TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60006 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (156ms).
 | – Problem 2 was processed with processor PolynomialLinearRange4iUR (4264ms).
 |    | – Problem 3 was processed with processor DependencyGraph (67ms).
 |    |    | – Problem 4 was processed with processor PolynomialLinearRange4iUR (2158ms).
 |    |    |    | – Problem 5 was processed with processor DependencyGraph (44ms).
 |    |    |    |    | – Problem 6 was processed with processor PolynomialLinearRange4iUR (3152ms).
 |    |    |    |    |    | – Problem 7 was processed with processor DependencyGraph (19ms).
 |    |    |    |    |    |    | – Problem 8 was processed with processor PolynomialLinearRange4iUR (926ms).
 |    |    |    |    |    |    |    | – Problem 9 was processed with processor DependencyGraph (11ms).
 |    |    |    |    |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (1ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (32ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (10ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 was processed with processor ForwardNarrowing (15ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 28 was processed with processor ForwardNarrowing (13ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 29 was processed with processor ForwardNarrowing (14ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 30 was processed with processor ForwardNarrowing (39ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 31 was processed with processor ForwardNarrowing (106ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 32 was processed with processor ForwardNarrowing (95ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 33 remains open; application of the following processors failed [ForwardNarrowing (148ms), ForwardNarrowing (73ms), ForwardNarrowing (152ms), ForwardNarrowing (73ms), ForwardNarrowing (80ms), ForwardNarrowing (85ms), ForwardNarrowing (161ms), ForwardNarrowing (73ms), ForwardNarrowing (56ms), ForwardNarrowing (51ms), ForwardNarrowing (64ms), ForwardNarrowing (58ms), ForwardNarrowing (58ms), ForwardNarrowing (58ms), ForwardNarrowing (58ms), ForwardNarrowing (56ms), ForwardNarrowing (63ms), ForwardNarrowing (58ms), ForwardNarrowing (65ms), ForwardNarrowing (64ms), ForwardNarrowing (64ms), ForwardNarrowing (65ms), ForwardNarrowing (146ms), ForwardNarrowing (66ms), ForwardNarrowing (79ms), ForwardNarrowing (86ms), ForwardNarrowing (82ms), ForwardNarrowing (87ms), ForwardNarrowing (89ms), ForwardNarrowing (84ms), ForwardNarrowing (72ms), ForwardNarrowing (159ms), ForwardNarrowing (87ms), ForwardNarrowing (186ms), ForwardNarrowing (79ms), ForwardNarrowing (155ms), ForwardNarrowing (63ms)].

The following open problems remain:

Open Dependency Pair Problem 10

Dependency Pairs

mark#(incr(X)) → a__incr#(mark(X))mark#(cons(X1, X2)) → mark#(X1)
mark#(s(X)) → mark#(X)a__incr#(cons(X, L)) → mark#(X)
mark#(incr(X)) → mark#(X)

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, head, a__head, nil, cons

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

a__adx#(cons(X, L)) → a__incr#(cons(mark(X), adx(L)))mark#(incr(X)) → a__incr#(mark(X))
a__nats# → a__adx#(a__zeros)mark#(zeros) → a__zeros#
mark#(cons(X1, X2)) → mark#(X1)mark#(nats) → a__nats#
a__tail#(cons(X, L)) → mark#(L)mark#(incr(X)) → mark#(X)
mark#(adx(X)) → a__adx#(mark(X))a__head#(cons(X, L)) → mark#(X)
mark#(head(X)) → mark#(X)mark#(adx(X)) → mark#(X)
mark#(tail(X)) → mark#(X)mark#(head(X)) → a__head#(mark(X))
a__nats# → a__zeros#a__adx#(cons(X, L)) → mark#(X)
a__incr#(cons(X, L)) → mark#(X)mark#(tail(X)) → a__tail#(mark(X))
mark#(s(X)) → mark#(X)

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The following SCCs where found

a__adx#(cons(X, L)) → a__incr#(cons(mark(X), adx(L)))mark#(incr(X)) → a__incr#(mark(X))
a__nats# → a__adx#(a__zeros)mark#(cons(X1, X2)) → mark#(X1)
mark#(nats) → a__nats#a__tail#(cons(X, L)) → mark#(L)
mark#(incr(X)) → mark#(X)mark#(adx(X)) → a__adx#(mark(X))
a__head#(cons(X, L)) → mark#(X)mark#(head(X)) → mark#(X)
mark#(adx(X)) → mark#(X)mark#(tail(X)) → mark#(X)
mark#(head(X)) → a__head#(mark(X))a__incr#(cons(X, L)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(tail(X)) → a__tail#(mark(X))
a__adx#(cons(X, L)) → mark#(X)

Problem 2: PolynomialLinearRange4iUR

Dependency Pair Problem

Dependency Pairs

a__adx#(cons(X, L)) → a__incr#(cons(mark(X), adx(L)))mark#(incr(X)) → a__incr#(mark(X))
a__nats# → a__adx#(a__zeros)mark#(cons(X1, X2)) → mark#(X1)
mark#(nats) → a__nats#a__tail#(cons(X, L)) → mark#(L)
mark#(incr(X)) → mark#(X)mark#(adx(X)) → a__adx#(mark(X))
a__head#(cons(X, L)) → mark#(X)mark#(head(X)) → mark#(X)
mark#(adx(X)) → mark#(X)mark#(tail(X)) → mark#(X)
mark#(head(X)) → a__head#(mark(X))a__incr#(cons(X, L)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(tail(X)) → a__tail#(mark(X))
a__adx#(cons(X, L)) → mark#(X)

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

Polynomial Interpretation

Improved Usable rules

a__head(X) → head(X)mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(head(X)) → a__head(mark(X))mark(0) → 0
a__tail(X) → tail(X)mark(tail(X)) → a__tail(mark(X))
a__adx(nil) → nila__adx(X) → adx(X)
a__head(cons(X, L)) → mark(X)a__zeros → zeros
a__incr(cons(X, L)) → cons(s(mark(X)), incr(L))a__nats → a__adx(a__zeros)
mark(nats) → a__natsmark(zeros) → a__zeros
mark(incr(X)) → a__incr(mark(X))a__incr(nil) → nil
a__nats → natsa__tail(cons(X, L)) → mark(L)
mark(s(X)) → s(mark(X))a__incr(X) → incr(X)
mark(nil) → nila__zeros → cons(0, zeros)
mark(adx(X)) → a__adx(mark(X))a__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))

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

a__nats# → a__adx#(a__zeros)

Problem 3: DependencyGraph

Dependency Pair Problem

Dependency Pairs

a__adx#(cons(X, L)) → a__incr#(cons(mark(X), adx(L)))mark#(incr(X)) → a__incr#(mark(X))
mark#(cons(X1, X2)) → mark#(X1)mark#(nats) → a__nats#
a__tail#(cons(X, L)) → mark#(L)mark#(incr(X)) → mark#(X)
mark#(adx(X)) → a__adx#(mark(X))a__head#(cons(X, L)) → mark#(X)
mark#(head(X)) → mark#(X)mark#(adx(X)) → mark#(X)
mark#(tail(X)) → mark#(X)mark#(head(X)) → a__head#(mark(X))
a__adx#(cons(X, L)) → mark#(X)mark#(tail(X)) → a__tail#(mark(X))
mark#(s(X)) → mark#(X)a__incr#(cons(X, L)) → mark#(X)

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, head, a__head, nil, cons

Strategy

The following SCCs where found

a__adx#(cons(X, L)) → a__incr#(cons(mark(X), adx(L)))mark#(incr(X)) → a__incr#(mark(X))
mark#(cons(X1, X2)) → mark#(X1)a__tail#(cons(X, L)) → mark#(L)
mark#(incr(X)) → mark#(X)mark#(adx(X)) → a__adx#(mark(X))
a__head#(cons(X, L)) → mark#(X)mark#(head(X)) → mark#(X)
mark#(adx(X)) → mark#(X)mark#(tail(X)) → mark#(X)
mark#(head(X)) → a__head#(mark(X))a__incr#(cons(X, L)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(tail(X)) → a__tail#(mark(X))
a__adx#(cons(X, L)) → mark#(X)

Problem 4: PolynomialLinearRange4iUR

Dependency Pair Problem

Dependency Pairs

a__adx#(cons(X, L)) → a__incr#(cons(mark(X), adx(L)))mark#(incr(X)) → a__incr#(mark(X))
mark#(cons(X1, X2)) → mark#(X1)a__tail#(cons(X, L)) → mark#(L)
mark#(incr(X)) → mark#(X)mark#(adx(X)) → a__adx#(mark(X))
a__head#(cons(X, L)) → mark#(X)mark#(head(X)) → mark#(X)
mark#(adx(X)) → mark#(X)mark#(tail(X)) → mark#(X)
mark#(head(X)) → a__head#(mark(X))a__incr#(cons(X, L)) → mark#(X)
mark#(s(X)) → mark#(X)a__adx#(cons(X, L)) → mark#(X)
mark#(tail(X)) → a__tail#(mark(X))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, head, a__head, nil, cons

Strategy

Polynomial Interpretation

Improved Usable rules

a__head(X) → head(X)mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(head(X)) → a__head(mark(X))mark(0) → 0
a__tail(X) → tail(X)mark(tail(X)) → a__tail(mark(X))
a__adx(nil) → nila__adx(X) → adx(X)
a__head(cons(X, L)) → mark(X)a__zeros → zeros
a__incr(cons(X, L)) → cons(s(mark(X)), incr(L))a__nats → a__adx(a__zeros)
mark(nats) → a__natsmark(zeros) → a__zeros
mark(incr(X)) → a__incr(mark(X))a__incr(nil) → nil
a__nats → natsa__tail(cons(X, L)) → mark(L)
mark(s(X)) → s(mark(X))a__incr(X) → incr(X)
mark(nil) → nila__zeros → cons(0, zeros)
mark(adx(X)) → a__adx(mark(X))a__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))

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

mark#(head(X)) → mark#(X)mark#(head(X)) → a__head#(mark(X))

Problem 5: DependencyGraph

Dependency Pair Problem

Dependency Pairs

a__adx#(cons(X, L)) → a__incr#(cons(mark(X), adx(L)))mark#(incr(X)) → a__incr#(mark(X))
mark#(cons(X1, X2)) → mark#(X1)a__tail#(cons(X, L)) → mark#(L)
mark#(incr(X)) → mark#(X)mark#(adx(X)) → a__adx#(mark(X))
a__head#(cons(X, L)) → mark#(X)mark#(adx(X)) → mark#(X)
mark#(tail(X)) → mark#(X)a__incr#(cons(X, L)) → mark#(X)
mark#(s(X)) → mark#(X)a__adx#(cons(X, L)) → mark#(X)
mark#(tail(X)) → a__tail#(mark(X))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The following SCCs where found

a__adx#(cons(X, L)) → a__incr#(cons(mark(X), adx(L)))mark#(incr(X)) → a__incr#(mark(X))
mark#(adx(X)) → mark#(X)mark#(tail(X)) → mark#(X)
mark#(cons(X1, X2)) → mark#(X1)a__incr#(cons(X, L)) → mark#(X)
mark#(s(X)) → mark#(X)a__adx#(cons(X, L)) → mark#(X)
mark#(tail(X)) → a__tail#(mark(X))a__tail#(cons(X, L)) → mark#(L)
mark#(incr(X)) → mark#(X)mark#(adx(X)) → a__adx#(mark(X))

Problem 6: PolynomialLinearRange4iUR

Dependency Pair Problem

Dependency Pairs

a__adx#(cons(X, L)) → a__incr#(cons(mark(X), adx(L)))mark#(adx(X)) → mark#(X)
mark#(incr(X)) → a__incr#(mark(X))mark#(tail(X)) → mark#(X)
mark#(cons(X1, X2)) → mark#(X1)a__incr#(cons(X, L)) → mark#(X)
mark#(s(X)) → mark#(X)a__adx#(cons(X, L)) → mark#(X)
mark#(tail(X)) → a__tail#(mark(X))a__tail#(cons(X, L)) → mark#(L)
mark#(incr(X)) → mark#(X)mark#(adx(X)) → a__adx#(mark(X))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

Polynomial Interpretation

Improved Usable rules

a__head(X) → head(X)mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(head(X)) → a__head(mark(X))mark(0) → 0
a__tail(X) → tail(X)mark(tail(X)) → a__tail(mark(X))
a__adx(nil) → nila__adx(X) → adx(X)
a__head(cons(X, L)) → mark(X)a__zeros → zeros
a__incr(cons(X, L)) → cons(s(mark(X)), incr(L))a__nats → a__adx(a__zeros)
mark(nats) → a__natsmark(zeros) → a__zeros
mark(incr(X)) → a__incr(mark(X))a__incr(nil) → nil
a__nats → natsa__tail(cons(X, L)) → mark(L)
mark(s(X)) → s(mark(X))a__incr(X) → incr(X)
mark(nil) → nila__zeros → cons(0, zeros)
mark(adx(X)) → a__adx(mark(X))a__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))

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

mark#(adx(X)) → a__adx#(mark(X))mark#(adx(X)) → mark#(X)
a__adx#(cons(X, L)) → mark#(X)

Problem 7: DependencyGraph

Dependency Pair Problem

Dependency Pairs

a__adx#(cons(X, L)) → a__incr#(cons(mark(X), adx(L)))mark#(incr(X)) → a__incr#(mark(X))
mark#(tail(X)) → mark#(X)mark#(cons(X1, X2)) → mark#(X1)
mark#(tail(X)) → a__tail#(mark(X))mark#(s(X)) → mark#(X)
a__incr#(cons(X, L)) → mark#(X)a__tail#(cons(X, L)) → mark#(L)
mark#(incr(X)) → mark#(X)

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, head, a__head, nil, cons

Strategy

The following SCCs where found

mark#(incr(X)) → a__incr#(mark(X))mark#(tail(X)) → mark#(X)
mark#(cons(X1, X2)) → mark#(X1)mark#(s(X)) → mark#(X)
mark#(tail(X)) → a__tail#(mark(X))a__incr#(cons(X, L)) → mark#(X)
a__tail#(cons(X, L)) → mark#(L)mark#(incr(X)) → mark#(X)

Problem 8: PolynomialLinearRange4iUR

Dependency Pair Problem

Dependency Pairs

mark#(incr(X)) → a__incr#(mark(X))mark#(tail(X)) → mark#(X)
mark#(cons(X1, X2)) → mark#(X1)mark#(s(X)) → mark#(X)
mark#(tail(X)) → a__tail#(mark(X))a__incr#(cons(X, L)) → mark#(X)
a__tail#(cons(X, L)) → mark#(L)mark#(incr(X)) → mark#(X)

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, head, a__head, nil, cons

Strategy

Polynomial Interpretation

Improved Usable rules

a__head(X) → head(X)mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(0) → 0mark(head(X)) → a__head(mark(X))
a__tail(X) → tail(X)mark(tail(X)) → a__tail(mark(X))
a__adx(nil) → nila__adx(X) → adx(X)
a__head(cons(X, L)) → mark(X)a__zeros → zeros
a__incr(cons(X, L)) → cons(s(mark(X)), incr(L))a__nats → a__adx(a__zeros)
mark(nats) → a__natsmark(zeros) → a__zeros
mark(incr(X)) → a__incr(mark(X))a__incr(nil) → nil
a__nats → natsa__tail(cons(X, L)) → mark(L)
mark(s(X)) → s(mark(X))a__incr(X) → incr(X)
mark(nil) → nila__zeros → cons(0, zeros)
mark(adx(X)) → a__adx(mark(X))a__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))

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

mark#(tail(X)) → mark#(X)mark#(tail(X)) → a__tail#(mark(X))

Problem 9: DependencyGraph

Dependency Pair Problem

Dependency Pairs

mark#(incr(X)) → a__incr#(mark(X))mark#(cons(X1, X2)) → mark#(X1)
a__incr#(cons(X, L)) → mark#(X)mark#(s(X)) → mark#(X)
a__tail#(cons(X, L)) → mark#(L)mark#(incr(X)) → mark#(X)

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The following SCCs where found

mark#(incr(X)) → a__incr#(mark(X))mark#(cons(X1, X2)) → mark#(X1)
a__incr#(cons(X, L)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(X)) → mark#(X)

Problem 10: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(X)) → a__incr#(mark(X))mark#(cons(X1, X2)) → mark#(X1)
a__incr#(cons(X, L)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(X)) → mark#(X)

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(X)) → a__incr#(mark(X)) is 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
a__incr#(a__adx(mark(_x21))) 
a__incr#(a__zeros) 
a__incr#(a__head(mark(_x21))) 
a__incr#(a__nats) 
a__incr#(nil) 
a__incr#(0) 
a__incr#(s(mark(_x21))) 
a__incr#(cons(mark(_x21), _x22)) 
a__incr#(a__incr(mark(_x21))) 
a__incr#(a__tail(mark(_x21))) 
Thus, the rule mark#(incr(X)) → a__incr#(mark(X)) is replaced by the following rules:
mark#(incr(0)) → a__incr#(0)mark#(incr(head(_x21))) → a__incr#(a__head(mark(_x21)))
mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21)))mark#(incr(incr(_x21))) → a__incr#(a__incr(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(zeros)) → a__incr#(a__zeros)mark#(incr(nil)) → a__incr#(nil)

Problem 11: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(0)) → a__incr#(0)mark#(incr(head(_x21))) → a__incr#(a__head(mark(_x21)))
mark#(incr(incr(_x21))) → a__incr#(a__incr(mark(_x21)))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(X)) → mark#(X)mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))mark#(s(X)) → mark#(X)
a__incr#(cons(X, L)) → mark#(X)mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(zeros)) → a__incr#(a__zeros)mark#(incr(nil)) → a__incr#(nil)

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(0)) → a__incr#(0) is 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
Thus, the rule mark#(incr(0)) → a__incr#(0) is deleted.

Problem 12: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(_x21))) → a__incr#(a__head(mark(_x21)))mark#(incr(incr(_x21))) → a__incr#(a__incr(mark(_x21)))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(X)) → mark#(X)
mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21)))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(s(X)) → mark#(X)a__incr#(cons(X, L)) → mark#(X)
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(zeros)) → a__incr#(a__zeros)
mark#(incr(nil)) → a__incr#(nil)

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(head(_x21))) → a__incr#(a__head(mark(_x21))) is 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
a__incr#(a__head(0)) 
a__incr#(a__head(a__adx(mark(_x41)))) 
a__incr#(a__head(a__zeros)) 
a__incr#(a__head(a__incr(mark(_x41)))) 
a__incr#(a__head(a__nats)) 
a__incr#(a__head(s(mark(_x41)))) 
a__incr#(a__head(a__head(mark(_x41)))) 
a__incr#(head(mark(_x21))) 
a__incr#(a__head(nil)) 
a__incr#(a__head(a__tail(mark(_x41)))) 
a__incr#(a__head(cons(mark(_x41), _x42))) 
Thus, the rule mark#(incr(head(_x21))) → a__incr#(a__head(mark(_x21))) is replaced by the following rules:
mark#(incr(head(nil))) → a__incr#(a__head(nil))mark#(incr(head(s(_x41)))) → a__incr#(a__head(s(mark(_x41))))
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(zeros))) → a__incr#(a__head(a__zeros))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))

Problem 13: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(_x41)))) → a__incr#(a__head(s(mark(_x41))))mark#(incr(head(nil))) → a__incr#(a__head(nil))
mark#(incr(incr(_x21))) → a__incr#(a__incr(mark(_x21)))mark#(incr(head(zeros))) → a__incr#(a__head(a__zeros))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(X)) → mark#(X)
mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21)))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(incr(nats)) → a__incr#(a__nats)a__incr#(cons(X, L)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(zeros)) → a__incr#(a__zeros)
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(s(_x41)))) → a__incr#(a__head(s(mark(_x41)))) is 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
a__incr#(a__head(s(a__tail(mark(_x51))))) 
a__incr#(a__head(s(0))) 
a__incr#(a__head(s(s(mark(_x51))))) 
a__incr#(a__head(s(a__adx(mark(_x51))))) 
a__incr#(a__head(s(a__head(mark(_x51))))) 
a__incr#(a__head(s(nil))) 
a__incr#(a__head(s(a__nats))) 
a__incr#(a__head(s(a__incr(mark(_x51))))) 
a__incr#(a__head(s(a__zeros))) 
a__incr#(a__head(s(cons(mark(_x51), _x52)))) 
a__incr#(head(s(mark(_x41)))) 
Thus, the rule mark#(incr(head(s(_x41)))) → a__incr#(a__head(s(mark(_x41)))) is replaced by the following rules:
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))

Problem 14: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(nil))) → a__incr#(a__head(nil))mark#(incr(incr(_x21))) → a__incr#(a__incr(mark(_x21)))
mark#(incr(head(zeros))) → a__incr#(a__head(a__zeros))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21)))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(s(X)) → mark#(X)a__incr#(cons(X, L)) → mark#(X)
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))
mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(X)) → mark#(X)mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(zeros)) → a__incr#(a__zeros)
mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(incr(_x21))) → a__incr#(a__incr(mark(_x21))) is 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
a__incr#(a__incr(a__nats)) 
a__incr#(a__incr(a__zeros)) 
a__incr#(a__incr(a__adx(mark(_x41)))) 
a__incr#(a__incr(nil)) 
a__incr#(incr(mark(_x21))) 
a__incr#(a__incr(a__tail(mark(_x41)))) 
a__incr#(a__incr(0)) 
a__incr#(a__incr(s(mark(_x41)))) 
a__incr#(a__incr(a__head(mark(_x41)))) 
a__incr#(a__incr(a__incr(mark(_x41)))) 
a__incr#(a__incr(cons(mark(_x41), _x42))) 
Thus, the rule mark#(incr(incr(_x21))) → a__incr#(a__incr(mark(_x21))) is replaced by the following rules:
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(a__incr(mark(_x41))))
mark#(incr(incr(nil))) → a__incr#(a__incr(nil))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))

Problem 15: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(nil))) → a__incr#(a__head(nil))mark#(incr(head(zeros))) → a__incr#(a__head(a__zeros))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(a__incr(mark(_x41))))mark#(incr(incr(nil))) → a__incr#(a__incr(nil))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))
mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21)))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(s(X)) → mark#(X)a__incr#(cons(X, L)) → mark#(X)
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(X)) → mark#(X)mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(zeros)) → a__incr#(a__zeros)
mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(nil))) → a__incr#(a__head(nil)) is 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
a__incr#(head(nil)) 
Thus, the rule mark#(incr(head(nil))) → a__incr#(a__head(nil)) is replaced by the following rules:
mark#(incr(head(nil))) → a__incr#(head(nil))

Problem 16: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(zeros))) → a__incr#(a__head(a__zeros))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(a__incr(mark(_x41))))
mark#(incr(incr(nil))) → a__incr#(a__incr(nil))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))
mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21)))mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))mark#(s(X)) → mark#(X)
a__incr#(cons(X, L)) → mark#(X)mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))
mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(X)) → mark#(X)mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(zeros)) → a__incr#(a__zeros)
mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(head(zeros))) → a__incr#(a__head(a__zeros)) is 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
a__incr#(a__head(cons(0, zeros))) 
a__incr#(a__head(zeros)) 
a__incr#(head(a__zeros)) 
Thus, the rule mark#(incr(head(zeros))) → a__incr#(a__head(a__zeros)) is replaced by the following rules:
mark#(incr(head(zeros))) → a__incr#(a__head(zeros))mark#(incr(head(zeros))) → a__incr#(head(a__zeros))
mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))

Problem 17: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(zeros))) → a__incr#(a__head(zeros))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(a__incr(mark(_x41))))
mark#(incr(incr(nil))) → a__incr#(a__incr(nil))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))
mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21)))mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))mark#(s(X)) → mark#(X)
a__incr#(cons(X, L)) → mark#(X)mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(X)) → mark#(X)mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))
mark#(incr(head(zeros))) → a__incr#(head(a__zeros))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(zeros)) → a__incr#(a__zeros)mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))
mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(zeros))) → a__incr#(a__head(zeros)) is 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
a__incr#(head(zeros)) 
Thus, the rule mark#(incr(head(zeros))) → a__incr#(a__head(zeros)) is replaced by the following rules:
mark#(incr(head(zeros))) → a__incr#(head(zeros))

Problem 18: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(a__incr(mark(_x41))))mark#(incr(incr(nil))) → a__incr#(a__incr(nil))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21)))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(s(X)) → mark#(X)a__incr#(cons(X, L)) → mark#(X)
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))mark#(incr(head(zeros))) → a__incr#(head(zeros))
mark#(incr(X)) → mark#(X)mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(zeros))) → a__incr#(head(a__zeros))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(zeros)) → a__incr#(a__zeros)mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))
mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(a__incr(mark(_x41)))) is 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
a__incr#(a__incr(a__incr(a__tail(mark(_x51))))) 
a__incr#(incr(a__incr(mark(_x41)))) 
a__incr#(a__incr(a__incr(cons(mark(_x51), _x52)))) 
a__incr#(a__incr(a__incr(a__adx(mark(_x51))))) 
a__incr#(a__incr(a__incr(a__zeros))) 
a__incr#(a__incr(a__incr(a__nats))) 
a__incr#(a__incr(a__incr(s(mark(_x51))))) 
a__incr#(a__incr(a__incr(nil))) 
a__incr#(a__incr(incr(mark(_x41)))) 
a__incr#(a__incr(a__incr(a__incr(mark(_x51))))) 
a__incr#(a__incr(a__incr(a__head(mark(_x51))))) 
a__incr#(a__incr(a__incr(0))) 
Thus, the rule mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(a__incr(mark(_x41)))) is replaced by the following rules:
mark#(incr(incr(incr(zeros)))) → a__incr#(a__incr(a__incr(a__zeros)))mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(incr(incr(adx(_x51))))) → a__incr#(a__incr(a__incr(a__adx(mark(_x51)))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))
mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))
mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))
mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))

Problem 19: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(incr(nil))) → a__incr#(a__incr(nil))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))
mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21)))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
a__incr#(cons(X, L)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))
mark#(incr(head(zeros))) → a__incr#(head(zeros))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))
mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(incr(incr(zeros)))) → a__incr#(a__incr(a__incr(a__zeros)))
mark#(incr(incr(incr(adx(_x51))))) → a__incr#(a__incr(a__incr(a__adx(mark(_x51)))))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(incr(X)) → mark#(X)
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))mark#(incr(head(zeros))) → a__incr#(head(a__zeros))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))mark#(incr(zeros)) → a__incr#(a__zeros)
mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(incr(nil))) → a__incr#(a__incr(nil)) is 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
a__incr#(nil) 
a__incr#(incr(nil)) 
Thus, the rule mark#(incr(incr(nil))) → a__incr#(a__incr(nil)) is replaced by the following rules:
mark#(incr(incr(nil))) → a__incr#(incr(nil))mark#(incr(incr(nil))) → a__incr#(nil)

Problem 20: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51)))))mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))
mark#(incr(incr(nil))) → a__incr#(incr(nil))mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21)))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(incr(nil))) → a__incr#(nil)
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))a__incr#(cons(X, L)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(zeros))) → a__incr#(head(zeros))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))
mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(incr(incr(zeros)))) → a__incr#(a__incr(a__incr(a__zeros)))mark#(incr(incr(incr(adx(_x51))))) → a__incr#(a__incr(a__incr(a__adx(mark(_x51)))))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(X)) → mark#(X)mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(head(zeros))) → a__incr#(head(a__zeros))mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))
mark#(incr(zeros)) → a__incr#(a__zeros)mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))
mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51))))) is 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
a__incr#(a__head(s(a__head(s(mark(_x61)))))) 
a__incr#(a__head(s(a__head(a__zeros)))) 
a__incr#(a__head(s(a__head(nil)))) 
a__incr#(a__head(s(a__head(a__head(mark(_x61)))))) 
a__incr#(a__head(s(a__head(cons(mark(_x61), _x62))))) 
a__incr#(a__head(s(a__head(a__nats)))) 
a__incr#(a__head(s(a__head(a__tail(mark(_x61)))))) 
a__incr#(a__head(s(a__head(a__incr(mark(_x61)))))) 
a__incr#(a__head(s(head(mark(_x51))))) 
a__incr#(head(s(a__head(mark(_x51))))) 
a__incr#(a__head(s(a__head(0)))) 
a__incr#(a__head(s(a__head(a__adx(mark(_x61)))))) 
Thus, the rule mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(a__head(mark(_x51))))) is replaced by the following rules:
mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(a__adx(mark(_x61))))))
mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(a__head(0))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))mark#(incr(head(s(head(zeros))))) → a__incr#(a__head(s(a__head(a__zeros))))
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))

Problem 21: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil)))mark#(incr(incr(nil))) → a__incr#(incr(nil))
mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21)))mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(a__head(0))))
mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(a__adx(mark(_x61))))))mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(incr(nil))) → a__incr#(nil)mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
a__incr#(cons(X, L)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(zeros))) → a__incr#(head(zeros))mark#(incr(head(s(head(zeros))))) → a__incr#(a__head(s(a__head(a__zeros))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))
mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(incr(incr(zeros)))) → a__incr#(a__incr(a__incr(a__zeros)))mark#(incr(incr(incr(adx(_x51))))) → a__incr#(a__incr(a__incr(a__adx(mark(_x51)))))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(X)) → mark#(X)mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))mark#(incr(head(zeros))) → a__incr#(head(a__zeros))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))mark#(incr(zeros)) → a__incr#(a__zeros)
mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil))) is 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
a__incr#(head(s(nil))) 
Thus, the rule mark#(incr(head(s(nil)))) → a__incr#(a__head(s(nil))) is replaced by the following rules:
mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))

Problem 22: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(incr(nil))) → a__incr#(incr(nil))mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21)))
mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(a__head(0))))mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(a__adx(mark(_x61))))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(incr(nil))) → a__incr#(nil)
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))a__incr#(cons(X, L)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(zeros))) → a__incr#(head(zeros))
mark#(incr(head(s(head(zeros))))) → a__incr#(a__head(s(a__head(a__zeros))))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))
mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))
mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(incr(incr(zeros)))) → a__incr#(a__incr(a__incr(a__zeros)))mark#(incr(incr(incr(adx(_x51))))) → a__incr#(a__incr(a__incr(a__adx(mark(_x51)))))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(X)) → mark#(X)mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))mark#(incr(head(zeros))) → a__incr#(head(a__zeros))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))mark#(incr(zeros)) → a__incr#(a__zeros)
mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(incr(nil))) → a__incr#(incr(nil)) is 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
Thus, the rule mark#(incr(incr(nil))) → a__incr#(incr(nil)) is deleted.

