TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60054 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (0ms).
 | – Problem 2 was processed with processor PolynomialLinearRange4iUR (0ms).
 | – Problem 3 was processed with processor SubtermCriterion (0ms).
 | – Problem 4 was processed with processor SubtermCriterion (0ms).
 | – Problem 5 was processed with processor BackwardsNarrowing (8ms).
 |    | – Problem 6 was processed with processor BackwardsNarrowing (9ms).
 |    |    | – Problem 7 was processed with processor BackwardsNarrowing (17ms).
 |    |    |    | – Problem 8 was processed with processor BackwardsNarrowing (16ms).
 |    |    |    |    | – Problem 9 was processed with processor BackwardsNarrowing (26ms).
 |    |    |    |    |    | – Problem 10 was processed with processor BackwardsNarrowing (62ms).
 |    |    |    |    |    |    | – Problem 11 was processed with processor BackwardsNarrowing (38ms).
 |    |    |    |    |    |    |    | – Problem 12 was processed with processor BackwardsNarrowing (85ms).
 |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor BackwardsNarrowing (36ms).
 |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor BackwardsNarrowing (39ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor BackwardsNarrowing (104ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor BackwardsNarrowing (54ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor BackwardsNarrowing (60ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor BackwardsNarrowing (149ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor BackwardsNarrowing (79ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor BackwardsNarrowing (88ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor BackwardsNarrowing (90ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor BackwardsNarrowing (221ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor BackwardsNarrowing (113ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor BackwardsNarrowing (264ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor BackwardsNarrowing (782ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 remains open; application of the following processors failed [BackwardsNarrowing (1119ms), BackwardsNarrowing (862ms), BackwardsNarrowing (809ms), BackwardsNarrowing (530ms), BackwardsNarrowing (871ms), BackwardsNarrowing (584ms), BackwardsNarrowing (652ms), BackwardsNarrowing (669ms), BackwardsNarrowing (713ms), BackwardsNarrowing (794ms), BackwardsNarrowing (833ms), BackwardsNarrowing (1367ms), BackwardsNarrowing (1201ms), BackwardsNarrowing (1621ms), BackwardsNarrowing (709ms), BackwardsNarrowing (1131ms), BackwardsNarrowing (1059ms), BackwardsNarrowing (1095ms), BackwardsNarrowing (930ms), BackwardsNarrowing (1309ms), BackwardsNarrowing (1555ms), BackwardsNarrowing (1311ms), BackwardsNarrowing (1611ms), BackwardsNarrowing (721ms), BackwardsNarrowing (1913ms), BackwardsNarrowing (timeout)].

The following open problems remain:

Open Dependency Pair Problem 5

Dependency Pairs

plus#(id(x), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))
plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: not, id, plus, 0, minus, s, if, false, true, gt, zero, quot

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

plus#(s(x), x) → id#(x)plus#(id(x), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), s(y)) → gt#(s(y), y)plus#(s(x), s(y)) → gt#(x, y)
plus#(s(x), s(y)) → if#(gt(x, y), x, y)plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))
plus#(s(x), x) → gt#(x, x)plus#(id(x), s(y)) → if#(gt(s(y), y), y, s(y))
quot#(s(x), s(y)) → minus#(x, y)plus#(s(x), s(y)) → id#(x)
plus#(s(x), x) → if#(gt(x, x), id(x), id(x))plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))
plus#(s(x), s(y)) → if#(not(gt(x, y)), id(x), id(y))gt#(s(x), s(y)) → gt#(x, y)
quot#(s(x), s(y)) → quot#(minus(x, y), s(y))minus#(s(x), s(y)) → minus#(x, y)
not#(x) → if#(x, false, true)plus#(s(x), s(y)) → id#(y)
plus#(s(x), s(y)) → not#(gt(x, y))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: id, not, plus, minus, 0, s, if, true, false, gt, zero, quot

Strategy

The following SCCs where found

plus#(id(x), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))
plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))
gt#(s(x), s(y)) → gt#(x, y)
quot#(s(x), s(y)) → quot#(minus(x, y), s(y))
minus#(s(x), s(y)) → minus#(x, y)

Problem 2: PolynomialLinearRange4iUR

Dependency Pair Problem

Dependency Pairs

quot#(s(x), s(y)) → quot#(minus(x, y), s(y))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: id, not, plus, minus, 0, s, if, true, false, gt, zero, quot

Strategy

Polynomial Interpretation

Improved Usable rules

minus(s(x), s(y)) → minus(x, y)minus(x, 0) → x

The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:

quot#(s(x), s(y)) → quot#(minus(x, y), s(y))

Problem 3: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

gt#(s(x), s(y)) → gt#(x, y)

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: id, not, plus, minus, 0, s, if, true, false, gt, zero, quot

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

gt#(s(x), s(y)) → gt#(x, y)

Problem 4: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

minus#(s(x), s(y)) → minus#(x, y)

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: id, not, plus, minus, 0, s, if, true, false, gt, zero, quot

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

minus#(s(x), s(y)) → minus#(x, y)

Problem 5: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(id(x), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))
plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: not, id, plus, 0, minus, s, if, false, true, gt, zero, quot

Strategy

The left-hand side of the rule plus#(id(x), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(id(x), minus(s(y), 0)) 
plus#(id(x), quot(s(_x32), s(_x31))) 
plus#(if(true, id(x), _x21), s(y)) 
plus#(id(id(x)), s(y)) 
plus#(id(x), if(true, s(y), _x31)) 
plus#(id(x), plus(s(_x32), s(_x31))) 
plus#(minus(id(x), 0), s(y)) 
plus#(id(x), if(false, _x32, s(y))) 
plus#(id(x), plus(id(_x32), s(_x31))) 
plus#(id(x), id(s(y))) 
plus#(plus(zero, id(x)), s(y)) 
plus#(if(false, _x22, id(x)), s(y)) 
plus#(id(x), plus(zero, s(y))) 
Thus, the rule plus#(id(x), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(id(id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 6: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(id(id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))
plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: id, not, plus, minus, 0, s, if, true, false, gt, zero, quot

Strategy

The left-hand side of the rule plus#(id(id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(id(minus(id(x), 0)), s(y)) 
plus#(if(true, id(id(x)), _x21), s(y)) 
plus#(id(id(id(x))), s(y)) 
plus#(id(id(x)), plus(zero, s(y))) 
plus#(id(if(false, _x32, id(x))), s(y)) 
plus#(minus(id(id(x)), 0), s(y)) 
plus#(id(id(x)), plus(id(_x32), s(_x31))) 
plus#(id(id(x)), id(s(y))) 
plus#(id(id(x)), plus(s(_x32), s(_x31))) 
plus#(plus(zero, id(id(x))), s(y)) 
plus#(id(id(x)), if(true, s(y), _x31)) 
plus#(id(if(true, id(x), _x31)), s(y)) 
plus#(id(id(x)), if(false, _x32, s(y))) 
plus#(id(id(x)), minus(s(y), 0)) 
plus#(id(id(x)), quot(s(_x32), s(_x31))) 
plus#(id(plus(zero, id(x))), s(y)) 
plus#(if(false, _x22, id(id(x))), s(y)) 
Thus, the rule plus#(id(id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(minus(id(id(x)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 7: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(minus(id(id(x)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))
plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: not, id, plus, 0, minus, s, if, false, true, gt, zero, quot

Strategy

The left-hand side of the rule plus#(minus(id(id(x)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(minus(minus(id(id(x)), 0), 0), s(y)) 
plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) 
plus#(minus(id(id(id(x))), 0), s(y)) 
plus#(minus(id(id(x)), 0), id(s(y))) 
plus#(minus(s(id(id(x))), s(0)), s(y)) 
plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) 
plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) 
plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) 
plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) 
plus#(id(minus(id(id(x)), 0)), s(y)) 
plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) 
plus#(minus(id(id(x)), id(0)), s(y)) 
plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) 
plus#(minus(id(id(x)), minus(0, 0)), s(y)) 
plus#(minus(plus(zero, id(id(x))), 0), s(y)) 
plus#(minus(id(minus(id(x), 0)), 0), s(y)) 
plus#(plus(zero, minus(id(id(x)), 0)), s(y)) 
plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) 
plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) 
plus#(minus(id(id(x)), 0), minus(s(y), 0)) 
plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) 
plus#(minus(id(id(x)), 0), plus(zero, s(y))) 
plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) 
plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) 
plus#(minus(id(id(x)), plus(zero, 0)), s(y)) 
plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) 
plus#(minus(id(plus(zero, id(x))), 0), s(y)) 
plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) 
Thus, the rule plus#(minus(id(id(x)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))

Problem 8: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(if(true, id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: id, not, plus, minus, 0, s, if, true, false, gt, zero, quot

Strategy

The left-hand side of the rule plus#(if(true, id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(if(true, id(id(id(x))), _x21), s(y)) 
plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) 
plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) 
plus#(plus(zero, if(true, id(id(x)), _x21)), s(y)) 
plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) 
plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) 
plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) 
plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) 
plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) 
plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) 
plus#(if(true, if(true, id(id(x)), _x21), _x31), s(y)) 
plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) 
plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) 
plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) 
plus#(id(if(true, id(id(x)), _x21)), s(y)) 
plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) 
plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) 
plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) 
plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) 
plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) 
plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) 
plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) 
plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) 
plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) 
plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) 
plus#(if(id(true), id(id(x)), _x21), s(y)) 
plus#(if(true, id(id(x)), _x21), id(s(y))) 
plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) 
Thus, the rule plus#(if(true, id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(if(true, if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 9: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(if(true, if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: not, id, plus, 0, minus, s, if, false, true, gt, zero, quot

Strategy

The left-hand side of the rule plus#(if(true, if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) 
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) 
plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) 
plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) 
plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) 
plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) 
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), s(y)) 
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) 
plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) 
plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) 
plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) 
plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) 
plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) 
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) 
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) 
plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) 
plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) 
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) 
plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) 
plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) 
plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) 
Thus, the rule plus#(if(true, if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 10: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: id, not, plus, minus, 0, s, if, true, false, gt, zero, quot

Strategy

The left-hand side of the rule plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) 
plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) 
plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) 
plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) 
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) 
plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) 
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) 
plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) 
plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) 
plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) 
plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) 
plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) 
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) 
plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) 
plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) 
plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) 
plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) 
Thus, the rule plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 11: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))
plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: not, id, plus, 0, minus, s, if, false, true, gt, zero, quot

Strategy

The left-hand side of the rule plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) 
plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) 
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) 
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) 
plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) 
plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) 
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) 
plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) 
plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) 
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) 
plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) 
plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) 
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) 
plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) 
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) 
plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) 
plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) 
Thus, the rule plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 12: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))
plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: id, not, plus, minus, 0, s, if, true, false, gt, zero, quot

Strategy

The left-hand side of the rule plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) 
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(if(false, _x102, true), id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(zero, s(y))) 
plus#(if(true, if(plus(zero, minus(true, id(0))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) 
plus#(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(if(true, 0, _x121)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(if(true, plus(zero, minus(true, id(0))), _x71), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(if(true, true, _x51), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, id(0)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) 
plus#(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) 
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(if(false, _x122, 0)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) 
plus#(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x41), s(y)) 
plus#(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(false, _x62, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), minus(s(y), 0)) 
plus#(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, if(true, minus(true, id(0)), _x91)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) 
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) 
plus#(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(quot(0, s(_x121))))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, if(true, id(0), _x111))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) 
Thus, the rule plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(quot(0, s(_x121))))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(true, 0, _x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(true, id(0), _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(false, _x102, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(false, _x122, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, id(0))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(true, minus(true, id(0)), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 13: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(plus(zero, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(if(false, _x122, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(false, _x112, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(true, 0, _x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, id(0)), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(true, zero, _x81), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(quot(0, s(_x121))))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(false, _x92, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(false, _x82, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(true, id(0), _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, id(0))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: not, id, plus, 0, minus, s, if, false, true, gt, zero, quot

Strategy

The left-hand side of the rule plus#(plus(zero, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) 
plus#(id(plus(zero, if(true, id(id(x)), _x21))), s(y)) 
plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), s(y)) 
plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), s(y)) 
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, s(y), _x31)) 
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), s(y)) 
plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), s(y)) 
plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), s(y)) 
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), s(y)) 
plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), s(y)) 
plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), s(y)) 
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), s(y)) 
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), s(y)) 
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(id(_x32), s(_x31))) 
plus#(plus(zero, id(if(true, id(id(x)), _x21))), s(y)) 
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(s(y), 0)) 
plus#(plus(zero, if(true, id(id(x)), _x21)), quot(s(_x32), s(_x31))) 
plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, s(y))) 
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), s(y)) 
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), s(y)) 
plus#(plus(zero, if(id(true), id(id(x)), _x21)), s(y)) 
plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), s(y)) 
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), s(y)) 
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), s(y)) 
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(s(_x32), s(_x31))) 
plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), s(y)) 
plus#(plus(zero, if(true, id(id(x)), _x21)), id(s(y))) 
plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), s(y)) 
plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), s(y)) 
plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), s(y)) 
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), s(y)) 
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, s(y))) 
plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), s(y)) 
plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), s(y)) 
plus#(plus(zero, if(true, id(id(id(x))), _x21)), s(y)) 
plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), s(y)) 
plus#(plus(id(zero), if(true, id(id(x)), _x21)), s(y)) 
Thus, the rule plus#(plus(zero, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))

Problem 14: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(plus(zero, if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(if(false, _x122, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(false, _x112, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(if(true, 0, _x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(false, _x102, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, id(0)), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(true, zero, _x81), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(quot(0, s(_x121))))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))plus#(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(true, id(0), _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, plus(zero, minus(true, id(0))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: id, not, plus, minus, 0, s, if, true, false, gt, zero, quot

Strategy

The left-hand side of the rule plus#(plus(zero, if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), id(s(y))) 
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), id(s(y))) 
plus#(plus(zero, if(true, id(id(x)), _x21)), id(quot(s(_x42), s(_x41)))) 
plus#(id(plus(zero, if(true, id(id(x)), _x21))), id(s(y))) 
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), id(s(y))) 
plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) 
plus#(plus(zero, id(if(true, id(id(x)), _x21))), id(s(y))) 
plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(false, _x42, s(y)))) 
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, id(s(y)))) 
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(id(_x42), s(_x41)))) 
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(zero, s(y)))) 
plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), id(s(y))) 
plus#(plus(id(zero), if(true, id(id(x)), _x21)), id(s(y))) 
plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), id(s(y))) 
plus#(plus(zero, if(id(true), id(id(x)), _x21)), id(s(y))) 
plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), id(s(y))) 
plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), id(s(y))) 
plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, id(s(y)))) 
plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(true, s(y), _x41))) 
plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) 
plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) 
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), id(s(y))) 
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(id(x)), _x21)), id(minus(s(y), 0))) 
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(s(_x42), s(_x41)))) 
plus#(plus(zero, if(true, id(id(x)), _x21)), id(id(s(y)))) 
plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), id(s(y))) 
plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), id(s(y))) 
plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), id(s(y))) 
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), id(s(y))) 
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(id(s(y)), 0)) 
plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(id(id(x))), _x21)), id(s(y))) 
plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), id(s(y))) 
plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), id(s(y))) 
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), id(s(y))) 
Thus, the rule plus#(plus(zero, if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(id(plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 15: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(false, _x122, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(true, 0, _x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(false, _x102, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(true, true, _x101), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(true, minus(true, id(0)), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(quot(0, s(_x121))))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(false, _x82, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(true, id(0), _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, id(id(x)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, plus(zero, minus(true, id(0))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: not, id, plus, 0, minus, s, if, false, true, gt, zero, quot

Strategy

The left-hand side of the rule plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(plus(zero, if(true, id(plus(zero, minus(id(x), 0))), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(minus(if(true, id(x), _x91), 0)), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(minus(id(x), id(0))), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(minus(minus(id(x), 0), 0)), _x21)), id(s(y))) 
plus#(plus(id(zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) 
plus#(plus(zero, if(true, plus(zero, id(minus(id(x), 0))), _x21)), id(s(y))) 
plus#(id(plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) 
plus#(plus(plus(zero, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(quot(s(_x42), s(_x41)))) 
plus#(plus(zero, if(if(true, true, _x61), id(minus(id(x), 0)), _x21)), id(s(y))) 
plus#(plus(zero, if(true, if(false, _x72, id(minus(id(x), 0))), _x21)), id(s(y))) 
plus#(plus(zero, id(if(true, id(minus(id(x), 0)), _x21))), id(s(y))) 
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(minus(s(y), 0))) 
plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x21), _x51)), id(s(y))) 
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(s(_x42), s(_x41)))) 
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), plus(zero, id(s(y)))) 
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(false, _x42, s(y)))) 
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(id(s(y)))) 
plus#(plus(zero, if(true, id(minus(id(x), quot(0, s(_x101)))), _x21)), id(s(y))) 
plus#(plus(zero, if(if(false, _x62, true), id(minus(id(x), 0)), _x21)), id(s(y))) 
plus#(plus(zero, if(plus(zero, true), id(minus(id(x), 0)), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(zero, s(y)))) 
plus#(plus(zero, if(true, id(minus(id(x), if(true, 0, _x101))), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(id(minus(id(x), 0))), _x21)), id(s(y))) 
plus#(plus(zero, if(id(true), id(minus(id(x), 0)), _x21)), id(s(y))) 
plus#(plus(zero, if(false, _x52, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) 
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(false, _x32, id(s(y)))) 
plus#(plus(zero, if(true, id(minus(if(false, _x92, id(x)), 0)), _x21)), id(s(y))) 
plus#(plus(zero, minus(if(true, id(minus(id(x), 0)), _x21), 0)), id(s(y))) 
plus#(plus(if(false, _x42, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(minus(id(x), plus(zero, 0))), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(minus(id(x), if(false, _x102, 0))), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(minus(plus(zero, id(x)), 0)), _x21)), id(s(y))) 
plus#(plus(minus(zero, 0), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(true, s(y), _x41))) 
plus#(plus(zero, if(minus(true, 0), id(minus(id(x), 0)), _x21)), id(s(y))) 
plus#(plus(zero, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) 
plus#(minus(plus(zero, if(true, id(minus(id(x), 0)), _x21)), 0), id(s(y))) 
plus#(plus(zero, if(true, id(minus(id(x), minus(0, 0))), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(true, id(s(y)), _x31)) 
plus#(plus(zero, if(true, minus(id(minus(id(x), 0)), 0), _x21)), id(s(y))) 
plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x71), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(minus(s(id(x)), s(0))), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(if(false, _x82, minus(id(x), 0))), _x21)), id(s(y))) 
plus#(if(true, plus(zero, if(true, id(minus(id(x), 0)), _x21)), _x31), id(s(y))) 
plus#(plus(if(true, zero, _x41), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) 
plus#(if(false, _x32, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) 
plus#(plus(zero, if(true, id(if(true, minus(id(x), 0), _x81)), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(minus(id(id(x)), 0)), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), minus(id(s(y)), 0)) 
plus#(plus(zero, if(gt(s(_x61), zero), id(minus(id(x), 0)), _x21)), id(s(y))) 
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(id(_x42), s(_x41)))) 
Thus, the rule plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(plus(id(zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(minus(id(x), 0), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), id(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(plus(zero, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), minus(0, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), plus(zero, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(false, _x82, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(s(id(x)), s(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(minus(id(x), 0)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), if(false, _x102, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(minus(id(x), 0)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(plus(zero, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(true, id(x), _x91), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(minus(id(x), 0)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(plus(zero, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(plus(zero, id(if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), quot(0, s(_x101)))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, minus(id(x), 0), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), if(true, 0, _x101))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x61), zero), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(false, _x92, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(false, _x52, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(minus(id(x), 0)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 16: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, id(id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(false, _x122, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(minus(id(x), 0)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(minus(id(x), 0)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(plus(zero, if(plus(zero, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(true, 0, _x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(minus(id(x), 0)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), quot(0, s(_x101)))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(if(true, true, _x51), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(minus(id(x), 0), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), minus(0, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(s(id(x)), s(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(true, id(x), _x91), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, minus(id(x), 0), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(quot(0, s(_x121))))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(false, _x92, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), plus(zero, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(false, _x82, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(true, id(0), _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(plus(zero, if(true, id(minus(id(id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), if(false, _x102, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(minus(id(x), 0)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(plus(zero, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(false, _x112, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(false, _x102, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, id(0)), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(false, _x92, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), id(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, plus(zero, minus(true, id(0))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(plus(zero, if(true, id(minus(id(x), if(true, 0, _x101))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x61), zero), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(false, _x52, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: id, not, plus, minus, 0, s, if, true, false, gt, zero, quot

Strategy

The left-hand side of the rule plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(minus(id(if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) 
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x62, 0)), s(y)) 
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(true, s(y), _x31)) 
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), quot(0, s(_x61))), s(y)) 
plus#(minus(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), 0), s(y)) 
plus#(minus(if(id(true), if(true, id(id(x)), _x21), _x31), 0), s(y)) 
plus#(minus(if(true, if(gt(s(_x81), zero), id(id(x)), _x21), _x31), 0), s(y)) 
plus#(minus(if(true, id(if(true, id(id(x)), _x21)), _x31), 0), s(y)) 
plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x51), 0), s(y)) 
plus#(minus(if(true, if(id(true), id(id(x)), _x21), _x31), 0), s(y)) 
plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x71), _x31), 0), s(y)) 
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), quot(s(_x32), s(_x31))) 
plus#(minus(if(if(false, _x62, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) 
plus#(minus(if(true, if(if(false, _x82, true), id(id(x)), _x21), _x31), 0), s(y)) 
plus#(id(minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) 
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(zero, s(y))) 
plus#(minus(if(true, if(if(true, true, _x81), id(id(x)), _x21), _x31), 0), s(y)) 
plus#(if(true, minus(if(true, if(true, id(id(x)), _x21), _x31), 0), _x41), s(y)) 
plus#(minus(if(true, if(true, id(if(true, id(x), _x101)), _x21), _x31), 0), s(y)) 
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(s(_x32), s(_x31))) 
plus#(minus(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), 0), s(y)) 
plus#(minus(if(true, if(true, id(id(id(x))), _x21), _x31), 0), s(y)) 
plus#(minus(s(if(true, if(true, id(id(x)), _x21), _x31)), s(0)), s(y)) 
plus#(minus(if(true, if(false, _x72, if(true, id(id(x)), _x21)), _x31), 0), s(y)) 
plus#(minus(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) 
plus#(minus(if(true, if(true, if(true, id(id(x)), _x91), _x21), _x31), 0), s(y)) 
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, 0)), s(y)) 
plus#(minus(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), 0), s(y)) 
plus#(minus(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), 0), s(y)) 
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(id(_x32), s(_x31))) 
plus#(minus(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), 0), s(y)) 
plus#(minus(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), 0), s(y)) 
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), id(s(y))) 
plus#(minus(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), 0), s(y)) 
plus#(if(false, _x42, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) 
plus#(minus(if(if(true, true, _x61), if(true, id(id(x)), _x21), _x31), 0), s(y)) 
plus#(minus(if(true, if(true, id(if(false, _x102, id(x))), _x21), _x31), 0), s(y)) 
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), minus(s(y), 0)) 
plus#(minus(if(true, if(true, if(false, _x92, id(id(x))), _x21), _x31), 0), s(y)) 
plus#(minus(if(gt(s(_x61), zero), if(true, id(id(x)), _x21), _x31), 0), s(y)) 
plus#(minus(if(false, _x52, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) 
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), minus(0, 0)), s(y)) 
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), id(0)), s(y)) 
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(false, _x32, s(y))) 
plus#(plus(zero, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) 
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(true, 0, _x61)), s(y)) 
plus#(minus(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), 0), s(y)) 
plus#(minus(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) 
plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) 
plus#(minus(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), 0), s(y)) 
Thus, the rule plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x51), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(true, if(true, id(id(x)), _x21), _x31), 0), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(if(false, _x102, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(true, 0, _x61)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(false, _x52, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x62, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(if(true, true, _x61), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(true, id(id(x)), _x91), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(if(true, true, _x81), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(gt(s(_x81), zero), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(minus(if(true, if(id(true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), quot(0, s(_x61))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(false, _x92, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(false, _x72, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(_x61), zero), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(s(if(true, if(true, id(id(x)), _x21), _x31)), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(minus(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(if(false, _x82, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x71), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(if(false, _x62, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(id(true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(if(true, id(x), _x101)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 17: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))
plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(minus(id(x), 0)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(false, _x122, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(s(if(true, if(true, id(id(x)), _x21), _x31)), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x71), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(id(true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, minus(id(minus(id(x), 0)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(plus(zero, if(plus(zero, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(if(true, 0, _x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, id(minus(id(x), 0)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), quot(0, s(_x101)))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(if(true, true, _x51), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(minus(id(x), 0), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), minus(0, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(s(id(x)), s(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(id(true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(if(true, id(x), _x91), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, minus(id(x), 0), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(if(true, id(x), _x101)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(true, if(true, id(id(x)), _x21), _x31), 0), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(quot(0, s(_x121))))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(if(false, _x102, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(false, _x92, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(true, 0, _x61)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), plus(zero, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(false, _x82, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(true, id(0), _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(if(false, _x62, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, plus(zero, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(if(false, _x52, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(if(true, true, _x61), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(plus(zero, if(true, id(minus(id(id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(false, _x92, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), if(false, _x102, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(minus(id(x), 0)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(plus(zero, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(false, _x112, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(false, _x52, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(if(true, true, _x81), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(gt(s(_x81), zero), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), quot(0, s(_x61))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(false, _x102, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(if(false, _x82, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, id(0)), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(false, _x92, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x51), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x91), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(false, _x72, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(plus(zero, if(true, id(minus(id(x), id(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x62, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(_x61), zero), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, id(0))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(plus(zero, if(true, id(minus(id(x), if(true, 0, _x101))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x61), zero), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(false, _x52, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: not, id, plus, 0, minus, s, if, false, true, gt, zero, quot

Strategy

The left-hand side of the rule plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) 
plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) 
plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) 
plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) 
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) 
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) 
plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) 
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) 
plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) 
plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) 
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) 
plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) 
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) 
plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) 
Thus, the rule plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 18: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(true, id(id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))
plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(false, _x122, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(minus(id(x), 0)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(s(if(true, if(true, id(id(x)), _x21), _x31)), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x71), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(id(true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, minus(id(minus(id(x), 0)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(plus(zero, if(plus(zero, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(true, 0, _x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, id(minus(id(x), 0)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(true, true, _x101), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), quot(0, s(_x101)))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(minus(id(x), 0), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), minus(0, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(id(true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(s(id(x)), s(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(true, id(x), _x91), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, minus(id(x), 0), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(if(true, id(x), _x101)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(true, if(true, id(id(x)), _x21), _x31), 0), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(quot(0, s(_x121))))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(if(false, _x102, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(true, 0, _x61)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), plus(zero, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(false, _x82, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(true, id(0), _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, id(id(x)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(if(false, _x62, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(if(true, true, _x61), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(false, _x92, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), if(false, _x102, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(minus(id(x), 0)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(plus(zero, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(false, _x52, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(if(true, true, _x81), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(gt(s(_x81), zero), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), quot(0, s(_x61))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(false, _x102, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(if(false, _x82, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(true, minus(true, id(0)), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(false, _x92, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x51), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x91), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(false, _x72, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), id(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x62, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(_x61), zero), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, plus(zero, minus(true, id(0))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), if(true, 0, _x101))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x61), zero), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(false, _x52, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: id, not, plus, minus, 0, s, if, true, false, gt, zero, quot

Strategy

The left-hand side of the rule plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) 
plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(s(y), 0)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) 
plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) 
plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), s(y)) 
plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) 
plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), s(y)) 
plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, s(y))) 
plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) 
plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) 
Thus, the rule plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 19: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(minus(id(x), 0)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(false, _x122, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(s(if(true, if(true, id(id(x)), _x21), _x31)), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x71), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(id(true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(true, minus(id(minus(id(x), 0)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(plus(zero, if(plus(zero, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(true, 0, _x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(minus(id(x), 0)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(true, true, _x101), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), quot(0, s(_x101)))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(minus(id(x), 0), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), minus(0, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(s(id(x)), s(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(id(true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(true, id(x), _x91), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, minus(id(x), 0), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(if(true, id(x), _x101)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(true, if(true, id(id(x)), _x21), _x31), 0), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(quot(0, s(_x121))))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(if(false, _x102, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(true, 0, _x61)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), plus(zero, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(false, _x82, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(true, id(0), _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, id(id(x)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(minus(if(if(false, _x62, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(if(true, true, _x61), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(false, _x92, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), if(false, _x102, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(minus(id(x), 0)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(plus(zero, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(false, _x52, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(if(true, true, _x81), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(gt(s(_x81), zero), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), quot(0, s(_x61))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(if(false, _x82, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, id(0)), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(false, _x92, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x51), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x91), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(false, _x72, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(plus(zero, if(true, id(minus(id(x), id(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x62, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(_x61), zero), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, id(0))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(plus(zero, if(true, id(minus(id(x), if(true, 0, _x101))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x61), zero), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(false, _x52, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: not, id, plus, 0, minus, s, if, false, true, gt, zero, quot

Strategy

The left-hand side of the rule plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(id(s(y)))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) 
plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) 
plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), id(s(y))) 
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) 
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) 
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) 
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), id(s(y))) 
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(minus(s(y), 0))) 
plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) 
plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), id(s(y))) 
plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) 
plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) 
plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), id(s(y))) 
plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) 
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) 
plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) 
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) 
Thus, the rule plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 20: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, id(id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(if(false, _x122, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(minus(id(x), 0)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(s(if(true, if(true, id(id(x)), _x21), _x31)), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x71), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(id(true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(true, minus(id(minus(id(x), 0)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(plus(zero, if(plus(zero, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(if(true, 0, _x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(minus(id(x), 0)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(true, true, _x101), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), quot(0, s(_x101)))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(minus(id(x), 0), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), minus(0, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(s(id(x)), s(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(id(true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(true, id(x), _x91), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, minus(id(x), 0), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(if(true, id(x), _x101)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(true, if(true, id(id(x)), _x21), _x31), 0), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(quot(0, s(_x121))))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(if(false, _x102, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(true, 0, _x61)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), plus(zero, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(false, _x82, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(true, id(0), _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(minus(if(if(false, _x62, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(if(false, _x52, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(if(true, true, _x61), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(false, _x92, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), if(false, _x102, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(minus(id(x), 0)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(true, zero, _x41), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(plus(zero, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(false, _x112, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(false, _x52, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(if(true, true, _x81), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(gt(s(_x81), zero), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), quot(0, s(_x61))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(if(false, _x82, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, id(0)), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(false, _x92, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x51), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(true, id(id(x)), _x91), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(false, _x72, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), id(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x62, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(_x61), zero), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, plus(zero, minus(true, id(0))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), if(true, 0, _x101))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x61), zero), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(false, _x52, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: id, not, plus, minus, 0, s, if, true, false, gt, zero, quot

Strategy

The left-hand side of the rule plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) 
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) 
plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), id(s(y))) 
plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) 
plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), id(s(y))) 
plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) 
plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), id(s(y))) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) 
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) 
plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(id(s(y)))) 
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) 
plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) 
plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) 
plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(minus(s(y), 0))) 
plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) 
plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), id(s(y))) 
plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) 
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) 
Thus, the rule plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 21: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(if(false, _x122, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(minus(id(x), 0)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(s(if(true, if(true, id(id(x)), _x21), _x31)), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x71), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(id(true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(true, minus(id(minus(id(x), 0)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(plus(zero, if(plus(zero, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(if(true, 0, _x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(minus(id(x), 0)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(id(plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), quot(0, s(_x101)))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(if(true, true, _x51), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(minus(id(x), 0), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), minus(0, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(s(id(x)), s(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(id(true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(true, id(x), _x91), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, minus(id(x), 0), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(if(true, id(x), _x101)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(true, if(true, id(id(x)), _x21), _x31), 0), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(quot(0, s(_x121))))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(if(false, _x102, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(true, 0, _x61)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), plus(zero, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(false, _x82, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(true, id(0), _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, id(id(x)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(minus(if(if(false, _x62, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, plus(zero, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(if(false, _x52, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(if(true, true, _x61), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(false, _x92, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), if(false, _x102, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(minus(id(x), 0)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(plus(zero, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(false, _x52, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(if(true, true, _x81), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(gt(s(_x81), zero), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), quot(0, s(_x61))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(if(false, _x82, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, id(0)), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(if(false, _x92, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(true, zero, _x81), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x51), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(true, id(id(x)), _x91), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(false, _x72, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(plus(zero, if(true, id(minus(id(x), id(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x62, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(_x61), zero), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, id(0))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), if(true, 0, _x101))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x61), zero), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(false, _x52, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: not, id, plus, 0, minus, s, if, false, true, gt, zero, quot

Strategy

The left-hand side of the rule plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), if(true, zero, _x81)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(s(_x51)), s(zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(plus(zero, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) 
plus#(if(gt(if(false, _x72, s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(minus(s(_x51), 0), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), plus(zero, zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(if(true, gt(s(_x51), zero), _x61), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), if(false, _x82, zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(plus(zero, s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) 
plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(if(true, s(_x51), _x71), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) 
plus#(id(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(id(s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(if(false, _x62, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(minus(gt(s(_x51), zero), 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), minus(zero, 0)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) 
plus#(minus(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) 
plus#(if(false, _x42, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(gt(s(_x51), zero), plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(plus(zero, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) 
plus#(if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), id(zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) 
Thus, the rule plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(if(gt(s(_x51), zero), if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(plus(zero, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(_x51), zero), 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), if(false, _x82, zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), id(zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(minus(s(_x51), 0), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, gt(s(_x51), zero), _x61), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(true, zero, _x81)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x62, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(true, s(_x51), _x71), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), minus(zero, 0)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(zero, s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), plus(zero, zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(false, _x72, s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(id(s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 22: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(true, s(_x51), _x71), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(minus(id(x), 0)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(s(if(true, if(true, id(id(x)), _x21), _x31)), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(false, _x82, zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(true, true, _x101), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), quot(0, s(_x101)))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(id(true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(true, id(x), _x91), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, minus(id(x), 0), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(true, if(true, id(id(x)), _x21), _x31), 0), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(quot(0, s(_x121))))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(if(false, _x102, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), plus(zero, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(true, zero, _x81)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), minus(zero, 0)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(plus(zero, minus(true, id(0))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(gt(s(_x51), zero), if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(if(true, true, _x61), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(false, _x92, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), if(false, _x102, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(minus(id(x), 0)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(false, _x52, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(if(true, true, _x81), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), quot(0, s(_x61))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(true, minus(true, id(0)), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(true, zero, _x81), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x51), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(true, id(id(x)), _x91), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(zero, s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(false, _x72, s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(plus(zero, if(true, id(minus(id(x), if(true, 0, _x101))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(if(false, _x122, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x71), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(id(true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, minus(id(minus(id(x), 0)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(plus(zero, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(minus(s(_x51), 0), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(true, 0, _x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(minus(id(x), 0)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(id(plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x62, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(minus(id(x), 0), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), minus(0, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(s(id(x)), s(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(plus(zero, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), plus(zero, zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(if(true, id(x), _x101)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(true, 0, _x61)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, gt(s(_x51), zero), _x61), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(true, id(0), _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(if(false, _x62, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(minus(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(plus(zero, if(true, id(id(x)), _x21)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(plus(zero, if(true, id(minus(id(id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(true, zero, _x41), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(plus(zero, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(id(s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(gt(s(_x81), zero), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(if(false, _x82, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(if(false, _x92, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(false, _x72, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), id(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(_x51), zero), 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x62, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), id(zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(_x61), zero), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, id(0))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x61), zero), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(false, _x52, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: id, not, plus, minus, 0, s, if, true, false, gt, zero, quot