Problem 23: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21)))mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(a__head(0))))
mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(a__adx(mark(_x61))))))mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(incr(nil))) → a__incr#(nil)mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
a__incr#(cons(X, L)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(zeros))) → a__incr#(head(zeros))mark#(incr(head(s(head(zeros))))) → a__incr#(a__head(s(a__head(a__zeros))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))
mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))
mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(incr(incr(zeros)))) → a__incr#(a__incr(a__incr(a__zeros)))
mark#(incr(incr(incr(adx(_x51))))) → a__incr#(a__incr(a__incr(a__adx(mark(_x51)))))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(incr(X)) → mark#(X)
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))
mark#(incr(head(zeros))) → a__incr#(head(a__zeros))mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))
mark#(incr(zeros)) → a__incr#(a__zeros)mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))
mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21))) is 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
a__incr#(a__adx(nil)) 
a__incr#(a__adx(0)) 
a__incr#(a__adx(s(mark(_x41)))) 
a__incr#(a__adx(a__nats)) 
a__incr#(a__adx(a__head(mark(_x41)))) 
a__incr#(a__adx(a__adx(mark(_x41)))) 
a__incr#(a__adx(a__zeros)) 
a__incr#(a__adx(a__tail(mark(_x41)))) 
a__incr#(a__adx(cons(mark(_x41), _x42))) 
a__incr#(adx(mark(_x21))) 
a__incr#(a__adx(a__incr(mark(_x41)))) 
Thus, the rule mark#(incr(adx(_x21))) → a__incr#(a__adx(mark(_x21))) is replaced by the following rules:
mark#(incr(adx(s(_x41)))) → a__incr#(a__adx(s(mark(_x41))))mark#(incr(adx(head(_x41)))) → a__incr#(a__adx(a__head(mark(_x41))))
mark#(incr(adx(nats))) → a__incr#(a__adx(a__nats))mark#(incr(adx(_x21))) → a__incr#(adx(mark(_x21)))
mark#(incr(adx(cons(_x41, _x42)))) → a__incr#(a__adx(cons(mark(_x41), _x42)))mark#(incr(adx(incr(_x41)))) → a__incr#(a__adx(a__incr(mark(_x41))))
mark#(incr(adx(nil))) → a__incr#(a__adx(nil))mark#(incr(adx(adx(_x41)))) → a__incr#(a__adx(a__adx(mark(_x41))))
mark#(incr(adx(0))) → a__incr#(a__adx(0))mark#(incr(adx(tail(_x41)))) → a__incr#(a__adx(a__tail(mark(_x41))))
mark#(incr(adx(zeros))) → a__incr#(a__adx(a__zeros))

Problem 24: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(a__head(0))))mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(a__adx(mark(_x61))))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(incr(nil))) → a__incr#(nil)
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))a__incr#(cons(X, L)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(adx(adx(_x41)))) → a__incr#(a__adx(a__adx(mark(_x41))))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(adx(zeros))) → a__incr#(a__adx(a__zeros))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(zeros))) → a__incr#(head(zeros))
mark#(incr(adx(incr(_x41)))) → a__incr#(a__adx(a__incr(mark(_x41))))mark#(incr(head(s(head(zeros))))) → a__incr#(a__head(s(a__head(a__zeros))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))mark#(incr(adx(0))) → a__incr#(a__adx(0))
mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(adx(s(_x41)))) → a__incr#(a__adx(s(mark(_x41))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(adx(nil))) → a__incr#(a__adx(nil))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))
mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(incr(incr(zeros)))) → a__incr#(a__incr(a__incr(a__zeros)))mark#(incr(adx(head(_x41)))) → a__incr#(a__adx(a__head(mark(_x41))))
mark#(incr(incr(incr(adx(_x51))))) → a__incr#(a__incr(a__incr(a__adx(mark(_x51)))))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(adx(nats))) → a__incr#(a__adx(a__nats))mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(X)) → mark#(X)mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(adx(_x21))) → a__incr#(adx(mark(_x21)))
mark#(incr(adx(cons(_x41, _x42)))) → a__incr#(a__adx(cons(mark(_x41), _x42)))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))mark#(incr(head(zeros))) → a__incr#(head(a__zeros))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))mark#(incr(zeros)) → a__incr#(a__zeros)
mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))
mark#(incr(adx(tail(_x41)))) → a__incr#(a__adx(a__tail(mark(_x41))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(a__head(0)))) is 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
a__incr#(head(s(a__head(0)))) 
a__incr#(a__head(s(head(0)))) 
Thus, the rule mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(a__head(0)))) is replaced by the following rules:
mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))

Problem 25: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(a__adx(mark(_x61))))))mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(incr(nil))) → a__incr#(nil)mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))a__incr#(cons(X, L)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(adx(adx(_x41)))) → a__incr#(a__adx(a__adx(mark(_x41))))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(adx(zeros))) → a__incr#(a__adx(a__zeros))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))
mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))mark#(incr(adx(incr(_x41)))) → a__incr#(a__adx(a__incr(mark(_x41))))
mark#(incr(head(zeros))) → a__incr#(head(zeros))mark#(incr(head(s(head(zeros))))) → a__incr#(a__head(s(a__head(a__zeros))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))mark#(incr(adx(0))) → a__incr#(a__adx(0))
mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))
mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))
mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(adx(s(_x41)))) → a__incr#(a__adx(s(mark(_x41))))mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))
mark#(incr(adx(nil))) → a__incr#(a__adx(nil))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(incr(incr(zeros)))) → a__incr#(a__incr(a__incr(a__zeros)))
mark#(incr(adx(head(_x41)))) → a__incr#(a__adx(a__head(mark(_x41))))mark#(incr(incr(incr(adx(_x51))))) → a__incr#(a__incr(a__incr(a__adx(mark(_x51)))))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))mark#(incr(adx(nats))) → a__incr#(a__adx(a__nats))
mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(incr(X)) → mark#(X)
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(adx(_x21))) → a__incr#(adx(mark(_x21)))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(adx(cons(_x41, _x42)))) → a__incr#(a__adx(cons(mark(_x41), _x42)))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))
mark#(incr(head(zeros))) → a__incr#(head(a__zeros))mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))
mark#(incr(zeros)) → a__incr#(a__zeros)mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))
mark#(incr(adx(tail(_x41)))) → a__incr#(a__adx(a__tail(mark(_x41))))mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(a__adx(mark(_x61)))))) is 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
a__incr#(a__head(s(a__head(a__adx(cons(mark(_x71), _x72)))))) 
a__incr#(a__head(s(a__head(a__adx(a__tail(mark(_x71))))))) 
a__incr#(head(s(a__head(a__adx(mark(_x61)))))) 
a__incr#(a__head(s(a__head(adx(mark(_x61)))))) 
a__incr#(a__head(s(head(a__adx(mark(_x61)))))) 
a__incr#(a__head(s(a__head(a__adx(a__incr(mark(_x71))))))) 
a__incr#(a__head(s(a__head(a__adx(a__nats))))) 
a__incr#(a__head(s(a__head(a__adx(0))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(mark(_x71))))))) 
a__incr#(a__head(s(a__head(a__adx(nil))))) 
a__incr#(a__head(s(a__head(a__adx(a__head(mark(_x71))))))) 
a__incr#(a__head(s(a__head(a__adx(s(mark(_x71))))))) 
a__incr#(a__head(s(a__head(a__adx(a__zeros))))) 
Thus, the rule mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(a__adx(mark(_x61)))))) is replaced by the following rules:
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(mark(_x71)))))))mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(mark(_x71)))))))
mark#(incr(head(s(head(adx(head(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__head(mark(_x71)))))))mark#(incr(head(s(head(adx(0)))))) → a__incr#(a__head(s(a__head(a__adx(0)))))
mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(mark(_x71), _x72))))))mark#(incr(head(s(head(adx(nil)))))) → a__incr#(a__head(s(a__head(a__adx(nil)))))
mark#(incr(head(s(head(adx(nats)))))) → a__incr#(a__head(s(a__head(a__adx(a__nats)))))mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(adx(mark(_x61))))))
mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(head(a__adx(mark(_x61))))))mark#(incr(head(s(head(adx(s(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(s(mark(_x71)))))))
mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(head(s(a__head(a__adx(mark(_x61))))))mark#(incr(head(s(head(adx(zeros)))))) → a__incr#(a__head(s(a__head(a__adx(a__zeros)))))
mark#(incr(head(s(head(adx(tail(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__tail(mark(_x71)))))))

Problem 26: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(mark(_x71)))))))mark#(incr(head(s(head(adx(0)))))) → a__incr#(a__head(s(a__head(a__adx(0)))))
mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(mark(_x71), _x72))))))mark#(incr(head(s(head(adx(nats)))))) → a__incr#(a__head(s(a__head(a__adx(a__nats)))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(incr(nil))) → a__incr#(nil)
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))
mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
a__incr#(cons(X, L)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(adx(adx(_x41)))) → a__incr#(a__adx(a__adx(mark(_x41))))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(head(s(head(adx(tail(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__tail(mark(_x71)))))))
mark#(incr(adx(zeros))) → a__incr#(a__adx(a__zeros))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))
mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(mark(_x71)))))))mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(adx(incr(_x41)))) → a__incr#(a__adx(a__incr(mark(_x41))))mark#(incr(head(zeros))) → a__incr#(head(zeros))
mark#(incr(head(s(head(zeros))))) → a__incr#(a__head(s(a__head(a__zeros))))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))
mark#(incr(adx(0))) → a__incr#(a__adx(0))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(head(s(a__head(a__adx(mark(_x61))))))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))
mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))
mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(adx(s(_x41)))) → a__incr#(a__adx(s(mark(_x41))))mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))
mark#(incr(adx(nil))) → a__incr#(a__adx(nil))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(incr(incr(zeros)))) → a__incr#(a__incr(a__incr(a__zeros)))
mark#(incr(head(s(head(adx(nil)))))) → a__incr#(a__head(s(a__head(a__adx(nil)))))mark#(incr(adx(head(_x41)))) → a__incr#(a__adx(a__head(mark(_x41))))
mark#(incr(incr(incr(adx(_x51))))) → a__incr#(a__incr(a__incr(a__adx(mark(_x51)))))mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(adx(mark(_x61))))))
mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(head(a__adx(mark(_x61))))))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(head(s(head(adx(s(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(s(mark(_x71)))))))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))
mark#(incr(head(nil))) → a__incr#(head(nil))mark#(incr(nil)) → a__incr#(nil)
mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))mark#(incr(adx(nats))) → a__incr#(a__adx(a__nats))
mark#(incr(head(s(head(adx(head(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__head(mark(_x71)))))))mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(X)) → mark#(X)mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(adx(_x21))) → a__incr#(adx(mark(_x21)))
mark#(incr(adx(cons(_x41, _x42)))) → a__incr#(a__adx(cons(mark(_x41), _x42)))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))mark#(incr(head(zeros))) → a__incr#(head(a__zeros))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))mark#(incr(head(s(head(adx(zeros)))))) → a__incr#(a__head(s(a__head(a__adx(a__zeros)))))
mark#(incr(zeros)) → a__incr#(a__zeros)mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))
mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))mark#(incr(adx(tail(_x41)))) → a__incr#(a__adx(a__tail(mark(_x41))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(mark(_x71))))))) is 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
a__incr#(a__head(s(a__head(a__adx(a__adx(nil)))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(a__incr(mark(_x81)))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(s(mark(_x81)))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(a__tail(mark(_x81)))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(cons(mark(_x81), _x82))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(a__adx(mark(_x81)))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(a__head(mark(_x81)))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(0)))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(a__zeros)))))) 
a__incr#(a__head(s(a__head(a__adx(adx(mark(_x71))))))) 
a__incr#(head(s(a__head(a__adx(a__adx(mark(_x71))))))) 
a__incr#(a__head(s(head(a__adx(a__adx(mark(_x71))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(a__nats)))))) 
a__incr#(a__head(s(a__head(adx(a__adx(mark(_x71))))))) 
Thus, the rule mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(mark(_x71))))))) is replaced by the following rules:
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(adx(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(nil))))))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(head(s(a__head(a__adx(a__adx(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(head(a__adx(a__adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(adx(a__adx(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__adx(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__zeros))))))
mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(0))))))mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__nats))))))
mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__tail(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__incr(mark(_x81))))))))

Problem 27: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(adx(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(mark(_x71), _x72))))))mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__nats))))))
mark#(incr(head(s(head(adx(nats)))))) → a__incr#(a__head(s(a__head(a__adx(a__nats)))))mark#(incr(incr(nil))) → a__incr#(nil)
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))a__incr#(cons(X, L)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(adx(adx(_x41)))) → a__incr#(a__adx(a__adx(mark(_x41))))mark#(incr(adx(zeros))) → a__incr#(a__adx(a__zeros))
mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(mark(_x71)))))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(s(head(zeros))))) → a__incr#(a__head(s(a__head(a__zeros))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__zeros))))))
mark#(incr(adx(0))) → a__incr#(a__adx(0))mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))
mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(head(s(a__head(a__adx(mark(_x61))))))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))
mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))
mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(nil))))))mark#(incr(adx(s(_x41)))) → a__incr#(a__adx(s(mark(_x41))))
mark#(incr(adx(nil))) → a__incr#(a__adx(nil))mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(incr(incr(zeros)))) → a__incr#(a__incr(a__incr(a__zeros)))
mark#(incr(adx(head(_x41)))) → a__incr#(a__adx(a__head(mark(_x41))))mark#(incr(head(s(head(adx(s(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(s(mark(_x71)))))))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(adx(nats))) → a__incr#(a__adx(a__nats))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(0))))))
mark#(incr(X)) → mark#(X)mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__tail(mark(_x81))))))))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(adx(cons(_x41, _x42)))) → a__incr#(a__adx(cons(mark(_x41), _x42)))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))mark#(incr(head(zeros))) → a__incr#(head(a__zeros))
mark#(incr(head(s(head(adx(zeros)))))) → a__incr#(a__head(s(a__head(a__adx(a__zeros)))))mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))
mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))mark#(incr(adx(tail(_x41)))) → a__incr#(a__adx(a__tail(mark(_x41))))
mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))mark#(incr(head(s(head(adx(0)))))) → a__incr#(a__head(s(a__head(a__adx(0)))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))
mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(cons(mark(_x81), _x82)))))))
mark#(incr(head(s(head(adx(tail(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__tail(mark(_x71)))))))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(head(s(a__head(a__adx(a__adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(head(a__adx(a__adx(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(adx(a__adx(mark(_x71)))))))
mark#(incr(head(zeros))) → a__incr#(head(zeros))mark#(incr(adx(incr(_x41)))) → a__incr#(a__adx(a__incr(mark(_x41))))
mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(head(s(head(adx(nil)))))) → a__incr#(a__head(s(a__head(a__adx(nil)))))
mark#(incr(incr(incr(adx(_x51))))) → a__incr#(a__incr(a__incr(a__adx(mark(_x51)))))mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(head(a__adx(mark(_x61))))))
mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(adx(mark(_x61))))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__head(mark(_x81))))))))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(head(s(head(adx(head(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__head(mark(_x71)))))))mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__adx(mark(_x81))))))))
mark#(incr(adx(_x21))) → a__incr#(adx(mark(_x21)))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))mark#(incr(zeros)) → a__incr#(a__zeros)
mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__incr(mark(_x81))))))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(adx(mark(_x71))))))) is 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
a__incr#(a__head(s(a__head(a__adx(adx(a__adx(mark(_x81)))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(nil)))))) 
a__incr#(a__head(s(a__head(a__adx(adx(0)))))) 
a__incr#(a__head(s(a__head(adx(adx(mark(_x71))))))) 
a__incr#(a__head(s(head(a__adx(adx(mark(_x71))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(a__tail(mark(_x81)))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(a__nats)))))) 
a__incr#(a__head(s(a__head(a__adx(adx(cons(mark(_x81), _x82))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(a__head(mark(_x81)))))))) 
a__incr#(head(s(a__head(a__adx(adx(mark(_x71))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(a__zeros)))))) 
a__incr#(a__head(s(a__head(a__adx(adx(a__incr(mark(_x81)))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(s(mark(_x81)))))))) 
Thus, the rule mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(adx(mark(_x71))))))) is replaced by the following rules:
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(adx(adx(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(head(a__adx(adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__zeros))))))
mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__nats))))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(head(s(a__head(a__adx(adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__tail(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(a__head(s(a__head(a__adx(adx(nil))))))
mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__incr(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(a__head(s(a__head(a__adx(adx(0))))))
mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__adx(mark(_x81))))))))

Problem 28: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(mark(_x81))))))))
mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(mark(_x71), _x72))))))mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__nats))))))
mark#(incr(head(s(head(adx(nats)))))) → a__incr#(a__head(s(a__head(a__adx(a__nats)))))mark#(incr(incr(nil))) → a__incr#(nil)
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(s(X)) → mark#(X)
a__incr#(cons(X, L)) → mark#(X)mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(adx(adx(_x41)))) → a__incr#(a__adx(a__adx(mark(_x41))))mark#(incr(adx(zeros))) → a__incr#(a__adx(a__zeros))
mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(mark(_x71)))))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(head(s(a__head(a__adx(adx(mark(_x71)))))))
mark#(incr(head(s(head(zeros))))) → a__incr#(a__head(s(a__head(a__zeros))))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__zeros))))))mark#(incr(adx(0))) → a__incr#(a__adx(0))
mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(a__head(s(a__head(a__adx(adx(nil))))))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))
mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(head(s(a__head(a__adx(mark(_x61))))))mark#(incr(head(nats))) → a__incr#(a__head(a__nats))
mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))mark#(incr(adx(s(_x41)))) → a__incr#(a__adx(s(mark(_x41))))
mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(nil))))))mark#(incr(adx(nil))) → a__incr#(a__adx(nil))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))
mark#(incr(incr(incr(zeros)))) → a__incr#(a__incr(a__incr(a__zeros)))mark#(incr(adx(head(_x41)))) → a__incr#(a__adx(a__head(mark(_x41))))
mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(s(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(s(mark(_x71)))))))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(adx(adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(head(a__adx(adx(mark(_x71)))))))mark#(incr(adx(nats))) → a__incr#(a__adx(a__nats))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(0))))))
mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__tail(mark(_x81))))))))mark#(incr(X)) → mark#(X)
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__tail(mark(_x81))))))))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(adx(cons(_x41, _x42)))) → a__incr#(a__adx(cons(mark(_x41), _x42)))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(head(zeros))) → a__incr#(head(a__zeros))mark#(incr(head(s(head(adx(zeros)))))) → a__incr#(a__head(s(a__head(a__adx(a__zeros)))))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))
mark#(incr(adx(tail(_x41)))) → a__incr#(a__adx(a__tail(mark(_x41))))mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))
mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__zeros))))))mark#(incr(head(s(head(adx(0)))))) → a__incr#(a__head(s(a__head(a__adx(0)))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))
mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(cons(mark(_x81), _x82)))))))
mark#(incr(head(s(head(adx(tail(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__tail(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(a__head(s(a__head(a__adx(adx(0))))))
mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(head(s(a__head(a__adx(a__adx(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(head(a__adx(a__adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(adx(a__adx(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__nats))))))
mark#(incr(head(zeros))) → a__incr#(head(zeros))mark#(incr(adx(incr(_x41)))) → a__incr#(a__adx(a__incr(mark(_x41))))
mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__incr(mark(_x81))))))))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__adx(mark(_x81))))))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(head(s(head(adx(nil)))))) → a__incr#(a__head(s(a__head(a__adx(nil)))))
mark#(incr(incr(incr(adx(_x51))))) → a__incr#(a__incr(a__incr(a__adx(mark(_x51)))))mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(adx(mark(_x61))))))
mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(head(a__adx(mark(_x61))))))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__head(mark(_x81))))))))mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))
mark#(incr(head(s(head(adx(head(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__head(mark(_x71)))))))mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__adx(mark(_x81))))))))
mark#(incr(adx(_x21))) → a__incr#(adx(mark(_x21)))mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))mark#(incr(zeros)) → a__incr#(a__zeros)
mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__incr(mark(_x81))))))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(mark(_x81)))))))) is 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
a__incr#(a__head(s(head(a__adx(adx(a__head(mark(_x81)))))))) 
a__incr#(a__head(s(a__head(adx(adx(a__head(mark(_x81)))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__zeros))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__incr(mark(_x91))))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__adx(mark(_x91))))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(a__head(s(mark(_x91))))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__head(mark(_x91))))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__nats))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(a__head(nil))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(a__head(0))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(a__head(cons(mark(_x91), _x92)))))))) 
a__incr#(head(s(a__head(a__adx(adx(a__head(mark(_x81)))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__tail(mark(_x91))))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(head(mark(_x81)))))))) 
Thus, the rule mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(mark(_x81)))))))) is replaced by the following rules:
mark#(incr(head(s(head(adx(adx(head(nats)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__nats)))))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__zeros)))))))mark#(incr(head(s(head(adx(adx(head(nil)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(nil)))))))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(head(s(a__head(a__adx(adx(a__head(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(head(head(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__head(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(head(0)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(0)))))))mark#(incr(head(s(head(adx(adx(head(s(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(s(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(head(tail(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__tail(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(head(adx(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__adx(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(head(cons(_x91, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(cons(mark(_x91), _x92))))))))mark#(incr(head(s(head(adx(adx(head(incr(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__incr(mark(_x91)))))))))

Problem 29: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(mark(_x71), _x72))))))
mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__nats))))))mark#(incr(head(s(head(adx(nats)))))) → a__incr#(a__head(s(a__head(a__adx(a__nats)))))
mark#(incr(incr(nil))) → a__incr#(nil)mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))
a__incr#(cons(X, L)) → mark#(X)mark#(s(X)) → mark#(X)
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(adx(adx(_x41)))) → a__incr#(a__adx(a__adx(mark(_x41))))
mark#(incr(adx(zeros))) → a__incr#(a__adx(a__zeros))mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__zeros)))))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(head(s(a__head(a__adx(adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(head(nil)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(nil)))))))mark#(incr(head(s(head(zeros))))) → a__incr#(a__head(s(a__head(a__zeros))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__zeros))))))
mark#(incr(adx(0))) → a__incr#(a__adx(0))mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(a__head(s(a__head(a__adx(adx(nil))))))
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))
mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))mark#(incr(head(s(head(adx(adx(head(tail(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__tail(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(adx(adx(head(cons(_x91, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(cons(mark(_x91), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(incr(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__incr(mark(_x91)))))))))mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(head(s(a__head(a__adx(mark(_x61))))))
mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(nil))))))mark#(incr(adx(s(_x41)))) → a__incr#(a__adx(s(mark(_x41))))
mark#(incr(adx(nil))) → a__incr#(a__adx(nil))mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(incr(incr(zeros)))) → a__incr#(a__incr(a__incr(a__zeros)))
mark#(incr(adx(head(_x41)))) → a__incr#(a__adx(a__head(mark(_x41))))mark#(incr(head(s(head(adx(adx(head(0)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(0)))))))
mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(s(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(s(mark(_x71)))))))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(adx(adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(head(a__adx(adx(mark(_x71)))))))mark#(incr(adx(nats))) → a__incr#(a__adx(a__nats))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(0))))))
mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__tail(mark(_x81))))))))mark#(incr(X)) → mark#(X)
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__tail(mark(_x81))))))))
mark#(incr(head(0))) → a__incr#(a__head(0))mark#(incr(adx(cons(_x41, _x42)))) → a__incr#(a__adx(cons(mark(_x41), _x42)))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))
mark#(incr(head(zeros))) → a__incr#(head(a__zeros))mark#(incr(head(s(head(adx(zeros)))))) → a__incr#(a__head(s(a__head(a__adx(a__zeros)))))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))
mark#(incr(adx(tail(_x41)))) → a__incr#(a__adx(a__tail(mark(_x41))))mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))
mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__zeros))))))mark#(incr(head(s(head(adx(0)))))) → a__incr#(a__head(s(a__head(a__adx(0)))))
mark#(incr(head(s(head(adx(adx(head(s(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(s(mark(_x91)))))))))mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(head(adx(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__adx(mark(_x91)))))))))mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))
mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(cons(mark(_x81), _x82)))))))
mark#(incr(head(s(head(adx(tail(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__tail(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(a__head(s(a__head(a__adx(adx(0))))))
mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(head(s(a__head(a__adx(a__adx(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(head(a__adx(a__adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(adx(a__adx(mark(_x71)))))))mark#(incr(adx(incr(_x41)))) → a__incr#(a__adx(a__incr(mark(_x41))))
mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__nats))))))mark#(incr(head(zeros))) → a__incr#(head(zeros))
mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__incr(mark(_x81))))))))mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__adx(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(head(nats)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__nats)))))))mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(head(s(a__head(a__adx(adx(a__head(mark(_x81))))))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))mark#(incr(head(s(head(adx(nil)))))) → a__incr#(a__head(s(a__head(a__adx(nil)))))
mark#(incr(head(s(head(adx(adx(head(head(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__head(mark(_x91)))))))))mark#(incr(incr(incr(adx(_x51))))) → a__incr#(a__incr(a__incr(a__adx(mark(_x51)))))
mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(head(a__adx(mark(_x61))))))mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(adx(mark(_x61))))))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__head(mark(_x81))))))))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))mark#(incr(head(s(head(adx(head(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__head(mark(_x71)))))))
mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__adx(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__head(mark(_x81))))))))mark#(incr(adx(_x21))) → a__incr#(adx(mark(_x21)))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))
mark#(incr(zeros)) → a__incr#(a__zeros)mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__incr(mark(_x81))))))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, head, a__head, nil, cons

Strategy

The right-hand side of the rule mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(mark(_x81)))))))) is 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
a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__nats))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(s(0))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(s(cons(mark(_x91), _x92)))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__adx(mark(_x91))))))))) 
a__incr#(head(s(a__head(a__adx(a__adx(s(mark(_x81)))))))) 
a__incr#(a__head(s(head(a__adx(a__adx(s(mark(_x81)))))))) 
a__incr#(a__head(s(a__head(adx(a__adx(s(mark(_x81)))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(s(nil))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__tail(mark(_x91))))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(mark(_x91))))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(s(s(mark(_x91))))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__head(mark(_x91))))))))) 
a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__zeros))))))) 
a__incr#(a__head(s(a__head(a__adx(adx(s(mark(_x81)))))))) 
Thus, the rule mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(mark(_x81)))))))) is replaced by the following rules:
mark#(incr(head(s(head(adx(adx(s(nil)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(nil)))))))mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__tail(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(0)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(0)))))))mark#(incr(head(s(head(adx(adx(s(adx(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__adx(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(cons(_x91, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(cons(mark(_x91), _x92))))))))mark#(incr(head(s(head(adx(adx(s(nats)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__nats)))))))
mark#(incr(head(s(head(adx(adx(s(head(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__head(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__zeros)))))))mark#(incr(head(s(head(adx(adx(s(s(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(s(mark(_x91)))))))))