Strategy

The left-hand side of the rule plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(if(gt(s(_x51), if(true, zero, _x81)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(plus(zero, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), s(y)) 
plus#(if(minus(gt(s(_x51), zero), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x71), _x31), s(y)) 
plus#(if(gt(s(_x51), minus(zero, 0)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), if(true, 0, _x121)), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), if(false, _x82, zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(if(true, minus(plus(zero, true), 0), _x101), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(if(false, _x122, zero), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(s(_x32), s(_x31))) 
plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), quot(s(_x32), s(_x31))) 
plus#(if(gt(s(_x51), zero), if(gt(s(_x81), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(if(false, _x122, id(x))), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, if(true, true, _x131)), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(true, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), _x41), s(y)) 
plus#(if(gt(s(_x51), id(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x121)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(if(false, _x72, s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(id(_x32), s(_x31))) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), 0), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(if(false, _x62, gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), s(y)) 
plus#(if(plus(zero, gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(if(true, true, _x81), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(if(true, zero, _x121), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), plus(zero, zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(if(false, _x82, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(zero, s(y))) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), quot(0, s(_x121))), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(if(true, s(_x51), _x71), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), if(false, _x112, id(id(x))), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x91), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(plus(zero, s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x111), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(false, _x32, s(y))) 
plus#(if(if(true, gt(s(_x51), zero), _x61), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x61), _x31), s(y)) 
plus#(minus(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), 0), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(if(false, _x102, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(true, s(y), _x31)) 
plus#(id(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), s(y)) 
plus#(if(gt(s(_x51), zero), if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(false, _x42, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), s(y)) 
plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x72, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), minus(s(y), 0)) 
plus#(if(id(gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(false, _x112, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), if(false, _x122, 0)), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(id(s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(false, _x92, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), s(y)) 
plus#(if(gt(minus(s(_x51), 0), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) 
Thus, the rule plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(if(false, _x102, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x72, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, if(true, true, _x131)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(gt(s(_x51), minus(zero, 0)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(false, _x92, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), if(true, zero, _x81)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), id(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), if(false, _x122, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(zero, s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x91), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x111), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(if(false, _x122, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(if(true, minus(plus(zero, true), 0), _x101), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(minus(s(_x51), 0), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), if(false, _x112, id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(true, true, _x81), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(false, _x112, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(gt(s(_x81), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), if(true, 0, _x121)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x71), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, gt(s(_x51), zero), _x61), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x121)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(_x51), zero), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(true, s(_x51), _x71), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), quot(0, s(_x121))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(id(gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), plus(zero, zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x62, gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(if(false, _x122, zero), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(false, _x82, zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(if(true, zero, _x121), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(false, _x82, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(false, _x72, s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(id(s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 23: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(false, _x92, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x111), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(if(false, _x122, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(true, s(_x51), _x71), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(minus(id(x), 0)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(minus(s(if(true, if(true, id(id(x)), _x21), _x31)), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x72, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(false, _x82, zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(gt(s(_x81), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(if(false, _x122, zero), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(true, true, _x101), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(if(true, zero, _x121), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), quot(0, s(_x101)))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(false, _x82, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), minus(zero, 0)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(id(true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(if(true, id(x), _x91), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, minus(id(x), 0), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(true, if(true, id(id(x)), _x21), _x31), 0), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(quot(0, s(_x121))))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(if(false, _x102, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), plus(zero, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), if(true, zero, _x81)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), minus(zero, 0)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, id(id(x)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(plus(zero, minus(true, id(0))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(if(false, _x52, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(minus(if(if(true, true, _x61), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(false, _x92, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), if(false, _x102, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(minus(id(x), 0)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), plus(zero, zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(false, _x52, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(if(true, true, _x81), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), quot(0, s(_x61))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, id(0)), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x51), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(gt(s(_x51), zero), if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x91), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x91), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), if(true, 0, _x121)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(zero, s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(plus(zero, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x62, gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(false, _x72, s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(plus(zero, if(true, id(minus(id(x), if(true, 0, _x101))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(id(s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(if(true, minus(plus(zero, true), 0), _x101), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(minus(s(_x51), 0), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(_x51), zero), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(if(false, _x122, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x71), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(id(true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, minus(id(minus(id(x), 0)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(if(false, _x102, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(true, zero, _x81)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(minus(s(_x51), 0), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), if(false, _x112, id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(true, 0, _x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(minus(id(x), 0)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(id(plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x62, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(if(true, gt(s(_x51), zero), _x61), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, if(true, true, _x131)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(minus(id(x), 0), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), minus(0, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(s(id(x)), s(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), plus(zero, zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(if(true, id(x), _x101)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(true, 0, _x61)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(false, _x82, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, gt(s(_x51), zero), _x61), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(true, id(0), _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), quot(0, s(_x121))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(if(false, _x62, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(minus(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(plus(zero, if(true, id(id(x)), _x21)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(plus(zero, if(true, id(minus(id(id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(true, zero, _x41), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(plus(zero, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(id(s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), id(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(gt(s(_x81), zero), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(false, _x112, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x121)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(if(false, _x82, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(false, _x92, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), if(false, _x122, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(if(true, true, _x81), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x71), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(true, s(_x51), _x71), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(false, _x72, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), id(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(zero, s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(_x51), zero), 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x62, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), id(zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(_x61), zero), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, id(0))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(false, _x82, zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(false, _x72, s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x61), zero), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(false, _x52, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: not, id, plus, 0, minus, s, if, false, true, gt, zero, quot

Strategy

The left-hand side of the rule plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(minus(s(y), 0))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) 
plus#(if(true, if(if(true, minus(s(plus(zero, true)), s(0)), _x71), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), minus(s(0), 0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(s(plus(zero, true))), s(s(0))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) 
plus#(minus(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), 0), id(s(y))) 
plus#(if(plus(zero, true), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(if(false, _x52, true), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(id(true), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(plus(zero, minus(s(plus(zero, true)), s(0))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(plus(zero, s(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(id(x))), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(if(true, 0, _x101))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) 
plus#(if(true, if(minus(if(true, s(plus(zero, true)), _x81), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, if(false, _x112, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(plus(zero, 0))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), if(true, s(0), _x91)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) 
plus#(if(true, if(minus(s(plus(zero, true)), plus(zero, s(0))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(minus(s(plus(zero, true)), s(0)), 0), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(minus(0, 0))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(if(false, _x102, 0))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), minus(id(id(x)), 0), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(id(zero), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(plus(zero, id(x))), _x21), _x31), id(s(y))) 
plus#(if(true, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), _x41), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), plus(zero, id(id(x))), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(if(false, _x92, plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(id(0))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) 
plus#(id(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31)), id(s(y))) 
plus#(if(true, plus(zero, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x101)))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(false, _x42, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31)), id(s(y))) 
plus#(if(true, if(minus(s(plus(minus(zero, 0), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(id(minus(s(plus(zero, true)), s(0))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, id(true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(plus(zero, zero), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) 
plus#(if(true, if(minus(s(minus(plus(zero, true), 0)), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(minus(true, 0), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(gt(s(_x51), zero), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(id(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(minus(id(x), 0)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), if(false, _x92, s(0))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(if(true, plus(zero, true), _x91)), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(if(false, _x82, s(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, if(true, true, _x111))), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, id(if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), id(s(y))) 
plus#(if(true, if(minus(id(s(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(if(false, _x72, minus(s(plus(zero, true)), s(0))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(minus(s(plus(zero, true)), 0), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, minus(if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), 0), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) 
plus#(plus(zero, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31)), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, minus(true, 0))), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, gt(s(_x111), zero))), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(if(true, true, _x51), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(false, _x62, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(if(true, zero, _x101), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(id(s(y)))) 
plus#(if(true, if(minus(s(plus(zero, true)), id(s(0))), id(id(x)), _x21), _x31), id(s(y))) 
plus#(if(true, if(minus(s(plus(if(false, _x102, zero), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) 
Thus, the rule plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(if(if(false, _x52, true), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(s(plus(zero, true)), s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(minus(plus(zero, true), 0)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(if(false, _x102, 0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(minus(zero, 0), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), plus(zero, s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), id(s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(true, if(minus(s(plus(zero, true)), minus(s(0), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(id(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), if(false, _x92, s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, gt(s(_x111), zero))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, s(plus(zero, true)), _x81), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(id(zero), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(true, plus(zero, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, minus(true, 0))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(s(plus(zero, true)), s(0)), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(minus(0, 0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(if(true, if(plus(zero, minus(s(plus(zero, true)), s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), if(true, s(0), _x91)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, s(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(if(true, 0, _x101))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(s(plus(zero, true)), s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(plus(zero, 0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(plus(zero, zero), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(if(false, _x102, zero), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, if(false, _x112, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x101)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, s(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(s(plus(zero, true))), s(s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, if(true, true, _x111))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(s(plus(zero, true)), s(0)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(s(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(if(false, _x92, plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(if(true, zero, _x101), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, id(true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(if(true, plus(zero, true), _x91)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(s(plus(zero, true)), 0), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 24: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(false, _x92, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x111), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(if(false, _x122, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(true, s(_x51), _x71), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(minus(id(x), 0)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(minus(s(if(true, if(true, id(id(x)), _x21), _x31)), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x72, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(false, _x82, zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(plus(zero, 0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(gt(s(_x81), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(if(false, _x122, zero), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(true, true, _x101), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(if(true, zero, _x121), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), quot(0, s(_x101)))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(false, _x82, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(id(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), minus(zero, 0)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, s(plus(zero, true)), _x81), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, minus(true, 0))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(id(true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(if(true, id(x), _x91), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(if(false, _x92, plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, id(true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, minus(id(x), 0), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(s(plus(zero, true)), 0), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(minus(zero, 0), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(if(false, _x102, 0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(true, if(true, id(id(x)), _x21), _x31), 0), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(quot(0, s(_x121))))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(if(false, _x102, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(false, _x92, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), plus(zero, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(false, _x82, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(true, zero, _x81)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), minus(zero, 0)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(s(plus(zero, true)), s(0)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(plus(zero, minus(true, id(0))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(gt(s(_x51), zero), if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), plus(zero, s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(if(true, true, _x61), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(false, _x92, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), if(false, _x102, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(minus(id(x), 0)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, if(true, true, _x111))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), plus(zero, zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(false, _x52, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(if(true, true, _x81), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, s(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), quot(0, s(_x61))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(false, _x62, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(true, minus(true, id(0)), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(true, zero, _x81), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(s(plus(zero, true)), s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(minus(plus(zero, true), 0)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x51), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x91), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(true, id(id(x)), _x91), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), if(true, s(0), _x91)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), if(true, 0, _x121)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(zero, s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), if(false, _x92, s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(if(true, plus(zero, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(s(plus(zero, true)), s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x62, gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(false, _x72, s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(s(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(plus(zero, if(true, id(minus(id(x), if(true, 0, _x101))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(id(s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), minus(s(0), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(minus(0, 0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(if(true, minus(plus(zero, true), 0), _x101), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(minus(s(_x51), 0), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(_x51), zero), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(false, _x122, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x71), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(id(true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(if(true, plus(zero, true), _x91)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, minus(id(minus(id(x), 0)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(if(false, _x102, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(plus(zero, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(true, zero, _x81)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(minus(s(_x51), 0), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), if(false, _x112, id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(if(true, 0, _x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, id(minus(id(x), 0)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(id(plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x62, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(if(true, gt(s(_x51), zero), _x61), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, if(true, true, _x131)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(minus(id(x), 0), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), minus(0, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(s(id(x)), s(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(s(plus(zero, true)), s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(if(false, _x102, zero), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), plus(zero, zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(if(true, zero, _x101), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(if(true, id(x), _x101)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, gt(s(_x111), zero))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(true, 0, _x61)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, gt(s(_x51), zero), _x61), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(true, id(0), _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(s(plus(zero, true))), s(s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), quot(0, s(_x121))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(if(false, _x62, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, plus(zero, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(minus(s(plus(id(zero), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(plus(zero, if(true, id(id(x)), _x21)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(plus(zero, if(true, id(minus(id(id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(if(true, 0, _x101))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(plus(zero, zero), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(true, zero, _x41), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(plus(zero, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(id(s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), id(s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, if(false, _x112, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), id(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(gt(s(_x81), zero), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(false, _x112, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(false, _x102, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, if(false, _x112, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x101)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x121)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(if(false, _x82, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(false, _x92, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), if(false, _x122, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(s(plus(zero, true)), s(0)), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(true, true, _x81), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x71), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, s(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(true, s(_x51), _x71), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(false, _x72, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), id(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(zero, s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(_x51), zero), 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x62, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), id(zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(_x61), zero), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, plus(zero, minus(true, id(0))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(false, _x82, zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(false, _x72, s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x61), zero), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(false, _x52, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: id, not, plus, minus, 0, s, if, true, false, gt, zero, quot

Strategy

The left-hand side of the rule plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), id(zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(if(true, gt(s(_x51), zero), _x61), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), plus(zero, s(y))) 
plus#(if(if(false, _x62, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(false, _x42, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), if(true, 0, _x131)), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(gt(zero, _x81), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(if(true, s(_x51), _x71), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(if(false, _x82, false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x101)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, if(false, _x142, true)), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), if(false, _x82, zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x72, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), if(false, _x32, s(y))) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), if(false, _x132, 0)), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(id(zero), true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), if(true, s(y), _x31)) 
plus#(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x41), s(y)) 
plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(plus(zero, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(minus(s(_x51), 0), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(plus(zero, false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), plus(id(_x32), s(_x31))) 
plus#(if(gt(s(_x51), zero), if(minus(false, 0), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), if(false, _x122, id(id(x))), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), minus(zero, 0)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(true, zero, _x131), true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x131))), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(id(x))), _x21)), _x31), s(y)) 
plus#(if(gt(if(false, _x72, s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), minus(if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), 0), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(id(gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(zero, true), 0), _x111), id(id(x)), _x21)), _x31), s(y)) 
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, if(true, true, _x141)), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(minus(gt(s(_x51), zero), 0), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21)), _x31), s(y)) 
plus#(if(gt(s(s(_x51)), s(zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), plus(s(_x32), s(_x31))) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(false, _x102, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) 
plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), plus(zero, zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(minus(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), 0), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x112, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), plus(zero, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) 
plus#(if(gt(id(s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, id(if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) 
plus#(if(gt(plus(zero, s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(if(true, id(x), _x131)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x121), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(if(false, _x132, id(x))), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, gt(s(_x141), zero)), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), if(true, zero, _x81)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), id(0)), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(if(true, false, _x81), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(if(true, plus(zero, true), _x121), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(id(false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(if(false, _x122, plus(zero, true)), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) 
plus#(if(gt(s(_x51), zero), if(false, _x62, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x132, zero), true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(plus(zero, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), id(if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), quot(s(_x32), s(_x31))) 
plus#(if(gt(s(_x51), zero), if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x71), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), minus(s(y), 0)) 
Thus, the rule plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, gt(s(_x51), zero), _x61), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x62, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x71), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x131))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x112, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(id(x))), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(true, zero, _x131), true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(true, s(_x51), _x71), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(id(s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(minus(s(_x51), 0), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(true, false, _x81), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(false, _x102, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(zero, s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(id(zero), true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x101)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(false, 0), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(gt(zero, _x81), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, if(true, true, _x141)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(false, _x72, s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), minus(if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(id(false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x72, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), if(true, zero, _x81)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(false, _x82, zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), plus(zero, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, gt(s(_x141), zero)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), if(true, 0, _x131)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), id(0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x121), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), minus(zero, 0)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x132, zero), true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(gt(s(_x51), zero), if(false, _x62, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(if(true, plus(zero, true), _x121), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(false, _x82, false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), plus(zero, zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), if(false, _x132, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(if(false, _x132, id(x))), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), id(zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(if(true, id(x), _x131)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, id(if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(if(false, _x122, plus(zero, true)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), id(if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(zero, true), 0), _x111), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, if(false, _x142, true)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), if(false, _x122, id(id(x))), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(_x51), zero), 0), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(plus(zero, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Problem 25: BackwardsNarrowing