Problem 30: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(s(X)) → mark#(X)
mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(mark(_x101), _x102)))))))))mark#(incr(incr(nats))) → a__incr#(a__incr(a__nats))
mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__zeros))))))mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(a__adx(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(a__head(s(a__head(a__adx(adx(nil))))))mark#(incr(adx(adx(cons(incr(_x61), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(a__head(s(mark(_x61))))))mark#(incr(head(s(head(adx(cons(adx(_x81), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(mark(_x81)), _x72))))))
mark#(incr(head(nats))) → a__incr#(a__head(a__nats))mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(mark(_x71), _x72))))))
mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(a__head(mark(_x51)))))mark#(incr(head(s(head(adx(cons(head(zeros), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__zeros), _x72))))))
mark#(incr(adx(adx(cons(tail(cons(_x71, _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(mark(_x71), _x72)), _x52))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(mark(_x111)))))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(a__incr(a__tail(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(a__incr(a__tail(mark(_x101))))))))))mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__zeros), _x72))))))
mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))mark#(incr(adx(head(_x41)))) → a__incr#(a__adx(a__head(mark(_x41))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(adx(s(a__tail(cons(cons(mark(_x111), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(s(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(s(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(s(incr(head(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__head(mark(_x101))))))))))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(adx(adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(head(a__adx(adx(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__adx(mark(_x111)), _x102)))))))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__tail(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(incr(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__incr(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(head(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__head(mark(_x121)), _x112), _x102)))))))))
mark#(incr(adx(adx(0)))) → a__incr#(a__adx(a__adx(0)))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(head(s(head(adx(cons(head(_x81), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__head(mark(_x81)), _x72))))))mark#(incr(head(s(head(adx(cons(head(_x81), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__head(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(incr(0))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(0))))))))mark#(incr(head(s(head(adx(cons(head(_x81), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(head(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(a__incr(a__tail(mark(_x101))))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(tail(a__incr(mark(_x131))), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(cons(0, zeros)))))))mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(nil), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(nil), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(s(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(s(mark(_x121)), _x112), _x102)))))))))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(adx(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__adx(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(a__head(adx(adx(s(a__tail(cons(mark(_x101), _x102)))))))))mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(cons(mark(_x81), _x82)))))))
mark#(incr(head(s(head(adx(tail(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__tail(mark(_x71)))))))mark#(incr(head(s(head(adx(cons(head(0), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(0), _x72))))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))mark#(incr(head(s(head(adx(adx(s(incr(s(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(s(mark(_x101))))))))))
mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))mark#(incr(head(zeros))) → a__incr#(head(zeros))
mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__zeros, _x102)))))))))mark#(incr(adx(adx(cons(tail(0), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(0), _x52))))
mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(head(s(head(a__adx(a__incr(mark(_x71)))))))mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(head(s(a__head(adx(a__incr(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__incr(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(incr(nil))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(nil))))))))
mark#(incr(head(s(head(adx(incr(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(incr(a__tail(mark(_x101))))))))))
mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))mark#(incr(head(s(head(adx(incr(s(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(head(s(a__head(a__adx(incr(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(incr(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__incr(mark(_x111)), _x102)))))))))
mark#(incr(incr(incr(adx(_x51))))) → a__incr#(a__incr(a__incr(a__adx(mark(_x51)))))mark#(incr(head(s(head(adx(cons(head(cons(_x91, _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(cons(mark(_x91), _x92)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(s(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(s(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(zeros, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__zeros, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(head(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__head(mark(_x101))))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(zeros)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__zeros)), _x112), _x102)))))))))
mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x81)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__adx(mark(_x81))))))))mark#(incr(adx(adx(cons(s(_x61), _x52))))) → a__incr#(a__adx(adx(cons(s(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(cons(0, zeros))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(tail(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__tail(mark(_x131))), _x112), _x102)))))))))
mark#(incr(adx(_x21))) → a__incr#(adx(mark(_x21)))mark#(incr(adx(adx(cons(nats, _x52))))) → a__incr#(a__adx(a__adx(cons(a__nats, _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(nats, _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__nats, _x102)))))))))mark#(incr(zeros)) → a__incr#(a__zeros)
mark#(incr(head(s(head(adx(incr(nil))))))) → a__incr#(head(s(a__head(a__adx(a__incr(nil))))))mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(zeros)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(s(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(s(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(s(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(s(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nats, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__nats, _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(zeros))))))
mark#(incr(adx(adx(cons(0, _x52))))) → a__incr#(a__adx(a__adx(cons(0, _x52))))mark#(incr(adx(adx(cons(s(_x61), _x52))))) → a__incr#(a__adx(a__adx(cons(s(mark(_x61)), _x52))))
mark#(incr(adx(adx(cons(nats, _x52))))) → a__incr#(a__adx(adx(cons(a__nats, _x52))))mark#(incr(head(s(head(adx(adx(s(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__zeros)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(s(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(s(mark(_x131))), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(head(_x121)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__head(mark(_x121))), _x102)))))))))
a__incr#(cons(X, L)) → mark#(X)mark#(incr(adx(zeros))) → a__incr#(a__adx(a__zeros))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(cons(_x121, _x122), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(cons(mark(_x121), _x122), _x112), _x102)))))))))mark#(incr(head(s(head(adx(cons(head(_x81), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__head(mark(_x81))), adx(_x51)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(s(_x121)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(s(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(a__zeros)))))))
mark#(incr(adx(adx(cons(zeros, _x52))))) → a__incr#(a__adx(a__adx(cons(zeros, _x52))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(head(adx(incr(cons(_x81, _x82)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(adx(adx(head(nil)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(nil)))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(incr(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__incr(mark(_x111)))))))))))mark#(incr(head(s(head(adx(cons(head(tail(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__tail(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(adx(s(nats)))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__nats)))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(0)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(0)))))))))
mark#(incr(head(s(head(adx(incr(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__head(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__tail(mark(_x91)))))))))
mark#(incr(adx(adx(cons(incr(s(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(s(mark(_x71))), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(nats, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__nats, _x102)))))))))
mark#(incr(head(s(head(adx(incr(nats))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__nats))))))mark#(incr(head(s(head(adx(incr(nil))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(nil))))))
mark#(incr(head(s(head(adx(adx(s(zeros)))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__zeros)))))))mark#(incr(incr(incr(zeros)))) → a__incr#(a__incr(a__incr(a__zeros)))
mark#(incr(head(s(head(adx(adx(s(nats)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__nats)))))))mark#(incr(head(s(head(adx(cons(0, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(0, _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(adx(_x141))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__adx(mark(_x141)))), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(tail(cons(cons(mark(_x111), _x112), _x102)))))))))
mark#(incr(adx(nats))) → a__incr#(a__adx(a__nats))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(tail(cons(cons(mark(_x111), _x112), _x102)))))))))
mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(mark(_x71), _x72))))))
mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(mark(_x71), _x72))))))mark#(incr(head(s(head(adx(cons(nats, _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__nats), adx(_x51)))))))
mark#(incr(adx(adx(cons(head(_x61), _x52))))) → a__incr#(a__adx(a__adx(cons(a__head(mark(_x61)), _x52))))mark#(incr(adx(cons(_x41, _x42)))) → a__incr#(a__adx(cons(mark(_x41), _x42)))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(zeros))) → a__incr#(head(a__zeros))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(adx(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__adx(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(zeros)))))) → a__incr#(a__head(s(a__head(a__adx(a__zeros)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(adx(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__adx(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))
mark#(incr(adx(tail(_x41)))) → a__incr#(a__adx(a__tail(mark(_x41))))mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(nil, _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(nil, _x102)))))))))mark#(incr(head(s(head(adx(0)))))) → a__incr#(a__head(s(a__head(a__adx(0)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(tail(cons(a__adx(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(adx(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__adx(mark(_x91)))))))))
mark#(incr(head(s(head(adx(cons(incr(_x81), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__incr(mark(_x81)), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(tail(_x121)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__tail(mark(_x121))), _x102)))))))))
mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(nats), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__nats), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(0, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(0, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(tail(cons(mark(_x101), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(0, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(0, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(s(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(s(mark(_x101))))))))))mark#(incr(head(s(head(adx(cons(head(_x81), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__head(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(cons(tail(_x81), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__tail(mark(_x81)), _x72))))))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(adx(a__adx(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(head(a__adx(a__adx(mark(_x71)))))))
mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))mark#(incr(adx(adx(cons(incr(head(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__head(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__nats))))))mark#(incr(adx(incr(_x41)))) → a__incr#(a__adx(a__incr(mark(_x41))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(head(s(a__head(a__adx(adx(s(a__tail(mark(_x91)))))))))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(adx(adx(cons(_x51, _x52))))) → a__incr#(adx(adx(cons(mark(_x51), _x52))))
mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(adx(a__adx(a__zeros))))))mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(head(a__adx(a__adx(a__zeros))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nats, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__nats, _x112), _x102)))))))))mark#(incr(adx(adx(cons(zeros, _x52))))) → a__incr#(a__adx(adx(cons(a__zeros, _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(tail(_x111), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__tail(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nats, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__nats, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))mark#(incr(adx(adx(cons(adx(_x61), _x52))))) → a__incr#(a__adx(adx(cons(a__adx(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(adx(s(head(_x91))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__head(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(incr(_x141))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__incr(mark(_x141)))), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(incr(mark(_x71)))))))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x81)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(a__head(s(head(a__adx(a__incr(mark(_x71)))))))
mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(a__head(s(a__head(adx(a__incr(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(adx(s(a__tail(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(head(s(a__head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(adx(adx(cons(incr(adx(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__adx(mark(_x71))), _x52))))mark#(incr(adx(adx(nil)))) → a__incr#(a__adx(a__adx(nil)))
mark#(incr(head(s(head(adx(head(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__head(mark(_x71)))))))mark#(incr(head(s(head(adx(incr(tail(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__tail(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(adx(s(a__tail(cons(cons(mark(_x111), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(adx(s(a__tail(cons(cons(mark(_x111), _x112), _x102)))))))))
mark#(incr(adx(adx(cons(tail(_x61), _x52))))) → a__incr#(adx(adx(cons(a__tail(mark(_x61)), _x52))))mark#(incr(adx(adx(cons(tail(adx(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__adx(mark(_x71))), _x52))))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(adx(s(a__tail(cons(a__adx(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(head(_x141))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__head(mark(_x141)))), _x112), _x102)))))))))
mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(adx(adx(cons(a__incr(a__nats), _x52))))mark#(incr(head(s(head(zeros))))) → a__incr#(a__head(s(a__head(a__zeros))))
mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))mark#(incr(head(s(head(adx(adx(s(s(_x91))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(s(mark(_x91)))))))))
mark#(incr(head(s(head(adx(cons(nil, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(nil, _x72))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(s(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(s(mark(_x111)))))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(0, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(0, _x102)))))))))mark#(incr(head(s(head(adx(cons(zeros, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__zeros, _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(tail(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__tail(mark(_x111)), _x102)))))))))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(head(s(head(adx(adx(s(tail(cons(nil, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(nil, _x102)))))))))mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))
mark#(incr(head(s(head(adx(adx(head(tail(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__tail(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x81)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x81)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__nats, _x72))))))
mark#(incr(adx(adx(cons(nil, _x52))))) → a__incr#(a__adx(adx(cons(nil, _x52))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(adx(adx(cons(incr(cons(_x71, _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(cons(mark(_x71), _x72)), _x52))))mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(nil))))))
mark#(incr(adx(adx(cons(tail(nats), _x52))))) → a__incr#(a__adx(adx(cons(tail(a__nats), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(mark(_x131))), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(incr(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__incr(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(incr(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__incr(mark(_x121)), _x112), _x102)))))))))
mark#(incr(adx(nil))) → a__incr#(a__adx(nil))mark#(incr(adx(adx(cons(incr(nil), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(nil), _x52))))
mark#(incr(adx(adx(cons(tail(_x61), _x52))))) → a__incr#(a__adx(adx(cons(tail(mark(_x61)), _x52))))mark#(incr(head(s(head(adx(adx(s(incr(tail(cons(_x111, _x112))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(cons(mark(_x111), _x112))))))))))
mark#(incr(head(s(head(adx(adx(s(head(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__head(mark(_x91)))))))))mark#(incr(head(s(head(adx(incr(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__adx(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(zeros))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__zeros))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(nats)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__nats)))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(zeros)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__zeros)))))))))mark#(incr(adx(adx(zeros)))) → a__incr#(a__adx(a__adx(a__zeros)))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x81)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(cons(head(nil), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(nil), _x72))))))
mark#(incr(adx(adx(cons(tail(head(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__head(mark(_x71))), _x52))))mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(0))))))
mark#(incr(head(s(head(adx(cons(head(nats), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__nats), _x72))))))mark#(incr(head(s(head(adx(incr(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__incr(mark(_x81))))))))
mark#(incr(adx(adx(cons(tail(tail(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__tail(mark(_x71))), _x52))))mark#(incr(adx(adx(cons(_x51, _x31))))) → a__incr#(a__adx(a__incr(cons(mark(mark(_x51)), adx(_x31)))))
mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(nats), _x52))))
mark#(incr(head(s(head(adx(cons(cons(_x81, _x82), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(cons(mark(_x81), _x82), _x72))))))mark#(incr(head(s(head(adx(cons(s(_x81), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(s(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__zeros, _x102)))))))))mark#(incr(adx(adx(cons(incr(0), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(0), _x52))))
mark#(incr(adx(adx(_x41)))) → a__incr#(a__adx(adx(mark(_x41))))mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__zeros))))))
mark#(incr(adx(adx(adx(_x51))))) → a__incr#(a__adx(a__adx(a__adx(mark(_x51)))))mark#(incr(head(s(head(adx(adx(s(incr(cons(_x101, _x102)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(cons(_x121, _x122)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(cons(mark(_x121), _x122)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(incr(_x121)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__incr(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nil, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(nil, _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nil, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(nil, _x112), _x102)))))))))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(adx(adx(_x41)))) → a__incr#(adx(a__adx(mark(_x41))))
mark#(incr(adx(adx(cons(nil, _x52))))) → a__incr#(a__adx(a__adx(cons(nil, _x52))))mark#(incr(adx(adx(cons(incr(zeros), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__zeros), _x52))))
mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(a__head(s(a__head(a__adx(adx(0))))))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(nats)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__nats)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(cons(head(adx(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__adx(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(0), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(0), _x112), _x102)))))))))mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(cons(_x141, _x142))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(cons(mark(_x141), _x142))), _x112), _x102)))))))))mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(incr(head(s(head(adx(incr(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(cons(mark(_x81), _x82)))))))mark#(incr(adx(adx(s(_x51))))) → a__incr#(a__adx(a__adx(s(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__incr(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(tail(tail(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__tail(mark(_x101))))))))))
mark#(incr(adx(adx(cons(incr(_x61), _x52))))) → a__incr#(a__adx(adx(cons(incr(mark(_x61)), _x52))))mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(tail(cons(cons(a__tail(a__incr(mark(_x131))), _x112), _x102)))))))))mark#(incr(adx(adx(cons(incr(_x61), _x52))))) → a__incr#(adx(adx(cons(a__incr(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(cons(_x131, _x132)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(cons(mark(_x131), _x132)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(incr(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__incr(mark(_x101))))))))))
mark#(incr(adx(adx(cons(zeros, _x52))))) → a__incr#(adx(a__adx(cons(a__zeros, _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(nil), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(nil), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(adx(s(a__tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(s(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(s(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(head(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__head(mark(_x111)))))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__head(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__adx(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(head(nats)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__nats)))))))
mark#(incr(adx(adx(cons(cons(_x61, _x62), _x52))))) → a__incr#(a__adx(a__adx(cons(cons(mark(_x61), _x62), _x52))))mark#(incr(head(s(head(adx(adx(s(cons(_x91, _x92))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(cons(mark(_x91), _x92))))))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x81)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(incr(incr(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__incr(mark(_x101))))))))))mark#(incr(head(s(head(adx(incr(head(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(head(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__head(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(head(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__head(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(head(head(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__head(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(adx(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__adx(mark(_x111)))))))))))mark#(incr(adx(adx(nats)))) → a__incr#(a__adx(a__adx(a__nats)))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(0), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(0), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(adx(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__adx(mark(_x131))), _x112), _x102)))))))))
mark#(incr(incr(0))) → a__incr#(a__incr(0))mark#(incr(adx(adx(head(_x51))))) → a__incr#(a__adx(a__adx(a__head(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(nats), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__nats), _x112), _x102)))))))))mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(a__adx(adx(cons(incr(a__nats), _x52))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(nil)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(nil)))))))))mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(nats, _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(s(_x111), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(s(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(incr(0))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(0))))))
mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__incr(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x81)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(adx(s(a__tail(cons(cons(a__tail(a__incr(mark(_x131))), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__nats))))))
mark#(incr(head(s(head(adx(nats)))))) → a__incr#(a__head(s(a__head(a__adx(a__nats)))))mark#(incr(adx(adx(cons(tail(incr(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__incr(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(nil)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(nil)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(cons(_x71, _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(mark(_x71)), adx(_x51)))))))
mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(a__incr(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(a__incr(mark(_x91)))))))))
mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(head(s(a__head(a__adx(a__adx(a__zeros))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(tail(mark(_x121)), _x112), _x102)))))))))mark#(incr(adx(adx(cons(incr(incr(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__incr(mark(_x71))), _x52))))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(head(s(a__head(a__adx(adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(adx(_x121)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__adx(mark(_x121))), _x102)))))))))mark#(incr(adx(0))) → a__incr#(a__adx(0))
mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(a__incr(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(head(s(a__head(a__adx(adx(a__head(a__zeros)))))))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(s(head(adx(adx(head(cons(_x91, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(cons(mark(_x91), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(incr(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__incr(mark(_x91)))))))))mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(head(s(a__head(a__adx(mark(_x61))))))
mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(incr(mark(_x91)))))))))
mark#(incr(adx(s(_x41)))) → a__incr#(a__adx(s(mark(_x41))))mark#(incr(adx(adx(cons(adx(_x61), _x52))))) → a__incr#(a__adx(a__adx(cons(a__adx(mark(_x61)), _x52))))
mark#(incr(adx(adx(cons(zeros, _x31))))) → a__incr#(a__adx(a__incr(cons(mark(a__zeros), adx(_x31)))))mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__zeros))))))
mark#(incr(head(s(head(adx(adx(s(tail(nil))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(nil))))))))mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))
mark#(incr(adx(adx(cons(head(_x61), _x52))))) → a__incr#(a__adx(adx(cons(a__head(mark(_x61)), _x52))))mark#(incr(adx(adx(cons(zeros, _x52))))) → a__incr#(a__adx(a__adx(cons(cons(0, zeros), _x52))))
mark#(incr(adx(adx(cons(_x51, _x52))))) → a__incr#(adx(a__adx(cons(mark(_x51), _x52))))mark#(incr(adx(adx(cons(0, _x52))))) → a__incr#(a__adx(adx(cons(0, _x52))))
mark#(incr(head(s(head(adx(adx(head(0)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(0)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(incr(_x111), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__incr(mark(_x111)), _x102)))))))))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(adx(adx(cons(tail(nats), _x52))))) → a__incr#(adx(adx(cons(a__tail(a__nats), _x52))))mark#(incr(adx(adx(incr(_x51))))) → a__incr#(a__adx(a__adx(a__incr(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(0)))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(0)))))))mark#(incr(head(s(head(adx(incr(0))))))) → a__incr#(head(s(a__head(a__adx(incr(0))))))
mark#(incr(X)) → mark#(X)mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(s(_x141))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(s(mark(_x141)))), _x112), _x102)))))))))
mark#(incr(adx(adx(cons(tail(zeros), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__zeros), _x52))))mark#(incr(head(s(head(adx(adx(s(cons(_x91, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(cons(mark(_x91), _x92))))))))
mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__tail(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nil, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(nil, _x112), _x102)))))))))
mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__adx(a__zeros)), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(head(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__head(mark(_x131))), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(head(s(a__head(a__adx(adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(zeros, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__zeros, _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(zeros, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__zeros, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(incr(adx(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__adx(mark(_x101))))))))))mark#(incr(head(s(head(adx(adx(s(tail(0))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(0))))))))
mark#(incr(adx(adx(cons(tail(_x61), _x52))))) → a__incr#(a__adx(a__adx(cons(a__tail(mark(_x61)), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(adx(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__adx(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(tail(mark(_x101))))))))))mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__nats, _x72))))))
mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__nats, _x72))))))mark#(incr(adx(adx(cons(incr(tail(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__tail(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(head(s(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(s(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(head(adx(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__adx(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(incr(nats))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__nats))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(0, _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(0, _x102)))))))))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(s(head(adx(incr(nats))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__nats))))))
mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(tail(mark(_x91)))))))))mark#(incr(head(s(head(adx(incr(0))))))) → a__incr#(head(s(head(a__adx(a__incr(0))))))
mark#(incr(head(s(head(adx(incr(0))))))) → a__incr#(head(s(a__head(adx(a__incr(0))))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(head(s(a__head(a__adx(a__adx(mark(_x71)))))))
mark#(incr(adx(adx(cons(tail(nats), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(nats), _x52))))mark#(incr(head(s(head(adx(adx(s(0)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(0)))))))
mark#(incr(adx(adx(tail(_x51))))) → a__incr#(a__adx(a__adx(a__tail(mark(_x51)))))mark#(incr(adx(adx(cons(tail(s(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(s(mark(_x71))), _x52))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(head(s(head(adx(cons(head(s(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(s(mark(_x91))), _x72))))))
mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(nats))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__nats))))))))mark#(incr(head(s(head(adx(incr(adx(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__adx(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(tail(_x141))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__tail(mark(_x141)))), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(adx(_x91))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__adx(mark(_x91)))))))))
mark#(incr(head(s(head(adx(incr(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__tail(mark(_x81))))))))mark#(incr(adx(adx(cons(tail(nil), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(nil), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(tail(cons(mark(_x101), _x102)))))))))mark#(incr(head(s(head(adx(cons(head(head(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__head(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(head(s(a__head(a__adx(adx(a__head(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(zeros), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__zeros), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(incr(mark(_x131))), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(0)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(0)), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(nil)))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(nil)))))))mark#(incr(head(s(head(adx(nil)))))) → a__incr#(a__head(s(a__head(a__adx(nil)))))
mark#(incr(head(s(head(adx(adx(s(incr(zeros))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__zeros))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(zeros), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__zeros), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(head(a__adx(mark(_x61))))))mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(adx(mark(_x61))))))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(head(s(head(adx(cons(head(incr(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__incr(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__adx(mark(_x111)), _x102)))))))))mark#(incr(adx(adx(cons(tail(nats), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__adx(a__zeros)), _x52))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(mark(_x101))))))))))mark#(incr(adx(adx(cons(cons(_x61, _x62), _x52))))) → a__incr#(a__adx(adx(cons(cons(mark(_x61), _x62), _x52))))
mark#(incr(head(s(head(adx(adx(s(nil)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(nil)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(0, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(0, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(incr(incr(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__incr(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(cons(mark(_x111), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x81)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__head(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(cons(_x121, _x122), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(cons(mark(_x121), _x122), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(cons(_x121, _x122), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(cons(mark(_x121), _x122), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(adx(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__head(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__head(a__zeros)))))))mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__head(a__zeros)))))))
mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(tail(cons(cons(mark(_x111), _x112), _x102)))))))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(mark(_x101), _x102))))))))) is 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
a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(mark(_x101), _x102))))))))) 
a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__head(mark(_x111)), _x102))))))))) 
a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(mark(_x111), _x112), _x102))))))))) 
a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__incr(mark(_x111)), _x102))))))))) 
a__incr#(head(s(head(a__adx(a__adx(s(tail(cons(mark(_x101), _x102))))))))) 
a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(s(mark(_x111)), _x102))))))))) 
a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(nil, _x102))))))))) 
a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__nats, _x102))))))))) 
a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81)))))))) 
a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__zeros, _x102))))))))) 
a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(0, _x102))))))))) 
a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__tail(mark(_x111)), _x102))))))))) 
a__incr#(head(s(head(a__adx(adx(s(a__tail(cons(mark(_x101), _x102))))))))) 
a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(mark(_x111)), _x102))))))))) 
Thus, the rule mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(mark(_x101), _x102))))))))) is replaced by the following rules:
mark#(incr(head(s(head(adx(adx(s(tail(cons(nil, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(nil, _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(tail(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__zeros, _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x81)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__head(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(mark(_x111), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(incr(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__incr(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(tail(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__tail(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(0, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(0, _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(head(a__adx(adx(s(a__tail(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(s(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(s(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(nats, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__nats, _x102)))))))))