Dependency Pair Problem

Dependency Pairs

plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, plus(zero, zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(plus(zero, zero), if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), id(true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(if(false, _x182, false), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), minus(id(id(x)), 0), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(false, _x72, if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), plus(zero, s(zero))), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(plus(zero, zero), true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), minus(id(id(x)), 0), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), if(false, _x172, true)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), minus(0, 0)), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), if(false, _x122, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(minus(false, 0), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x91), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(minus(false, 0), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, plus(zero, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(if(false, _x92, zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), if(true, 0, _x121)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(plus(zero, s(_x51)), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(plus(zero, if(false, _x162, minus(plus(zero, true), 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(minus(s(if(true, if(true, id(id(x)), _x21), _x31)), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(true, s(_x51), _x71), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(plus(zero, true), false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(if(true, plus(zero, true), _x211), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(id(zero), if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, id(zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, if(false, _x212, zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), plus(zero, id(id(x))), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), id(if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x72, if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x92, id(gt(s(_x51), zero))), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(quot(s(_x92), s(_x91))), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), if(false, _x222, id(id(x))), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(if(true, if(minus(true, if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), minus(true, 0)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(plus(zero, false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, gt(s(_x51), zero), _x61), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(false, _x92, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), id(0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(false, _x162, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21))), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x72, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(zero, s(_x51)), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), if(false, _x82, zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(quot(s(_x152), s(_x151)), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), quot(0, s(_x131))), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, if(true, zero, _x221)), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(id(zero), true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), plus(zero, true)), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), if(true, 0, _x191)), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(plus(zero, minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), minus(s(zero), 0)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, if(true, true, _x231)), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(x), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(if(false, _x132, id(id(x))), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), plus(zero, true)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, minus(zero, 0)), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(if(false, _x112, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(s(_x51))), s(s(zero))), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(true, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x171)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x91), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(false, _x82, s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(plus(zero, true), minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0)), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), plus(zero, zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), quot(0, s(_x261)))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(id(if(false, _x152, zero)), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), if(false, _x122, 0)), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(zero, true), 0), _x161), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(minus(plus(if(false, _x152, zero), true), 0), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(s(_x51)), s(zero)), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), minus(zero, 0)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, s(plus(zero, true)), _x81), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(true, id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(id(true), if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(s(_x51)), s(zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(id(false), _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), plus(zero, 0)), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(false, _x122, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(0, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x52, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, minus(plus(zero, true), 0), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), quot(0, s(_x121))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, if(true, minus(plus(zero, true), 0), _x201)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), quot(0, s(_x261)))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(plus(zero, false), _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, plus(zero, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(plus(s(_x112), s(_x111)), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(id(true), s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x122, if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(false, _x102, minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(plus(zero, zero), true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, id(if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), plus(zero, 0))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, minus(zero, 0)), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(plus(zero, zero))), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(minus(s(_x51), 0), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), if(true, 0, _x221)), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, if(true, true, _x101), _x111)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(false, _x82, s(_x51))), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(true, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21), _x151)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), if(false, _x112, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(if(true, plus(zero, if(false, _x142, zero)), _x161), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), if(true, zero, _x141)), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(true, minus(id(x), 0), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(if(true, true, _x101), if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, gt(s(if(true, s(_x51), _x81)), s(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), id(if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21))), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, id(s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(minus(s(_x51), 0)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(if(false, _x132, zero), if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(minus(id(id(x)), 0), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(true, s(s(_x51)), _x71), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(minus(zero, 0), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(id(zero), true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(quot(0, s(_x121))))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(plus(zero, id(x))), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), id(0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(s(_x51)), s(zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(gt(s(_x51), plus(zero, zero)), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(quot(s(_x132), s(_x131)), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(if(true, zero, _x121), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), if(true, s(zero), _x81)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(gt(s(_x111), zero), id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(if(true, s(_x51), _x81))), s(s(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(if(true, true, _x51), id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(plus(s(_x122), s(_x121)), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), plus(zero, zero)), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x91), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, id(quot(0, s(_x131))))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), plus(zero, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, 0)), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), quot(0, s(_x141))), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, gt(s(s(_x51)), s(zero)), _x61), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), if(false, _x182, id(id(x))), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(if(true, id(x), _x141)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(false, _x92, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, id(if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), plus(zero, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(minus(s(_x51), 0), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(if(false, _x192, false), _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(minus(true, 0), zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(minus(id(x), 0)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(s(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true)), s(0)), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(plus(zero, true), true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, if(false, _x142, id(x)))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, if(false, _x272, true)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), if(true, 0, _x121)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(plus(zero, if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(minus(plus(zero, true), 0), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), if(false, _x92, s(zero))), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(s(id(id(x))), s(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x182, if(true, minus(plus(if(false, _x152, zero), true), 0), _x171)), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(quot(s(_x112), s(_x111)), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(id(s(_x51)), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(plus(zero, s(_x51)), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(quot(s(_x92), s(_x91))), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(quot(s(_x92), s(_x91)), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(plus(zero, gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), id(true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(id(s(_x51)), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(true, s(_x51), _x71), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(true, if(false, _x152, zero), _x161), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, plus(zero, zero)), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(true, id(s(y)), _x31))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), plus(zero, zero))), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(if(true, false, _x191), _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(if(false, _x132, zero), true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x72, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(if(false, _x122, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(if(true, gt(s(s(_x51)), s(zero)), _x71), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), plus(zero, minus(id(id(x)), 0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(true, 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(if(true, true, _x151), false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(plus(zero, false), _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(if(true, zero, _x91))), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), id(0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(minus(id(x), 0)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), minus(if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, minus(if(false, _x142, if(true, zero, _x181)), 0)), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, id(zero), _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x71), zero), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(false, _x82, false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), id(zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), minus(if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), 0), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), id(if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21))), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, if(true, id(s(y)), _x61), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(if(true, id(x), _x181)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), plus(zero, zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, plus(if(false, _x152, zero), true)), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, minus(if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), 0), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x71), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(id(plus(if(false, _x152, zero), true)), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(if(false, _x132, zero), zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), if(true, true, _x131)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(id(s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(minus(gt(s(s(_x51)), s(zero)), 0), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(plus(zero, zero), zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(false, _x92, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(if(true, true, _x101), 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, minus(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71), 0))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(minus(zero, 0), if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, minus(zero, 0))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, if(true, s(_x51), _x111), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), minus(0, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), plus(zero, id(id(x))), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, if(false, _x192, zero)), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(if(true, s(_x51), _x91)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(if(true, s(_x51), _x91), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), if(true, id(id(x)), _x181), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(id(false), _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x141), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), id(if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), minus(id(id(x)), 0), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, id(true), _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(if(false, _x92, true), if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(id(id(x)), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), if(false, _x132, zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, s(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x101)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(gt(s(s(_x51)), s(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), plus(zero, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31)), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), minus(true, 0)), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(if(true, true, _x101), s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(if(false, _x112, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(plus(zero, gt(s(s(_x51)), s(zero))), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(if(true, zero, _x91), true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), if(true, 0, _x151)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(true, zero, _x81), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(id(gt(s(s(_x51)), s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(plus(zero, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(if(false, _x122, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(id(plus(plus(zero, zero), true)), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, plus(zero, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), if(false, _x172, id(id(x))), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(plus(zero, minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(if(false, _x122, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), if(false, _x132, 0))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), if(false, _x162, zero))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(if(true, s(_x51), _x121), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), quot(0, s(_x151))), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(plus(s(_x92), s(_x91)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(minus(s(_x51), 0), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(s(plus(zero, true)), s(0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(false, _x92, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(id(true), if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), minus(zero, 0)), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(gt(s(_x131), zero), if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(quot(s(_x92), s(_x91))), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(minus(true, 0), s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(true, s(if(true, s(_x51), _x81)), _x71), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(zero, true), 0), _x131), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(minus(plus(if(false, _x152, zero), true), 0), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x162, if(false, _x152, zero)), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(if(true, zero, _x131), if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, gt(s(_x231), zero)), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), id(true)), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x91), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(plus(id(_x102), s(_x101)), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), quot(0, s(_x121))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x91), zero), if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(id(plus(zero, if(false, _x142, if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), plus(zero, s(zero))), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(id(gt(s(_x51), zero))), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, gt(s(_x51), zero)), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(if(true, true, _x191), minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(if(true, zero, _x121), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), if(true, 0, _x121)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), id(if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(plus(zero, zero))), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, if(true, zero, _x221), _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(plus(zero, s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(minus(id(x), 0)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, true), if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(if(true, plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), _x111), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, plus(zero, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(plus(zero, true), if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(minus(false, 0), _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, minus(if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), 0), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(if(false, _x222, zero), true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x172, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(false, _x72, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(if(false, _x162, false), _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(id(plus(zero, gt(s(_x131), zero))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), plus(zero, true)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(minus(id(id(x)), quot(0, s(_x41))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), plus(zero, zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), id(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), if(false, _x82, s(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), plus(zero, zero)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(plus(id(_x92), s(_x91)), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(s(plus(zero, true)), s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(id(true), if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(id(if(true, if(gt(if(false, _x122, s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(minus(true, 0), id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(minus(id(x), 0)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x91), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(false, _x102, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(gt(s(_x81), zero), if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(minus(plus(zero, true), 0), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(true, 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), plus(zero, id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), minus(0, 0)), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(if(false, _x212, true), zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, id(if(false, _x142, zero))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(id(if(gt(if(true, s(_x51), _x91), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(minus(plus(zero, id(x)), 0)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), if(false, _x102, s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(if(true, id(x), _x131)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, gt(s(_x161), zero)), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), if(false, _x122, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x62, gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x92, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), id(if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(if(true, zero, _x91))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(if(true, s(_x51), _x111), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(s(_x51))), s(s(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), minus(true, 0)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(minus(false, 0), _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), 0), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, minus(if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), 0), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), minus(0, 0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(if(false, _x72, gt(s(s(_x51)), s(zero))), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(id(zero), true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(if(true, id(x), _x221)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(minus(zero, 0))), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), minus(s(0), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), if(false, _x222, 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x81), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), quot(0, s(_x191))), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, if(true, true, _x101))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), if(false, _x202, true)), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(id(s(s(_x51))), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(plus(id(_x72), s(_x71))), _x31)) → plus#(x, if(gt(s(plus(_x72, if(gt(s(_x71), _x71), _x71, s(_x71)))), plus(_x72, if(gt(s(_x71), _x71), _x71, s(_x71)))), plus(_x72, if(gt(s(_x71), _x71), _x71, s(_x71))), s(plus(_x72, if(gt(s(_x71), _x71), _x71, s(_x71))))))
plus#(if(gt(s(s(_x51)), s(if(false, _x92, zero))), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x42, if(true, id(s(y)), _x31))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(plus(s(_x162), s(_x161)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), minus(if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), 0), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(gt(s(_x81), zero), if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(if(false, _x112, minus(plus(plus(zero, zero), true), 0))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(id(false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), if(false, _x152, 0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(id(x))), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(gt(s(_x51), zero), if(true, if(plus(zero, minus(plus(zero, true), 0)), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, if(true, id(x), _x141))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(minus(plus(zero, true), 0), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(if(false, _x252, plus(zero, true)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, if(false, _x202, minus(plus(if(false, _x152, zero), true), 0)), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(false, _x92, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(if(false, _x112, plus(zero, if(false, _x132, true))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(id(zero), if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(gt(s(_x101), zero), if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, gt(s(_x131), zero), _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x91), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(id(zero), true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(plus(s(_x82), s(_x81))), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(gt(s(_x101), zero), s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(x), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(true, if(false, _x162, minus(plus(zero, true), 0)), _x171), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), if(true, 0, _x131)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(if(true, plus(zero, true), _x91)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), _x101)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), plus(zero, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(if(false, _x122, plus(zero, if(false, _x142, zero))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(true, if(false, _x162, minus(plus(zero, true), 0)), _x211), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(plus(zero, s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(if(false, _x162, false), _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(if(false, _x102, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(false, _x72, if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, plus(zero, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), minus(id(plus(zero, id(x))), 0), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(id(plus(zero, if(false, _x142, zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(id(s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), minus(true, 0)), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(id(false), _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(id(true), minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(minus(id(x), 0)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(quot(s(_x72), s(_x71))), _x31)) → plus#(x, if(gt(s(quot(minus(_x72, _x71), s(_x71))), quot(minus(_x72, _x71), s(_x71))), quot(minus(_x72, _x71), s(_x71)), s(quot(minus(_x72, _x71), s(_x71)))))
plus#(id(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), plus(zero, if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21))), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(plus(id(_x82), s(_x81))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, plus(zero, true)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(if(true, gt(s(s(_x51)), s(zero)), _x81), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), _x71)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), plus(zero, s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), if(false, _x82, s(zero))), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(if(false, _x132, s(_x51)), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(false, _x82, s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), quot(0, s(_x81))), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(plus(zero, false), _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, gt(s(_x51), zero), _x61), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(minus(false, 0), _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(plus(zero, minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0)), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, id(if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(id(zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(minus(false, 0), _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(if(true, false, _x131), _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(gt(s(if(true, s(_x51), _x81)), s(if(true, zero, _x91))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(plus(zero, id(x))), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(plus(id(_x82), s(_x81))), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, if(true, false, _x161), _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), id(if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(minus(zero, 0), if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(id(zero), if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), quot(0, s(_x121))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, minus(if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), 0)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x101), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(plus(zero, minus(plus(if(false, _x152, zero), true), 0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), id(0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(true, if(false, _x152, zero), _x191), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, gt(s(s(_x51)), s(zero)), _x61), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), id(true)), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(plus(id(_x82), s(_x81))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(minus(s(_x51), 0), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), minus(if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, id(zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, id(if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(plus(id(_x122), s(_x121)), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(true, s(_x51), _x71), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(plus(zero, true), if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), if(true, id(id(x)), _x111), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(s(id(x)), s(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, if(true, id(s(y)), _x31))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(if(true, s(_x51), _x91)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), plus(zero, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21)), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(plus(zero, true), if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x72, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(if(false, _x102, zero), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, false), _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), quot(0, s(_x121))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), gt(s(_x141), zero)), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(id(x))), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(if(false, _x202, true), zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(if(true, true, _x121), minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, minus(if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21), 0))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, id(gt(s(_x131), zero))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x71), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, gt(s(_x51), zero), _x61), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), minus(id(id(x)), 0), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), if(false, _x112, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(if(true, plus(zero, zero), _x121), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(true, s(s(_x51)), _x71), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(if(true, id(x), _x101)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(if(false, _x132, zero), true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(if(true, false, _x191), _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), minus(id(id(x)), 0), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), if(false, _x172, id(id(x))), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, gt(s(_x111), zero))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(zero, s(s(_x51))), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(id(s(_x51)), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(plus(zero, gt(s(s(_x51)), s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, id(true)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(id(s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(true, 0, _x61)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), quot(0, s(_x101))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(if(false, _x172, zero), if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, if(true, minus(plus(if(false, _x152, zero), true), 0), _x201), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, gt(s(_x51), zero), _x61), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(minus(true, 0), if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(if(false, _x212, plus(if(false, _x152, zero), true)), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(if(false, _x92, zero))), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(id(plus(zero, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(plus(zero, if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(false, _x92, zero), if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(minus(id(x), 0)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(if(false, _x102, true), s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), minus(0, 0)), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x62, if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), minus(if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), 0), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), if(true, minus(id(id(x)), 0), _x121), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, id(0))), if(false, _x92, id(id(x))), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, gt(s(_x161), zero)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(s(plus(zero, true))), s(s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(gt(zero, _x171), _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(plus(zero, true), if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(false, _x192, if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), quot(0, s(_x121))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(false, _x72, s(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(gt(s(_x151), zero), false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x121), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71), _x81)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(id(s(s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x142, gt(s(_x131), zero))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, if(true, id(s(y)), _x31), _x41)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(if(false, _x62, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(if(true, zero, _x91))), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(id(s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), quot(0, s(_x121))), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(true, minus(plus(zero, true), 0), _x71), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(id(plus(zero, true)), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(if(false, _x222, id(x))), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), if(true, id(id(x)), _x131), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(id(plus(if(false, _x152, zero), true)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), plus(zero, if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x101), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), quot(0, s(_x131)))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(plus(zero, s(_x51))), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, plus(zero, true)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(if(false, _x82, plus(zero, true)), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(id(zero), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(plus(zero, minus(if(true, plus(zero, true), _x111), 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(id(plus(zero, true)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(if(false, _x122, zero), gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(zero, s(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, plus(zero, minus(plus(zero, true), 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(false, _x102, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(minus(true, 0), if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x62, minus(gt(s(s(_x51)), s(zero)), 0)), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(if(true, 0, _x101))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(id(true), zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(plus(zero, zero), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(plus(zero, false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(s(plus(zero, true)), s(0)), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), if(true, 0, _x131)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(s(_x51))), s(s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), quot(0, s(_x121))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(_x51), zero), 0), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(if(false, _x92, zero), true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(if(false, _x122, zero), if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(zero, true), 0), _x201), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(id(if(false, _x162, minus(plus(zero, true), 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(true, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x171)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(true, if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x121), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(if(true, true, _x81), if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, plus(zero, true)), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(plus(zero, true), plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), plus(zero, 0)), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), if(true, 0, _x131))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(if(false, _x182, id(x))), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(gt(s(_x51), zero), 0)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, id(true)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(gt(s(_x81), zero), if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(if(true, gt(s(_x51), zero), _x121), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(s(plus(zero, true)), s(0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), minus(zero, 0)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(minus(zero, 0))), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), minus(id(id(x)), 0), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, true, _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(if(true, id(x), _x121)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(true, if(false, _x142, if(true, zero, _x181)), _x171)), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x131))), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(false, _x112, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(id(zero))), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, id(if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21))), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, minus(zero, 0)), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(id(if(false, _x82, if(true, if(if(false, _x152, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(id(gt(s(_x51), zero)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(gt(zero, _x131), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), minus(s(zero), 0)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(s(plus(plus(zero, if(false, _x142, zero)), true)), s(0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), minus(if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x172, if(false, _x142, if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), if(true, zero, _x81)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(id(false), _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x152, if(false, _x142, if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x62, gt(s(_x51), zero)), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), plus(zero, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(if(true, minus(plus(zero, true), 0), _x111), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(if(true, gt(s(_x51), zero), _x151), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(gt(zero, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(if(false, _x172, false), _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), if(false, _x122, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, if(false, _x112, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), if(false, _x82, 0)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(plus(zero, id(id(x))), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x101)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x121)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, minus(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), 0), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(zero, _x101), _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(plus(zero, false), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(plus(zero, zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(false, _x112, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(minus(false, 0), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(gt(zero, _x231), _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), if(false, _x82, 0)), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, plus(zero, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21)), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(false, _x72, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), plus(zero, if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), minus(0, 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, plus(zero, zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(plus(zero, zero), if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(id(plus(zero, true)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, id(minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), quot(0, s(_x141))), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), minus(s(zero), 0)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(id(gt(s(s(_x51)), s(zero))), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), if(false, _x172, true)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), if(false, _x122, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(s(plus(zero, true)), s(0)), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), if(true, zero, _x101)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, id(minus(plus(if(false, _x152, zero), true), 0)), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, if(false, _x132, minus(plus(plus(zero, if(false, _x142, zero)), true), 0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(if(false, _x122, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(true, minus(id(id(x)), 0), _x121), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(gt(s(_x201), zero), zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), minus(true, 0)), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(s(gt(s(s(_x51)), s(zero))), s(0)), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), minus(zero, 0)), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), plus(zero, zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(minus(false, 0), _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, if(true, true, _x101)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), if(false, _x162, true)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(if(false, _x82, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(gt(zero, _x171), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), id(s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), minus(0, 0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(false, _x72, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(if(false, _x122, plus(zero, true)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, id(if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, plus(zero, if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x111), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(id(gt(s(_x51), zero)), 0), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(if(true, gt(s(s(_x51)), s(zero)), _x71), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), id(zero))), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(if(false, _x82, s(s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(plus(zero, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), if(false, _x172, zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x221))), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(false, _x72, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(if(true, id(x), _x121)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, minus(id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(true, zero, _x81)), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(plus(zero, false), _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(if(true, s(_x51), _x121), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(s(_x51)), s(zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, if(false, _x122, id(0)))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(zero, s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), if(false, _x112, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), if(true, id(id(x)), _x111), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(if(true, false, _x161), _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), id(zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, gt(s(_x271), zero)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(if(true, gt(s(_x51), zero), _x111), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(if(true, zero, _x101))), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, plus(zero, zero), _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(id(x))), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, if(true, true, _x131)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(minus(gt(s(_x51), zero), 0), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(true, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21), _x161)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), if(false, _x142, 0)), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(minus(false, 0), _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(id(true), minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(plus(id(_x82), s(_x81))), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), plus(zero, if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(plus(s(_x132), s(_x131)), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(plus(zero, false), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), if(false, _x92, s(zero))), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(zero, plus(plus(zero, zero), true)), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(plus(id(_x102), s(_x101))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), plus(zero, s(zero))), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(if(true, s(_x51), _x131), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(if(false, _x82, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(id(plus(zero, true)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), if(true, id(id(x)), _x111), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, plus(zero, minus(true, id(0))), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, if(false, _x132, minus(plus(plus(zero, if(false, _x142, zero)), true), 0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(if(false, _x152, false), _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(id(if(false, _x162, minus(plus(zero, true), 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(plus(zero, id(x))), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(minus(zero, 0), true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(id(zero), true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), minus(if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), 0), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(minus(id(x), 0)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, id(true)), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(false, _x72, s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(s(plus(zero, gt(s(_x131), zero))), s(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), if(true, s(zero), _x101)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(if(false, _x162, plus(zero, if(false, _x142, zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(plus(zero, if(false, _x52, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(true, zero, _x81)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(gt(zero, _x221), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, id(if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21))), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, minus(gt(s(s(_x51)), s(zero)), 0), _x61), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(plus(zero, true), if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(plus(s(_x82), s(_x81))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(plus(zero, false), _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(if(true, false, _x221), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), id(if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21)), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(if(true, gt(s(_x51), zero), _x111), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(plus(id(_x92), s(_x91))), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, if(true, id(0), _x121))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(if(false, _x72, s(y))), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x141), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), id(0)), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), id(s(zero))), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), if(false, _x122, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(plus(zero, true), minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(id(plus(plus(zero, if(false, _x142, zero)), true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, if(true, zero, _x191)), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x72, if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, minus(zero, 0), _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(minus(id(x), 0)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), _x61), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(gt(s(_x81), zero), if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(gt(if(true, s(_x51), _x71), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), id(0)), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, if(true, true, _x131)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(minus(id(x), 0)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(gt(zero, _x181), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(plus(s(_x92), s(_x91)), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x91), zero), if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, gt(s(s(_x51)), s(zero))), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, if(true, true, _x101)), 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(minus(zero, 0), true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(if(true, plus(zero, true), _x121), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x62, gt(s(s(_x51)), s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), minus(zero, 0)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), plus(zero, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(if(true, gt(s(_x51), zero), _x111), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(true, if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x131), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(if(false, _x162, plus(zero, if(false, _x142, zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(if(false, _x152, s(_x131)), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, plus(zero, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(if(false, _x192, false), _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(false, _x92, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(false, _x72, s(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(true, zero, _x181), true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(id(zero))), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(minus(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31), 0))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(minus(id(x), 0)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), plus(zero, 0)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, if(false, _x242, minus(plus(zero, true), 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(if(false, _x152, plus(zero, if(false, _x142, if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(false, _x122, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(if(false, _x192, true), minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(minus(id(x), 0)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x72, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, minus(if(true, zero, _x181), 0))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), if(true, zero, _x81)), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(minus(id(x), 0)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), if(true, 0, _x141)), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(false, _x112, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, minus(if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), 0), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(minus(if(true, plus(zero, true), _x111), 0), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(minus(false, 0), _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(false, _x112, if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(id(false), _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, minus(gt(s(s(_x51)), s(zero)), 0)), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(plus(s(_x82), s(_x81))), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(true, 0, _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(if(false, _x192, id(x))), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(if(true, true, _x81), if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(s(_x51))), s(s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), minus(0, 0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(if(false, _x122, zero), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(gt(s(_x81), zero), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(false, _x82, minus(id(id(x)), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(false, 0), _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(if(true, zero, _x121), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), quot(0, s(_x101)))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(plus(zero, zero), if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(false, _x42, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(id(x))), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, plus(zero, if(false, _x132, true))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(id(s(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(if(false, _x82, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(id(x)), _x21))), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(if(false, _x112, id(gt(s(_x51), zero))), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(gt(s(_x51), zero), 0), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), if(true, 0, _x221))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), quot(0, s(_x221))), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(plus(zero, id(x))), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), _x71), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, minus(true, 0))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), if(true, 0, _x121)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), quot(0, s(_x221)))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(minus(plus(zero, if(false, _x142, zero)), 0), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), minus(0, 0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(if(true, plus(zero, true), _x81), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(minus(s(_x51), 0)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(false, _x92, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, if(false, _x202, minus(plus(zero, true), 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(id(zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(minus(true, 0), minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), id(true)), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(id(zero), true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), minus(id(id(x)), 0), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(id(x))), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(id(zero), zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), plus(zero, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(plus(zero, s(_x51)), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, if(true, zero, _x151)), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(false, _x92, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), if(false, _x112, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(if(true, id(x), _x91), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(id(true), id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(id(true), if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(id(false), _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), minus(if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), 0), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(if(true, s(_x51), _x101)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, plus(zero, id(s(y))), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x71), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(s(plus(zero, true)), 0), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(id(s(_x131)), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), gt(s(_x231), zero)), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(minus(zero, 0), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(id(s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, plus(zero, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), if(false, _x142, true)), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(plus(zero, gt(s(s(_x51)), s(zero))), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, gt(s(_x101), zero)), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), _x111), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), id(true)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), minus(if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(false, _x92, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x71), if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(if(true, zero, _x101))), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(minus(false, 0), _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(if(true, true, _x121), true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(false, _x102, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31)), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), if(true, zero, _x111)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x122, if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), plus(zero, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(if(true, plus(zero, id(x)), _x121)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(minus(id(x), 0)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(if(false, _x122, minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0)), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(gt(zero, _x181), _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(false, _x102, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31)), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, minus(true, 0), _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, plus(zero, minus(plus(if(false, _x152, zero), true), 0)), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(id(s(_x51)), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(s(_x51))), s(s(zero))), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), plus(zero, id(id(x))), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), gt(s(_x201), zero)), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), minus(zero, 0)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(minus(false, 0), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, not(false)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x71), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(plus(zero, true), s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(id(s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(plus(zero, true), if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(if(false, _x82, true), if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, plus(zero, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21))), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(if(true, id(gt(s(_x51), zero)), _x111), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(if(false, _x102, true), if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), if(false, _x122, zero))), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), if(true, 0, _x121)), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(plus(zero, gt(s(_x51), zero))), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(plus(zero, true), if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(id(plus(zero, true)), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x171), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), if(true, 0, _x181)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x182, false), _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71), _x121))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(plus(s(_x122), s(_x121)), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(minus(if(true, false, _x131), 0), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(id(s(_x51))), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(minus(if(true, s(_x51), _x81), 0)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), plus(zero, s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(plus(zero, true), if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), plus(zero, id(id(x))), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(id(zero), if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, minus(if(false, _x142, if(true, zero, _x181)), 0)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(plus(zero, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(if(false, _x162, minus(plus(zero, true), 0)), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), plus(zero, 0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(plus(zero, minus(plus(zero, true), 0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(plus(zero, true), if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), id(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(minus(false, 0), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(minus(gt(s(s(_x51)), s(zero)), 0)), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(plus(zero, true), zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(if(false, _x122, plus(zero, true)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, gt(s(_x51), zero), _x61), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(if(true, zero, _x101))), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(false, _x82, s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), id(if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(if(true, id(x), _x191)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(plus(s(_x82), s(_x81)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(if(false, _x232, id(x))), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31)), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(if(false, _x62, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, plus(zero, minus(plus(plus(zero, if(false, _x142, zero)), true), 0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x142, if(false, _x132, true))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, if(true, true, _x111))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x101), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(false, _x92, if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61)), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(true, s(s(_x51)), _x71), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, gt(s(_x51), zero)), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(id(if(true, if(gt(s(_x51), zero), if(if(false, _x132, false), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), minus(0, 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x132, minus(plus(if(false, _x152, zero), true), 0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), if(true, zero, _x171)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, id(zero)), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, minus(zero, 0), _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(false, _x82, s(_x51))), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x121)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(plus(zero, s(s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, id(if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(if(true, gt(s(_x51), zero), _x101)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, minus(plus(zero, true), 0), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, plus(zero, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), plus(zero, 0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(false, _x52, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(plus(zero, s(_x51)), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(minus(s(_x51), 0)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(id(x)), _x21))), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), id(0)), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(if(false, _x82, gt(s(s(_x51)), s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), id(0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(s(plus(plus(zero, if(false, _x142, zero)), true)), s(0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(plus(zero, false), _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x81), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), if(true, id(id(x)), _x111), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(id(s(s(_x51))), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), if(true, s(zero), _x81)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(if(true, plus(plus(zero, if(false, _x142, zero)), true), _x111), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(minus(s(_x51), 0), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(minus(id(x), 0)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, if(false, _x232, true)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(gt(s(if(true, s(_x51), _x81)), s(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(if(true, plus(plus(zero, if(false, _x142, zero)), true), _x151), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(plus(zero, false), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(gt(s(_x51), zero), 0), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), if(true, true, _x171)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(id(true), true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), if(true, zero, _x131)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), plus(zero, 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), if(true, s(zero), _x91)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(true, if(false, _x132, true), _x141)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(if(false, _x182, id(x))), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, id(plus(zero, true)), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x42, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, if(false, _x212, zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(minus(s(s(_x51)), 0), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, if(false, _x162, false), _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), minus(s(zero), 0)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, minus(if(false, _x142, zero), 0)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(false, _x112, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, if(false, _x192, true)), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, minus(if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), 0), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, plus(zero, false), _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(if(false, _x82, plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(plus(zero, if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(id(gt(s(_x51), zero)), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x91), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(minus(plus(zero, true), 0)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(plus(zero, s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, plus(plus(zero, if(false, _x142, zero)), true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(minus(s(_x51), 0)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), plus(zero, if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(id(if(false, _x82, if(true, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(zero, s(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), minus(0, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, plus(zero, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, if(false, _x272, true)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(if(true, minus(plus(zero, if(false, _x132, true)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, if(false, _x222, zero)), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), id(0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(if(true, true, _x131), plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(plus(zero, false), _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(minus(plus(zero, if(false, _x142, zero)), 0), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(if(false, _x92, s(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(id(true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(id(false), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(plus(id(_x122), s(_x121)), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(id(if(false, _x152, zero)), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), minus(if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), 0), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(plus(zero, true), 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, if(true, false, _x131), _x141), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(id(minus(plus(zero, true), 0)), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(true, zero, _x221), true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(plus(zero, false), _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(if(true, false, _x201), _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(id(if(true, if(id(id(gt(s(_x51), zero))), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(if(true, true, _x81), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, id(zero)), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), if(false, _x122, minus(id(id(x)), 0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(if(true, id(x), _x121)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, minus(if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21), 0)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, plus(zero, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(minus(gt(s(s(_x51)), s(zero)), 0), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), if(false, _x112, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(if(false, _x152, plus(plus(zero, if(false, _x142, zero)), true)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), if(false, _x92, s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(if(true, s(s(_x51)), _x81), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), plus(zero, 0)), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(id(gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), if(true, 0, _x221)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(id(false), _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(id(s(_x51)), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(plus(id(_x92), s(_x91))), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), if(false, _x122, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(x)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(s(_x72), s(_x71)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(if(if(false, _x52, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), plus(zero, 0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), minus(zero, 0))), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), id(zero)), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, plus(zero, id(x)))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(id(zero))), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, minus(if(false, _x142, zero), 0)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(plus(s(_x152), s(_x151)), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(false, _x72, if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(id(gt(s(s(_x51)), s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(if(true, plus(plus(zero, if(false, _x142, zero)), true), _x151), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(plus(zero, s(_x51))), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(false, _x62, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(plus(zero, minus(plus(zero, gt(s(_x131), zero)), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(if(false, _x112, minus(plus(zero, true), 0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(true, gt(s(_x51), zero), _x91), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), id(0)), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(plus(zero, id(id(x))), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), gt(s(_x151), zero)), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(id(plus(zero, if(false, _x132, true))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(id(s(if(true, s(_x51), _x81))), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(gt(s(_x81), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(minus(s(_x131), 0), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(s(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(if(false, _x132, false), _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(id(minus(plus(zero, true), 0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(minus(gt(if(true, s(s(_x51)), _x81), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, id(if(false, _x142, if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(if(true, zero, _x131), true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), minus(id(id(x)), 0), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), _x51)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(plus(zero, if(false, _x152, zero)), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), id(0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(id(s(_x51)), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(if(true, true, _x81), if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x52, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(minus(0, 0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(if(true, true, _x201), zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(if(true, plus(zero, true), _x251), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(true, id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, plus(zero, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x72, true), if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, if(false, _x252, zero)), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), plus(zero, if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x91), zero), if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(minus(s(s(_x51)), 0), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(if(true, 0, _x111), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(if(true, false, _x231), _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(id(x))), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x32, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(plus(zero, if(true, false, _x131)), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(if(false, _x102, id(x))), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(minus(gt(s(s(_x51)), s(zero)), 0)), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(plus(zero, s(_x51)), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(false, _x102, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, if(true, true, _x161)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(if(false, _x152, true), false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, minus(true, 0)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), plus(zero, 0)), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(if(true, plus(zero, gt(s(_x131), zero)), _x111), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), minus(s(zero), 0)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, minus(gt(s(s(_x51)), s(zero)), 0), _x61), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(quot(s(_x82), s(_x81))), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(minus(plus(zero, if(false, _x142, zero)), 0), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(id(true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(id(zero))), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(if(true, s(_x51), _x91)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(minus(true, 0), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(id(true), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), 0), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, id(if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21))), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(plus(zero, minus(plus(plus(zero, zero), true), 0))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(if(true, s(_x51), _x131), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(if(true, s(s(_x51)), _x81), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(minus(if(false, _x162, minus(plus(zero, true), 0)), 0), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), plus(zero, 0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), minus(zero, 0)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(id(true), plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, id(true)), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(if(true, id(x), _x121)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), minus(if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(id(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, plus(id(_x112), s(_x111)), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(true, if(false, _x142, zero), _x181)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x62, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x161), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(false, _x72, s(s(_x51))), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(id(gt(s(s(_x51)), s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(minus(s(if(true, s(_x51), _x81)), 0), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x82, false), _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), plus(zero, id(id(x))), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(if(false, _x92, true), if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(if(false, _x112, s(_x51)), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(quot(s(_x82), s(_x81))), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(minus(plus(zero, zero), 0), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(false, _x72, s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, minus(zero, 0)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(if(false, _x162, zero), if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), if(true, id(id(x)), _x181), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(id(zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, id(if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(true, 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31)), _x101)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(if(true, zero, _x121), if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(gt(id(s(s(_x51))), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(gt(zero, _x181), _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), id(if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, if(true, true, _x131)), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(false, _x72, if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), plus(zero, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(id(gt(s(_x51), zero)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(minus(id(x), 0)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(quot(s(_x162), s(_x161)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31)), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(if(false, _x192, id(x))), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), minus(0, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, id(if(false, _x142, zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(gt(s(_x101), zero), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(if(true, false, _x101), _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(minus(zero, 0))), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(id(s(_x51)), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(plus(zero, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(id(if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(s(plus(zero, true)), s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, minus(true, 0)), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), minus(if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(gt(s(_x81), zero), if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(plus(zero, false), _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(gt(s(_x51), zero), if(minus(plus(plus(zero, zero), true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(zero, s(s(_x51))), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(id(if(true, plus(zero, true), _x111)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x131), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(plus(zero, false), _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), if(false, _x132, 0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(true, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21), _x121)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(if(false, _x122, plus(zero, if(false, _x142, if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(false, _x72, if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(plus(zero, if(false, _x162, minus(plus(zero, true), 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, if(true, minus(plus(zero, true), 0), _x201)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(if(true, false, _x181), _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(true, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21), _x161)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), id(0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(if(true, zero, _x101), true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(plus(zero, id(x)))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31)), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), 0), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(plus(zero, false), _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, id(minus(plus(zero, true), 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), if(true, zero, _x131)), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(gt(zero, _x101), _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(if(true, false, _x221), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(plus(s(_x82), s(_x81)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(if(true, true, _x121), minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(minus(zero, 0), if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(id(false), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(true, if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x121), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(if(true, zero, _x161), if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(if(false, _x122, s(_x51)), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(if(true, false, _x161), _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), id(0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71), _x81)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, minus(if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), 0), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(if(false, _x102, false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), if(true, 0, _x81)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, plus(zero, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, plus(zero, minus(plus(zero, true), 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, id(if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(if(false, _x102, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(plus(zero, zero))), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(minus(false, 0), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), if(true, zero, _x131)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, minus(zero, 0)), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), minus(0, 0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(s(_x51)), s(zero)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(quot(s(_x132), s(_x131)), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(if(false, _x132, id(x))), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, id(minus(plus(zero, true), 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, gt(s(_x231), zero)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, zero), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, minus(true, 0)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x72, if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), quot(0, s(_x221)))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, plus(zero, true)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(gt(s(s(_x51)), s(zero))), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(true, if(false, _x142, zero), _x151)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), id(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, id(true)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(s(gt(s(s(_x51)), s(zero))), s(0)), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), if(false, _x262, 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, id(s(_x51)), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), if(true, true, _x131)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(minus(true, 0), zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(_x51), zero), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x71), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), minus(id(id(x)), 0), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), if(true, 0, _x141)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(gt(s(s(_x51)), id(s(zero))), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(if(false, _x92, s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(zero, s(_x51)), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, id(if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), plus(zero, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(s(_x72), s(_x71)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x91), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(minus(false, 0), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(minus(true, 0), if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(minus(id(x), 0)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), plus(zero, true)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x71), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(if(true, id(x), _x231)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(plus(zero, s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(if(true, plus(zero, true), _x141), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(id(true), zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(if(true, zero, _x121), gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(plus(zero, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(if(false, _x132, plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true)), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(minus(true, 0), if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(id(false), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(quot(s(_x82), s(_x81))), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, minus(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(id(s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(false, _x92, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, minus(gt(s(s(_x51)), s(zero)), 0), _x61), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(if(true, plus(zero, true), _x251), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(plus(zero, id(x))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x131))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), id(s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(id(x))), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), if(false, _x152, true)), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, false, _x81), _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(plus(zero, true), if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(if(true, id(x), _x121)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), if(false, _x82, zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, minus(true, 0)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x92, if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), id(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(true, false, _x81), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), id(if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(id(gt(s(s(_x51)), s(zero))), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), id(zero))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(id(zero), gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, gt(s(s(_x51)), s(zero)), _x61), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, plus(zero, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(if(true, plus(zero, if(false, _x142, if(true, zero, _x181))), _x151), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, minus(true, 0)), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, minus(if(plus(zero, minus(true, id(0))), id(id(x)), _x21), 0), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(quot(s(_x82), s(_x81))), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), if(false, _x222, 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(plus(s(_x132), s(_x131)), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(x), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, minus(false, 0), _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(plus(s(_x82), s(_x81)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(false, _x102, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21)), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), _x121), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, minus(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), 0), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), plus(zero, 0)), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(gt(s(s(_x51)), s(zero)), if(plus(zero, true), if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x121), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(id(true), if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), if(true, true, _x231)), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, id(gt(s(_x51), zero))), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), minus(s(zero), 0)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), plus(zero, zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, if(false, _x162, true)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(plus(zero, false), _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x71), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(minus(true, 0), if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(id(true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), if(false, _x112, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(if(true, gt(s(s(_x51)), s(zero)), _x71), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), minus(zero, 0)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(plus(zero, id(x))), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(plus(s(_x122), s(_x121)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(gt(zero, _x181), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x132, if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21))), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(s(id(id(x))), s(0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), if(false, _x112, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, plus(zero, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, if(true, true, _x161)), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(plus(id(_x152), s(_x151)), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(_x51), zero), 0), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(if(false, _x122, true), true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x182, zero), true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(minus(if(false, _x162, minus(plus(zero, true), 0)), 0), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(if(false, _x112, gt(s(_x51), zero)), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(false, _x72, if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, if(false, _x132, true), _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, plus(zero, if(false, _x142, if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(if(false, _x62, gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, plus(zero, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21))), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(gt(s(_x51), zero), if(minus(false, 0), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, minus(s(_x51), 0), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, plus(zero, if(false, _x142, zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), if(true, true, _x151)), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(false, _x82, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, gt(s(_x141), zero)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, plus(zero, true)), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(if(true, true, _x81), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(if(false, _x112, minus(plus(zero, true), 0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), id(zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(id(plus(zero, if(false, _x142, zero))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), id(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, id(true)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(if(false, _x122, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(true, if(false, _x142, zero), _x181)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x71), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(false, _x112, plus(zero, true)), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), minus(0, 0))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(minus(true, 0), if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(if(true, false, _x181), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, plus(zero, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, id(if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x222, zero), true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(id(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(true, s(_x51), _x71), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(gt(s(_x51), zero), minus(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(if(true, false, _x181), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(minus(true, 0), plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, minus(true, 0)), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(true, false, _x181), _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, 0), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), minus(0, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), if(true, 0, _x151)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x62, gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(minus(zero, 0))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), minus(0, 0)), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), if(false, _x122, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), plus(zero, true)), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(false, _x102, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, plus(zero, true)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(gt(s(_x121), zero), minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(plus(zero, zero), if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, plus(zero, zero))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), minus(if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), 0), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(gt(s(s(_x51)), s(if(true, zero, _x91))), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(if(true, zero, _x221), true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x62, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(true, if(minus(true, 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(if(true, false, _x151), _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x62, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), quot(0, s(_x121))), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(gt(s(s(_x51)), s(zero))), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), id(zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(minus(plus(zero, true), 0), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), if(false, _x112, id(plus(zero, id(x)))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x72, if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(minus(if(false, _x152, zero), 0), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(id(true), if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x62, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), id(0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, quot(s(_x112), s(_x111)), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), minus(zero, 0)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(minus(plus(zero, if(false, _x142, if(true, zero, _x181))), 0), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(plus(zero, id(x))), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, if(true, zero, _x211))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(plus(id(_x122), s(_x121)), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), if(true, 0, _x101)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x51), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(if(true, zero, _x151), true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(plus(zero, true), id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), if(true, s(zero), _x81)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(s(gt(s(s(_x51)), s(zero))), s(0)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, plus(zero, gt(s(_x131), zero))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(if(true, id(x), _x181)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), if(false, _x82, zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, minus(if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), 0), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(minus(s(_x51), 0)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, plus(zero, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31)), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), id(zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(s(_x51))), s(s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(false, _x82, zero)), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, id(minus(plus(plus(zero, if(false, _x142, zero)), true), 0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(id(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), id(0)), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(minus(zero, 0), zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(s(plus(zero, true)), s(0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x111), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(if(false, _x122, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, id(zero), _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(quot(s(_x92), s(_x91)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), s(y)) → plus#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))