Problem 31: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(s(X)) → mark#(X)mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__zeros), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__adx(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__adx(mark(_x91))), _x72))))))
mark#(incr(head(s(head(incr(adx(nats))))))) → a__incr#(head(s(a__head(a__incr(a__adx(a__nats))))))mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(a__adx(mark(_x41))))
mark#(incr(head(s(head(adx(cons(adx(cons(_x91, _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(cons(mark(_x91), _x92)), _x72))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(a__head(s(head(a__adx(adx(head(cons(nil, _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(a__head(s(a__head(adx(adx(head(cons(nil, _x92))))))))mark#(incr(adx(head(_x41)))) → a__incr#(a__adx(a__head(mark(_x41))))
mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(s(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(s(mark(_x71)))))))
mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(a__nats), _x72))))))mark#(incr(adx(adx(cons(incr(zeros), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(a__zeros), _x52))))
mark#(incr(nil)) → a__incr#(nil)mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(head(a__adx(adx(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(adx(adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__adx(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(head(cons(_x91, _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(mark(_x91), _x92))))))))
mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(a__head(adx(incr(a__zeros))))))mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(head(a__adx(incr(a__zeros))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(adx(nil), _x92))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(tail(_x121)))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(a__tail(mark(_x121))))))))))))
mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__tail(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(incr(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__incr(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(head(incr(adx(_x71))))))) → a__incr#(head(s(head(a__incr(a__adx(mark(_x71)))))))mark#(incr(adx(adx(0)))) → a__incr#(a__adx(a__adx(0)))
mark#(incr(head(s(head(adx(cons(head(_x81), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__head(mark(_x81)), _x72))))))mark#(incr(head(s(head(adx(cons(head(_x81), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__head(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(tail(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(a__tail(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(a__head(a__incr(a__nats)))))
mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(cons(0, zeros)))))))mark#(incr(head(s(head(adx(cons(cons(_x81, _x82), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(cons(mark(_x81), _x82), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(tail(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__tail(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(adx(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__adx(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(tail(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__tail(mark(_x71)))))))mark#(incr(head(s(head(adx(cons(head(0), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(0), _x72))))))
mark#(incr(head(s(head(adx(adx(s(incr(s(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(s(mark(_x101))))))))))mark#(incr(head(zeros))) → a__incr#(head(zeros))
mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__zeros, _x102)))))))))mark#(incr(head(s(head(adx(cons(head(zeros), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(cons(0, zeros)), _x72))))))
mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__incr(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(incr(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(a__incr(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(incr(nil))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(nil))))))))mark#(incr(head(s(head(adx(incr(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(incr(a__tail(mark(_x101))))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(tail(cons(a__zeros, _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(nats), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(a__nats)), adx(_x51)))))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(head(adx(incr(s(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(s(mark(_x81))))))))mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(head(s(a__head(a__adx(incr(mark(_x71)))))))
mark#(incr(head(nats))) → a__incr#(a__head(nats))mark#(incr(head(s(head(adx(cons(adx(incr(0)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(0)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(s(_x121)))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(s(mark(_x121))))))))))))mark#(incr(head(s(head(adx(adx(head(0)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(0)))))))
mark#(incr(head(s(head(adx(adx(cons(s(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(s(mark(_x91)), _x82)))))))mark#(incr(head(s(head(adx(cons(head(cons(_x91, _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(cons(mark(_x91), _x92)), _x72))))))
mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(adx(a__adx(cons(incr(a__nats), _x52))))mark#(incr(head(s(head(adx(cons(adx(s(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(s(mark(_x91))), _x72))))))
mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x81)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(mark(_x91)))))))))mark#(incr(head(s(head(adx(cons(adx(_x81), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__adx(mark(_x81))))))))
mark#(incr(adx(adx(cons(incr(_x61), _x31))))) → a__incr#(adx(a__incr(cons(mark(incr(mark(_x61))), adx(_x31)))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(tail(a__tail(mark(_x111)))))))))))
mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(cons(0, zeros))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(tail(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__tail(mark(_x131))), _x112), _x102)))))))))
mark#(incr(head(nats))) → a__incr#(a__head(a__adx(a__zeros)))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(a__head(s(a__head(cons(s(mark(mark(a__adx(a__adx(nil))))), incr(adx(_x51)))))))
mark#(incr(adx(_x21))) → a__incr#(adx(mark(_x21)))mark#(incr(head(s(head(adx(incr(nil))))))) → a__incr#(head(s(a__head(a__adx(a__incr(nil))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(s(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(s(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(s(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(s(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(incr(adx(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(a__adx(mark(_x101)))), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nats, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__nats, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(0), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(0), _x72))))))mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(zeros))))))
mark#(incr(adx(adx(cons(tail(cons(_x71, _x72)), _x52))))) → a__incr#(adx(adx(cons(a__tail(cons(mark(_x71), _x72)), _x52))))mark#(incr(adx(adx(cons(incr(head(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(a__head(mark(_x71))), _x52))))
mark#(incr(incr(nats))) → a__incr#(a__incr(nats))mark#(incr(adx(adx(cons(0, _x52))))) → a__incr#(a__adx(a__adx(cons(0, _x52))))
mark#(incr(adx(adx(cons(s(_x61), _x52))))) → a__incr#(a__adx(a__adx(cons(s(mark(_x61)), _x52))))mark#(incr(adx(adx(cons(nats, _x52))))) → a__incr#(a__adx(adx(cons(a__nats, _x52))))
mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(head(s(head(a__adx(adx(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(head(s(a__head(adx(adx(cons(mark(_x81), _x82)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(head(_x121)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__head(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(s(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(s(mark(_x131))), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(head(_x121)), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(a__head(mark(_x121))), _x102)))))))))a__incr#(cons(X, L)) → mark#(X)
mark#(incr(adx(adx(cons(tail(cons(nil, _x72)), _x52))))) → a__incr#(adx(adx(cons(a__tail(cons(nil, _x72)), _x52))))mark#(incr(head(s(head(adx(cons(zeros, _x51))))))) → a__incr#(head(s(a__head(a__incr(cons(mark(a__zeros), adx(_x51)))))))
mark#(incr(adx(zeros))) → a__incr#(a__adx(a__zeros))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(cons(_x121, _x122), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(cons(mark(_x121), _x122), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(s(_x121)), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(s(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(s(_x121)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(s(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(adx(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(a__adx(mark(_x101)))), _x72))))))mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(a__zeros)))))))
mark#(incr(head(s(head(adx(cons(adx(incr(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(incr(mark(_x91))), _x72))))))mark#(incr(adx(adx(cons(zeros, _x52))))) → a__incr#(a__adx(a__adx(cons(zeros, _x52))))
mark#(cons(X1, X2)) → mark#(X1)mark#(incr(adx(adx(cons(tail(cons(incr(_x81), _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(a__incr(mark(_x81)), _x72)), _x52))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(nil)), adx(_x51)))))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(adx(adx(nil)), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(adx(adx(nil)), _x72))))))mark#(incr(head(s(head(adx(cons(head(tail(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__tail(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(head(s(a__head(a__adx(adx(nil))))))mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(head(s(head(a__adx(cons(mark(_x71), _x72))))))
mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(head(s(a__head(adx(cons(mark(_x71), _x72))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(0)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(0)))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(head(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(a__head(mark(_x101)))), _x72))))))mark#(incr(adx(adx(cons(incr(s(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(s(mark(_x71))), _x52))))
mark#(incr(head(s(adx(_x51))))) → a__incr#(head(s(a__adx(mark(_x51)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(zeros, _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(nats, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__nats, _x102)))))))))mark#(incr(head(s(head(adx(incr(nil))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(nil))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(incr(a__tail(a__tail(mark(_x111)))))))))))mark#(incr(head(s(head(adx(cons(adx(incr(zeros)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(a__zeros)), _x72))))))
mark#(incr(head(s(head(adx(cons(0, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(0, _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(head(s(a__head(a__incr(cons(mark(a__adx(a__adx(nil))), adx(_x51)))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(tail(mark(_x111)))))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(tail(cons(cons(mark(_x111), _x112), _x102)))))))))
mark#(incr(adx(nats))) → a__incr#(a__adx(a__nats))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(tail(cons(cons(mark(_x111), _x112), _x102)))))))))
mark#(incr(adx(adx(cons(incr(0), _x52))))) → a__incr#(a__adx(adx(cons(incr(0), _x52))))mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(mark(_x71), _x72))))))
mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(mark(_x71), _x72))))))mark#(incr(adx(cons(_x41, _x42)))) → a__incr#(a__adx(cons(mark(_x41), _x42)))
mark#(incr(head(zeros))) → a__incr#(head(a__zeros))mark#(incr(head(s(head(adx(adx(head(cons(adx(s(_x111)), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(s(mark(_x111))), _x92))))))))
mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))mark#(incr(adx(tail(_x41)))) → a__incr#(a__adx(a__tail(mark(_x41))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(nil, _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(nil, _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(nil, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(nil, _x102)))))))))
mark#(incr(adx(adx(cons(incr(0), _x31))))) → a__incr#(a__adx(a__incr(cons(mark(incr(0)), adx(_x31)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(tail(cons(a__adx(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(tail(cons(a__adx(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(tail(_x121)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__tail(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(tail(_x121)), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(a__tail(mark(_x121))), _x102)))))))))mark#(incr(adx(adx(cons(incr(adx(_x71)), _x52))))) → a__incr#(adx(a__adx(cons(incr(a__adx(mark(_x71))), _x52))))
mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(0, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(0, _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(tail(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(0, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(0, _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(s(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(s(mark(_x101))))))))))
mark#(incr(head(s(head(adx(cons(tail(_x81), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__tail(mark(_x81)), _x72))))))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(head(s(head(s(zeros)))))) → a__incr#(a__head(s(a__head(s(a__zeros)))))mark#(incr(head(s(head(s(head(_x71))))))) → a__incr#(a__head(s(a__head(s(a__head(mark(_x71)))))))
mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__nats))))))
mark#(incr(adx(incr(_x41)))) → a__incr#(a__adx(a__incr(mark(_x41))))mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(a__head(adx(a__incr(cons(0, zeros)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(head(a__adx(a__incr(cons(0, zeros)))))))
mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(head(s(a__head(a__adx(adx(s(a__tail(mark(_x91)))))))))mark#(incr(head(s(head(s(tail(_x71))))))) → a__incr#(a__head(s(a__head(s(a__tail(mark(_x71)))))))
mark#(incr(head(s(adx(tail(_x61)))))) → a__incr#(a__head(s(a__adx(a__tail(mark(_x61))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nats, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__nats, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(tail(_x111), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__tail(mark(_x111)), _x102)))))))))mark#(incr(adx(adx(cons(zeros, _x52))))) → a__incr#(a__adx(adx(cons(a__zeros, _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nats, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__nats, _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(head(a__adx(a__adx(a__zeros))))))
mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(adx(a__adx(a__zeros))))))mark#(incr(head(s(adx(nats))))) → a__incr#(a__head(s(a__adx(a__nats))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(nil), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(nil), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(adx(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(a__adx(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(a__head(s(a__head(adx(a__incr(mark(_x71)))))))mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(a__head(s(head(a__adx(a__incr(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x81)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(adx(s(a__tail(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(head(s(a__head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(adx(adx(cons(incr(adx(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__adx(mark(_x71))), _x52))))mark#(incr(head(s(head(incr(adx(incr(_x81)))))))) → a__incr#(head(s(a__head(a__incr(a__adx(a__incr(mark(_x81))))))))
mark#(incr(adx(adx(nil)))) → a__incr#(a__adx(a__adx(nil)))mark#(incr(head(s(head(adx(adx(cons(adx(_x91), _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(a__adx(mark(_x91)), _x82)))))))
mark#(incr(head(s(head(adx(adx(cons(adx(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(a__adx(mark(_x91)), _x82)))))))mark#(incr(head(s(head(incr(adx(_x71))))))) → a__incr#(head(s(a__head(incr(a__adx(mark(_x71)))))))
mark#(incr(head(s(head(incr(adx(_x71))))))) → a__incr#(head(s(a__head(a__incr(adx(mark(_x71)))))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(adx(adx(nil))), adx(_x51)))))))
mark#(incr(adx(adx(cons(tail(adx(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__adx(mark(_x71))), _x52))))mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(head(s(head(a__adx(adx(head(cons(adx(nil), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(head(s(a__head(adx(adx(head(cons(adx(nil), _x92))))))))mark#(incr(head(s(head(head(_x61)))))) → a__incr#(head(s(a__head(a__head(mark(_x61))))))
mark#(incr(head(s(head(adx(cons(adx(zeros), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__zeros), _x72))))))mark#(incr(head(s(head(adx(adx(head(nats)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(a__nats)))))))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(adx(adx(cons(incr(tail(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(a__tail(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(0), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(0), _x102)))))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(0), _x92))))))))) → a__incr#(a__head(s(head(a__adx(adx(head(cons(a__adx(0), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(0), _x92))))))))) → a__incr#(a__head(s(a__head(adx(adx(head(cons(a__adx(0), _x92))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(zeros), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(a__zeros), _x102)))))))))
mark#(incr(head(s(head(incr(adx(nil))))))) → a__incr#(head(s(a__head(a__incr(a__adx(nil))))))mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(adx(adx(cons(a__incr(a__nats), _x52))))
mark#(incr(head(s(head(zeros))))) → a__incr#(a__head(s(a__head(a__zeros))))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(s(_x91))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(s(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(s(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(s(mark(_x111)))))))))))
mark#(incr(head(s(head(adx(adx(head(s(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(s(mark(_x91)))))))))mark#(incr(head(s(head(adx(cons(tail(_x81), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__tail(mark(_x81)), _x72))))))
mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))mark#(incr(head(s(head(s(nats)))))) → a__incr#(a__head(s(a__head(s(a__nats)))))
mark#(incr(head(s(head(adx(adx(head(tail(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__tail(mark(_x91)))))))))mark#(incr(adx(adx(cons(nil, _x52))))) → a__incr#(a__adx(adx(cons(nil, _x52))))
mark#(incr(head(s(head(adx(cons(_x71, _x51))))))) → a__incr#(head(s(a__head(a__incr(cons(mark(mark(_x71)), adx(_x51)))))))mark#(incr(adx(adx(cons(tail(nats), _x52))))) → a__incr#(a__adx(adx(cons(tail(a__nats), _x52))))
mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(nil))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(0), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(adx(0), _x92))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(incr(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__incr(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(incr(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__incr(mark(_x121)), _x112), _x102)))))))))
mark#(incr(adx(adx(cons(incr(incr(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(a__incr(mark(_x71))), _x52))))mark#(incr(adx(adx(cons(incr(nil), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(nil), _x52))))
mark#(incr(adx(adx(cons(tail(_x61), _x52))))) → a__incr#(a__adx(adx(cons(tail(mark(_x61)), _x52))))mark#(incr(head(s(head(adx(adx(s(head(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__head(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(zeros)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__zeros)))))))))mark#(incr(head(s(head(adx(adx(head(adx(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(a__adx(mark(_x91)))))))))
mark#(incr(head(s(head(adx(cons(head(nil), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(nil), _x72))))))mark#(incr(adx(adx(cons(tail(cons(s(_x81), _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(s(mark(_x81)), _x72)), _x52))))
mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(0))))))mark#(incr(head(s(head(adx(incr(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__incr(mark(_x81))))))))
mark#(incr(head(s(head(s(incr(_x71))))))) → a__incr#(a__head(s(a__head(s(a__incr(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(a__head(s(head(adx(adx(head(cons(a__adx(nil), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(tail(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(a__tail(mark(_x91)))))))))mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(nats), _x52))))
mark#(incr(head(s(head(incr(head(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__head(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(head(_x111)), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(a__head(mark(_x111))), _x92))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__zeros, _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__zeros, _x102)))))))))
mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(head(s(mark(_x61))))))mark#(incr(head(s(head(adx(adx(s(incr(cons(_x101, _x102)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(adx(nil)), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(cons(_x121, _x122)), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(cons(mark(_x121), _x122)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(cons(_x121, _x122)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(cons(mark(_x121), _x122)), _x102)))))))))mark#(incr(adx(adx(cons(incr(head(_x71)), _x52))))) → a__incr#(adx(a__adx(cons(incr(a__head(mark(_x71))), _x52))))
mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))mark#(incr(adx(adx(cons(nil, _x52))))) → a__incr#(a__adx(a__adx(cons(nil, _x52))))
mark#(incr(adx(adx(cons(incr(zeros), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__zeros), _x52))))mark#(incr(head(s(head(incr(nil)))))) → a__incr#(head(s(a__head(a__incr(nil)))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(nil, _x92))))))))mark#(incr(head(s(head(adx(cons(head(adx(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__adx(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(0), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(0), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(cons(_x141, _x142))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(cons(mark(_x141), _x142))), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(incr(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(cons(mark(_x81), _x82)))))))mark#(incr(adx(adx(s(_x51))))) → a__incr#(a__adx(a__adx(s(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__incr(mark(_x91)))))))))mark#(incr(adx(adx(cons(incr(_x61), _x52))))) → a__incr#(a__adx(adx(cons(incr(mark(_x61)), _x52))))
mark#(incr(adx(adx(cons(incr(_x61), _x52))))) → a__incr#(adx(adx(cons(a__incr(mark(_x61)), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(incr(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__incr(mark(_x101))))))))))
mark#(incr(adx(adx(cons(zeros, _x52))))) → a__incr#(adx(a__adx(cons(a__zeros, _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(adx(s(a__tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(s(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(s(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(nil, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(nil, _x102)))))))))
mark#(incr(adx(adx(cons(incr(_x61), _x52))))) → a__incr#(adx(adx(cons(incr(mark(_x61)), _x52))))mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__adx(mark(_x81))))))))
mark#(incr(head(s(head(adx(cons(adx(incr(s(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(s(mark(_x101)))), _x72))))))mark#(incr(adx(adx(cons(cons(_x61, _x62), _x52))))) → a__incr#(a__adx(a__adx(cons(cons(mark(_x61), _x62), _x52))))
mark#(incr(head(s(head(adx(adx(s(cons(_x91, _x92))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(cons(mark(_x91), _x92))))))))mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))
mark#(incr(head(s(head(adx(cons(incr(_x81), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__incr(mark(_x81)), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x81)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x81)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(a__adx(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(incr(head(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__head(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(incr(incr(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__incr(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(head(s(a__head(a__adx(adx(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(adx(adx(head(head(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__head(mark(_x91)))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(s(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(s(mark(_x101)))), _x72))))))mark#(incr(adx(adx(cons(incr(0), _x52))))) → a__incr#(adx(a__adx(cons(incr(0), _x52))))
mark#(incr(head(s(adx(0))))) → a__incr#(a__head(s(a__adx(0))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(head(s(a__head(a__adx(adx(head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(adx(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__adx(mark(_x111)))))))))))mark#(incr(adx(adx(nats)))) → a__incr#(a__adx(a__adx(a__nats)))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(0), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(0), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(0), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(0), _x102)))))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(_x101), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__adx(mark(_x101)), _x92))))))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(adx(adx(cons(incr(cons(_x71, _x72)), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(cons(mark(_x71), _x72)), _x52))))mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(adx(mark(_x91))), _x72))))))
mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(a__adx(adx(cons(incr(a__nats), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x81)))))))))) → a__incr#(head(s(head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(nats, _x72))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(zeros))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(a__zeros))))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(s(_x111), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(s(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(incr(0))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(0))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x81)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(incr(incr(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__incr(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(cons(zeros, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(a__zeros, _x82)))))))mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__nats))))))
mark#(incr(head(s(head(adx(nats)))))) → a__incr#(a__head(s(a__head(a__adx(a__nats)))))mark#(incr(head(s(head(adx(cons(adx(incr(_x91)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__incr(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(incr(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__incr(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(cons(_x71, _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(mark(_x71)), adx(_x51)))))))
mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(a__incr(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(a__incr(mark(_x91)))))))))
mark#(incr(head(s(head(s(adx(_x71))))))) → a__incr#(a__head(s(a__head(s(a__adx(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(a__head(s(head(a__adx(adx(nil))))))
mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(a__head(s(a__head(adx(adx(nil))))))mark#(incr(adx(adx(cons(incr(incr(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__incr(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(head(s(a__head(a__adx(adx(mark(_x71)))))))mark#(incr(head(s(head(incr(adx(cons(_x81, _x82)))))))) → a__incr#(head(s(a__head(a__incr(a__adx(cons(mark(_x81), _x82)))))))
mark#(incr(head(s(head(adx(cons(adx(incr(incr(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(a__incr(mark(_x101)))), _x72))))))mark#(incr(head(s(adx(s(_x61)))))) → a__incr#(a__head(s(a__adx(s(mark(_x61))))))
mark#(incr(head(s(head(incr(adx(adx(_x81)))))))) → a__incr#(head(s(a__head(a__incr(a__adx(a__adx(mark(_x81))))))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__adx(nil)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(cons(_x121, _x122)))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(cons(mark(_x121), _x122)))))))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(cons(_x111, _x112)), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(cons(mark(_x111), _x112)), _x92))))))))
mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(head(s(a__head(a__adx(mark(_x61))))))mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(incr(mark(_x91)))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(adx(nil)), _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(adx(nil)), _x72))))))
mark#(incr(adx(adx(cons(adx(_x61), _x52))))) → a__incr#(a__adx(a__adx(cons(a__adx(mark(_x61)), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(cons(0, zeros), _x102)))))))))
mark#(incr(head(s(head(adx(cons(head(zeros), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__head(a__zeros)), adx(_x51)))))))mark#(incr(adx(adx(cons(tail(cons(0, _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(0, _x72)), _x52))))
mark#(incr(adx(adx(cons(zeros, _x52))))) → a__incr#(a__adx(a__adx(cons(cons(0, zeros), _x52))))mark#(incr(adx(adx(cons(_x51, _x52))))) → a__incr#(adx(a__adx(cons(mark(_x51), _x52))))
mark#(incr(head(s(head(adx(adx(head(0)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(0)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(incr(_x111), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__incr(mark(_x111)), _x102)))))))))
mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))
mark#(incr(adx(adx(cons(tail(nats), _x52))))) → a__incr#(adx(adx(cons(a__tail(a__nats), _x52))))mark#(incr(adx(adx(incr(_x51))))) → a__incr#(a__adx(a__adx(a__incr(mark(_x51)))))
mark#(incr(head(s(head(adx(incr(0))))))) → a__incr#(head(s(a__head(a__adx(incr(0))))))mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(head(mark(_x51)))))
mark#(incr(X)) → mark#(X)mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(nats))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(a__nats))))))))))
mark#(incr(head(s(head(adx(cons(adx(_x81), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(mark(_x81)), _x72))))))mark#(incr(head(s(head(adx(cons(adx(_x81), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(s(_x141))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(s(mark(_x141)))), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(head(mark(_x111)), _x102)))))))))
mark#(incr(adx(adx(cons(tail(zeros), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__zeros), _x52))))mark#(incr(head(s(head(adx(adx(s(cons(_x91, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(cons(mark(_x91), _x92))))))))
mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__tail(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nil, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(nil, _x112), _x102)))))))))
mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))mark#(incr(head(s(head(nats))))) → a__incr#(head(s(a__head(a__nats))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(head(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__head(mark(_x131))), _x112), _x102)))))))))mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__adx(a__zeros)), _x52))))
mark#(incr(head(s(head(adx(cons(adx(adx(tail(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(a__tail(mark(_x101)))), _x72))))))mark#(incr(head(s(head(adx(adx(s(incr(adx(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__adx(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(cons(nats, _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(a__nats, _x82)))))))mark#(incr(head(s(head(adx(adx(cons(nats, _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(a__nats, _x82)))))))
mark#(incr(head(s(head(adx(adx(s(tail(0))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(0))))))))mark#(incr(head(s(head(adx(adx(s(tail(adx(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__adx(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(head(s(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(s(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(head(adx(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__adx(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(incr(nats))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__nats))))))))mark#(incr(head(s(head(adx(cons(head(zeros), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(head(a__zeros), _x72))))))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(nats), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(a__nats), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(tail(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(0)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(0)))))))
mark#(incr(adx(adx(tail(_x51))))) → a__incr#(a__adx(a__adx(a__tail(mark(_x51)))))mark#(incr(adx(adx(cons(tail(cons(_x71, _x72)), _x52))))) → a__incr#(a__adx(adx(cons(tail(cons(mark(_x71), _x72)), _x52))))
mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(a__nats), _x52))))
mark#(incr(head(s(head(adx(incr(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__tail(mark(_x81))))))))mark#(incr(adx(adx(cons(tail(nil), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(nil), _x52))))
mark#(incr(head(s(head(adx(adx(head(cons(0, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(0, _x92))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(tail(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(tail(cons(mark(_x101), _x102)))))))))mark#(incr(adx(adx(cons(tail(cons(cons(_x81, _x82), _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(cons(mark(_x81), _x82), _x72)), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(0)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(0)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(incr(zeros))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__zeros))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(zeros), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__zeros), _x112), _x102)))))))))mark#(incr(adx(adx(cons(tail(cons(nil, _x72)), _x52))))) → a__incr#(a__adx(adx(cons(tail(cons(nil, _x72)), _x52))))
mark#(incr(head(s(head(adx(cons(head(incr(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__incr(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(adx(head(cons(s(_x101), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(s(mark(_x101)), _x92))))))))
mark#(incr(adx(adx(cons(tail(nats), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__adx(a__zeros)), _x52))))mark#(incr(head(s(head(adx(adx(s(nil)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(nil)))))))
mark#(incr(adx(adx(cons(cons(_x61, _x62), _x52))))) → a__incr#(a__adx(adx(cons(cons(mark(_x61), _x62), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(cons(mark(_x111), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(incr(incr(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__incr(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(_x111))))))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(a__incr(a__tail(a__tail(mark(_x111)))))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(_x111))))))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(a__incr(a__tail(a__tail(mark(_x111)))))))))))mark#(incr(adx(adx(cons(incr(_x61), _x31))))) → a__incr#(a__adx(a__incr(cons(mark(incr(mark(_x61))), adx(_x31)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__head(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__head(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(cons(_x121, _x122), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(cons(mark(_x121), _x122), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(cons(_x121, _x122), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(cons(mark(_x121), _x122), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(incr(cons(_x101, _x102))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(cons(mark(_x101), _x102))), _x72))))))mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__head(a__zeros)))))))
mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__head(a__zeros)))))))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))
mark#(incr(head(s(adx(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__adx(cons(mark(_x61), _x62)))))mark#(incr(adx(adx(cons(incr(s(_x71)), _x52))))) → a__incr#(adx(a__adx(cons(incr(s(mark(_x71))), _x52))))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(adx(a__adx(nil))), adx(_x51)))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(a__incr(a__tail(mark(_x101))))))))))mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__nats), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__nats), _x72))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(a__incr(a__tail(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(s(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(s(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__nats), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(adx(s(a__tail(cons(cons(mark(_x111), _x112), _x102)))))))))mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(head(s(a__head(a__tail(mark(_x61))))))
mark#(incr(head(s(head(adx(adx(s(incr(head(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__head(mark(_x101))))))))))mark#(incr(head(s(head(adx(cons(adx(adx(zeros)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(a__zeros)), _x72))))))
mark#(incr(head(s(head(adx(adx(cons(s(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(s(mark(_x91)), _x82)))))))mark#(incr(head(s(head(adx(adx(cons(s(_x91), _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(s(mark(_x91)), _x82)))))))