plus#(id(if(true, if(gt(s(_x51), id(zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(plus(zero, if(false, _x162, minus(plus(zero, true), 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, if(false, _x62, id(s(y))), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(if(true, false, _x171), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, minus(true, 0)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), minus(true, 0)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(id(x))), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(minus(s(s(_x51)), 0), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(minus(s(_x51), 0), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(false, _x202, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(if(false, _x122, gt(s(_x51), zero))), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(s(_x51)), s(zero))), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(true, if(false, _x162, minus(plus(zero, true), 0)), _x171), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), plus(zero, 0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), if(false, _x132, zero)), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(minus(id(x), 0)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(id(s(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x82, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31)), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(id(true), minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(minus(false, 0), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), plus(zero, 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(if(true, true, _x91), if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), plus(zero, zero)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(false, _x182, zero))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), minus(zero, 0)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), if(true, 0, _x131)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(id(false), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(if(false, _x92, s(_x51)), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(id(x))), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, id(plus(zero, 0)))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(id(true), if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x62, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(false, _x102, minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(minus(zero, 0))), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(if(false, _x132, s(_x51)), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(plus(zero, s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), minus(if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), 0), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(minus(false, 0), _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), plus(zero, zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(id(zero), if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, id(zero))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(id(true), id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x71), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(id(if(minus(true, 0), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), plus(zero, 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(if(true, true, _x111), id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(plus(zero, false), _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x121)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, id(if(false, _x142, if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(minus(plus(zero, if(true, true, _x101)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, id(if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), if(true, 0, _x121)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), minus(true, 0)), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), plus(zero, s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, plus(zero, if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(true, zero, _x141)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(if(true, s(_x51), _x101), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), plus(zero, zero)), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(plus(zero, 0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(id(true), if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x191)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x41), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(id(zero), minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(if(false, _x102, zero))), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(false, _x102, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21)), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(if(false, _x122, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, plus(zero, zero)), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, gt(s(_x231), zero)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(plus(zero, zero), if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), if(true, zero, _x101)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(if(false, _x122, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), _x71), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(gt(s(_x121), zero), true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(s(plus(zero, true)), s(0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x91), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x101)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(gt(s(_x51), zero), 0), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x91), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(false, _x122, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21))), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(if(false, _x112, true), id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(if(false, _x82, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), id(if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(_x51), zero), 0), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), plus(zero, if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(id(zero), zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(id(plus(zero, true)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(id(plus(plus(zero, if(false, _x142, zero)), true)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), if(true, id(id(x)), _x221), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), if(false, _x102, zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, false, _x81), _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(id(x))), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, id(x), _x41)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(minus(zero, 0), if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), minus(if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), 0), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), id(if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21)), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), id(s(zero))), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(plus(id(_x162), s(_x161)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), id(if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(id(0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(if(true, s(_x51), _x161), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(true, 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, gt(s(if(true, s(_x51), _x81)), s(zero)), _x61), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(id(true), if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x172, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(id(if(true, false, _x131)), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), plus(zero, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), if(true, id(id(x)), _x111), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(if(true, id(x), _x91)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(plus(zero, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(plus(zero, true), if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(plus(zero, zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(minus(s(y), 0)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(if(true, zero, _x131), true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(if(false, _x102, false), _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(plus(zero, true), id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(plus(zero, zero), if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(if(false, _x122, plus(zero, true)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(if(true, false, _x101), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), if(false, _x102, 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(gt(zero, _x141), _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x101), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x91), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(plus(zero, if(false, _x152, zero)), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), id(0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, id(true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(id(gt(s(_x51), zero)), 0), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(if(false, _x102, 0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), plus(zero, zero)), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x192, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x172, minus(plus(if(false, _x152, zero), true), 0)), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(id(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171)), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(id(false), _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x62, if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(gt(s(s(_x51)), s(zero))), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(false, _x92, minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), if(true, zero, _x121))), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(id(false), _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), if(true, 0, _x81)), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), minus(0, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(minus(false, 0), _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, if(true, true, _x141)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(if(false, _x112, plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), plus(zero, true)), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, minus(true, 0)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), if(true, true, _x201)), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), if(false, _x132, id(id(x))), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x71), if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), if(true, id(id(x)), _x111), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, plus(s(_x112), s(_x111)), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(gt(s(_x81), zero), if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, if(true, zero, _x181), _x201))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(plus(zero, zero), if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(id(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, id(if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), if(true, id(id(x)), _x141), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(if(false, _x92, s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(id(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(gt(s(_x81), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(plus(zero, id(x))), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(if(false, _x122, gt(s(_x51), zero)), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(gt(s(_x81), zero), if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x152, if(false, _x142, zero))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(if(false, _x102, minus(plus(zero, if(false, _x132, true)), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(false, _x132, false), _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), if(false, _x142, 0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(if(true, zero, _x141), zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), if(true, s(zero), _x91)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), minus(zero, 0)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, minus(if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), 0), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, id(if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, minus(id(id(x)), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(if(false, _x122, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(minus(s(_x51), 0)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, id(if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(minus(id(x), 0)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), if(true, 0, _x121)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), id(zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(if(true, plus(zero, if(false, _x142, zero)), _x121), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, plus(zero, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31)), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(minus(if(false, _x152, zero), 0), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), id(s(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(id(false), _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(plus(zero, if(false, _x152, zero)), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(if(false, _x212, plus(zero, true)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(id(s(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(plus(zero, s(_x51)), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(if(false, _x132, zero), id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(if(false, _x92, id(id(x))), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), id(if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(gt(s(if(true, if(false, _x112, s(_x51)), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), if(true, 0, _x121)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), quot(0, s(_x121))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(gt(zero, _x101), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(if(true, minus(plus(zero, true), 0), _x111), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), id(0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), minus(0, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(minus(false, 0), _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(if(true, zero, _x91))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(true, if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x121), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), minus(if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(id(s(_x51)), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, minus(if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21), 0)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(zero, _x81), _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(if(false, _x252, plus(zero, true)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(gt(zero, _x131), _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), minus(quot(0, s(_x91)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(plus(zero, zero), zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(true, if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x131), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), plus(zero, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), if(true, 0, _x81)), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(minus(s(_x51), 0), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), if(false, _x152, 0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x62, minus(gt(s(s(_x51)), s(zero)), 0)), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(gt(zero, _x141), _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x62, gt(s(s(_x51)), s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), if(false, _x82, zero)), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x181))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(if(false, _x132, plus(zero, zero)), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(gt(s(_x81), zero), if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(if(true, zero, _x41), if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(minus(s(_x51), 0), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(minus(true, 0), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(minus(id(x), 0)), _x21), _x51)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(if(false, _x82, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), id(if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(false), _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31)), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(false, _x62, true), id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, if(true, plus(zero, true), _x111)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(true), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(plus(zero, id(x))), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), minus(id(id(x)), 0), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(id(if(false, _x152, zero)), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), if(true, 0, _x151)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(id(true), if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), _x111), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(if(false, _x172, zero), if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, plus(zero, true)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(plus(zero, s(_x51)), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(id(s(y))), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(if(true, true, _x91), if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, minus(if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), 0)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, if(true, true, _x101)), _x81), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), quot(0, s(_x61))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(if(true, id(x), _x191)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), id(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(gt(s(_x121), zero), minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(plus(id(_x82), s(_x81))), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(if(false, _x122, s(_x51)), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(false, _x202, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(if(true, minus(plus(zero, true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), if(true, 0, _x261))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(s(_x51))), s(s(zero))), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(if(false, _x212, plus(zero, true)), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(if(false, _x232, false), _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x122, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(if(false, _x222, zero), true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), gt(s(_x161), zero)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), plus(zero, if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(s(plus(if(false, _x152, zero), true)), s(0)), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x62, gt(s(s(_x51)), s(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), plus(zero, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(if(true, true, _x81), if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(s(plus(zero, true)), s(0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, if(true, plus(zero, true), _x141), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(minus(plus(zero, gt(s(_x131), zero)), 0), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71), _x81)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(if(true, s(_x131), _x151), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(if(false, _x152, plus(plus(zero, if(false, _x142, zero)), true)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), id(true)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(minus(plus(zero, true), 0), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(if(true, zero, _x221), true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x212, if(false, _x162, minus(plus(zero, true), 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(if(false, _x142, id(x))), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(if(true, zero, _x81), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(if(true, zero, _x131), zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(s(plus(zero, true)), s(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x71), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x31), _x51), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(plus(zero, if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(true, id(id(x)), _x21))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(minus(s(_x51), 0), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(id(if(false, _x162, minus(plus(zero, true), 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), plus(zero, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(minus(true, 0), if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(minus(true, 0), if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, plus(zero, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31)), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(minus(zero, 0), true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x91), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(if(true, plus(zero, true), _x211), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, if(true, true, _x191)), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x92, if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21))), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(id(zero), true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), plus(zero, if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21))), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, if(true, true, _x231)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(false, _x72, s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(if(false, _x92, zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(id(false), _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), if(true, true, _x161)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(if(true, true, _x61), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, if(false, _x152, zero)), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(minus(id(id(x)), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, if(false, _x142, true)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(zero, s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, minus(id(id(x)), 0), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(if(false, _x122, true), minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(if(true, s(y), _x71)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(if(false, _x102, minus(plus(zero, gt(s(_x131), zero)), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, id(zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(id(zero), if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(s(plus(if(false, _x152, zero), true)), s(0)), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(plus(zero, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, if(true, true, _x141)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(minus(gt(s(_x51), zero), 0)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(minus(zero, 0), true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(s(plus(plus(zero, zero), true)), s(0))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), plus(zero, 0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(plus(zero, minus(true, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(plus(zero, minus(plus(zero, true), 0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(id(if(false, _x162, minus(plus(zero, true), 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(plus(zero, minus(gt(s(s(_x51)), s(zero)), 0)), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), plus(zero, zero)), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), if(true, 0, _x121)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), if(false, _x142, id(id(x))), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, plus(zero, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), plus(zero, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(true, id(x), _x61)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(if(false, _x132, s(_x51)), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), id(0))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(minus(s(_x51), 0), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x72, if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(minus(s(s(_x51)), 0), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(plus(zero, minus(plus(plus(zero, if(false, _x142, zero)), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(id(plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(false, _x102, id(minus(plus(plus(zero, zero), true), 0))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(_x51), zero), 0), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(plus(s(_x92), s(_x91))), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(if(true, true, _x91), if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, plus(zero, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21))), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(if(false, _x122, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(id(x))), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, if(true, true, _x271)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, plus(zero, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, minus(id(s(y)), 0), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, id(if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21)), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(if(false, _x142, plus(zero, true)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), if(true, true, _x141)), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(if(false, _x72, gt(s(s(_x51)), s(zero))), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(minus(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31), 0))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), plus(zero, 0)), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, minus(true, 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(minus(s(_x51), 0)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(if(true, gt(s(_x51), zero), _x81), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, if(true, true, _x171))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(gt(s(_x81), zero), if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, gt(s(s(_x51)), s(zero)), _x61), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), if(true, 0, _x101))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(plus(zero, if(false, _x162, minus(plus(zero, true), 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(id(s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(if(false, _x182, id(x))), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(if(false, _x122, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(if(false, _x112, plus(plus(zero, if(false, _x142, zero)), true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(minus(s(_x51), 0)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(false, _x92, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(minus(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(plus(zero, false), _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(true, true, _x101), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), if(true, 0, _x141)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(id(0)))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(if(false, _x132, zero), if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(quot(s(_x82), s(_x81))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(id(zero), id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), plus(zero, if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(if(true, minus(plus(zero, true), 0), _x101), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(if(true, false, _x171), _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(zero, s(if(true, s(_x51), _x81))), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(if(true, zero, _x131), id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(if(false, _x82, true), if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x22, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x151))), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(false, _x102, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31)), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, id(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(if(true, true, _x81), if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(plus(zero, minus(true, 0)), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), _x181), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(plus(zero, true), quot(0, s(_x91))), _x71), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(if(true, id(id(x)), _x131), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(plus(id(_x92), s(_x91)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(if(false, _x202, false), _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(if(true, gt(s(_x51), zero), _x121), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(plus(zero, zero), true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(true, true, _x81), if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), id(true)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(minus(gt(s(_x51), zero), 0), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(minus(false, 0), _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(s(plus(plus(zero, if(false, _x142, zero)), true)), s(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(if(true, plus(zero, true), _x211), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(minus(zero, 0), true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(if(false, _x142, plus(if(false, _x152, zero), true)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(_x51), zero), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, minus(true, 0)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(true, if(false, _x162, minus(plus(zero, true), 0)), _x211), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(if(false, _x122, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(plus(zero, if(id(true), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), plus(zero, if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, if(true, true, _x131), _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(if(true, zero, _x261), true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(s(id(id(x))), s(0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(id(minus(plus(zero, true), 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(if(true, plus(plus(zero, zero), true), _x121), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(plus(s(_x132), s(_x131)), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(id(x), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), minus(id(id(x)), 0), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), quot(0, s(_x121))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(id(false), _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), quot(0, s(_x151))), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x111), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, if(true, minus(plus(zero, true), 0), _x241)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), minus(0, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(false, _x82, true), if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(plus(s(_x92), s(_x91)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(true, zero, _x81)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), if(true, 0, _x221))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(plus(id(_x132), s(_x131)), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), minus(zero, 0)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(if(true, true, _x81), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(if(true, plus(zero, if(false, _x142, zero)), _x161), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(minus(s(_x51), 0), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), if(true, zero, _x141))), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, id(if(true, 0, _x131)))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(gt(zero, _x81), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), id(s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(id(s(_x51))), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, id(if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(minus(id(x), 0)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(plus(s(_x92), s(_x91))), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, if(false, _x142, plus(zero, true)), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(if(true, true, _x61), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(id(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(if(false, _x82, plus(zero, minus(true, id(0)))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), if(false, _x82, s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(if(false, _x102, false), _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), if(false, _x152, 0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(id(gt(s(s(_x51)), s(zero))), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), plus(zero, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(minus(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(s(if(true, plus(zero, true), _x111)), s(0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(minus(zero, 0), id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(plus(zero, true), minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), plus(zero, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), minus(true, 0)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(id(minus(plus(zero, true), 0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(true, id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, if(true, true, _x131)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(minus(id(x), 0), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(false, 0), _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(if(false, _x132, true), plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x62, gt(s(s(_x51)), s(zero))), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x72, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(minus(true, 0), if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, if(false, _x222, zero), _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), id(if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21))), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(if(true, id(x), _x181)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), plus(zero, s(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(if(true, zero, _x111))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(id(false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, id(true)), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(plus(zero, s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(minus(0, 0), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, id(id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), if(true, id(id(x)), _x171), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(id(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(if(true, id(x), _x151)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, gt(s(s(_x51)), s(zero)), _x61), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(if(true, s(s(_x51)), _x91), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), plus(zero, zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), if(false, _x222, 0)), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), id(0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, id(minus(true, id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, id(true))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), if(false, _x122, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), if(false, _x112, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(quot(s(_x122), s(_x121)), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(zero, plus(plus(zero, if(false, _x142, zero)), true)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(false, _x112, if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(minus(zero, 0))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, id(if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(if(false, _x182, false), _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(id(s(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, minus(if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), 0), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(minus(true, 0), false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, plus(zero, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(if(false, _x112, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(s(_x72), s(_x71)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(if(true, plus(zero, true), _x81), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(plus(zero, gt(s(s(_x51)), s(zero))), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(plus(s(_x72), s(_x71))), _x31)) → plus#(x, if(gt(s(s(plus(if(gt(_x72, _x71), _x72, _x71), if(not(gt(_x72, _x71)), id(_x72), id(_x71))))), s(plus(if(gt(_x72, _x71), _x72, _x71), if(not(gt(_x72, _x71)), id(_x72), id(_x71))))), s(plus(if(gt(_x72, _x71), _x72, _x71), if(not(gt(_x72, _x71)), id(_x72), id(_x71)))), s(s(plus(if(gt(_x72, _x71), _x72, _x71), if(not(gt(_x72, _x71)), id(_x72), id(_x71)))))))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), quot(0, s(_x151))), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(id(minus(plus(zero, gt(s(_x131), zero)), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(true, s(s(_x51)), _x71), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(plus(s(_x102), s(_x101)), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(if(false, _x122, plus(plus(zero, zero), true)), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(gt(zero, _x131), _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(minus(true, 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), if(true, 0, _x121)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(plus(zero, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(plus(zero, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(false, _x72, minus(plus(zero, true), 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(gt(s(_x51), zero), 0), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), id(0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, if(true, id(0), _x111))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(if(true, minus(plus(zero, gt(s(_x131), zero)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), if(false, _x102, zero)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(if(true, id(x), _x231)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, gt(s(_x141), zero)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(if(true, id(x), _x141)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), minus(0, 0)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x212, if(false, _x162, minus(plus(zero, true), 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, id(true)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), minus(if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x182, if(false, _x142, zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(plus(zero, true), if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), plus(zero, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(false, _x72, s(s(_x51))), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(false, _x102, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31)), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(true, s(_x51), _x71), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(plus(id(_x122), s(_x121)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(if(true, s(_x51), _x81)), s(zero)), 0), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, 0)), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, id(id(x)), _x21), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x121)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), minus(id(id(x)), 0), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, if(true, true, _x231)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(id(if(true, s(_x51), _x81))), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(id(false), _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(minus(id(x), 0)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(quot(s(_x132), s(_x131)), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(plus(zero, true), id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(minus(id(x), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(if(false, _x142, false), _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, minus(if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), 0), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(if(true, id(x), _x121)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, id(true)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x112, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(id(true), if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(gt(zero, _x161), _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(id(x))), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(if(true, id(x), _x121)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(true, 0), if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, plus(zero, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31)), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(if(false, _x142, zero), zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), minus(zero, 0)), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), if(false, _x122, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, if(false, _x102, minus(true, id(0)))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, minus(true, id(0))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(plus(zero, false), _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(id(if(gt(s(s(_x51)), s(zero)), id(if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61)), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(if(false, _x122, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(id(zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), minus(zero, 0)), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(plus(zero, if(true, s(_x51), _x81))), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), quot(0, s(_x91))), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(if(true, plus(if(false, _x152, zero), true), _x181), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(id(minus(plus(if(false, _x152, zero), true), 0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(minus(s(_x51), 0), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), if(true, 0, _x261))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(minus(s(_x51), 0)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(plus(zero, zero))), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(true, 0), if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), if(false, _x82, 0)), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(if(gt(s(_x51), zero), if(false, _x62, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(gt(zero, _x181), _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(if(true, zero, _x131), if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(true, plus(zero, true), _x81), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(if(true, true, _x91), if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), minus(0, 0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(zero, _x81), _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), plus(zero, s(zero))), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(id(zero))), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), minus(true, 0)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), _x91)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71), _x81)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(if(true, zero, _x121), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), gt(s(_x171), zero)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(true), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x62, minus(gt(s(s(_x51)), s(zero)), 0)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(s(_x72), s(_x71)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(if(false, _x82, true), if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(quot(s(_x122), s(_x121)), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(minus(gt(s(_x51), zero), 0), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(id(true), if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x71), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), plus(zero, zero))), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), minus(zero, 0))), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(if(false, _x72, gt(s(s(_x51)), s(zero))), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(false, _x112, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21)), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(s(plus(zero, true)), s(0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(false, _x162, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21))), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(false, _x142, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(plus(zero, true), zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(s(plus(if(false, _x152, zero), true)), s(0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(plus(zero, zero))), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), if(true, id(plus(zero, id(x))), _x111), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, gt(s(s(_x51)), s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(gt(s(_x81), zero), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(if(false, _x122, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, plus(plus(zero, zero), true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(if(false, _x82, true), if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(false, _x112, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(if(true, zero, _x91), minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(id(false), _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), minus(id(id(x)), 0), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(if(false, _x112, zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(id(s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(if(false, _x92, true), if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(plus(s(_x82), s(_x81))), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(gt(s(_x81), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), minus(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(id(if(gt(s(s(_x51)), minus(s(zero), 0)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(id(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(false, _x72, s(if(true, s(_x51), _x81))), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(id(x))), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, if(false, _x212, zero), _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), id(zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(id(plus(if(false, _x152, zero), true)), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, if(true, minus(plus(zero, true), 0), _x241)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), if(true, true, _x131)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x91), zero), if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(false, _x102, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(gt(s(_x41), zero), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(if(false, _x52, true), id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(id(true), false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(if(false, _x92, id(x)), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(plus(zero, zero), if(true, id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(minus(zero, 0), zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x61), zero), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), if(false, _x82, s(zero))), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x62, gt(s(s(_x51)), s(zero))), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, plus(zero, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31)), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(plus(zero, false), _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(minus(true, 0), if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), plus(zero, 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(if(true, minus(plus(zero, true), 0), _x101), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(if(false, _x112, plus(zero, gt(s(_x131), zero))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(minus(true, 0), if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), minus(0, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x222, if(false, _x152, zero)), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(minus(id(id(x)), 0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), minus(0, 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), plus(zero, 0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(x), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(minus(s(_x51), 0), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, minus(if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21), 0)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(true, if(false, _x152, zero), _x221), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, if(true, zero, _x181), _x191))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), plus(zero, zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(id(minus(plus(zero, if(false, _x132, true)), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x71), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(minus(zero, 0))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, plus(zero, minus(plus(zero, true), 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x132, if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21))), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(plus(zero, zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(if(false, _x92, true), if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x122, if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(gt(s(s(_x51)), if(true, s(zero), _x81)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(if(true, zero, _x261), true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, s(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(id(s(s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(gt(s(_x81), zero), if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), plus(zero, s(zero))), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(plus(s(_x92), s(_x91))), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(plus(zero, gt(s(_x51), zero))), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(plus(zero, false), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), if(false, _x132, 0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), minus(s(zero), 0)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), minus(s(zero), 0)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, plus(zero, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(true, 0, _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(true, zero, _x151), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(minus(s(_x51), 0)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, plus(zero, minus(plus(plus(zero, if(false, _x142, zero)), true), 0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(minus(plus(zero, true), 0), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, id(if(false, _x132, true))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(if(false, _x182, false), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(minus(s(s(_x51)), 0), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, true), if(true, id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(false, _x82, id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(true, zero, _x91), if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(gt(zero, _x191), _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, minus(plus(zero, if(true, true, _x101)), 0), _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(gt(s(_x191), zero), minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), plus(zero, id(plus(zero, id(x)))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(_x51), zero), 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x192, if(false, _x152, zero)), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x91), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(plus(zero, zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(id(true), if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(if(false, _x122, zero), true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), minus(if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(plus(zero, minus(plus(if(false, _x152, zero), true), 0)), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(if(false, _x262, zero), true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(true, gt(s(_x131), zero), _x141)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(id(true), if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(if(true, id(x), _x101)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(if(false, _x82, true), if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(plus(zero, true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(minus(id(x), 0)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), if(true, 0, _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(x)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, plus(zero, if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(s(_x51))), s(s(zero))), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(minus(plus(zero, zero), 0), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(plus(id(_x82), s(_x81))), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), id(zero)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, id(zero)), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(gt(s(_x61), zero), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(plus(zero, if(true, minus(plus(if(false, _x152, zero), true), 0), _x171)), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(false, _x92, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, id(minus(plus(plus(zero, if(false, _x142, zero)), true), 0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(false, _x82, zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(minus(true, 0), minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x61), zero), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, if(true, zero, _x211))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), minus(id(id(x)), 0), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(false, _x202, if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x62, gt(s(if(true, s(_x51), _x81)), s(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(true, 0, _x91)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, plus(zero, if(false, _x142, if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), id(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), id(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(if(true, plus(zero, zero), _x131), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(minus(zero, 0), true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(false, _x72, s(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x71), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(false, _x92, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, id(if(false, _x142, zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), id(0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(true, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21), _x151)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(false, _x92, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(s(plus(plus(zero, zero), true)), s(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(plus(zero, false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), if(true, id(id(x)), _x111), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(id(plus(plus(zero, if(false, _x142, zero)), true)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(minus(plus(plus(zero, zero), true), 0), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(minus(id(x), 0)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(quot(s(_x122), s(_x121)), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, quot(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), id(zero)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(minus(false, 0), _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), if(true, id(id(x)), _x111), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, if(false, _x122, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, plus(if(false, _x152, zero), true)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(if(false, _x92, true), if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(plus(zero, id(id(x))), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(if(true, true, _x81), if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), if(false, _x132, zero)), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x71), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), minus(0, 0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(if(true, false, _x141), _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), if(false, _x122, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(if(true, zero, _x171), if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), minus(s(zero), 0)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), id(true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(plus(zero, if(true, true, _x101)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(id(false), _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(minus(s(s(_x51)), 0), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, minus(id(id(x)), 0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(minus(zero, 0), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(if(false, _x122, plus(zero, id(x)))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), if(true, id(id(x)), _x111), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), plus(zero, if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x111), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(id(zero))), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), id(if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), if(false, _x192, 0)), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(zero, s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, plus(zero, id(id(x))), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(if(true, plus(zero, true), _x171), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(gt(s(_x211), zero), zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, gt(s(s(_x51)), s(zero)), _x61), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(minus(id(x), 0)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(gt(s(_x81), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(plus(zero, zero), gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), plus(zero, zero))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(id(s(_x51))), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(if(false, _x102, gt(s(_x51), zero))), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(if(false, _x122, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(minus(s(_x51), 0), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(minus(true, 0), if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(s(_x51))), s(s(zero))), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, gt(s(_x171), zero))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(minus(gt(s(_x51), zero), 0), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, if(true, minus(true, id(0)), _x101)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(minus(s(s(_x51)), 0), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(if(true, gt(s(_x51), zero), _x61), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), if(true, s(zero), _x81)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(false, _x72, s(_x51)), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), minus(if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), 0), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), minus(if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), 0), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, if(true, true, _x101))), s(0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, minus(id(id(x)), 0), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x121))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(id(plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(if(true, gt(s(_x51), zero), _x81), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(id(minus(plus(if(false, _x152, zero), true), 0)), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, plus(zero, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(if(true, plus(zero, if(false, _x142, if(true, zero, _x181))), _x121), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(false, _x92, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(minus(plus(zero, if(false, _x132, true)), 0), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, if(false, _x162, true)), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(quot(s(_x82), s(_x81))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), plus(zero, s(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, minus(if(false, _x132, true), 0)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(plus(zero, minus(plus(zero, if(false, _x132, true)), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(id(true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), id(if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), minus(0, 0)), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(true), id(id(x)), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), _x61), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, minus(if(false, _x142, zero), 0)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), if(false, _x42, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(if(false, _x92, zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(if(true, s(_x51), _x121), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, id(minus(plus(zero, true), 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, minus(if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), 0), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), if(false, _x112, id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(if(false, _x152, zero), true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31)), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(minus(s(s(_x51)), 0), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(minus(plus(zero, true), quot(0, s(_x91)))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), if(false, _x142, zero)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(if(false, _x102, zero))), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), minus(zero, 0))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(minus(zero, 0), gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(zero, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(if(false, _x92, s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(not(true), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(true, if(minus(s(if(false, _x92, plus(zero, true))), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, plus(zero, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(if(true, gt(s(_x51), zero), _x111), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(if(false, _x172, plus(zero, true)), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, gt(s(_x51), zero)), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, plus(zero, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(if(true, s(_x51), _x121), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(s(_x131)), s(zero))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, plus(zero, if(true, true, _x101))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(zero, plus(plus(zero, if(false, _x142, zero)), true)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, minus(if(true, if(true, id(id(x)), _x21), _x31), 0), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), if(true, id(id(x)), _x221), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x111), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(id(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(if(false, _x102, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), id(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), if(false, _x142, 0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(id(plus(zero, if(false, _x142, zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(false, _x62, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(if(false, _x162, s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(gt(zero, _x201), _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(if(true, false, _x181), _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(minus(true, id(0)), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, gt(s(_x191), zero)), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x91), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x91), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), if(false, _x172, id(id(x))), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(true, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21), _x201))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), if(false, _x82, s(zero))), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), if(true, zero, _x81)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(true, minus(id(id(x)), 0), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(id(minus(plus(plus(zero, zero), true), 0))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, plus(zero, if(false, _x142, zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(plus(zero, s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(if(false, _x102, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(if(true, plus(zero, minus(true, id(0))), _x81), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, if(true, s(_x91), _x121))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(if(false, _x42, zero), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(s(plus(zero, true)), s(0)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(id(true), if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(if(false, _x112, gt(s(_x51), zero)), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(true, if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x121), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(id(plus(zero, true)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(id(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(plus(zero, true), if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(if(false, _x72, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(if(false, _x142, id(x))), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x131), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(true, if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x91), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), plus(zero, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(id(x))), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(minus(zero, 0), true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(id(x))), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(true, 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), plus(zero, s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x61), zero), id(id(x)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(false, _x32, id(id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), if(true, quot(0, s(_x91)), _x101)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), if(false, _x182, 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), if(true, 0, _x121)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(true, if(true, id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(if(true, true, _x61), if(true, id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), if(false, _x112, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(zero, s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), minus(true, 0)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(if(false, _x212, plus(zero, true)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(minus(plus(zero, true), 0), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(true, id(id(x)), _x71), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(if(true, true, _x81), if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(minus(s(_x51), 0), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), quot(0, s(_x81))), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(id(s(_x51)), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(true, true, _x131)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(plus(s(_x122), s(_x121)), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, if(false, _x92, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(if(true, minus(plus(plus(zero, zero), true), 0), _x111)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(id(zero), true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(false, _x72, s(s(_x51))), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(true, if(if(true, true, _x71), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(minus(zero, 0), if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, minus(zero, 0))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(minus(id(x), if(false, _x102, 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, if(false, _x232, true)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(false, _x92, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21)), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), id(s(zero))), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, plus(zero, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x151)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), if(false, _x112, zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), plus(zero, if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), if(false, _x142, zero))), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(if(true, zero, _x171), if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(id(s(_x51)), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(minus(zero, 0), if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, minus(zero, 0))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(true, s(_x51), _x71), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), id(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, plus(zero, true)), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(false, _x92, if(true, s(_x51), _x81))), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(if(false, _x82, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(id(_x42), s(_x41)))) → plus#(x, if(gt(s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41)))), plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))), s(plus(_x42, if(gt(s(_x41), _x41), _x41, s(_x41))))))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(if(true, zero, _x121), true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(true, zero, _x131), true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(if(false, _x152, id(x))), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), if(true, id(id(x)), _x171), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(s(plus(zero, true)), s(0)), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), id(if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, id(if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(if(false, _x132, id(id(x))), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x71), zero), if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(if(true, true, _x81), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, minus(if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21), 0)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(if(true, true, _x81), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, plus(zero, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(plus(zero, 0), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, minus(gt(s(_x131), zero), 0)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(if(false, _x102, zero))), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, if(true, true, _x101))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(minus(gt(s(_x51), zero), 0), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(plus(s(_x82), s(_x81))), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, id(id(x)), _x21), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(plus(zero, zero), if(true, id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(if(true, id(gt(s(_x51), zero)), _x91), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(if(false, _x82, true), if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(s(true), s(id(0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(plus(zero, id(x))), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, plus(zero, zero)), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), plus(zero, id(id(x))), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(minus(id(x), 0)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(plus(zero, false), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x132, zero), true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(plus(id(_x92), s(_x91))), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(minus(plus(zero, true), 0), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x101), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), if(false, _x92, s(zero))), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(id(false), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(quot(s(_x42), s(_x41)))) → plus#(x, if(gt(s(quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41))), quot(minus(_x42, _x41), s(_x41)), s(quot(minus(_x42, _x41), s(_x41)))))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(gt(s(_x51), zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(true, 0), if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(if(true, true, _x131), if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, plus(zero, zero)), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), if(false, _x222, id(id(x))), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, if(true, minus(true, id(0)), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x71), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), minus(0, 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(if(true, id(x), _x81)), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(plus(zero, s(_x51))), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(plus(zero, true), if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(id(zero), true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(s(_x51)), s(zero))), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(true, true, _x101)), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, gt(s(s(_x51)), s(zero))), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(s(_x51)), s(zero)), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(false), _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(if(false, _x92, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(plus(zero, s(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, id(minus(plus(plus(zero, zero), true), 0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(zero, plus(if(false, _x152, zero), true)), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(s(plus(zero, true)), if(true, s(0), _x91)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(if(false, _x82, plus(zero, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), minus(id(id(x)), 0), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, plus(s(_x122), s(_x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), minus(zero, 0)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), id(0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31), _x111))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), if(true, zero, _x81)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, if(true, zero, _x211), _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(plus(zero, true), if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(if(true, plus(plus(zero, zero), true), _x111), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(true, 0), if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(id(zero), true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, minus(if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), 0), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), if(false, _x212, id(id(x))), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), id(zero)), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(minus(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x132, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(if(true, false, _x141), _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(plus(id(_x112), s(_x111)), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), if(false, _x122, id(id(x))), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true)), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(plus(zero, zero), id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, id(true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(minus(id(id(x)), 0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(plus(zero, id(x))), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), plus(zero, 0)), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), if(true, s(zero), _x91)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(id(minus(if(true, plus(zero, true), _x111), 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(id(s(s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(gt(zero, _x161), _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), if(gt(s(_x51), zero), id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(quot(s(_x102), s(_x101))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, id(id(x)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(id(zero), true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), if(true, zero, _x141)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), plus(zero, if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(s(x), x) → plus#(if(gt(x, x), id(x), id(x)), s(x))
plus#(id(if(gt(if(false, _x92, s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(gt(zero, _x151), _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(plus(zero, false), _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(if(false, _x82, true), if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x131), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), plus(zero, if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21))), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(minus(id(id(x)), 0), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), if(false, _x232, true)), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(if(false, _x142, false), _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(plus(zero, s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), id(zero))), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31), _x111))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, if(false, _x202, minus(plus(zero, true), 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), minus(0, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(if(false, _x122, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(if(true, plus(zero, if(false, _x132, true)), _x111), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(if(true, true, _x211), zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, if(false, _x172, true))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), minus(if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), 0), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(minus(true, 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(minus(zero, 0), if(true, id(id(x)), _x21)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(if(true, true, _x91), if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, if(true, minus(true, 0), _x91)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), if(true, zero, _x131)), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, id(if(plus(zero, minus(true, id(0))), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(false, _x112, if(true, true, _x101))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(false, _x82, s(_x51))), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(false, _x72, s(_x51)), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(plus(zero, id(x))), _x21), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(id(minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(minus(s(s(_x51)), 0), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(id(x)), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(true, if(minus(plus(zero, gt(s(_x101), zero)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, gt(s(_x51), zero), _x61), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(s(plus(zero, if(false, _x132, true))), s(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, minus(if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21), 0)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(if(false, _x262, zero), true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(plus(zero, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(minus(gt(s(s(_x51)), s(zero)), 0)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(minus(id(id(x)), 0), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, minus(if(true, zero, _x181), 0))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, minus(if(true, if(true, id(id(x)), _x21), _x31), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(zero, s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x52, true), if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(minus(false, 0), _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, minus(if(minus(plus(zero, true), 0), id(id(x)), _x21), 0)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), quot(0, s(_x141))), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, minus(true, 0)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(if(false, _x232, id(x))), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), minus(s(zero), 0)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(if(false, _x92, zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x101), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(id(x))), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(minus(s(_x51), 0), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, plus(zero, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(if(true, id(id(x)), _x91), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(id(true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(if(false, _x82, s(s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(id(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true)), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(id(plus(zero, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), id(s(zero))), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(false, _x122, minus(id(id(x)), 0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(false, _x62, gt(s(s(_x51)), s(zero))), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, id(if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(minus(minus(gt(s(s(_x51)), s(zero)), 0), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), plus(zero, 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), if(false, _x112, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(true, if(minus(true, 0), id(if(false, _x92, id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(minus(zero, 0))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, id(zero)), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x32, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, id(gt(s(_x51), zero))), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(minus(s(plus(zero, true)), s(0)), id(id(x)), _x21), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(plus(zero, id(x))), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, if(true, plus(zero, true), _x111), _x121), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, if(true, id(id(x)), _x21), _x71), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(id(true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(if(false, _x122, true), minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), if(false, _x142, id(id(x))), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, minus(id(minus(id(x), 0)), 0), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, minus(s(_x91), 0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x162, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(false, _x82, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(false, _x82, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31)), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(plus(zero, gt(s(_x51), zero)), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(if(true, s(y), _x41))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, id(id(x)), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(gt(s(s(_x51)), s(plus(zero, zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x91), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(zero, true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(if(true, true, _x81), if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(if(true, s(_x51), _x131), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(if(false, _x132, true), if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(plus(zero, gt(s(_x51), zero)), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, gt(s(s(_x51)), s(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(minus(gt(s(_x51), zero), 0), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(id(false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(id(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(minus(true, 0), id(minus(id(x), 0)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), minus(id(id(x)), 0), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(id(plus(zero, zero)), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x72, true), if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(minus(zero, 0), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, id(if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), id(s(zero))), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(plus(zero, s(_x51)), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(id(s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, if(true, true, _x141)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), id(0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x91), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), if(false, _x112, id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(plus(zero, gt(s(s(_x51)), s(zero))), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, id(if(true, 0, _x121)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, plus(zero, true)), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), minus(id(id(x)), 0), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, if(false, _x232, true)), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x101), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(if(true, true, _x51), if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(if(false, _x142, id(x))), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(plus(zero, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(minus(s(y), 0))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), minus(if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), 0), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(if(true, plus(zero, true), _x121), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, id(if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(id(x)), _x21), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, gt(s(_x141), zero)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, quot(0, s(_x111)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), plus(zero, id(id(x))), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(minus(plus(if(false, _x152, zero), true), 0), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, id(if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, if(true, zero, _x251)), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), minus(0, 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(plus(s(_x82), s(_x81))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(minus(s(_x51), 0), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(true, if(minus(plus(zero, if(true, plus(zero, true), _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(quot(s(_x102), s(_x101)), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(if(true, true, _x51), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, plus(zero, true)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(if(true, id(x), _x121)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), id(0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(plus(zero, s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), minus(0, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), minus(if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), 0), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), if(false, _x112, id(id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, id(id(x)), _x21), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(id(if(gt(id(s(_x51)), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(if(false, _x102, s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, plus(zero, minus(plus(zero, true), 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(plus(zero, zero), true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), if(true, s(zero), _x81)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(s(_x51)), s(zero)), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(id(minus(plus(plus(zero, zero), true), 0)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), id(if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), id(s(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, plus(zero, if(true, id(minus(id(x), 0)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(plus(id(_x132), s(_x131)), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(if(true, minus(plus(zero, true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), minus(id(s(y)), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, minus(true, 0))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, minus(gt(s(s(_x51)), s(zero)), 0)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), if(false, _x82, s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(false, _x102, true)), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(id(false), _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, id(true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, plus(zero, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(minus(false, 0), _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(plus(zero, s(_x131)), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, gt(s(s(_x51)), s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, id(minus(plus(zero, true), 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(true, if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(if(false, _x102, s(_x51)), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(s(_x72), s(_x71)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), if(false, _x262, 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(id(zero), true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(plus(zero, minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), if(false, _x182, id(id(x))), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, if(true, true, _x271)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(minus(s(_x51), 0), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(x), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(plus(zero, zero), true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), if(false, _x142, zero)), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(false, _x72, if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x91)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(minus(id(x), 0)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), minus(id(id(x)), 0), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), minus(zero, 0)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(if(false, _x182, plus(if(false, _x152, zero), true)), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(plus(zero, id(x))), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), id(zero)), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(zero, s(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(minus(id(x), 0)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), plus(zero, zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(minus(true, 0), if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), plus(zero, s(zero))), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, gt(zero, _x161), _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, id(if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(if(false, _x222, false), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(id(plus(plus(zero, zero), true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), plus(zero, 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(if(false, _x122, plus(zero, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, plus(zero, if(false, _x142, zero))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(if(false, _x122, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(minus(zero, 0), true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(minus(false, 0), _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, plus(zero, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x71), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, if(true, s(_x51), _x81), _x91)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, id(if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), minus(id(id(x)), 0), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x82, false), _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(if(false, _x122, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x92, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(id(true), if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(plus(zero, id(minus(plus(plus(zero, zero), true), 0))), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(if(false, _x82, zero), minus(true, id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(if(true, true, _x81), if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x172, if(false, _x162, minus(plus(zero, true), 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x52, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), id(0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(minus(plus(plus(zero, zero), true), 0), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(plus(zero, zero))), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), if(true, zero, _x161))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(if(true, false, _x101), _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, gt(s(_x271), zero)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(id(gt(s(_x51), zero)), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(id(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(plus(zero, if(true, id(id(x)), _x21)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(if(true, plus(if(false, _x152, zero), true), _x211), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, 0), id(id(x)), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(gt(s(_x131), zero), plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(id(false), _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(minus(zero, 0))), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), minus(zero, 0)), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(plus(zero, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(true), if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(id(x)), _x21)), id(plus(zero, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, plus(zero, id(minus(id(x), 0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(false, _x72, s(_x51)), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(id(s(_x51))), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, minus(id(x), 0))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(if(false, _x222, false), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(false, _x72, if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, minus(if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), 0), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(s(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true)), s(0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), plus(zero, if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61)), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(0, s(_x91))), if(true, id(id(x)), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(if(false, _x102, minus(plus(zero, true), 0)), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(if(true, plus(if(false, _x152, zero), true), _x141), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), 0)), _x21)), id(if(false, _x42, s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(plus(zero, s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, true, _x51), if(minus(plus(zero, true), quot(0, s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(plus(zero, s(s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, false), _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), 0), if(false, _x82, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(id(x)))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(id(if(true, if(plus(plus(zero, zero), minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(minus(false, 0), _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(id(x)), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))
plus#(if(true, id(id(x)), _x21), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), plus(zero, if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(plus(zero, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(if(true, id(x), _x141)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(if(true, plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), _x131), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(minus(id(x), 0)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(plus(zero, id(x))), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x182, if(false, _x142, zero))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), if(false, _x132, 0)), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), plus(zero, if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61)), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(id(minus(plus(plus(zero, if(false, _x142, zero)), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(false, _x112, if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(id(zero), if(true, id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, if(false, _x72, id(id(x))), _x21)), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(plus(zero, id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(minus(zero, 0))), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), if(true, id(id(x)), _x211), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, minus(if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21), 0))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(0))), id(if(false, _x102, id(x))), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(if(false, _x102, minus(plus(zero, true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), id(0)), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(minus(if(false, _x152, zero), 0), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(minus(s(s(_x51)), 0), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(gt(zero, _x191), _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(true, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21), _x201))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(if(true, id(x), _x121)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(minus(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, plus(zero, if(true, id(id(x)), _x21))), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), if(false, _x222, 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, true), if(false, _x102, quot(0, s(_x91)))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, plus(zero, if(true, id(id(x)), _x21)), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(false, _x72, s(_x51)), zero), if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(true, s(s(_x51)), _x71), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, minus(if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), 0), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(id(plus(zero, if(false, _x142, if(true, zero, _x181)))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71), _x81)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), plus(zero, if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), id(zero)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(plus(zero, if(true, id(id(x)), _x21)), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(s(id(id(x))), s(0)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(false, _x142, if(true, false, _x131)), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), plus(zero, zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(plus(zero, minus(if(false, _x102, true), id(0))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(minus(true, 0), if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(minus(plus(zero, if(false, _x142, if(true, zero, _x181))), 0), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(s(_x51)), s(zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(if(true, id(x), _x151)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, plus(zero, true))), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, if(minus(true, 0), true, _x101)), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(plus(if(false, _x92, zero), minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(if(true, minus(if(true, plus(zero, true), _x111), 0), _x101), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(minus(true, 0), minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, minus(id(0), 0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(id(if(false, _x42, id(x))), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(if(false, _x112, gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(if(false, _x82, true), id(id(x)), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(if(false, _x112, plus(plus(zero, zero), true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(minus(id(x), 0)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(true, if(minus(plus(zero, true), 0), id(plus(zero, id(x))), _x21), _x91), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(minus(0, 0)))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), quot(0, s(_x81))), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), plus(zero, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(minus(true, 0), if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), if(true, id(s(y)), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, plus(zero, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x71), zero), if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), id(0)), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), if(false, _x82, s(zero))), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), if(false, _x32, id(s(y)))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(if(false, _x92, zero))), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(minus(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), 0)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(false, _x42, id(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), 0), id(id(x)), _x21)), _x31)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(minus(plus(zero, true), 0), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(s(_x72), s(_x71)), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(plus(zero, true), if(plus(zero, minus(true, id(0))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(if(true, id(x), _x121)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, id(if(true, true, _x101))), 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), if(true, id(plus(zero, s(y))), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x172, if(false, _x162, minus(plus(zero, true), 0))), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(if(false, _x152, zero), true), if(true, 0, _x151)), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, true), if(minus(plus(zero, true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(quot(s(_x122), s(_x121)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(true, 0)), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(if(false, _x122, s(_x51)), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), minus(0, 0)), id(plus(zero, id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), plus(zero, if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21)), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(if(false, _x82, true), if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(id(false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(false, _x92, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(true, if(false, _x142, if(true, zero, _x181)), _x151)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(id(plus(zero, true)), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(plus(s(_x102), s(_x101))), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, minus(true, 0)), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(zero, s(s(_x51))), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), if(false, _x132, zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(zero, true), quot(quot(0, s(_x111)), s(_x91))), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, minus(minus(plus(zero, true), 0), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x91), zero), if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(if(false, _x152, id(x))), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(false, _x102, minus(plus(plus(zero, if(false, _x142, zero)), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(true, s(s(_x51)), _x71), s(zero)), if(true, if(id(minus(plus(plus(zero, zero), true), 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(if(false, _x122, if(true, plus(zero, true), _x111)), 0), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(gt(s(s(_x51)), s(zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(false, _x82, id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, if(false, _x142, true)), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(s(_x51))), s(s(zero))), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, plus(zero, s(_x51)), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(if(false, _x82, true), if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(false, _x152, if(if(false, _x162, if(false, _x242, minus(plus(zero, true), 0))), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), gt(s(_x171), zero)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), if(true, true, _x171)), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21))), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(zero, true), 0), _x111), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(plus(zero, s(_x51)), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, if(false, _x142, true)), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, id(if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31)), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(plus(zero, minus(true, id(if(false, _x132, 0)))), id(id(x)), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(minus(zero, 0), true), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), minus(if(true, id(id(x)), _x131), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), id(s(zero))), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), plus(zero, id(id(x))), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(if(false, _x172, false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(true, 0), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(false, _x102, true)), 0), minus(id(id(x)), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), id(if(minus(plus(zero, true), 0), minus(id(id(x)), 0), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x62, if(minus(if(false, _x162, minus(plus(zero, true), 0)), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(s(_x51)), s(zero)), if(true, minus(if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), 0), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(if(false, _x102, minus(if(true, plus(zero, true), _x111), 0)), id(id(x)), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), if(true, id(id(x)), _x81), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, id(if(gt(plus(id(_x132), s(_x131)), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(if(true, zero, _x91))), if(true, if(minus(plus(plus(zero, if(false, _x142, zero)), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(minus(zero, 0), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(if(false, _x182, false), _x142, if(true, zero, _x181))), true), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(true, id(minus(id(x), id(0))), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(plus(zero, s(s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, if(false, _x132, true)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(id(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), id(if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))plus#(if(true, if(gt(s(_x51), zero), if(minus(if(true, plus(zero, true), _x121), 0), minus(id(id(x)), 0), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), id(zero)), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), plus(zero, 0)), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(true, id(id(x)), _x21)), minus(if(true, id(s(y)), _x31), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(id(s(_x51)), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), plus(zero, if(true, if(minus(if(true, plus(zero, true), _x111), 0), id(id(x)), _x21), _x61)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, plus(zero, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(id(if(true, if(gt(s(_x51), zero), if(if(false, _x132, false), _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x202, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(if(true, gt(s(_x51), zero), _x121)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, false, _x131), _x62, if(false, _x152, if(if(gt(zero, _x221), _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(true, quot(0, s(_x91))), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(plus(zero, minus(plus(zero, true), 0)), id(id(x)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(if(false, _x82, s(s(_x51))), s(zero)), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(zero, true), 0), id(id(x)), _x21), _x61), _x31), id(plus(s(_x42), s(_x41)))) → plus#(x, if(gt(s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41))))), s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))), s(s(plus(if(gt(_x42, _x41), _x42, _x41), if(not(gt(_x42, _x41)), id(_x42), id(_x41)))))))
plus#(if(false, _x22, minus(id(id(x)), 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), if(false, _x82, zero)), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), id(zero)), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(false, _x82, if(true, if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(id(zero), true), 0), id(id(x)), _x21)), _x31), _x71))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(false, _x42, id(if(gt(s(_x51), zero), if(false, _x62, if(if(true, minus(plus(if(false, _x152, zero), true), 0), _x171), id(id(x)), _x21)), _x31))), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))plus#(if(gt(s(s(_x51)), if(true, s(zero), _x81)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), 0), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(id(id(x)), plus(zero, 0)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(false, _x52, if(true, id(id(x)), _x21))), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), id(id(x)), _x21)), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(true, if(gt(s(_x51), zero), if(if(true, id(false), _x131), _x62, if(false, _x152, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(false, _x92, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21)), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(id(if(id(true), if(id(gt(s(_x51), zero)), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(gt(s(_x51), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))plus#(id(if(true, if(gt(minus(s(_x51), 0), zero), if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21)), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, zero, _x181))), id(true)), 0), id(id(x)), _x21), _x61), _x31)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(zero)), 0), if(true, if(minus(plus(plus(zero, zero), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(true, if(id(gt(s(_x51), zero)), if(false, _x122, if(false, _x62, if(if(false, _x162, minus(plus(zero, true), 0)), id(id(x)), _x21))), _x31), _x71)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(true, if(minus(s(plus(zero, true)), s(0)), id(if(false, _x92, id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(minus(if(true, if(true, id(id(x)), _x21), _x31), 0), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, if(false, _x142, if(true, plus(zero, zero), _x181))), true), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(minus(plus(if(true, zero, _x91), true), 0), id(id(x)), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, id(id(x))), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(true, if(minus(plus(plus(zero, zero), true), 0), id(minus(id(x), 0)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(minus(gt(s(s(_x51)), s(minus(zero, 0))), 0), if(true, if(minus(plus(zero, gt(s(_x131), zero)), 0), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(if(true, s(_x51), _x81)), s(zero)), if(true, if(if(true, minus(plus(plus(zero, if(false, _x142, zero)), true), if(false, _x152, 0)), _x101), id(id(x)), _x21), _x61), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(plus(zero, if(minus(true, 0), id(id(x)), _x21)), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(true, if(minus(plus(zero, if(true, true, _x101)), 0), id(id(x)), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))