mark#(incr(adx(adx(cons(tail(cons(adx(_x81), _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(a__adx(mark(_x81)), _x72)), _x52))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(head(s(a__head(a__incr(cons(mark(adx(adx(nil))), adx(_x51)))))))
mark#(incr(head(s(head(adx(cons(head(zeros), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__head(a__zeros), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__adx(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(incr(adx(0))))))) → a__incr#(head(s(a__head(a__incr(a__adx(0))))))mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(head(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__head(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(incr(_x91)), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(a__incr(mark(_x91)))), adx(_x51)))))))
mark#(incr(head(s(head(adx(adx(cons(adx(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(a__adx(mark(_x91)), _x82)))))))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(adx(adx(cons(tail(cons(nil, _x51)), nil))))) → a__incr#(a__adx(adx(cons(mark(_x51), _x52))))mark#(incr(head(s(head(adx(cons(nil, _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(nil, _x72))))))
mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(a__nats), _x52))))mark#(incr(head(s(head(adx(adx(s(incr(0))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(0))))))))
mark#(incr(head(s(head(adx(cons(head(_x81), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(head(mark(_x81)), _x72))))))mark#(incr(adx(adx(cons(incr(s(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(s(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(adx(adx(head(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(head(a__adx(adx(head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(cons(tail(_x91), _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(a__tail(mark(_x91)), _x82)))))))mark#(incr(head(s(head(adx(adx(cons(tail(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(a__tail(mark(_x91)), _x82)))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(a__incr(a__tail(mark(_x101))))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(tail(a__incr(mark(_x131))), _x112), _x102)))))))))
mark#(incr(head(s(head(incr(adx(s(_x81)))))))) → a__incr#(head(s(a__head(a__incr(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(incr(cons(_x71, _x72))))))) → a__incr#(head(s(a__head(a__incr(cons(mark(_x71), _x72))))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(nil), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(nil), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(s(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(s(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(nil), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(nil), _x102)))))))))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(a__head(adx(adx(s(a__tail(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(head(a__adx(adx(s(a__tail(cons(mark(_x101), _x102)))))))))mark#(incr(adx(adx(cons(incr(incr(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(a__incr(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(a__zeros)), _x72))))))
mark#(incr(adx(adx(cons(tail(0), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(0), _x52))))mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(head(s(a__head(adx(a__incr(mark(_x71)))))))
mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(head(s(head(a__adx(a__incr(mark(_x71)))))))mark#(incr(head(s(head(adx(cons(zeros, _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(cons(0, zeros), _x72))))))
mark#(incr(adx(adx(cons(incr(adx(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(a__adx(mark(_x71))), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(incr(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__incr(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(incr(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__incr(mark(_x111)), _x102)))))))))mark#(incr(incr(incr(adx(_x51))))) → a__incr#(a__incr(a__incr(a__adx(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(head(_x121)))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(a__head(mark(_x121))))))))))))mark#(incr(adx(adx(cons(incr(_x61), _x31))))) → a__incr#(a__adx(a__incr(cons(mark(a__incr(mark(_x61))), adx(_x31)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(s(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(s(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(s(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(s(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(zeros, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__zeros, _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(head(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__head(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(zeros)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__zeros)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(0), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__adx(0), _x92))))))))
mark#(incr(adx(adx(cons(s(_x61), _x52))))) → a__incr#(a__adx(adx(cons(s(mark(_x61)), _x52))))mark#(incr(adx(adx(cons(incr(_x61), _x52))))) → a__incr#(adx(a__adx(cons(a__incr(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(adx(head(cons(incr(_x101), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__incr(mark(_x101)), _x92))))))))mark#(incr(head(s(head(incr(adx(head(_x81)))))))) → a__incr#(head(s(a__head(a__incr(a__adx(a__head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(cons(head(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(a__head(mark(_x91)), _x82)))))))mark#(incr(head(s(head(nil))))) → a__incr#(head(s(a__head(nil))))
mark#(incr(adx(adx(cons(nats, _x52))))) → a__incr#(a__adx(a__adx(cons(a__nats, _x52))))mark#(incr(zeros)) → a__incr#(a__zeros)
mark#(incr(head(s(head(adx(adx(s(tail(cons(nats, _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__nats, _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(nats, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__nats, _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(a__head(s(a__head(incr(cons(mark(a__adx(a__adx(nil))), adx(_x51)))))))mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(zeros)))))))
mark#(incr(adx(adx(cons(incr(nil), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(nil), _x52))))mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__adx(nil), _x92))))))))
mark#(incr(head(s(adx(incr(_x61)))))) → a__incr#(a__head(s(a__adx(a__incr(mark(_x61))))))mark#(incr(adx(adx(cons(incr(cons(_x71, _x72)), _x52))))) → a__incr#(adx(a__adx(cons(incr(cons(mark(_x71), _x72)), _x52))))
mark#(incr(head(s(head(adx(adx(s(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__zeros)))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(nats), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(a__nats), _x92))))))))
mark#(incr(head(s(head(s(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__head(s(cons(mark(_x71), _x72))))))mark#(incr(head(s(head(adx(cons(head(_x81), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__head(mark(_x81))), adx(_x51)))))))
mark#(incr(head(s(head(adx(incr(cons(_x81, _x82)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(adx(adx(head(nil)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(nil)))))))
mark#(incr(adx(adx(cons(tail(cons(_x71, _x51)), mark(_x71)))))) → a__incr#(a__adx(adx(cons(mark(_x51), _x52))))mark#(incr(head(s(head(adx(cons(adx(head(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__head(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(incr(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__incr(mark(_x111)))))))))))mark#(incr(head(s(head(adx(cons(adx(incr(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(a__incr(mark(_x91))), _x72))))))
mark#(incr(adx(adx(cons(tail(cons(nats, _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(a__nats, _x72)), _x52))))mark#(incr(head(s(head(adx(adx(s(nats)))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__nats)))))))
mark#(incr(head(s(head(adx(incr(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__head(mark(_x81))))))))mark#(incr(adx(adx(cons(incr(cons(_x71, _x72)), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(cons(mark(_x71), _x72)), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__tail(mark(_x91)))))))))mark#(incr(adx(adx(cons(tail(cons(head(_x81), _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(a__head(mark(_x81)), _x72)), _x52))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(head(s(head(a__adx(adx(head(cons(a__adx(nil), _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(head(s(a__head(adx(adx(head(cons(a__adx(nil), _x92))))))))
mark#(incr(head(s(head(adx(incr(nats))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__nats))))))mark#(incr(head(s(head(adx(adx(s(zeros)))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__zeros)))))))
mark#(incr(incr(incr(zeros)))) → a__incr#(a__incr(a__incr(a__zeros)))mark#(incr(head(s(head(adx(adx(s(nats)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__nats)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(adx(_x141))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__adx(mark(_x141)))), _x112), _x102)))))))))mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(head(s(head(adx(cons(nats, _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__nats), adx(_x51)))))))mark#(incr(head(s(adx(head(_x61)))))) → a__incr#(a__head(s(a__adx(a__head(mark(_x61))))))
mark#(incr(adx(adx(cons(head(_x61), _x52))))) → a__incr#(a__adx(a__adx(cons(a__head(mark(_x61)), _x52))))mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(adx(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__adx(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(zeros)))))) → a__incr#(a__head(s(a__head(a__adx(a__zeros)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(adx(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__adx(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(0))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(0))))))))))
mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))mark#(incr(head(s(head(adx(cons(adx(adx(incr(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(a__incr(mark(_x101)))), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(_x81), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(mark(_x81)), _x72))))))mark#(incr(head(s(head(adx(0)))))) → a__incr#(a__head(s(a__head(a__adx(0)))))
mark#(incr(head(s(head(adx(adx(s(adx(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__adx(mark(_x91)))))))))mark#(incr(head(s(head(adx(cons(incr(_x81), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__incr(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(nats), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(a__nats), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(nats), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__nats), _x102)))))))))
mark#(incr(head(s(head(adx(cons(head(_x81), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__head(mark(_x81)), _x72))))))mark#(incr(head(s(head(adx(adx(head(cons(nats, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__nats, _x92))))))))
mark#(incr(head(s(head(adx(adx(cons(tail(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(a__tail(mark(_x91)), _x82)))))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(adx(a__adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(head(a__adx(a__adx(mark(_x71)))))))mark#(incr(adx(adx(cons(incr(head(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__head(mark(_x71))), _x52))))
mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(adx(mark(_x51)))))mark#(incr(adx(adx(cons(incr(zeros), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(a__zeros), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(s(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(s(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(head(head(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(a__head(mark(_x91)))))))))
mark#(incr(head(s(head(adx(cons(adx(_x81), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(mark(_x81))), adx(_x51)))))))mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))
mark#(incr(adx(adx(cons(_x51, _x52))))) → a__incr#(adx(adx(cons(mark(_x51), _x52))))mark#(incr(head(s(head(incr(adx(zeros))))))) → a__incr#(head(s(a__head(a__incr(a__adx(a__zeros))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))mark#(incr(adx(adx(cons(adx(_x61), _x52))))) → a__incr#(a__adx(adx(cons(a__adx(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(adx(head(incr(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(a__incr(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(head(_x91))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__head(mark(_x91)))))))))
mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(incr(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(incr(_x141))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__incr(mark(_x141)))), _x112), _x102)))))))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(head(s(head(a__incr(mark(_x61))))))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(a__head(s(head(a__incr(cons(mark(a__adx(a__adx(nil))), adx(_x51)))))))mark#(incr(incr(nats))) → a__incr#(a__incr(a__adx(a__zeros)))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(adx(nil))), adx(_x51)))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(_x111))))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(mark(_x111)))))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(cons(_x101, _x102))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(cons(mark(_x101), _x102))), _x72))))))mark#(incr(head(s(head(adx(head(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__head(mark(_x71)))))))
mark#(incr(head(s(head(adx(incr(tail(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__tail(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(adx(s(a__tail(cons(cons(mark(_x111), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(adx(s(a__tail(cons(cons(mark(_x111), _x112), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(nil), _x72))))))
mark#(incr(head(s(head(adx(adx(cons(nil, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(nil, _x82)))))))mark#(incr(adx(adx(cons(tail(_x61), _x52))))) → a__incr#(adx(adx(cons(a__tail(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(_x101), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(adx(mark(_x101)), _x92))))))))mark#(incr(head(s(adx(nil))))) → a__incr#(a__head(s(a__adx(nil))))
mark#(incr(head(s(adx(adx(_x61)))))) → a__incr#(a__head(s(a__adx(a__adx(mark(_x61))))))mark#(incr(head(s(head(adx(adx(head(cons(nil, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(nil, _x92))))))))
mark#(incr(adx(adx(cons(incr(tail(_x71)), _x52))))) → a__incr#(adx(a__adx(cons(incr(a__tail(mark(_x71))), _x52))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(nil))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(nil))))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(adx(s(a__tail(cons(a__adx(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(adx(s(a__tail(cons(a__adx(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(nil), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(nil), _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(a__adx(mark(_x91)))), adx(_x51)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))
mark#(incr(incr(nats))) → a__incr#(incr(a__nats))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(head(_x141))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__head(mark(_x141)))), _x112), _x102)))))))))
mark#(incr(adx(adx(cons(incr(adx(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(a__adx(mark(_x71))), _x52))))mark#(incr(head(s(head(adx(adx(head(cons(adx(incr(_x111)), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(a__incr(mark(_x111))), _x92))))))))
mark#(incr(head(s(head(adx(cons(nil, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(nil, _x72))))))mark#(incr(head(s(head(adx(cons(zeros, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__zeros, _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(0, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(0, _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(tail(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__tail(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(tail(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__tail(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__adx(nil)), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__adx(nil)), _x72))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(a__head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(nil, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(nil, _x102)))))))))mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x81)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x81)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__nats, _x72))))))mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))
mark#(incr(adx(adx(cons(incr(cons(_x71, _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(cons(mark(_x71), _x72)), _x52))))mark#(incr(adx(adx(cons(tail(cons(zeros, _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(a__zeros, _x72)), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(mark(_x131))), _x112), _x102)))))))))mark#(incr(adx(nil))) → a__incr#(a__adx(nil))
mark#(incr(head(s(head(adx(adx(s(incr(tail(cons(_x111, _x112))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(cons(mark(_x111), _x112))))))))))mark#(incr(head(s(adx(zeros))))) → a__incr#(a__head(s(a__adx(a__zeros))))
mark#(incr(head(s(head(adx(incr(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__adx(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(zeros))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__zeros))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(nats)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__nats)))))))))mark#(incr(head(s(head(adx(cons(head(zeros), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(zeros), _x72))))))
mark#(incr(adx(adx(zeros)))) → a__incr#(a__adx(a__adx(a__zeros)))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x81)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x81)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(adx(adx(cons(tail(head(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__head(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(adx(_x111)), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(a__adx(mark(_x111))), _x92))))))))mark#(incr(head(s(head(adx(cons(adx(incr(nil)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(nil)), _x72))))))
mark#(incr(head(s(head(adx(cons(head(nats), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__nats), _x72))))))mark#(incr(adx(adx(cons(tail(tail(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__tail(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(head(cons(_x91, _x92))))))))) → a__incr#(a__head(s(a__head(adx(adx(head(cons(mark(_x91), _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(_x91, _x92))))))))) → a__incr#(a__head(s(head(a__adx(adx(head(cons(mark(_x91), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(cons(_x101, _x102), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(cons(mark(_x101), _x102), _x92))))))))mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))
mark#(incr(adx(adx(cons(_x51, _x31))))) → a__incr#(a__adx(a__incr(cons(mark(mark(_x51)), adx(_x31)))))mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(a__head(a__adx(a__incr(cons(0, zeros)))))))
mark#(incr(head(s(head(adx(adx(cons(nats, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(a__nats, _x82)))))))mark#(incr(head(s(head(adx(cons(cons(_x81, _x82), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(cons(mark(_x81), _x82), _x72))))))
mark#(incr(head(s(head(adx(cons(s(_x81), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(s(mark(_x81)), _x72))))))mark#(incr(head(nats))) → a__incr#(head(a__nats))
mark#(incr(adx(adx(_x41)))) → a__incr#(a__adx(adx(mark(_x41))))mark#(incr(adx(adx(cons(incr(0), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(0), _x52))))
mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__zeros))))))mark#(incr(adx(adx(adx(_x51))))) → a__incr#(a__adx(a__adx(a__adx(mark(_x51)))))
mark#(incr(adx(adx(cons(incr(nil), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(nil), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(incr(_x121)), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(a__incr(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(incr(_x121)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__incr(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nil, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(nil, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nil, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(nil, _x112), _x102)))))))))mark#(incr(adx(adx(_x41)))) → a__incr#(adx(a__adx(mark(_x41))))
mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(a__head(s(a__head(a__adx(adx(0))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(nats)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__nats)), _x112), _x102)))))))))
mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))mark#(incr(head(s(head(s(nil)))))) → a__incr#(a__head(s(a__head(s(nil)))))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))
mark#(incr(head(s(head(adx(adx(s(tail(tail(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__tail(mark(_x101))))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(tail(cons(cons(a__tail(a__incr(mark(_x131))), _x112), _x102)))))))))
mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))mark#(incr(adx(adx(cons(incr(nil), _x52))))) → a__incr#(adx(a__adx(cons(incr(nil), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(cons(_x131, _x132)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(cons(mark(_x131), _x132)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(nil), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(nil), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(cons(0, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(0, _x82)))))))mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(head(adx(a__incr(a__zeros))))))
mark#(incr(head(s(head(adx(cons(head(zeros), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__head(a__zeros), _x72))))))mark#(incr(head(s(head(adx(cons(head(zeros), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__head(a__zeros), _x72))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(head(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__head(mark(_x111)))))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__head(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(head(nats)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__nats)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(tail(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__zeros, _x102)))))))))mark#(incr(head(s(head(adx(cons(0, _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(0, _x72))))))
mark#(incr(head(s(head(adx(cons(adx(tail(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__tail(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(head(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__head(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(head(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__head(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(incr(_x91)), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__incr(mark(_x91))), _x72))))))
mark#(incr(head(s(head(zeros))))) → a__incr#(head(s(a__head(a__zeros))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__head(mark(_x81))))))))
mark#(incr(head(s(head(s(s(_x71))))))) → a__incr#(a__head(s(a__head(s(s(mark(_x71)))))))mark#(incr(head(s(head(incr(0)))))) → a__incr#(head(s(a__head(a__incr(0)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(adx(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__adx(mark(_x131))), _x112), _x102)))))))))mark#(incr(head(s(head(adx(cons(zeros, _x72))))))) → a__incr#(head(s(a__head(adx(cons(a__zeros, _x72))))))
mark#(incr(head(s(head(adx(cons(zeros, _x72))))))) → a__incr#(head(s(head(a__adx(cons(a__zeros, _x72))))))mark#(incr(adx(adx(head(_x51))))) → a__incr#(a__adx(a__adx(a__head(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(nats), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__nats), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(nil)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(nil)))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(incr(_x121)))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(a__incr(mark(_x121))))))))))))mark#(incr(head(s(head(incr(s(_x71))))))) → a__incr#(head(s(a__head(a__incr(s(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(a__head(s(head(adx(adx(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(head(s(a__head(s(mark(_x61))))))
mark#(incr(head(s(head(adx(adx(cons(incr(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(a__incr(mark(_x91)), _x82)))))))mark#(incr(head(s(head(adx(adx(head(cons(zeros, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__zeros, _x92))))))))
mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__incr(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(adx(_x121)))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(a__adx(mark(_x121))))))))))))
mark#(incr(head(s(head(incr(adx(tail(_x81)))))))) → a__incr#(head(s(a__head(a__incr(a__adx(a__tail(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(nats, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__nats, _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(0)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(0)), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(adx(s(a__tail(cons(cons(a__tail(a__incr(mark(_x131))), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(cons(head(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(a__head(mark(_x91)), _x82)))))))mark#(incr(head(s(head(adx(adx(cons(head(_x91), _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(a__head(mark(_x91)), _x82)))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(head(s(head(a__adx(cons(adx(adx(nil)), _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(head(s(a__head(adx(cons(adx(adx(nil)), _x72))))))
mark#(incr(head(s(head(incr(zeros)))))) → a__incr#(head(s(a__head(a__incr(a__zeros)))))mark#(incr(head(s(head(adx(cons(adx(incr(head(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(a__head(mark(_x101)))), _x72))))))
mark#(incr(adx(adx(cons(tail(incr(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__incr(mark(_x71))), _x52))))mark#(incr(head(s(head(adx(adx(head(cons(adx(tail(_x111)), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(a__tail(mark(_x111))), _x92))))))))
mark#(incr(head(s(head(adx(adx(cons(zeros, _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(a__zeros, _x82)))))))mark#(incr(head(s(head(adx(adx(cons(zeros, _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(a__zeros, _x82)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(nil)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(nil)), _x112), _x102)))))))))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(head(s(a__head(a__adx(a__adx(a__zeros))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(tail(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(adx(_x121)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__adx(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(adx(_x121)), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(a__adx(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(a__incr(mark(_x91)))))))))
mark#(incr(adx(0))) → a__incr#(a__adx(0))mark#(incr(head(s(head(adx(cons(zeros, _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(zeros, _x72))))))
mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(head(s(a__head(a__adx(adx(a__head(a__zeros)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x81)))))))))) → a__incr#(head(s(head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(s(head(adx(adx(head(incr(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__incr(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(head(cons(_x91, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(cons(mark(_x91), _x92))))))))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(head(s(head(adx(adx(cons(0, _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(0, _x82)))))))mark#(incr(head(s(head(adx(adx(cons(0, _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(0, _x82)))))))
mark#(incr(adx(s(_x41)))) → a__incr#(a__adx(s(mark(_x41))))mark#(incr(head(s(head(adx(adx(s(tail(cons(0, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(0, _x102)))))))))
mark#(incr(adx(adx(cons(zeros, _x31))))) → a__incr#(a__adx(a__incr(cons(mark(a__zeros), adx(_x31)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x81)))))))))) → a__incr#(head(s(head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__zeros))))))mark#(incr(head(s(head(incr(tail(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__tail(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(s(tail(nil))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(nil))))))))mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))
mark#(incr(adx(adx(cons(head(_x61), _x52))))) → a__incr#(a__adx(adx(cons(a__head(mark(_x61)), _x52))))mark#(incr(head(s(head(adx(cons(s(_x81), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(s(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nats)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(a__nats)), _x72))))))mark#(incr(adx(adx(cons(0, _x52))))) → a__incr#(a__adx(adx(cons(0, _x52))))
mark#(incr(nats)) → a__incr#(a__nats)mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(head(s(head(adx(adx(head(cons(adx(zeros), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(a__zeros), _x92))))))))mark#(incr(head(s(head(adx(adx(s(0)))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(0)))))))
mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(a__head(a__adx(incr(a__zeros))))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(a__head(a__adx(a__incr(zeros))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(head(s(a__head(a__adx(adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(zeros, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__zeros, _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(zeros, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__zeros, _x112), _x102)))))))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(head(s(a__head(incr(mark(_x61))))))mark#(incr(adx(adx(cons(tail(_x61), _x52))))) → a__incr#(a__adx(a__adx(cons(a__tail(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(tail(mark(_x101))))))))))mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__nats, _x72))))))
mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__nats, _x72))))))mark#(incr(adx(adx(cons(incr(tail(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__tail(mark(_x71))), _x52))))
mark#(incr(adx(adx(cons(incr(s(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(s(mark(_x71))), _x52))))mark#(incr(adx(adx(cons(incr(tail(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(a__tail(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(tail(cons(a__head(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(0, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(0, _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(0, _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(0, _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(adx(head(cons(tail(_x101), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__tail(mark(_x101)), _x92))))))))mark#(incr(head(s(head(adx(incr(nats))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__nats))))))
mark#(incr(head(s(head(adx(incr(0))))))) → a__incr#(head(s(head(a__adx(a__incr(0))))))mark#(incr(head(s(head(adx(incr(0))))))) → a__incr#(head(s(a__head(adx(a__incr(0))))))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(head(s(a__head(a__adx(a__adx(mark(_x71)))))))mark#(incr(head(s(head(s(0)))))) → a__incr#(a__head(s(a__head(s(0)))))
mark#(incr(adx(adx(cons(tail(nats), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(nats), _x52))))mark#(incr(head(s(head(adx(adx(cons(nil, _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(nil, _x82)))))))
mark#(incr(head(s(head(adx(adx(cons(nil, _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(nil, _x82)))))))mark#(incr(adx(adx(cons(tail(s(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(s(mark(_x71))), _x52))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(adx(adx(cons(incr(head(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(a__head(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(a__adx(nil)), _x72))))))mark#(incr(head(s(head(adx(cons(head(s(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(s(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(incr(nats)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(a__nats)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(nats))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__nats))))))))mark#(incr(head(s(head(adx(incr(adx(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__adx(mark(_x81))))))))
mark#(incr(adx(adx(cons(tail(cons(tail(_x81), _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(a__tail(mark(_x81)), _x72)), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(tail(_x141))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__tail(mark(_x141)))), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(adx(_x91))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__adx(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(a__head(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(cons(head(head(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__head(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(zeros), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(a__zeros), _x102)))))))))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(head(s(a__head(a__adx(adx(a__head(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(zeros), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__zeros), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(a__incr(a__tail(a__tail(mark(_x111)))))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(incr(mark(_x131))), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(head(nil)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(nil)))))))mark#(incr(head(s(head(adx(adx(s(nil)))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(nil)))))))
mark#(incr(head(s(head(adx(nil)))))) → a__incr#(a__head(s(a__head(a__adx(nil)))))mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(head(a__adx(mark(_x61))))))
mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(adx(mark(_x61))))))mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))
mark#(incr(head(s(head(adx(adx(cons(cons(_x91, _x92), _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(cons(mark(_x91), _x92), _x82)))))))mark#(incr(head(s(head(adx(adx(cons(cons(_x91, _x92), _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(cons(mark(_x91), _x92), _x82)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__adx(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(_x101), _x92))))))))) → a__incr#(a__head(s(a__head(adx(adx(head(cons(a__adx(mark(_x101)), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(_x101), _x92))))))))) → a__incr#(a__head(s(head(a__adx(adx(head(cons(a__adx(mark(_x101)), _x92))))))))mark#(incr(head(s(head(adx(adx(cons(incr(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(a__incr(mark(_x91)), _x82)))))))
mark#(incr(head(s(head(adx(adx(cons(incr(_x91), _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(a__incr(mark(_x91)), _x82)))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(cons(cons(_x91, _x92), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(cons(mark(_x91), _x92), _x82)))))))mark#(incr(adx(adx(cons(incr(0), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(0), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(incr(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__incr(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(0, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(0, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(cons(_x121, _x122)), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(cons(mark(_x121), _x122)), _x102)))))))))mark#(incr(head(s(head(adx(adx(head(cons(head(_x101), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__head(mark(_x101)), _x92))))))))
mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x81)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(mark(_x81))))))))
mark#(incr(adx(adx(cons(incr(zeros), _x52))))) → a__incr#(adx(a__adx(cons(incr(a__zeros), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(adx(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(adx(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(nats), _x72))))))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__head(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__head(mark(_x81))))))))
mark#(incr(adx(adx(cons(incr(incr(_x71)), _x52))))) → a__incr#(adx(a__adx(cons(incr(a__incr(mark(_x71))), _x52))))mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(head(a__adx(a__incr(zeros))))))
mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(a__head(adx(a__incr(zeros))))))mark#(incr(head(s(head(adx(cons(adx(incr(tail(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(a__tail(mark(_x101)))), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(tail(cons(cons(mark(_x111), _x112), _x102)))))))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__zeros), _x72)))))) is 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
a__incr#(head(s(a__head(a__adx(cons(a__adx(a__zeros), _x72)))))) 
a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(a__zeros)), adx(_x51))))))) 
a__incr#(a__head(s(a__head(adx(cons(a__adx(a__zeros), _x72)))))) 
a__incr#(a__head(s(head(a__adx(cons(a__adx(a__zeros), _x72)))))) 
a__incr#(a__head(s(a__head(a__adx(cons(a__adx(cons(0, zeros)), _x72)))))) 
a__incr#(a__head(s(a__head(a__adx(cons(adx(a__zeros), _x72)))))) 
a__incr#(a__head(s(a__head(a__adx(cons(a__adx(zeros), _x72)))))) 
Thus, the rule mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__zeros), _x72)))))) is replaced by the following rules:
mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(zeros), _x72))))))mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(a__zeros), _x72))))))
mark#(incr(head(s(head(adx(cons(nats, _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(a__zeros)), adx(_x51)))))))mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__zeros), _x72))))))
mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__zeros), _x72))))))mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__zeros), _x72))))))
mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(cons(0, zeros)), _x72))))))

Problem 32: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(s(X)) → mark#(X)mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(_x121))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(mark(_x121)))), _x92))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(zeros))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(s(zeros))), _x102)))))))))mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(head(a__adx(incr(a__zeros))))))
mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(a__head(adx(incr(a__zeros))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(adx(nil), _x92))))))))
mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__tail(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(tail(_x121)))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(a__tail(mark(_x121))))))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(incr(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__incr(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(incr(adx(_x71))))))) → a__incr#(head(s(head(a__incr(a__adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x51))))))) → a__incr#(head(s(a__head(a__incr(cons(mark(a__adx(a__adx(mark(_x91)))), adx(_x51)))))))mark#(incr(adx(adx(0)))) → a__incr#(a__adx(a__adx(0)))
mark#(incr(head(s(head(adx(adx(tail(0)))))))) → a__incr#(head(s(head(a__adx(adx(a__tail(0)))))))mark#(incr(head(s(head(adx(adx(tail(0)))))))) → a__incr#(head(s(a__head(adx(adx(a__tail(0)))))))
mark#(incr(head(s(head(adx(adx(head(cons(zeros, _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__zeros, _x92))))))))mark#(incr(head(s(head(adx(cons(head(_x81), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__head(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(cons(head(_x81), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__head(mark(_x81)), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(tail(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(a__tail(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(incr(nats)))))) → a__incr#(head(s(a__head(a__incr(a__nats)))))mark#(incr(head(s(head(adx(cons(cons(_x81, _x82), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(cons(mark(_x81), _x82), _x72))))))
mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(cons(0, zeros)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(tail(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__tail(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(s(cons(_x81, _x82)))))))) → a__incr#(head(s(a__head(a__adx(s(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(adx(adx(head(cons(head(s(tail(_x121))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__tail(mark(_x121)))), _x92))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(adx(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__adx(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(head(cons(head(nil), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(nil), _x92))))))))
mark#(incr(head(s(head(adx(tail(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__tail(mark(_x71)))))))mark#(incr(head(s(head(adx(s(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(adx(s(cons(mark(_x81), _x82)))))))
mark#(incr(head(s(head(adx(s(cons(_x81, _x82)))))))) → a__incr#(a__head(s(head(a__adx(s(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(adx(cons(head(0), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(0), _x72))))))
mark#(incr(head(s(head(adx(adx(s(incr(s(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(s(mark(_x101))))))))))mark#(incr(head(zeros))) → a__incr#(head(zeros))
mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__zeros, _x102)))))))))mark#(incr(head(s(head(adx(s(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(s(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(nil)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(nil)), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(adx(cons(_x101, _x102))), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__adx(cons(mark(_x101), _x102))), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(cons(_x101, _x102))), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__adx(cons(mark(_x101), _x102))), _x72))))))mark#(incr(head(s(head(adx(cons(head(zeros), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(cons(0, zeros)), _x72))))))
mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__incr(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(incr(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(a__incr(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(incr(nil))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(nil))))))))mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(a__head(s(a__head(adx(adx(0))))))
mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(a__head(s(head(a__adx(adx(0))))))mark#(incr(head(s(head(adx(incr(s(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(head(s(head(a__adx(cons(a__adx(a__adx(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(incr(a__tail(mark(_x101))))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(head(s(a__head(adx(cons(a__adx(a__adx(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(tail(cons(a__zeros, _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(nats), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(a__nats)), adx(_x51)))))))mark#(incr(head(s(cons(_x51, _x52))))) → a__incr#(a__head(s(cons(mark(_x51), _x52))))
mark#(incr(head(s(head(adx(incr(s(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(s(mark(_x81))))))))mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(head(s(a__head(a__adx(incr(mark(_x71)))))))
mark#(incr(head(nats))) → a__incr#(a__head(nats))mark#(incr(head(s(head(adx(cons(adx(incr(0)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(0)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(s(_x121)))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(s(mark(_x121))))))))))))mark#(incr(head(s(head(adx(adx(head(0)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(0)))))))
mark#(incr(head(s(head(adx(adx(cons(s(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(s(mark(_x91)), _x82)))))))mark#(incr(head(s(head(adx(cons(head(cons(_x91, _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(cons(mark(_x91), _x92)), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(incr(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__adx(a__incr(mark(_x101)))), _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(incr(_x101))), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__adx(a__incr(mark(_x101)))), _x72))))))
mark#(incr(head(s(head(adx(s(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(s(a__incr(mark(_x81))))))))mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(adx(a__adx(cons(incr(a__nats), _x52))))
mark#(incr(head(s(head(adx(adx(incr(zeros)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__incr(a__zeros)))))))mark#(incr(head(s(head(adx(adx(incr(zeros)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__incr(a__zeros)))))))
mark#(incr(head(s(head(adx(cons(adx(s(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(s(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(adx(head(cons(head(incr(_x111)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(a__incr(mark(_x111))), _x92))))))))
mark#(incr(incr(incr(head(_x51))))) → a__incr#(a__incr(a__incr(a__head(mark(_x51)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x81)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(mark(_x91)))))))))mark#(incr(head(s(head(adx(cons(adx(_x81), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(mark(_x91)))))))))mark#(incr(adx(adx(cons(incr(zeros), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(cons(0, zeros)), _x52))))
mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__adx(mark(_x81))))))))mark#(incr(adx(adx(cons(incr(_x61), _x31))))) → a__incr#(adx(a__incr(cons(mark(incr(mark(_x61))), adx(_x31)))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(tail(a__tail(mark(_x111)))))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(tail(cons(a__head(a__head(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(cons(0, zeros))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(tail(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__tail(mark(_x131))), _x112), _x102)))))))))
mark#(incr(head(nats))) → a__incr#(a__head(a__adx(a__zeros)))mark#(incr(head(s(head(adx(adx(head(cons(head(s(adx(_x121))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__adx(mark(_x121)))), _x92))))))))
mark#(incr(incr(adx(tail(_x51))))) → a__incr#(a__incr(a__adx(a__tail(mark(_x51)))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(a__head(s(a__head(cons(s(mark(mark(a__adx(a__adx(nil))))), incr(adx(_x51)))))))
mark#(incr(adx(_x21))) → a__incr#(adx(mark(_x21)))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(head(s(a__head(adx(adx(a__head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(head(s(head(a__adx(adx(a__head(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(a__tail(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(head(cons(s(_x101), _x92))))))))) → a__incr#(head(s(a__head(adx(adx(head(cons(s(mark(_x101)), _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(s(_x101), _x92))))))))) → a__incr#(head(s(head(a__adx(adx(head(cons(s(mark(_x101)), _x92))))))))
mark#(incr(head(s(head(adx(incr(nil))))))) → a__incr#(head(s(a__head(a__adx(a__incr(nil))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(s(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(s(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(s(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(s(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(tail(incr(adx(_x101)))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(a__incr(a__adx(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(tail(incr(adx(_x101)))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(a__incr(a__adx(mark(_x101))))))))))mark#(incr(head(s(head(adx(cons(adx(incr(adx(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(a__adx(mark(_x101)))), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nats, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__nats, _x112), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(0), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(0), _x72))))))
mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(zeros))))))mark#(incr(head(s(head(adx(adx(s(cons(_x91, _x92))))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(cons(mark(_x91), _x92))))))))
mark#(incr(head(s(head(adx(adx(s(cons(_x91, _x92))))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(cons(mark(_x91), _x92))))))))mark#(incr(adx(adx(cons(tail(cons(_x71, _x72)), _x52))))) → a__incr#(adx(adx(cons(a__tail(cons(mark(_x71), _x72)), _x52))))
mark#(incr(adx(adx(cons(incr(head(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(a__head(mark(_x71))), _x52))))mark#(incr(adx(adx(cons(0, _x52))))) → a__incr#(a__adx(a__adx(cons(0, _x52))))
mark#(incr(incr(nats))) → a__incr#(a__incr(nats))mark#(incr(head(s(head(incr(adx(nats))))))) → a__incr#(head(s(a__head(a__incr(a__adx(a__adx(a__zeros)))))))
mark#(incr(adx(adx(cons(s(_x61), _x52))))) → a__incr#(a__adx(a__adx(cons(s(mark(_x61)), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(tail(_x131))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(a__head(a__tail(mark(_x131)))), _x102)))))))))
mark#(incr(adx(adx(cons(nats, _x52))))) → a__incr#(a__adx(adx(cons(a__nats, _x52))))mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(head(s(a__head(adx(adx(cons(mark(_x81), _x82)))))))
mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(head(s(head(a__adx(adx(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(adx(adx(head(cons(incr(_x101), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__incr(mark(_x101)), _x92))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(head(_x121)), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(a__head(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(s(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(s(mark(_x131))), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(head(_x121)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__head(mark(_x121))), _x102)))))))))a__incr#(cons(X, L)) → mark#(X)
mark#(incr(adx(adx(cons(tail(cons(nil, _x72)), _x52))))) → a__incr#(adx(adx(cons(a__tail(cons(nil, _x72)), _x52))))mark#(incr(adx(head(s(_x51))))) → a__incr#(a__adx(a__head(s(mark(_x51)))))
mark#(incr(head(s(head(adx(cons(zeros, _x51))))))) → a__incr#(head(s(a__head(a__incr(cons(mark(a__zeros), adx(_x51)))))))mark#(incr(adx(zeros))) → a__incr#(a__adx(a__zeros))
mark#(incr(head(s(head(adx(adx(tail(tail(_x91))))))))) → a__incr#(head(s(a__head(adx(adx(a__tail(a__tail(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(tail(tail(_x91))))))))) → a__incr#(head(s(head(a__adx(adx(a__tail(a__tail(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(cons(_x121, _x122), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(cons(mark(_x121), _x122), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(s(_x121)), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(s(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(s(_x121)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(s(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(adx(adx(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(a__adx(mark(_x101)))), _x72))))))
mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(a__zeros)))))))mark#(incr(head(s(head(adx(cons(adx(incr(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(incr(mark(_x91))), _x72))))))
mark#(incr(adx(adx(cons(zeros, _x52))))) → a__incr#(a__adx(a__adx(cons(zeros, _x52))))mark#(cons(X1, X2)) → mark#(X1)
mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(a__head(adx(adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(head(a__adx(adx(s(mark(_x81))))))))
mark#(incr(adx(adx(cons(tail(cons(incr(_x81), _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(a__incr(mark(_x81)), _x72)), _x52))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(nil)), adx(_x51)))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(adx(adx(nil)), _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(adx(adx(nil)), _x72))))))
mark#(incr(head(s(head(adx(cons(head(tail(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__tail(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(s(cons(head(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(s(cons(a__head(mark(_x91)), _x82)))))))
mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(head(s(a__head(a__adx(adx(nil))))))mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(head(s(head(a__adx(cons(mark(_x71), _x72))))))
mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(head(s(a__head(adx(cons(mark(_x71), _x72))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(0)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(0)))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(head(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(a__head(mark(_x101)))), _x72))))))mark#(incr(adx(adx(cons(incr(s(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(s(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(cons(adx(cons(nats, _x92)), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(cons(a__nats, _x92))), adx(_x51)))))))mark#(incr(head(s(adx(_x51))))) → a__incr#(head(s(a__adx(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(zeros, _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(nats, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__nats, _x102)))))))))
mark#(incr(head(s(head(adx(adx(tail(s(_x91))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(s(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(tail(s(_x91))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(s(mark(_x91)))))))))
mark#(incr(head(s(head(adx(incr(nil))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(nil))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(incr(_x131))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(a__incr(mark(_x131)))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(incr(a__tail(a__tail(mark(_x111)))))))))))mark#(incr(adx(head(zeros)))) → a__incr#(a__adx(a__head(a__zeros)))
mark#(incr(head(s(head(adx(cons(adx(cons(nats, _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(cons(a__adx(a__zeros), _x92)), _x72))))))mark#(incr(head(s(head(adx(cons(adx(incr(zeros)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(a__zeros)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(_x131))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(head(s(mark(_x131)))), _x102)))))))))mark#(incr(head(s(head(adx(s(_x71))))))) → a__incr#(head(s(a__head(a__adx(s(mark(_x71)))))))
mark#(incr(head(s(head(adx(cons(0, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(0, _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(head(s(a__head(a__incr(cons(mark(a__adx(a__adx(nil))), adx(_x51)))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(tail(mark(_x111)))))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(0)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(0)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(tail(cons(cons(mark(_x111), _x112), _x102)))))))))mark#(incr(adx(nats))) → a__incr#(a__adx(a__nats))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(tail(cons(cons(mark(_x111), _x112), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(nats), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(adx(a__nats)), adx(_x51)))))))
mark#(incr(adx(adx(cons(incr(0), _x52))))) → a__incr#(a__adx(adx(cons(incr(0), _x52))))mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(mark(_x71), _x72))))))
mark#(incr(head(s(head(adx(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(mark(_x71), _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(s(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__adx(s(mark(_x101)))), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(s(_x101))), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__adx(s(mark(_x101)))), _x72))))))mark#(incr(adx(cons(_x41, _x42)))) → a__incr#(a__adx(cons(mark(_x41), _x42)))
mark#(incr(head(zeros))) → a__incr#(head(a__zeros))mark#(incr(head(s(head(adx(adx(head(cons(adx(s(_x111)), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(s(mark(_x111))), _x92))))))))
mark#(incr(head(zeros))) → a__incr#(a__head(cons(0, zeros)))mark#(incr(adx(tail(_x41)))) → a__incr#(a__adx(a__tail(mark(_x41))))
mark#(incr(head(s(head(adx(adx(tail(tail(_x91))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(a__tail(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(tail(tail(_x91))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(a__tail(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(nil, _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(nil, _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(nil, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(nil, _x102)))))))))
mark#(incr(adx(adx(cons(incr(0), _x31))))) → a__incr#(a__adx(a__incr(cons(mark(incr(0)), adx(_x31)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(head(_x131))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(a__head(a__head(mark(_x131)))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(tail(cons(a__adx(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(tail(cons(a__adx(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(head(cons(s(s(_x111)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(s(s(mark(_x111))), _x92))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(tail(_x121)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__tail(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(tail(_x121)), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(a__tail(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(cons(_x91, _x71)), mark(_x91)))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__incr(cons(mark(mark(_x91)), adx(_x71))), _x72))))))
mark#(incr(adx(adx(cons(incr(adx(_x71)), _x52))))) → a__incr#(adx(a__adx(cons(incr(a__adx(mark(_x71))), _x52))))mark#(incr(incr(zeros))) → a__incr#(a__incr(a__zeros))
mark#(incr(head(s(head(0))))) → a__incr#(head(s(a__head(0))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(0, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(0, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(tail(cons(mark(_x101), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(0, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(0, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(s(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(s(mark(_x101))))))))))mark#(incr(head(s(head(adx(cons(tail(_x81), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__tail(mark(_x81)), _x72))))))
mark#(incr(head(s(head(s(zeros)))))) → a__incr#(a__head(s(a__head(s(a__zeros)))))mark#(incr(head(incr(_x41)))) → a__incr#(a__head(a__incr(mark(_x41))))
mark#(incr(head(s(head(adx(s(cons(nats, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(s(cons(a__nats, _x82)))))))mark#(incr(head(s(head(s(head(_x71))))))) → a__incr#(a__head(s(a__head(s(a__head(mark(_x71)))))))
mark#(incr(head(s(zeros)))) → a__incr#(a__head(s(a__zeros)))mark#(incr(adx(incr(_x41)))) → a__incr#(a__adx(a__incr(mark(_x41))))
mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__nats))))))mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(a__head(adx(a__incr(cons(0, zeros)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(head(a__adx(a__incr(cons(0, zeros)))))))
mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(head(s(a__head(a__adx(adx(s(a__tail(mark(_x91)))))))))mark#(incr(incr(adx(nil)))) → a__incr#(a__incr(a__adx(nil)))
mark#(incr(head(s(head(s(tail(_x71))))))) → a__incr#(a__head(s(a__head(s(a__tail(mark(_x71)))))))mark#(incr(head(s(head(adx(s(cons(nil, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(s(cons(nil, _x82)))))))
mark#(incr(head(s(adx(tail(_x61)))))) → a__incr#(a__head(s(a__adx(a__tail(mark(_x61))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(adx(_x131))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(a__adx(mark(_x131)))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(adx(a__adx(a__zeros))))))mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(head(a__adx(a__adx(a__zeros))))))
mark#(incr(adx(adx(cons(zeros, _x52))))) → a__incr#(a__adx(adx(cons(a__zeros, _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nats, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__nats, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nats, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__nats, _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(tail(_x111), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__tail(mark(_x111)), _x102)))))))))
mark#(incr(head(s(adx(nats))))) → a__incr#(a__head(s(a__adx(a__nats))))mark#(incr(head(s(head(adx(adx(tail(incr(nil))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(a__incr(nil))))))))
mark#(incr(head(s(head(adx(adx(tail(incr(nil))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(a__incr(nil))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(nil), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(nil), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(adx(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(a__adx(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(a__head(s(a__head(adx(a__incr(mark(_x71)))))))
mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(a__head(s(head(a__adx(a__incr(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x81)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(s(_x91))))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(s(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(s(_x91))))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(s(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(adx(s(a__tail(cons(mark(_x101), _x102)))))))))mark#(incr(head(s(head(adx(adx(tail(incr(s(_x101)))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(a__incr(s(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(tail(incr(s(_x101)))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(a__incr(s(mark(_x101))))))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(head(s(a__head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(zeros))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(s(cons(0, zeros)))), _x102)))))))))
mark#(incr(adx(adx(cons(incr(adx(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__adx(mark(_x71))), _x52))))mark#(incr(head(s(head(incr(adx(incr(_x81)))))))) → a__incr#(head(s(a__head(a__incr(a__adx(a__incr(mark(_x81))))))))
mark#(incr(adx(adx(nil)))) → a__incr#(a__adx(a__adx(nil)))mark#(incr(head(s(head(adx(adx(cons(adx(_x91), _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(a__adx(mark(_x91)), _x82)))))))
mark#(incr(head(s(head(adx(adx(cons(adx(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(a__adx(mark(_x91)), _x82)))))))mark#(incr(head(s(head(adx(adx(tail(cons(_x91, _x92))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(cons(mark(_x91), _x92))))))))
mark#(incr(head(s(head(adx(adx(tail(cons(_x91, _x92))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(cons(mark(_x91), _x92))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(head(_x141)))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(tail(cons(head(a__head(s(a__head(mark(_x141))))), _x102)))))))))
mark#(incr(head(s(head(incr(adx(_x71))))))) → a__incr#(head(s(a__head(a__incr(adx(mark(_x71)))))))mark#(incr(head(s(head(incr(adx(_x71))))))) → a__incr#(head(s(a__head(incr(a__adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(adx(adx(nil))), adx(_x51)))))))mark#(incr(adx(adx(cons(tail(adx(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__adx(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(head(s(head(a__adx(adx(head(cons(adx(nil), _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(head(s(a__head(adx(adx(head(cons(adx(nil), _x92))))))))
mark#(incr(head(s(head(head(_x61)))))) → a__incr#(head(s(a__head(a__head(mark(_x61))))))mark#(incr(head(s(head(adx(cons(adx(zeros), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__zeros), _x72))))))
mark#(incr(head(s(head(adx(adx(head(cons(0, _x92))))))))) → a__incr#(head(s(a__head(adx(adx(head(cons(0, _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(0, _x92))))))))) → a__incr#(head(s(head(a__adx(adx(head(cons(0, _x92))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(cons(_x141, _x142)))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(s(cons(mark(_x141), _x142)))), _x102)))))))))mark#(incr(head(s(head(adx(adx(head(nats)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(a__nats)))))))
mark#(incr(head(s(nats)))) → a__incr#(a__head(s(a__nats)))mark#(incr(adx(adx(cons(incr(zeros), _x52))))) → a__incr#(a__adx(adx(cons(incr(a__zeros), _x52))))
mark#(incr(adx(adx(cons(incr(tail(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(a__tail(mark(_x71))), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(0), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(0), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(cons(tail(_x101), _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(cons(a__tail(mark(_x101)), _x92)), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(nats))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(tail(cons(head(a__head(s(a__nats))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(0), _x92))))))))) → a__incr#(a__head(s(head(a__adx(adx(head(cons(a__adx(0), _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(0), _x92))))))))) → a__incr#(a__head(s(a__head(adx(adx(head(cons(a__adx(0), _x92))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(zeros), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(a__zeros), _x102)))))))))mark#(incr(head(s(head(incr(adx(nil))))))) → a__incr#(head(s(a__head(a__incr(a__adx(nil))))))
mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(adx(adx(cons(a__incr(a__nats), _x52))))mark#(incr(head(s(head(adx(cons(adx(cons(adx(_x101), _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(cons(a__adx(mark(_x101)), _x92)), _x72))))))
mark#(incr(head(s(head(zeros))))) → a__incr#(a__head(s(a__head(a__zeros))))mark#(incr(incr(incr(tail(_x51))))) → a__incr#(a__incr(a__incr(a__tail(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(s(_x91))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(s(mark(_x91)))))))))mark#(incr(head(s(head(adx(cons(adx(cons(s(_x101), _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(cons(s(mark(_x101)), _x92)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(s(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(s(mark(_x111)))))))))))mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(cons(0, zeros)), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(cons(nil, _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(cons(nil, _x92)), _x72))))))mark#(incr(head(s(head(adx(adx(head(s(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(s(mark(_x91)))))))))
mark#(incr(head(s(head(adx(cons(tail(_x81), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__tail(mark(_x81)), _x72))))))mark#(incr(head(_x21))) → a__incr#(head(mark(_x21)))
mark#(incr(head(s(head(s(nats)))))) → a__incr#(a__head(s(a__head(s(a__nats)))))mark#(incr(head(s(head(adx(adx(head(tail(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__tail(mark(_x91)))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(adx(a__adx(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(s(cons(incr(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(s(cons(a__incr(mark(_x91)), _x82)))))))
mark#(incr(head(s(head(adx(s(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(s(a__zeros))))))mark#(incr(adx(adx(cons(nil, _x52))))) → a__incr#(a__adx(adx(cons(nil, _x52))))
mark#(incr(head(s(head(adx(cons(_x71, _x51))))))) → a__incr#(head(s(a__head(a__incr(cons(mark(mark(_x71)), adx(_x51)))))))mark#(incr(incr(adx(0)))) → a__incr#(a__incr(a__adx(0)))
mark#(incr(head(s(head(adx(adx(head(cons(head(s(_x111)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(head(s(mark(_x111))), _x92))))))))mark#(incr(head(s(head(adx(cons(adx(cons(nil, _x92)), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(cons(nil, _x92))), adx(_x51)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(0))), _x81)))))))))) → a__incr#(head(s(head(adx(adx(s(mark(_x81))))))))mark#(incr(adx(adx(cons(tail(nats), _x52))))) → a__incr#(a__adx(adx(cons(tail(a__nats), _x52))))
mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(nil))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(0), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(adx(0), _x92))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(incr(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__incr(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(incr(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__incr(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(cons(nil, _x92)), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(cons(nil, _x92)), _x72))))))mark#(incr(adx(adx(cons(incr(incr(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(a__incr(mark(_x71))), _x52))))
mark#(incr(adx(adx(cons(incr(nil), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(nil), _x52))))mark#(incr(adx(adx(cons(tail(_x61), _x52))))) → a__incr#(a__adx(adx(cons(tail(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(adx(s(head(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__head(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(head(cons(head(_x101), _x92))))))))) → a__incr#(head(s(head(a__adx(adx(head(cons(a__head(mark(_x101)), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(head(_x101), _x92))))))))) → a__incr#(head(s(a__head(adx(adx(head(cons(a__head(mark(_x101)), _x92))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(zeros)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__zeros)))))))))
mark#(incr(head(s(head(adx(adx(head(adx(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(a__adx(mark(_x91)))))))))mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(adx(a__nats), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(adx(a__nats), _x72))))))mark#(incr(head(s(head(adx(adx(head(cons(s(nats), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(s(a__nats), _x92))))))))
mark#(incr(head(s(head(adx(adx(tail(nil)))))))) → a__incr#(head(s(a__head(adx(adx(tail(nil)))))))mark#(incr(head(s(head(adx(adx(tail(nil)))))))) → a__incr#(head(s(head(a__adx(adx(tail(nil)))))))
mark#(incr(head(s(head(adx(cons(head(nil), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(nil), _x72))))))mark#(incr(adx(adx(cons(tail(cons(s(_x81), _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(s(mark(_x81)), _x72)), _x52))))
mark#(incr(head(s(head(adx(adx(head(cons(head(head(_x111)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(a__head(mark(_x111))), _x92))))))))mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(0))))))
mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(head(s(head(adx(adx(a__tail(mark(_x81))))))))mark#(incr(head(s(head(adx(cons(adx(cons(nats, _x92)), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(cons(a__nats, _x92)), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(cons(nil, _x71)), nil))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__incr(cons(mark(nil), adx(_x71))), _x72))))))mark#(incr(head(s(head(adx(incr(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__incr(mark(_x81))))))))
mark#(incr(head(s(head(adx(cons(adx(cons(nil, _x92)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(cons(nil, _x92)), _x72))))))mark#(incr(head(s(head(adx(cons(adx(cons(nil, _x92)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(cons(nil, _x92)), _x72))))))
mark#(incr(adx(head(_x41)))) → a__incr#(a__adx(head(mark(_x41))))mark#(incr(head(s(head(s(incr(_x71))))))) → a__incr#(a__head(s(a__head(s(a__incr(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(a__head(s(head(adx(adx(head(cons(a__adx(nil), _x92))))))))mark#(incr(head(s(head(adx(adx(head(tail(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(a__tail(mark(_x91)))))))))
mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(nats), _x52))))mark#(incr(adx(head(tail(_x51))))) → a__incr#(a__adx(a__head(a__tail(mark(_x51)))))
mark#(incr(head(s(head(incr(head(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__head(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(head(_x111)), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(a__head(mark(_x111))), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(tail(_x101), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__tail(mark(_x101)), _x92))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__zeros, _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__zeros, _x102)))))))))mark#(incr(head(s(head(s(_x61)))))) → a__incr#(a__head(s(head(s(mark(_x61))))))
mark#(incr(head(s(head(adx(adx(s(incr(cons(_x101, _x102)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(cons(mark(_x101), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(adx(nil)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(cons(_x121, _x122)), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(cons(mark(_x121), _x122)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(cons(_x121, _x122)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(cons(mark(_x121), _x122)), _x102)))))))))
mark#(incr(adx(adx(cons(incr(head(_x71)), _x52))))) → a__incr#(adx(a__adx(cons(incr(a__head(mark(_x71))), _x52))))mark#(incr(head(s(0)))) → a__incr#(a__head(s(0)))
mark#(incr(adx(adx(cons(nil, _x52))))) → a__incr#(a__adx(a__adx(cons(nil, _x52))))mark#(incr(adx(adx(cons(incr(zeros), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__zeros), _x52))))
mark#(incr(head(s(head(incr(nil)))))) → a__incr#(head(s(a__head(a__incr(nil)))))mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(nil, _x92))))))))
mark#(incr(head(s(head(adx(cons(head(adx(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__adx(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(0), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(0), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(cons(_x141, _x142))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(cons(mark(_x141), _x142))), _x112), _x102)))))))))mark#(incr(head(s(head(adx(incr(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(cons(mark(_x81), _x82)))))))
mark#(incr(adx(adx(s(_x51))))) → a__incr#(a__adx(a__adx(s(mark(_x51)))))mark#(incr(head(s(head(adx(cons(adx(adx(adx(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__adx(a__adx(mark(_x101)))), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(adx(_x101))), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__adx(a__adx(mark(_x101)))), _x72))))))mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__incr(mark(_x91)))))))))
mark#(incr(adx(adx(cons(incr(_x61), _x52))))) → a__incr#(a__adx(adx(cons(incr(mark(_x61)), _x52))))mark#(incr(head(s(head(adx(adx(head(cons(s(head(_x111)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(s(a__head(mark(_x111))), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(head(cons(_x111, _x112)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(cons(mark(_x111), _x112)), _x92))))))))mark#(incr(adx(adx(cons(incr(_x61), _x52))))) → a__incr#(adx(adx(cons(a__incr(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(incr(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__incr(mark(_x101))))))))))mark#(incr(adx(adx(cons(zeros, _x52))))) → a__incr#(adx(a__adx(cons(a__zeros, _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(adx(s(a__tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(s(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(s(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(nil, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(nil, _x102)))))))))mark#(incr(adx(adx(cons(incr(_x61), _x52))))) → a__incr#(adx(adx(cons(incr(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__adx(mark(_x81))))))))mark#(incr(head(s(head(adx(cons(adx(incr(s(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(s(mark(_x101)))), _x72))))))
mark#(incr(adx(adx(cons(cons(_x61, _x62), _x52))))) → a__incr#(a__adx(a__adx(cons(cons(mark(_x61), _x62), _x52))))mark#(incr(head(s(head(adx(adx(s(cons(_x91, _x92))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(cons(mark(_x91), _x92))))))))
mark#(incr(incr(incr(_x41)))) → a__incr#(incr(a__incr(mark(_x41))))mark#(incr(head(s(head(adx(cons(incr(_x81), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__incr(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x81)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x81)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(a__adx(mark(_x91))), _x72))))))mark#(incr(incr(adx(nats)))) → a__incr#(a__incr(a__adx(a__nats)))
mark#(incr(head(s(head(adx(adx(tail(incr(nats))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(a__incr(a__nats))))))))mark#(incr(head(s(head(adx(adx(tail(incr(nats))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(a__incr(a__nats))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(nats), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(a__nats), _x102)))))))))mark#(incr(head(s(head(adx(incr(head(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(incr(incr(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__incr(mark(_x101))))))))))mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(head(s(a__head(a__adx(adx(cons(mark(_x81), _x82)))))))
mark#(incr(head(s(head(adx(adx(head(head(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__head(mark(_x91)))))))))mark#(incr(head(s(head(adx(cons(adx(adx(s(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(s(mark(_x101)))), _x72))))))
mark#(incr(adx(adx(cons(incr(0), _x52))))) → a__incr#(adx(a__adx(cons(incr(0), _x52))))mark#(incr(head(s(adx(0))))) → a__incr#(a__head(s(a__adx(0))))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(head(s(a__head(a__adx(adx(head(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(adx(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__adx(mark(_x111)))))))))))
mark#(incr(adx(adx(nats)))) → a__incr#(a__adx(a__adx(a__nats)))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(tail(_x141)))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(s(a__tail(mark(_x141))))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(0), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(0), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(0), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(0), _x102)))))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(_x101), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__adx(mark(_x101)), _x92))))))))mark#(incr(incr(0))) → a__incr#(a__incr(0))
mark#(incr(adx(adx(cons(incr(cons(_x71, _x72)), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(cons(mark(_x71), _x72)), _x52))))mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(adx(mark(_x91))), _x72))))))
mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(a__adx(adx(cons(incr(a__nats), _x52))))mark#(incr(head(s(head(incr(adx(nats))))))) → a__incr#(head(s(head(a__incr(a__adx(a__nats))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x81)))))))))) → a__incr#(head(s(head(adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(nats, _x72))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(zeros))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(a__zeros))))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(s(_x111), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(s(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(incr(0))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(0))))))mark#(incr(head(s(head(adx(adx(head(cons(s(adx(_x111)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(s(a__adx(mark(_x111))), _x92))))))))
mark#(incr(head(s(head(adx(cons(adx(cons(nats, _x71)), a__nats))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__incr(cons(mark(a__nats), adx(_x71))), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(incr(_x141)))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(s(a__incr(mark(_x141))))), _x102)))))))))