Rewrite Rules

minus(x, 0) → xminus(s(x), s(y)) → minus(x, y)
quot(0, s(y)) → 0quot(s(x), s(y)) → s(quot(minus(x, y), s(y)))
plus(s(x), s(y)) → s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))plus(s(x), x) → plus(if(gt(x, x), id(x), id(x)), s(x))
plus(zero, y) → yplus(id(x), s(y)) → s(plus(x, if(gt(s(y), y), y, s(y))))
id(x) → xif(true, x, y) → x
if(false, x, y) → ynot(x) → if(x, false, true)
gt(s(x), zero) → truegt(zero, y) → false
gt(s(x), s(y)) → gt(x, y)

Original Signature

Termination of terms over the following signature is verified: not, id, plus, 0, minus, s, if, false, true, gt, zero, quot

Strategy

The left-hand side of the rule plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is backward narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
plus#(if(gt(s(_x51), zero), if(minus(plus(id(zero), true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(plus(zero, zero), true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(minus(zero, 0), id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(minus(plus(zero, true), 0), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), plus(zero, s(y))) 
plus#(if(gt(if(true, s(_x51), _x71), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), plus(s(_x32), s(_x31))) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), plus(zero, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), if(false, _x82, zero)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), id(if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x61), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), minus(if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), 0), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), id(s(y))) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, if(true, id(id(x)), _x101)), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(false, _x102, true)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), minus(0, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(minus(s(_x51), 0), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(id(minus(plus(zero, true), 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(s(plus(zero, true)), s(0)), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(plus(zero, id(id(x))), 0), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(plus(zero, id(id(x)))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), id(zero)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), minus(s(y), 0)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, gt(s(_x101), zero)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(id(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31)), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(if(true, zero, _x91), true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(if(false, _x112, id(x)))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(if(true, zero, _x91), id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(plus(zero, true), 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), plus(zero, zero)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(if(true, id(x), _x111))), _x21), _x31), s(y)) 
plus#(plus(zero, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31)), s(y)) 
plus#(if(gt(s(_x51), zero), if(if(false, _x72, minus(plus(zero, true), 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(false, _x92, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), plus(id(_x32), s(_x31))) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, plus(zero, id(id(x)))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(if(false, _x92, zero), true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(false, _x82, plus(zero, id(id(x)))), _x21), _x31), s(y)) 
plus#(if(gt(if(false, _x72, s(_x51)), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(minus(gt(s(_x51), zero), 0), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(id(x)))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, if(false, _x102, id(id(x)))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, plus(zero, true)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(if(true, gt(s(_x51), zero), _x61), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), if(true, zero, _x81)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(s(_x51)), s(zero)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(if(true, plus(zero, true), _x81), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(plus(zero, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(id(plus(zero, true)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), if(true, s(y), _x31)) 
plus#(if(gt(s(_x51), minus(zero, 0)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(minus(id(x), 0))), _x21), _x31), s(y)) 
plus#(minus(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), 0), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(true, true, _x101)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(true, plus(zero, id(id(x))), _x81), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(minus(zero, 0), true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), plus(zero, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21)), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(true, 0, _x91)), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(plus(zero, s(_x51)), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), id(0)), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(plus(zero, zero), id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(if(true, minus(plus(zero, true), 0), _x71), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), _x41), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(plus(zero, id(x)))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(if(false, _x92, zero), id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), if(false, _x32, s(y))) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, minus(true, 0)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), quot(s(_x32), s(_x31))) 
plus#(if(false, _x42, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31)), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, id(true)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, minus(id(id(x)), 0)), _x21), _x31), s(y)) 
plus#(if(gt(id(s(_x51)), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(if(false, _x82, plus(zero, true)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(if(false, _x62, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) 
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(id(zero), id(id(x))), _x21), _x31), s(y)) 
Thus, the rule plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y))) is replaced by the following rules:
plus#(if(gt(s(_x51), zero), if(minus(id(plus(zero, true)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(false, _x42, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(false, _x82, zero)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, plus(zero, id(id(x)))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(id(gt(s(_x51), zero)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, minus(true, 0)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(quot(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(id(zero), true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, id(true)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(true, gt(s(_x51), zero), _x61), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, if(false, _x102, id(id(x)))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(true, true, _x101)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), if(true, zero, _x81)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(true, 0, _x91)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(true, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), _x41), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(plus(zero, s(_x51)), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(minus(zero, 0), true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(if(false, _x92, zero), true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(if(false, _x72, s(_x51)), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(if(true, s(_x51), _x71), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(plus(zero, zero), true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(if(false, _x72, minus(plus(zero, true), 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(false, _x82, plus(zero, id(id(x)))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(id(s(_x51)), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), plus(zero, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(id(minus(plus(zero, true), 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), id(zero)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), plus(zero, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), id(0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), plus(zero, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(minus(gt(s(_x51), zero), 0), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), if(true, s(y), _x31)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), quot(s(_x32), s(_x31))) → plus#(x, if(gt(s(quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31))), quot(minus(_x32, _x31), s(_x31)), s(quot(minus(_x32, _x31), s(_x31)))))plus#(if(gt(s(_x51), zero), id(if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, gt(s(_x101), zero)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), id(s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(if(false, _x92, zero), id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(false, _x62, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21)), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(id(zero), id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(if(false, _x112, id(x)))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(s(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(plus(zero, zero), id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), if(true, plus(zero, id(id(x))), _x81), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), minus(s(y), 0)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(minus(zero, 0), id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(if(false, _x62, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(plus(zero, id(x)))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(if(true, minus(plus(zero, true), 0), _x71), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), if(false, _x92, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), minus(if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), 0), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, minus(id(id(x)), 0)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), plus(zero, zero)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(id(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, plus(zero, true)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(if(false, _x82, plus(zero, true)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), minus(zero, 0)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(if(true, zero, _x91), id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), plus(s(_x32), s(_x31))) → plus#(x, if(gt(s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31))))), s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))), s(s(plus(if(gt(_x32, _x31), _x32, _x31), if(not(gt(_x32, _x31)), id(_x32), id(_x31)))))))
plus#(if(gt(s(_x51), zero), if(plus(zero, minus(plus(zero, true), 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(plus(zero, gt(s(_x51), zero)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), minus(0, 0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(id(x)))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(plus(zero, if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31)), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), minus(plus(zero, id(id(x))), 0), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(s(_x51)), s(zero)), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), quot(0, s(_x91))), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(if(true, plus(zero, true), _x81), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), plus(id(_x32), s(_x31))) → plus#(x, if(gt(s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31)))), plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))), s(plus(_x32, if(gt(s(_x31), _x31), _x31, s(_x31))))))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), id(plus(zero, id(id(x)))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(minus(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), 0), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(if(true, id(x), _x111))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, if(true, id(id(x)), _x101)), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(plus(id(_x72), s(_x71)), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(minus(plus(zero, true), 0), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(if(true, zero, _x91), true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(s(plus(zero, true)), s(0)), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(minus(s(_x51), 0), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(minus(plus(zero, if(false, _x102, true)), 0), plus(zero, id(id(x))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(minus(id(x), 0))), _x21), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))plus#(if(gt(s(_x51), zero), if(true, if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x61), _x31), s(y)) → plus#(x, if(gt(s(y), y), y, s(y)))
plus#(if(gt(s(_x51), zero), if(minus(plus(zero, true), 0), plus(zero, id(id(x))), _x21), _x31), if(false, _x32, s(y))) → plus#(x, if(gt(s(y), y), y, s(y)))