mark#(incr(incr(adx(head(_x51))))) → a__incr#(a__incr(a__adx(a__head(mark(_x51)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x81)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(zeros)))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(a__zeros)))))))mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(head(a__adx(adx(tail(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(a__head(adx(adx(tail(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(zeros)))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(a__zeros)))))))
mark#(incr(head(s(head(incr(incr(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__incr(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(cons(zeros, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(a__zeros, _x82)))))))
mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__nats))))))mark#(incr(head(s(head(adx(nats)))))) → a__incr#(a__head(s(a__head(a__adx(a__nats)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(0), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(0), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(incr(_x91)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__incr(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(incr(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__incr(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(a__incr(mark(_x91)))))))))
mark#(incr(head(s(head(adx(cons(_x71, _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(mark(_x71)), adx(_x51)))))))mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(a__incr(mark(_x91)))))))))
mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__zeros), _x72))))))mark#(incr(head(s(head(s(adx(_x71))))))) → a__incr#(a__head(s(a__head(s(a__adx(mark(_x71)))))))
mark#(incr(adx(adx(cons(incr(incr(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__incr(mark(_x71))), _x52))))mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(a__head(s(a__head(adx(adx(nil))))))
mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(a__head(s(head(a__adx(adx(nil))))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(head(s(a__head(a__adx(adx(mark(_x71)))))))
mark#(incr(head(s(head(incr(adx(cons(_x81, _x82)))))))) → a__incr#(head(s(a__head(a__incr(a__adx(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(head(_x141)))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(s(a__head(mark(_x141))))), _x102)))))))))
mark#(incr(head(s(head(adx(s(cons(adx(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(s(cons(a__adx(mark(_x91)), _x82)))))))mark#(incr(head(s(head(incr(adx(adx(_x81)))))))) → a__incr#(head(s(a__head(a__incr(a__adx(a__adx(mark(_x81))))))))
mark#(incr(head(s(adx(s(_x61)))))) → a__incr#(a__head(s(a__adx(s(mark(_x61))))))mark#(incr(head(s(head(adx(cons(adx(incr(incr(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(a__incr(mark(_x101)))), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__adx(nil)), _x72))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(cons(_x121, _x122)))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(cons(mark(_x121), _x122)))))))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(cons(_x111, _x112)), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(cons(mark(_x111), _x112)), _x92))))))))mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(head(s(a__head(a__adx(mark(_x61))))))
mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(incr(mark(_x91)))))))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(adx(nil)), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(adx(nil)), _x72))))))mark#(incr(adx(adx(cons(adx(_x61), _x52))))) → a__incr#(a__adx(a__adx(cons(a__adx(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(cons(0, zeros), _x102)))))))))mark#(incr(head(s(head(adx(cons(head(zeros), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__head(a__zeros)), adx(_x51)))))))
mark#(incr(head(s(head(adx(cons(adx(cons(_x91, _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(cons(mark(_x91), _x92)), _x72))))))mark#(incr(head(s(head(adx(adx(tail(s(_x91))))))))) → a__incr#(head(s(a__head(adx(adx(a__tail(s(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(tail(s(_x91))))))))) → a__incr#(head(s(head(a__adx(adx(a__tail(s(mark(_x91)))))))))mark#(incr(adx(adx(cons(tail(cons(0, _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(0, _x72)), _x52))))
mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(adx(a__nats), _x72))))))mark#(incr(adx(adx(cons(zeros, _x52))))) → a__incr#(a__adx(a__adx(cons(cons(0, zeros), _x52))))
mark#(incr(adx(adx(cons(_x51, _x52))))) → a__incr#(adx(a__adx(cons(mark(_x51), _x52))))mark#(incr(head(s(head(adx(adx(head(0)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(0)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(nats)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(a__head(a__nats)), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x51))))))) → a__incr#(a__head(s(head(a__incr(cons(mark(a__adx(a__adx(mark(_x91)))), adx(_x51)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(incr(_x111), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__incr(mark(_x111)), _x102)))))))))mark#(incr(incr(cons(_x41, _x42)))) → a__incr#(a__incr(cons(mark(_x41), _x42)))
mark#(incr(head(s(head(nats))))) → a__incr#(a__head(s(a__head(a__nats))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(tail(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(a__tail(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(incr(0)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__incr(0)))))))mark#(incr(head(s(head(adx(adx(incr(0)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__incr(0)))))))
mark#(incr(adx(adx(cons(tail(nats), _x52))))) → a__incr#(adx(adx(cons(a__tail(a__nats), _x52))))mark#(incr(adx(adx(incr(_x51))))) → a__incr#(a__adx(a__adx(a__incr(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(0))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(tail(cons(head(head(s(0))), _x102)))))))))mark#(incr(head(s(head(adx(incr(0))))))) → a__incr#(head(s(a__head(a__adx(incr(0))))))
mark#(incr(head(s(head(_x51))))) → a__incr#(head(s(head(mark(_x51)))))mark#(incr(X)) → mark#(X)
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(nats))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(a__nats))))))))))mark#(incr(head(s(head(adx(adx(head(cons(cons(_x101, _x102), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(cons(mark(_x101), _x102), _x92))))))))
mark#(incr(head(s(head(adx(cons(adx(_x81), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(mark(_x81)), _x72))))))mark#(incr(head(s(head(adx(cons(adx(_x81), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(s(_x141))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(s(mark(_x141)))), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(tail(adx(_x91))))))))) → a__incr#(head(s(a__head(adx(adx(a__tail(a__adx(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(tail(adx(_x91))))))))) → a__incr#(head(s(head(a__adx(adx(a__tail(a__adx(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(head(mark(_x111)), _x102)))))))))
mark#(incr(adx(adx(cons(tail(zeros), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__zeros), _x52))))mark#(incr(adx(head(adx(_x51))))) → a__incr#(a__adx(a__head(a__adx(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(cons(_x91, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(cons(mark(_x91), _x92))))))))mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__tail(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(incr(s(_x91))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__incr(s(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(incr(s(_x91))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__incr(s(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nil, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(nil, _x112), _x102)))))))))mark#(incr(head(s(head(nats))))) → a__incr#(head(s(a__head(a__nats))))
mark#(incr(incr(incr(nats)))) → a__incr#(a__incr(a__incr(a__nats)))mark#(incr(head(s(head(adx(adx(tail(head(_x91))))))))) → a__incr#(head(s(a__head(adx(adx(a__tail(a__head(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(tail(head(_x91))))))))) → a__incr#(head(s(head(a__adx(adx(a__tail(a__head(mark(_x91)))))))))mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__adx(a__zeros)), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(head(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__head(mark(_x131))), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(nats)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(a__nats)))))))
mark#(incr(head(s(head(adx(cons(adx(adx(tail(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(a__tail(mark(_x101)))), _x72))))))mark#(incr(head(s(head(adx(adx(s(incr(adx(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__adx(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(cons(nats, _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(a__nats, _x82)))))))mark#(incr(head(s(head(adx(adx(cons(nats, _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(a__nats, _x82)))))))
mark#(incr(head(s(head(adx(adx(s(tail(0))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(0))))))))mark#(incr(head(s(head(adx(adx(s(tail(adx(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__adx(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(head(s(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(s(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(head(adx(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__adx(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(incr(nats))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__nats))))))))mark#(incr(head(s(head(adx(cons(head(zeros), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(head(a__zeros), _x72))))))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(a__head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(s(head(adx(adx(incr(cons(_x91, _x92))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__incr(cons(mark(_x91), _x92))))))))
mark#(incr(head(s(head(adx(adx(incr(cons(_x91, _x92))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__incr(cons(mark(_x91), _x92))))))))mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(a__head(s(a__head(adx(adx(a__nats))))))
mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(a__head(s(head(a__adx(adx(a__nats))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(nats), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(a__nats), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(tail(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(a__head(s(head(adx(adx(head(cons(nil, _x92))))))))
mark#(incr(head(s(head(adx(adx(s(0)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(0)))))))mark#(incr(adx(adx(tail(_x51))))) → a__incr#(a__adx(a__adx(a__tail(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(zeros)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(a__zeros)), _x102)))))))))mark#(incr(adx(adx(cons(tail(cons(_x71, _x72)), _x52))))) → a__incr#(a__adx(adx(cons(tail(cons(mark(_x71), _x72)), _x52))))
mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(head(s(a__head(adx(adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(head(s(head(a__adx(adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(tail(incr(tail(_x101)))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(a__incr(a__tail(mark(_x101))))))))))mark#(incr(head(s(head(adx(adx(tail(incr(tail(_x101)))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(a__incr(a__tail(mark(_x101))))))))))
mark#(incr(head(s(head(0))))) → a__incr#(a__head(s(head(0))))mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(a__nats), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(_x121)), _x81)))))))))) → a__incr#(head(s(head(adx(adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(incr(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__tail(mark(_x81))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(incr(_x101))), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__adx(a__incr(mark(_x101)))), _x72))))))mark#(incr(head(s(head(adx(s(nats))))))) → a__incr#(a__head(s(a__head(a__adx(s(a__nats))))))
mark#(incr(adx(adx(cons(tail(nil), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(nil), _x52))))mark#(incr(head(s(head(adx(adx(head(cons(0, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(0, _x92))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(tail(cons(mark(_x101), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(tail(cons(mark(_x101), _x102)))))))))
mark#(incr(incr(adx(s(_x51))))) → a__incr#(a__incr(a__adx(s(mark(_x51)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(nats)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(a__nats)), _x102)))))))))
mark#(incr(adx(adx(cons(tail(cons(cons(_x81, _x82), _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(cons(mark(_x81), _x82), _x72)), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(0)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(0)), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(cons(_x91, _x92)), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(cons(mark(_x91), _x92)), _x72))))))mark#(incr(head(s(head(adx(adx(s(incr(zeros))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__zeros))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(zeros), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__zeros), _x112), _x102)))))))))mark#(incr(adx(adx(cons(tail(cons(nil, _x72)), _x52))))) → a__incr#(a__adx(adx(cons(tail(cons(nil, _x72)), _x52))))
mark#(incr(head(s(head(adx(cons(head(incr(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__incr(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(adx(head(cons(s(_x101), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(s(mark(_x101)), _x92))))))))
mark#(incr(adx(adx(cons(tail(nats), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__adx(a__zeros)), _x52))))mark#(incr(head(s(head(adx(adx(s(nil)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(nil)))))))
mark#(incr(adx(adx(cons(cons(_x61, _x62), _x52))))) → a__incr#(a__adx(adx(cons(cons(mark(_x61), _x62), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(cons(mark(_x111), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(incr(incr(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__incr(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(_x111))))))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(a__incr(a__tail(a__tail(mark(_x111)))))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(_x111))))))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(a__incr(a__tail(a__tail(mark(_x111)))))))))))mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(a__tail(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(a__tail(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__head(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__head(mark(_x111)), _x102)))))))))mark#(incr(adx(adx(cons(incr(_x61), _x31))))) → a__incr#(a__adx(a__incr(cons(mark(incr(mark(_x61))), adx(_x31)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(cons(_x121, _x122), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(cons(mark(_x121), _x122), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(cons(_x121, _x122), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(cons(mark(_x121), _x122), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(adx(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(a__adx(mark(_x91)))))))))mark#(incr(head(s(head(adx(cons(adx(incr(cons(_x101, _x102))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(cons(mark(_x101), _x102))), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(tail(cons(head(a__head(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__head(a__zeros)))))))
mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__head(a__zeros)))))))mark#(incr(head(s(head(_x51))))) → a__incr#(a__head(s(head(mark(_x51)))))
mark#(incr(head(s(adx(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__adx(cons(mark(_x61), _x62)))))mark#(incr(adx(adx(cons(incr(s(_x71)), _x52))))) → a__incr#(adx(a__adx(cons(incr(s(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(head(cons(s(0), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(s(0), _x92))))))))mark#(incr(head(s(head(adx(cons(adx(adx(0)), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__adx(0)), _x72))))))
mark#(incr(head(s(head(adx(adx(head(cons(head(s(0)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(0)), _x92))))))))mark#(incr(head(s(head(adx(adx(incr(tail(_x91))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__incr(a__tail(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(incr(tail(_x91))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__incr(a__tail(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(head(cons(head(s(_x111)), _x92))))))))) → a__incr#(head(s(head(a__adx(adx(head(cons(a__head(s(mark(_x111))), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(head(s(_x111)), _x92))))))))) → a__incr#(head(s(a__head(adx(adx(head(cons(a__head(s(mark(_x111))), _x92))))))))mark#(incr(head(s(head(adx(adx(s(nil)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(nil)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(s(_x141)))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(s(s(mark(_x141))))), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(cons(_x91, _x92)), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(cons(mark(_x91), _x92))), adx(_x51)))))))
mark#(incr(cons(_x21, _x22))) → a__incr#(cons(mark(_x21), _x22))mark#(incr(adx(head(head(_x51))))) → a__incr#(a__adx(a__head(a__head(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(incr(nats)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__incr(a__nats)))))))mark#(incr(head(s(head(adx(adx(incr(nats)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__incr(a__nats)))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(head(s(a__head(adx(adx(head(cons(nil, _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(head(s(head(a__adx(adx(head(cons(nil, _x92))))))))
mark#(incr(head(s(head(adx(s(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(s(a__adx(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(head(s(a__head(adx(adx(a__zeros))))))
mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(head(s(head(a__adx(adx(a__zeros))))))mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(head(s(a__head(adx(adx(a__adx(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(head(s(head(a__adx(adx(a__adx(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(head(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(cons(nats, _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(cons(a__nats, _x92)), _x72))))))mark#(incr(head(s(head(adx(adx(head(cons(head(s(zeros)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__zeros)), _x92))))))))
mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(mark(_x81), _x82)))))))
mark#(incr(head(s(head(adx(s(cons(cons(_x91, _x92), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(s(cons(cons(mark(_x91), _x92), _x82)))))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(adx(a__adx(nil))), adx(_x51)))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(a__incr(a__tail(mark(_x101))))))))))mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__nats), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__nats), _x72))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(a__incr(a__tail(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(head(cons(head(tail(_x111)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(a__tail(mark(_x111))), _x92))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(s(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(s(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__nats), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(adx(s(a__tail(cons(cons(mark(_x111), _x112), _x102)))))))))
mark#(incr(head(s(head(tail(_x61)))))) → a__incr#(head(s(a__head(a__tail(mark(_x61))))))mark#(incr(head(s(head(adx(adx(s(incr(head(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__head(mark(_x101))))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(zeros)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(a__zeros)), _x72))))))mark#(incr(head(s(head(adx(adx(cons(s(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(s(mark(_x91)), _x82)))))))
mark#(incr(head(s(head(adx(adx(cons(s(_x91), _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(s(mark(_x91)), _x82)))))))mark#(incr(adx(adx(cons(tail(cons(adx(_x81), _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(a__adx(mark(_x81)), _x72)), _x52))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(head(s(a__head(a__incr(cons(mark(adx(adx(nil))), adx(_x51)))))))mark#(incr(head(s(head(adx(cons(head(zeros), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__head(a__zeros), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__adx(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(incr(adx(0))))))) → a__incr#(head(s(a__head(a__incr(a__adx(0))))))
mark#(incr(incr(incr(_x41)))) → a__incr#(a__incr(incr(mark(_x41))))mark#(incr(head(s(head(adx(adx(head(cons(head(s(head(_x121))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__head(mark(_x121)))), _x92))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(zeros)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__adx(a__zeros)), _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(zeros)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__adx(a__zeros)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(cons(_x121, _x122)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(cons(mark(_x121), _x122)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(head(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__head(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(incr(_x91)), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(a__incr(mark(_x91)))), adx(_x51)))))))mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(a__adx(a__zeros)), _x72))))))
mark#(incr(head(s(head(adx(adx(cons(adx(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(a__adx(mark(_x91)), _x82)))))))mark#(incr(head(0))) → a__incr#(a__head(0))
mark#(incr(adx(adx(cons(tail(cons(nil, _x51)), nil))))) → a__incr#(a__adx(adx(cons(mark(_x51), _x52))))mark#(incr(head(s(head(adx(adx(s(adx(_x91))))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(a__adx(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(adx(_x91))))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(a__adx(mark(_x91)))))))))mark#(incr(incr(adx(zeros)))) → a__incr#(a__incr(a__adx(a__zeros)))
mark#(incr(head(s(head(adx(cons(nil, _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(nil, _x72))))))mark#(incr(adx(adx(cons(incr(nats), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(a__nats), _x52))))
mark#(incr(head(s(head(adx(adx(s(incr(0))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(0))))))))mark#(incr(head(s(head(adx(cons(head(_x81), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(head(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(head(s(a__head(adx(adx(a__incr(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(head(s(head(a__adx(adx(a__incr(mark(_x81))))))))
mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(a__zeros), _x72))))))mark#(incr(head(s(head(adx(adx(head(cons(head(s(s(_x121))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(s(mark(_x121)))), _x92))))))))
mark#(incr(adx(adx(cons(incr(s(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(s(mark(_x71))), _x52))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(adx(adx(head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(head(a__adx(adx(head(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(head(cons(head(nats), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(a__nats), _x92))))))))
mark#(incr(head(s(head(adx(adx(cons(tail(_x91), _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(a__tail(mark(_x91)), _x82)))))))mark#(incr(head(s(head(adx(adx(cons(tail(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(a__tail(mark(_x91)), _x82)))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(a__incr(a__tail(mark(_x101))))))))))mark#(incr(head(s(head(adx(adx(tail(0)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(0)))))))
mark#(incr(head(s(head(adx(adx(tail(0)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(0)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(tail(a__incr(mark(_x131))), _x112), _x102)))))))))
mark#(incr(head(s(head(incr(adx(s(_x81)))))))) → a__incr#(head(s(a__head(a__incr(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(incr(cons(_x71, _x72))))))) → a__incr#(head(s(a__head(a__incr(cons(mark(_x71), _x72))))))
mark#(incr(head(s(tail(_x51))))) → a__incr#(a__head(s(a__tail(mark(_x51)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(nil), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(nil), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(s(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(s(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(nil), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(nil), _x102)))))))))
mark#(incr(s(_x21))) → a__incr#(s(mark(_x21)))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(a__head(adx(adx(s(a__tail(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(head(a__adx(adx(s(a__tail(cons(mark(_x101), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(cons(nats, _x92)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(cons(a__nats, _x92)), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(cons(nats, _x92)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(cons(a__nats, _x92)), _x72))))))mark#(incr(adx(adx(cons(incr(incr(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(a__incr(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(a__head(s(a__head(a__incr(mark(_x61))))))
mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(a__head(s(a__head(cons(mark(_x61), _x62)))))mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(a__zeros)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(head(_x91))))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(a__head(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(head(_x91))))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(a__head(mark(_x91)))))))))
mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__zeros), _x72))))))mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__zeros), _x72))))))
mark#(incr(adx(adx(cons(tail(0), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(0), _x52))))mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(head(s(a__head(adx(a__incr(mark(_x71)))))))
mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(head(s(head(a__adx(a__incr(mark(_x71)))))))mark#(incr(head(s(head(adx(cons(adx(adx(head(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__adx(a__head(mark(_x101)))), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(head(_x101))), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__adx(a__head(mark(_x101)))), _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(adx(_x101))), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__adx(a__adx(mark(_x101)))), _x72))))))
mark#(incr(head(s(head(adx(s(tail(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(s(a__tail(mark(_x81))))))))mark#(incr(head(s(head(adx(cons(zeros, _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(cons(0, zeros), _x72))))))
mark#(incr(head(s(head(adx(adx(head(cons(head(zeros), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(a__zeros), _x92))))))))mark#(incr(adx(adx(cons(incr(adx(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(a__adx(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(s(cons(s(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(s(cons(s(mark(_x91)), _x82)))))))mark#(incr(head(s(head(adx(cons(adx(adx(s(_x101))), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__adx(s(mark(_x101)))), _x72))))))
mark#(incr(head(s(head(adx(adx(head(cons(head(s(nil)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(nil)), _x92))))))))mark#(incr(head(s(head(adx(adx(tail(incr(_x91))))))))) → a__incr#(a__head(s(a__head(adx(adx(tail(a__incr(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(tail(incr(_x91))))))))) → a__incr#(a__head(s(head(a__adx(adx(tail(a__incr(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(nil))))))) → a__incr#(head(s(head(adx(adx(nil))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(incr(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__incr(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(incr(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__incr(mark(_x111)), _x102)))))))))
mark#(incr(incr(incr(adx(_x51))))) → a__incr#(a__incr(a__incr(a__adx(mark(_x51)))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(head(_x121)))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(a__head(mark(_x121))))))))))))
mark#(incr(adx(adx(cons(incr(_x61), _x31))))) → a__incr#(a__adx(a__incr(cons(mark(a__incr(mark(_x61))), adx(_x31)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(s(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(s(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(s(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(s(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(zeros, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__zeros, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(head(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__head(mark(_x101))))))))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(head(s(head(adx(adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(zeros)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__zeros)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(0), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__adx(0), _x92))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(adx(a__adx(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(adx(a__adx(mark(_x91))), _x72))))))
mark#(incr(adx(adx(cons(s(_x61), _x52))))) → a__incr#(a__adx(adx(cons(s(mark(_x61)), _x52))))mark#(incr(adx(adx(cons(incr(_x61), _x52))))) → a__incr#(adx(a__adx(cons(a__incr(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(adx(head(cons(incr(_x101), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__incr(mark(_x101)), _x92))))))))mark#(incr(head(s(head(adx(cons(adx(adx(0)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__adx(0)), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(0)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__adx(0)), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(s(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(s(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(incr(adx(head(_x81)))))))) → a__incr#(head(s(a__head(a__incr(a__adx(a__head(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(tail(zeros)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(a__zeros)))))))
mark#(incr(head(s(head(adx(adx(tail(zeros)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(a__zeros)))))))mark#(incr(head(s(head(adx(adx(cons(head(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(a__head(mark(_x91)), _x82)))))))
mark#(incr(head(s(head(nil))))) → a__incr#(head(s(a__head(nil))))mark#(incr(adx(adx(cons(nats, _x52))))) → a__incr#(a__adx(a__adx(cons(a__nats, _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(nil)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(a__head(nil)), _x102)))))))))mark#(incr(zeros)) → a__incr#(a__zeros)
mark#(incr(head(s(head(adx(adx(s(tail(cons(nats, _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__nats, _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(nats, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__nats, _x102)))))))))
mark#(incr(head(s(head(adx(adx(tail(nats)))))))) → a__incr#(head(s(a__head(adx(adx(a__tail(a__nats)))))))mark#(incr(head(s(head(adx(adx(tail(nats)))))))) → a__incr#(head(s(head(a__adx(adx(a__tail(a__nats)))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(a__head(s(a__head(incr(cons(mark(a__adx(a__adx(nil))), adx(_x51)))))))mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(zeros)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(incr(_x131))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(a__head(a__incr(mark(_x131)))), _x102)))))))))mark#(incr(adx(adx(cons(incr(nil), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(nil), _x52))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__adx(nil), _x92))))))))mark#(incr(head(s(adx(incr(_x61)))))) → a__incr#(a__head(s(a__adx(a__incr(mark(_x61))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(adx(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(a__adx(mark(_x121))), _x102)))))))))mark#(incr(incr(adx(incr(_x51))))) → a__incr#(a__incr(a__adx(a__incr(mark(_x51)))))
mark#(incr(adx(adx(cons(incr(cons(_x71, _x72)), _x52))))) → a__incr#(adx(a__adx(cons(incr(cons(mark(_x71), _x72)), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(0))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(head(s(0))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__zeros)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(incr(_x141)))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(tail(cons(head(a__head(s(a__incr(mark(_x141))))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(nats), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(a__nats), _x92))))))))mark#(incr(head(s(head(s(cons(_x71, _x72))))))) → a__incr#(a__head(s(a__head(s(cons(mark(_x71), _x72))))))
mark#(incr(head(s(head(adx(cons(head(_x81), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__head(mark(_x81))), adx(_x51)))))))mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(head(s(a__head(adx(adx(a__nats))))))
mark#(incr(head(s(head(adx(adx(nats))))))) → a__incr#(head(s(head(a__adx(adx(a__nats))))))mark#(incr(head(s(head(adx(adx(tail(incr(incr(_x101)))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(a__incr(a__incr(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(tail(incr(incr(_x101)))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(a__incr(a__incr(mark(_x101))))))))))mark#(incr(head(s(head(adx(incr(cons(_x81, _x82)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(cons(mark(_x81), _x82)))))))
mark#(incr(head(s(head(adx(adx(head(nil)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(nil)))))))mark#(incr(adx(adx(cons(tail(cons(_x71, _x51)), mark(_x71)))))) → a__incr#(a__adx(adx(cons(mark(_x51), _x52))))
mark#(incr(head(s(head(adx(cons(adx(head(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__head(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(incr(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__incr(mark(_x111)))))))))))
mark#(incr(head(s(head(incr(adx(nats))))))) → a__incr#(head(s(a__head(incr(a__adx(a__nats))))))mark#(incr(head(s(head(incr(adx(nats))))))) → a__incr#(head(s(a__head(a__incr(adx(a__nats))))))
mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(a__head(s(head(adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(s(nil))))))) → a__incr#(a__head(s(a__head(a__adx(s(nil))))))
mark#(incr(head(s(head(adx(cons(adx(incr(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(a__incr(mark(_x91))), _x72))))))mark#(incr(adx(adx(cons(tail(cons(nats, _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(a__nats, _x72)), _x52))))
mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(head(adx(adx(a__incr(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(nats)))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__nats)))))))
mark#(incr(incr(adx(cons(_x51, _x52))))) → a__incr#(a__incr(a__adx(cons(mark(_x51), _x52))))mark#(incr(head(s(head(adx(incr(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(adx(_x131))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(a__head(a__adx(mark(_x131)))), _x102)))))))))mark#(incr(adx(adx(cons(incr(cons(_x71, _x72)), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(cons(mark(_x71), _x72)), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__tail(mark(_x91)))))))))mark#(incr(adx(adx(cons(tail(cons(head(_x81), _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(a__head(mark(_x81)), _x72)), _x52))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(head(s(head(a__adx(adx(head(cons(a__adx(nil), _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(head(s(a__head(adx(adx(head(cons(a__adx(nil), _x92))))))))
mark#(incr(head(s(head(adx(incr(nats))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__nats))))))mark#(incr(head(s(head(adx(adx(s(zeros)))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__zeros)))))))
mark#(incr(incr(incr(zeros)))) → a__incr#(a__incr(a__incr(a__zeros)))mark#(incr(head(s(head(adx(cons(adx(adx(head(_x101))), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__adx(a__head(mark(_x101)))), _x72))))))
mark#(incr(head(s(head(adx(adx(s(nats)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__nats)))))))mark#(incr(head(s(head(adx(cons(adx(adx(tail(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__adx(a__tail(mark(_x101)))), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(tail(_x101))), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__adx(a__tail(mark(_x101)))), _x72))))))mark#(incr(adx(head(_x41)))) → a__incr#(adx(a__head(mark(_x41))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(adx(_x141))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__adx(mark(_x141)))), _x112), _x102)))))))))mark#(incr(head(s(head(adx(s(_x71))))))) → a__incr#(a__head(s(a__head(adx(s(mark(_x71)))))))
mark#(incr(head(s(head(adx(s(_x71))))))) → a__incr#(a__head(s(head(a__adx(s(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(tail(head(_x91))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(a__head(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(tail(head(_x91))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(a__head(mark(_x91)))))))))mark#(incr(incr(head(_x41)))) → a__incr#(a__incr(a__head(mark(_x41))))
mark#(incr(head(s(head(adx(cons(nats, _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__nats), adx(_x51)))))))mark#(incr(head(s(head(adx(adx(tail(incr(cons(_x101, _x102)))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(a__incr(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(adx(tail(incr(cons(_x101, _x102)))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(a__incr(cons(mark(_x101), _x102)))))))))mark#(incr(head(s(adx(head(_x61)))))) → a__incr#(a__head(s(a__adx(a__head(mark(_x61))))))
mark#(incr(adx(adx(cons(head(_x61), _x52))))) → a__incr#(a__adx(a__adx(cons(a__head(mark(_x61)), _x52))))mark#(incr(head(s(head(adx(s(cons(0, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(s(cons(0, _x82)))))))
mark#(incr(head(tail(_x41)))) → a__incr#(a__head(a__tail(mark(_x41))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(adx(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__adx(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(zeros)))))) → a__incr#(a__head(s(a__head(a__adx(a__zeros)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(adx(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__adx(mark(_x121)), _x112), _x102)))))))))
mark#(incr(adx(head(nil)))) → a__incr#(a__adx(a__head(nil)))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(0))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(0))))))))))
mark#(incr(head(s(head(adx(s(cons(zeros, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(s(cons(a__zeros, _x82)))))))mark#(incr(head(adx(_x41)))) → a__incr#(a__head(a__adx(mark(_x41))))
mark#(incr(head(s(head(adx(cons(adx(adx(incr(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(a__incr(mark(_x101)))), _x72))))))mark#(incr(head(s(head(adx(cons(adx(_x81), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(0)))))) → a__incr#(a__head(s(a__head(a__adx(0)))))mark#(incr(head(s(head(adx(adx(s(adx(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__adx(mark(_x91)))))))))
mark#(incr(head(s(head(adx(cons(adx(cons(cons(_x101, _x102), _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(cons(cons(mark(_x101), _x102), _x92)), _x72))))))mark#(incr(head(s(head(adx(cons(incr(_x81), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__incr(mark(_x81)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(nats), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(a__nats), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(nats), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__nats), _x102)))))))))
mark#(incr(head(s(head(adx(cons(head(_x81), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__head(mark(_x81)), _x72))))))mark#(incr(head(s(head(adx(adx(head(cons(nats, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__nats, _x92))))))))
mark#(incr(head(s(head(adx(adx(cons(tail(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(a__tail(mark(_x91)), _x82)))))))mark#(incr(head(s(head(adx(adx(tail(nats)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(a__nats)))))))
mark#(incr(head(s(head(adx(adx(tail(nats)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(a__nats)))))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(a__head(adx(a__adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(head(a__adx(a__adx(mark(_x71)))))))mark#(incr(adx(adx(cons(incr(head(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__head(mark(_x71))), _x52))))
mark#(incr(head(s(adx(_x51))))) → a__incr#(a__head(s(adx(mark(_x51)))))mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(nats), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(head(_x131))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(a__head(mark(_x131)))), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(nil)))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(nil)))))))
mark#(incr(head(s(head(adx(adx(s(nil)))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(nil)))))))mark#(incr(adx(adx(cons(incr(zeros), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(a__zeros), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(nil))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(s(nil))), _x102)))))))))mark#(incr(head(s(head(adx(adx(head(head(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(a__head(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(s(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(s(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(_x81), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(mark(_x81))), adx(_x51)))))))
mark#(incr(tail(_x21))) → a__incr#(a__tail(mark(_x21)))mark#(incr(head(s(head(adx(adx(tail(nil)))))))) → a__incr#(head(s(head(adx(adx(a__tail(nil)))))))
mark#(incr(adx(adx(cons(_x51, _x52))))) → a__incr#(adx(adx(cons(mark(_x51), _x52))))mark#(incr(head(s(head(incr(adx(zeros))))))) → a__incr#(head(s(a__head(a__incr(a__adx(a__zeros))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))mark#(incr(adx(adx(cons(adx(_x61), _x52))))) → a__incr#(a__adx(adx(cons(a__adx(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(adx(tail(incr(zeros))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(a__incr(a__zeros))))))))mark#(incr(head(s(head(adx(adx(tail(incr(zeros))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(a__incr(a__zeros))))))))
mark#(incr(head(s(head(adx(adx(head(incr(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(a__incr(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(head(_x91))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__head(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(incr(_x141))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__incr(mark(_x141)))), _x112), _x102)))))))))mark#(incr(head(s(head(adx(incr(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(incr(mark(_x71)))))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(head(s(head(a__incr(mark(_x61))))))mark#(incr(head(s(s(_x51))))) → a__incr#(a__head(s(s(mark(_x51)))))
mark#(incr(head(s(head(adx(s(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(s(a__head(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(tail(_x141)))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(tail(cons(head(a__head(s(a__tail(mark(_x141))))), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(a__head(s(head(a__incr(cons(mark(a__adx(a__adx(nil))), adx(_x51)))))))mark#(incr(incr(nats))) → a__incr#(a__incr(a__adx(a__zeros)))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(adx(nil))), adx(_x51)))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(_x111))))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(mark(_x111)))))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(cons(_x101, _x102))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(cons(mark(_x101), _x102))), _x72))))))mark#(incr(head(s(head(adx(head(_x71))))))) → a__incr#(a__head(s(a__head(a__adx(a__head(mark(_x71)))))))
mark#(incr(head(s(head(adx(incr(tail(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__tail(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(adx(s(a__tail(cons(cons(mark(_x111), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(adx(s(a__tail(cons(cons(mark(_x111), _x112), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(adx(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(nil), _x72))))))mark#(incr(head(s(head(adx(adx(cons(nil, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(nil, _x82)))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(_x101), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(adx(mark(_x101)), _x92))))))))mark#(incr(adx(adx(cons(tail(_x61), _x52))))) → a__incr#(adx(adx(cons(a__tail(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(cons(adx(cons(_x91, _x92)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(cons(mark(_x91), _x92)), _x72))))))mark#(incr(head(s(head(adx(cons(adx(cons(_x91, _x92)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(cons(mark(_x91), _x92)), _x72))))))
mark#(incr(head(s(adx(nil))))) → a__incr#(a__head(s(a__adx(nil))))mark#(incr(head(s(adx(adx(_x61)))))) → a__incr#(a__head(s(a__adx(a__adx(mark(_x61))))))
mark#(incr(head(s(head(adx(adx(head(cons(head(s(cons(_x121, _x122))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(cons(mark(_x121), _x122))), _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(nil, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(nil, _x92))))))))
mark#(incr(adx(adx(cons(incr(tail(_x71)), _x52))))) → a__incr#(adx(a__adx(cons(incr(a__tail(mark(_x71))), _x52))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(nil))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(nil))))))))))
mark#(incr(head(s(head(adx(cons(adx(cons(zeros, _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(cons(a__zeros, _x92)), _x72))))))mark#(incr(head(s(head(adx(adx(s(0)))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(0)))))))
mark#(incr(head(s(head(adx(adx(s(0)))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(0)))))))mark#(incr(head(s(head(adx(adx(head(cons(head(adx(_x111)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(a__adx(mark(_x111))), _x92))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(adx(s(a__tail(cons(a__adx(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(adx(s(a__tail(cons(a__adx(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(incr(head(_x91))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__incr(a__head(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(incr(head(_x91))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__incr(a__head(mark(_x91)))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(a__adx(mark(_x91)))), adx(_x51)))))))mark#(incr(head(s(head(adx(cons(adx(nil), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(nil), _x72))))))
mark#(incr(head(s(head(adx(adx(s(cons(_x91, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(cons(mark(_x91), _x92))))))))mark#(incr(incr(nats))) → a__incr#(incr(a__nats))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))
mark#(incr(adx(adx(cons(incr(zeros), _x31))))) → a__incr#(a__adx(a__incr(cons(mark(incr(a__zeros)), adx(_x31)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(head(_x141))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__head(mark(_x141)))), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(nats)))))))) → a__incr#(a__head(s(head(a__adx(a__adx(s(a__nats)))))))mark#(incr(adx(adx(cons(incr(adx(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(a__adx(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(s(nats)))))))) → a__incr#(a__head(s(a__head(adx(a__adx(s(a__nats)))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(incr(_x111)), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(a__incr(mark(_x111))), _x92))))))))
mark#(incr(head(s(head(adx(cons(adx(cons(head(_x101), _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(cons(a__head(mark(_x101)), _x92)), _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(a__head(s(head(adx(cons(a__adx(a__adx(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(cons(nil, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(nil, _x72))))))mark#(incr(head(s(head(adx(cons(zeros, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__zeros, _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(0, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(0, _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(adx(_x141)))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(tail(cons(head(a__head(s(a__adx(mark(_x141))))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))) → a__incr#(a__head(s(head(adx(adx(head(cons(adx(nil), _x92))))))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__adx(nil)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(tail(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__tail(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(tail(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__tail(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__adx(nil)), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(nil, _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(nil, _x102)))))))))
mark#(incr(head(s(nil)))) → a__incr#(head(s(nil)))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x81)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x81)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__nats, _x72))))))
mark#(incr(incr(incr(cons(_x51, _x52))))) → a__incr#(a__incr(a__incr(cons(mark(_x51), _x52))))mark#(incr(adx(adx(cons(incr(cons(_x71, _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(cons(mark(_x71), _x72)), _x52))))
mark#(incr(head(s(head(adx(adx(head(cons(head(0), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(0), _x92))))))))mark#(incr(adx(adx(cons(tail(cons(zeros, _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(a__zeros, _x72)), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(mark(_x131))), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(tail(_x131))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(a__tail(mark(_x131)))), _x102)))))))))
mark#(incr(adx(nil))) → a__incr#(a__adx(nil))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(nil), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(nil), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(cons(_x111, _x112))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(cons(mark(_x111), _x112))))))))))mark#(incr(head(s(adx(zeros))))) → a__incr#(a__head(s(a__adx(a__zeros))))
mark#(incr(head(s(head(adx(adx(s(tail(zeros))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__zeros))))))))mark#(incr(head(s(head(adx(incr(adx(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__adx(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(nats)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__nats)))))))))
mark#(incr(head(s(head(adx(cons(head(zeros), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(zeros), _x72))))))mark#(incr(adx(adx(zeros)))) → a__incr#(a__adx(a__adx(a__zeros)))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x81)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x81)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(zeros))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(tail(cons(head(a__head(s(a__zeros))), _x102)))))))))mark#(incr(adx(adx(cons(tail(head(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__head(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(adx(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(adx(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(adx(_x111)), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(a__adx(mark(_x111))), _x92))))))))mark#(incr(head(s(head(adx(cons(adx(incr(nil)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(nil)), _x72))))))
mark#(incr(head(s(head(adx(cons(head(nats), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__nats), _x72))))))mark#(incr(incr(adx(_x41)))) → a__incr#(incr(a__adx(mark(_x41))))
mark#(incr(incr(adx(_x41)))) → a__incr#(a__incr(adx(mark(_x41))))mark#(incr(adx(adx(cons(tail(tail(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__tail(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(head(a__adx(adx(a__zeros))))))mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(adx(adx(a__zeros))))))
mark#(incr(head(s(head(adx(adx(head(cons(nil, _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(nil, _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(s(tail(_x111)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(s(a__tail(mark(_x111))), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(_x91, _x92))))))))) → a__incr#(a__head(s(head(a__adx(adx(head(cons(mark(_x91), _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(_x91, _x92))))))))) → a__incr#(a__head(s(a__head(adx(adx(head(cons(mark(_x91), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(cons(_x101, _x102), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(cons(mark(_x101), _x102), _x92))))))))mark#(incr(incr(incr(nil)))) → a__incr#(a__incr(a__incr(nil)))
mark#(incr(adx(adx(cons(_x51, _x31))))) → a__incr#(a__adx(a__incr(cons(mark(mark(_x51)), adx(_x31)))))mark#(incr(head(s(head(adx(adx(s(s(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(s(mark(_x91)))))))))
mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(a__head(a__adx(a__incr(cons(0, zeros)))))))mark#(incr(head(s(head(adx(adx(cons(nats, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(a__nats, _x82)))))))
mark#(incr(head(s(head(adx(cons(cons(_x81, _x82), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(cons(mark(_x81), _x82), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(cons(_x141, _x142)))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(tail(cons(head(a__head(s(cons(mark(_x141), _x142)))), _x102)))))))))
mark#(incr(head(s(head(adx(cons(s(_x81), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(s(mark(_x81)), _x72))))))mark#(incr(head(nats))) → a__incr#(head(a__nats))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(_x131))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(tail(cons(head(head(s(mark(_x131)))), _x102)))))))))mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(a__head(adx(adx(incr(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(head(a__adx(adx(incr(mark(_x81))))))))mark#(incr(adx(adx(cons(incr(0), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(0), _x52))))
mark#(incr(adx(adx(_x41)))) → a__incr#(a__adx(adx(mark(_x41))))mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__zeros))))))
mark#(incr(adx(adx(adx(_x51))))) → a__incr#(a__adx(a__adx(a__adx(mark(_x51)))))mark#(incr(adx(adx(cons(incr(nil), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(nil), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(incr(_x121)), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(a__incr(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(incr(_x121)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__incr(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nil, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(nil, _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(nil, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(nil, _x112), _x102)))))))))
mark#(incr(adx(adx(_x41)))) → a__incr#(adx(a__adx(mark(_x41))))mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(a__head(s(a__head(a__adx(adx(0))))))
mark#(incr(head(s(head(head(_x61)))))) → a__incr#(a__head(s(a__head(a__head(mark(_x61))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(nats)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__nats)), _x112), _x102)))))))))
mark#(incr(incr(incr(s(_x51))))) → a__incr#(a__incr(a__incr(s(mark(_x51)))))mark#(incr(head(s(head(s(nil)))))) → a__incr#(a__head(s(a__head(s(nil)))))
mark#(incr(incr(tail(_x41)))) → a__incr#(a__incr(a__tail(mark(_x41))))mark#(incr(head(s(head(adx(adx(s(tail(tail(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__tail(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(s(head(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(a__head(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(tail(cons(cons(a__tail(a__incr(mark(_x131))), _x112), _x102)))))))))
mark#(incr(incr(incr(0)))) → a__incr#(a__incr(a__incr(0)))mark#(incr(adx(adx(cons(incr(nil), _x52))))) → a__incr#(adx(a__adx(cons(incr(nil), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(cons(_x131, _x132)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(cons(mark(_x131), _x132)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(head(cons(_x91, _x92))))))))) → a__incr#(head(s(a__head(adx(adx(head(cons(mark(_x91), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(_x91, _x92))))))))) → a__incr#(head(s(head(a__adx(adx(head(cons(mark(_x91), _x92))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(_x131))), _x81)))))))))) → a__incr#(head(s(head(adx(adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(nil), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(nil), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(s(_x141)))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(tail(cons(head(a__head(s(s(mark(_x141))))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(cons(0, _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(0, _x82)))))))mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(head(adx(a__incr(a__zeros))))))
mark#(incr(head(s(head(adx(adx(tail(zeros)))))))) → a__incr#(head(s(head(a__adx(adx(a__tail(a__zeros)))))))mark#(incr(head(s(head(adx(adx(tail(zeros)))))))) → a__incr#(head(s(a__head(adx(adx(a__tail(a__zeros)))))))
mark#(incr(head(s(head(adx(cons(head(zeros), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__head(a__zeros), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(cons(_x131, _x132))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(a__head(cons(mark(_x131), _x132))), _x102)))))))))
mark#(incr(head(s(head(adx(cons(head(zeros), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__head(a__zeros), _x72))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(head(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__head(mark(_x111)))))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(a__head(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(tail(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(adx(head(nats)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__nats)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__zeros, _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(incr(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(a__incr(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(adx(cons(0, _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(0, _x72))))))
mark#(incr(adx(head(nats)))) → a__incr#(a__adx(a__head(a__nats)))mark#(incr(head(s(head(adx(adx(head(cons(s(zeros), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(s(a__zeros), _x92))))))))
mark#(incr(head(s(head(adx(adx(s(0)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(0)))))))mark#(incr(head(s(head(adx(cons(adx(cons(0, _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(cons(0, _x92)), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(tail(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__tail(mark(_x91))), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(head(_x121), _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__head(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(head(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__head(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(incr(_x91)), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__incr(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(_x131))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(a__head(s(mark(_x131)))), _x102)))))))))mark#(incr(head(s(head(zeros))))) → a__incr#(head(s(a__head(a__zeros))))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__head(mark(_x81))))))))mark#(incr(head(s(head(s(s(_x71))))))) → a__incr#(a__head(s(a__head(s(s(mark(_x71)))))))
mark#(incr(head(s(head(incr(0)))))) → a__incr#(head(s(a__head(a__incr(0)))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(adx(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__adx(mark(_x131))), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(cons(zeros, _x72))))))) → a__incr#(head(s(head(a__adx(cons(a__zeros, _x72))))))mark#(incr(head(s(head(adx(cons(zeros, _x72))))))) → a__incr#(head(s(a__head(adx(cons(a__zeros, _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(nats), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__nats), _x112), _x102)))))))))mark#(incr(adx(adx(head(_x51))))) → a__incr#(a__adx(a__adx(a__head(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(0)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(a__head(0)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(nil)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(nil)))))))))
mark#(incr(head(s(head(incr(s(_x71))))))) → a__incr#(head(s(a__head(a__incr(s(mark(_x71)))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(incr(_x121)))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(a__incr(mark(_x121))))))))))))
mark#(incr(head(s(head(adx(adx(cons(_x81, _x82)))))))) → a__incr#(a__head(s(head(adx(adx(cons(mark(_x81), _x82)))))))mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(a__head(s(head(adx(adx(a__tail(mark(_x81))))))))
mark#(incr(head(s(head(s(_x61)))))) → a__incr#(head(s(a__head(s(mark(_x61))))))mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__adx(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(adx(_x81)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__adx(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(cons(incr(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(a__incr(mark(_x91)), _x82)))))))
mark#(incr(head(s(head(adx(adx(head(cons(zeros, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__zeros, _x92))))))))mark#(incr(head(s(head(adx(adx(tail(incr(0))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(a__incr(0))))))))
mark#(incr(head(s(head(adx(adx(tail(incr(0))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(a__incr(0))))))))mark#(incr(head(s(head(adx(adx(incr(_x81)))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(a__incr(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(head(cons(s(incr(_x111)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(s(a__incr(mark(_x111))), _x92))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(adx(_x121)))))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(a__tail(a__adx(mark(_x121))))))))))))
mark#(incr(head(s(head(incr(adx(tail(_x81)))))))) → a__incr#(head(s(a__head(a__incr(a__adx(a__tail(mark(_x81))))))))mark#(incr(head(s(head(adx(cons(adx(adx(cons(_x101, _x102))), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__adx(cons(mark(_x101), _x102))), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(nats, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__nats, _x102)))))))))mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(head(s(head(a__adx(adx(tail(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(tail(_x81)))))))) → a__incr#(head(s(a__head(adx(adx(tail(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(head(cons(head(_x101), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(head(mark(_x101)), _x92))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(0)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(0)), _x72))))))mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(head(s(a__head(adx(adx(0))))))
mark#(incr(head(s(head(adx(adx(0))))))) → a__incr#(head(s(head(a__adx(adx(0))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(adx(s(a__tail(cons(cons(a__tail(a__incr(mark(_x131))), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(cons(nats, _x51))))))) → a__incr#(a__head(s(a__head(a__incr(cons(mark(a__adx(a__zeros)), adx(_x51)))))))mark#(incr(head(s(head(adx(adx(cons(head(_x91), _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(a__head(mark(_x91)), _x82)))))))
mark#(incr(head(s(head(adx(adx(cons(head(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(a__head(mark(_x91)), _x82)))))))mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(head(s(a__head(adx(cons(adx(adx(nil)), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(head(s(head(a__adx(cons(adx(adx(nil)), _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(tail(_x101))), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__adx(a__tail(mark(_x101)))), _x72))))))
mark#(incr(head(s(head(incr(zeros)))))) → a__incr#(head(s(a__head(a__incr(a__zeros)))))mark#(incr(head(s(head(adx(cons(adx(adx(nats)), _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__adx(a__adx(a__nats)), _x72))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nats)), _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__adx(a__adx(a__nats)), _x72))))))mark#(incr(head(s(head(adx(cons(adx(incr(head(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(a__head(mark(_x101)))), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(head(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(adx(s(0))))))) → a__incr#(a__head(s(a__head(a__adx(s(0))))))
mark#(incr(adx(adx(cons(tail(incr(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(a__incr(mark(_x71))), _x52))))mark#(incr(head(s(head(adx(adx(head(cons(adx(tail(_x111)), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(a__tail(mark(_x111))), _x92))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(nil)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(nil)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(cons(zeros, _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(a__zeros, _x82)))))))
mark#(incr(head(s(head(adx(adx(cons(zeros, _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(a__zeros, _x82)))))))mark#(incr(head(head(_x41)))) → a__incr#(a__head(a__head(mark(_x41))))
mark#(incr(head(s(head(adx(adx(tail(incr(_x91))))))))) → a__incr#(a__head(s(head(adx(adx(a__tail(a__incr(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(zeros), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(a__zeros), _x102)))))))))
mark#(incr(head(s(head(adx(adx(zeros))))))) → a__incr#(head(s(a__head(a__adx(a__adx(a__zeros))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(tail(mark(_x121)), _x112), _x102)))))))))
mark#(incr(head(s(_x41)))) → a__incr#(head(s(mark(_x41))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(adx(_x121)), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(a__adx(mark(_x121))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(adx(_x121)), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__adx(mark(_x121))), _x102)))))))))mark#(incr(adx(head(incr(_x51))))) → a__incr#(a__adx(a__head(a__incr(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(s(incr(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(a__incr(mark(_x91)))))))))mark#(incr(adx(0))) → a__incr#(a__adx(0))
mark#(incr(head(s(head(adx(cons(zeros, _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(zeros, _x72))))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(a__head(s(head(adx(adx(mark(_x71)))))))
mark#(incr(head(s(head(adx(adx(head(zeros)))))))) → a__incr#(head(s(a__head(a__adx(adx(a__head(a__zeros)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(zeros, _x81)))))))))) → a__incr#(head(s(head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(incr(_x21))) → a__incr#(incr(mark(_x21)))mark#(incr(head(s(head(adx(adx(head(incr(_x91))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(a__incr(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(head(cons(_x91, _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(a__head(cons(mark(_x91), _x92))))))))mark#(incr(incr(s(_x41)))) → a__incr#(a__incr(s(mark(_x41))))
mark#(incr(head(s(head(adx(adx(cons(0, _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(0, _x82)))))))mark#(incr(head(s(head(adx(adx(cons(0, _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(0, _x82)))))))
mark#(incr(adx(s(_x41)))) → a__incr#(a__adx(s(mark(_x41))))mark#(incr(adx(adx(cons(zeros, _x31))))) → a__incr#(a__adx(a__incr(cons(mark(a__zeros), adx(_x31)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(0, _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(0, _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x81)))))))))) → a__incr#(head(s(head(adx(a__adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(nats)), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__adx(a__nats)), _x72))))))mark#(incr(head(s(head(incr(tail(_x71))))))) → a__incr#(head(s(a__head(a__incr(a__tail(mark(_x71)))))))
mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(a__head(s(a__head(a__adx(a__incr(a__zeros))))))mark#(incr(head(s(head(adx(adx(s(tail(nil))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(nil))))))))
mark#(incr(incr(incr(incr(_x51))))) → a__incr#(a__incr(a__incr(a__incr(mark(_x51)))))mark#(incr(adx(adx(cons(head(_x61), _x52))))) → a__incr#(a__adx(adx(cons(a__head(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(cons(s(_x81), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(s(mark(_x81)), _x72))))))mark#(incr(head(s(head(adx(cons(adx(adx(nats)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__adx(a__nats)), _x72))))))
mark#(incr(adx(adx(cons(0, _x52))))) → a__incr#(a__adx(adx(cons(0, _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(nats))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(s(a__nats))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(incr(incr(_x91))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__incr(a__incr(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(incr(incr(_x91))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__incr(a__incr(mark(_x91)))))))))
mark#(incr(head(s(head(adx(cons(adx(cons(incr(_x101), _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(cons(a__incr(mark(_x101)), _x92)), _x72))))))mark#(incr(nats)) → a__incr#(a__nats)
mark#(incr(head(s(head(adx(adx(s(zeros)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(a__zeros)))))))mark#(incr(head(nil))) → a__incr#(head(nil))
mark#(incr(head(s(head(adx(adx(head(cons(adx(zeros), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__adx(a__zeros), _x92))))))))mark#(incr(head(s(head(adx(adx(s(0)))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(0)))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(tail(cons(a__head(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(zeros), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(zeros)), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(a__head(a__head(a__zeros)), _x102)))))))))mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(a__head(a__adx(incr(a__zeros))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(adx(_x141)))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(s(a__adx(mark(_x141))))), _x102)))))))))mark#(incr(head(s(head(cons(_x61, _x62)))))) → a__incr#(head(s(a__head(cons(mark(_x61), _x62)))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x81)))))))))) → a__incr#(head(s(head(adx(adx(s(mark(_x81))))))))mark#(incr(incr(adx(adx(_x51))))) → a__incr#(a__incr(a__adx(a__adx(mark(_x51)))))
mark#(incr(head(s(head(adx(adx(head(cons(nats, _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__nats, _x92))))))))mark#(incr(adx(adx(cons(incr(zeros), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(zeros), _x52))))
mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(a__head(a__adx(a__incr(zeros))))))mark#(incr(head(s(head(adx(adx(s(_x81)))))))) → a__incr#(head(s(a__head(a__adx(adx(s(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(zeros, _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__zeros, _x112), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(zeros, _x112), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(cons(a__zeros, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(tail(incr(_x91))))))))) → a__incr#(head(s(head(a__adx(adx(a__tail(a__incr(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(tail(incr(_x91))))))))) → a__incr#(head(s(a__head(adx(adx(a__tail(a__incr(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(tail(cons(_x91, _x92))))))))) → a__incr#(head(s(head(a__adx(adx(a__tail(cons(mark(_x91), _x92))))))))mark#(incr(head(s(head(adx(adx(tail(cons(_x91, _x92))))))))) → a__incr#(head(s(a__head(adx(adx(a__tail(cons(mark(_x91), _x92))))))))
mark#(incr(head(s(head(adx(adx(incr(nil)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__incr(nil)))))))mark#(incr(head(s(head(adx(adx(incr(nil)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__incr(nil)))))))
mark#(incr(head(s(head(incr(_x61)))))) → a__incr#(head(s(a__head(incr(mark(_x61))))))mark#(incr(adx(adx(cons(tail(_x61), _x52))))) → a__incr#(a__adx(a__adx(cons(a__tail(mark(_x61)), _x52))))
mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(a__head(s(a__head(a__adx(a__adx(s(a__incr(tail(mark(_x101))))))))))mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(head(a__adx(cons(a__nats, _x72))))))
mark#(incr(head(s(head(adx(cons(nats, _x72))))))) → a__incr#(a__head(s(a__head(adx(cons(a__nats, _x72))))))mark#(incr(adx(adx(cons(incr(tail(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__incr(a__tail(mark(_x71))), _x52))))
mark#(incr(adx(adx(cons(incr(tail(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(incr(a__tail(mark(_x71))), _x52))))mark#(incr(adx(adx(cons(incr(s(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(s(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(head(cons(s(nil), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(s(nil), _x92))))))))mark#(incr(adx(head(cons(_x51, _x52))))) → a__incr#(a__adx(a__head(cons(mark(_x51), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(tail(cons(a__head(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(0, _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(0, _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(0, _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(0, _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(mark(_x101), _x102)))))))))
mark#(incr(head(s(head(adx(adx(head(cons(tail(_x101), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__tail(mark(_x101)), _x92))))))))mark#(incr(head(s(head(adx(incr(nats))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__nats))))))
mark#(incr(adx(head(0)))) → a__incr#(a__adx(a__head(0)))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(cons(_x131, _x132))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(a__head(cons(mark(_x131), _x132))), _x102)))))))))
mark#(incr(head(s(head(adx(incr(0))))))) → a__incr#(head(s(head(a__adx(a__incr(0))))))mark#(incr(head(s(head(adx(incr(0))))))) → a__incr#(head(s(a__head(adx(a__incr(0))))))
mark#(incr(head(s(head(adx(adx(head(cons(head(s(nats)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__nats)), _x92))))))))mark#(incr(head(s(head(adx(adx(incr(adx(_x91))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__incr(a__adx(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(incr(adx(_x91))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__incr(a__adx(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(_x71))))))) → a__incr#(head(s(a__head(a__adx(a__adx(mark(_x71)))))))
mark#(incr(head(s(head(s(0)))))) → a__incr#(a__head(s(a__head(s(0)))))mark#(incr(adx(adx(cons(tail(nats), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(nats), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(zeros))), _x81)))))))))) → a__incr#(head(s(head(adx(adx(s(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(cons(nil, _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(nil, _x82)))))))
mark#(incr(head(s(head(adx(adx(cons(nil, _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(nil, _x82)))))))mark#(incr(head(s(head(adx(adx(tail(incr(_x91))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(incr(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(tail(incr(_x91))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(incr(mark(_x91)))))))))mark#(incr(adx(adx(cons(tail(s(_x71)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(s(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(adx(tail(nil)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(nil)))))))mark#(incr(head(s(head(adx(adx(tail(nil)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(nil)))))))
mark#(incr(head(s(incr(_x51))))) → a__incr#(a__head(s(a__incr(mark(_x51)))))mark#(incr(adx(adx(cons(incr(head(_x71)), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(a__head(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(cons(adx(adx(nil)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(adx(a__adx(nil)), _x72))))))mark#(incr(head(s(head(adx(cons(head(s(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(s(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(_x121), _x112), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(cons(a__tail(mark(_x121)), _x112), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(incr(nats)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(a__nats)), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(nats))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(a__nats))))))))mark#(incr(head(s(head(adx(incr(adx(_x81)))))))) → a__incr#(head(s(a__head(a__adx(a__incr(a__adx(mark(_x81))))))))
mark#(incr(adx(adx(cons(tail(cons(tail(_x81), _x72)), _x52))))) → a__incr#(a__adx(adx(cons(a__tail(cons(a__tail(mark(_x81)), _x72)), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(tail(_x141))), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(a__incr(a__tail(mark(_x141)))), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(adx(_x91))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__adx(mark(_x91)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(nil))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(tail(cons(head(a__head(s(nil))), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(_x121)), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(a__head(mark(_x121))), _x102)))))))))mark#(incr(head(s(head(adx(adx(tail(incr(head(_x101)))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(a__incr(a__head(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(tail(incr(head(_x101)))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(a__incr(a__head(mark(_x101))))))))))mark#(incr(head(s(head(adx(cons(head(head(_x91)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__head(a__head(mark(_x91))), _x72))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(zeros), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(a__adx(a__zeros), _x102)))))))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(head(s(a__head(a__adx(adx(a__head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(zeros), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(a__adx(a__zeros), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(tail(_x111))))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(s(a__incr(a__tail(a__tail(mark(_x111)))))))))))
mark#(incr(head(s(head(adx(adx(head(nil)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(nil)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(tail(incr(_x131)), _x112), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(cons(a__tail(incr(mark(_x131))), _x112), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(adx(zeros)), _x72))))))) → a__incr#(head(s(a__head(a__adx(cons(a__adx(a__adx(a__zeros)), _x72))))))mark#(incr(head(s(head(adx(nil)))))) → a__incr#(a__head(s(a__head(a__adx(nil)))))
mark#(incr(head(s(head(adx(adx(s(nil)))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(nil)))))))mark#(incr(head(s(head(adx(s(cons(tail(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(s(cons(a__tail(mark(_x91)), _x82)))))))
mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(a__head(adx(mark(_x61))))))mark#(incr(head(s(head(adx(_x61)))))) → a__incr#(a__head(s(head(a__adx(mark(_x61))))))
mark#(incr(head(cons(_x41, _x42)))) → a__incr#(a__head(cons(mark(_x41), _x42)))mark#(incr(head(s(head(adx(adx(cons(cons(_x91, _x92), _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(cons(mark(_x91), _x92), _x82)))))))
mark#(incr(head(s(head(adx(adx(cons(cons(_x91, _x92), _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(cons(mark(_x91), _x92), _x82)))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__adx(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(cons(adx(cons(nats, _x92)), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(cons(nats, _x92)), _x72))))))mark#(incr(head(s(head(adx(adx(head(cons(adx(_x101), _x92))))))))) → a__incr#(a__head(s(a__head(adx(adx(head(cons(a__adx(mark(_x101)), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(adx(_x101), _x92))))))))) → a__incr#(a__head(s(head(a__adx(adx(head(cons(a__adx(mark(_x101)), _x92))))))))mark#(incr(head(s(head(adx(adx(cons(incr(_x91), _x82)))))))) → a__incr#(a__head(s(a__head(adx(adx(cons(a__incr(mark(_x91)), _x82)))))))
mark#(incr(head(s(head(adx(adx(cons(incr(_x91), _x82)))))))) → a__incr#(a__head(s(head(a__adx(adx(cons(a__incr(mark(_x91)), _x82)))))))mark#(incr(head(s(head(adx(adx(s(incr(tail(_x101)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__incr(a__tail(mark(_x101))))))))))
mark#(incr(head(s(head(adx(adx(cons(cons(_x91, _x92), _x82)))))))) → a__incr#(a__head(s(a__head(a__adx(adx(cons(cons(mark(_x91), _x92), _x82)))))))mark#(incr(adx(adx(cons(incr(0), _x52))))) → a__incr#(a__adx(a__adx(cons(a__incr(0), _x52))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(incr(_x111), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__incr(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(0, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(a__tail(cons(cons(0, _x112), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(cons(_x121, _x122)), _x102)))))))))) → a__incr#(head(s(head(adx(a__adx(s(a__tail(cons(a__head(cons(mark(_x121), _x122)), _x102)))))))))mark#(incr(head(s(head(adx(adx(head(cons(head(_x101), _x92))))))))) → a__incr#(a__head(s(a__head(a__adx(adx(head(cons(a__head(mark(_x101)), _x92))))))))
mark#(incr(head(s(head(nil))))) → a__incr#(a__head(s(a__head(nil))))mark#(incr(head(s(head(adx(adx(s(tail(cons(_x101, _x81)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(mark(_x81))))))))
mark#(incr(adx(adx(cons(incr(zeros), _x52))))) → a__incr#(adx(a__adx(cons(incr(a__zeros), _x52))))mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(a__head(adx(a__adx(s(a__tail(cons(adx(mark(_x111)), _x102)))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(adx(_x111), _x102)))))))))) → a__incr#(head(s(head(a__adx(a__adx(s(a__tail(cons(adx(mark(_x111)), _x102)))))))))mark#(incr(head(s(head(adx(adx(head(cons(s(cons(_x111, _x112)), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(s(cons(mark(_x111), _x112)), _x92))))))))
mark#(incr(head(s(head(adx(adx(s(tail(cons(head(head(s(zeros))), _x102)))))))))) → a__incr#(head(s(head(adx(adx(s(a__tail(cons(head(head(s(a__zeros))), _x102)))))))))mark#(incr(head(s(head(adx(cons(adx(nats), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(nats), _x72))))))
mark#(incr(head(s(head(incr(adx(nats))))))) → a__incr#(head(s(a__head(a__incr(a__adx(nats))))))mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(a__head(adx(adx(a__head(mark(_x81))))))))
mark#(incr(head(s(head(adx(adx(head(_x81)))))))) → a__incr#(a__head(s(head(a__adx(adx(a__head(mark(_x81))))))))mark#(incr(head(s(head(adx(adx(tail(adx(_x91))))))))) → a__incr#(a__head(s(head(a__adx(adx(a__tail(a__adx(mark(_x91)))))))))
mark#(incr(head(s(head(adx(adx(tail(adx(_x91))))))))) → a__incr#(a__head(s(a__head(adx(adx(a__tail(a__adx(mark(_x91)))))))))mark#(incr(adx(adx(cons(incr(incr(_x71)), _x52))))) → a__incr#(adx(a__adx(cons(incr(a__incr(mark(_x71))), _x52))))
mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(head(a__adx(a__incr(zeros))))))mark#(incr(head(s(head(adx(incr(zeros))))))) → a__incr#(head(s(a__head(adx(a__incr(zeros))))))
mark#(incr(head(s(head(adx(cons(adx(incr(tail(_x101))), _x72))))))) → a__incr#(a__head(s(a__head(a__adx(cons(a__adx(a__incr(a__tail(mark(_x101)))), _x72))))))mark#(incr(head(s(head(adx(adx(s(tail(cons(cons(_x111, _x112), _x102)))))))))) → a__incr#(head(s(a__head(a__adx(a__adx(s(tail(cons(cons(mark(_x111), _x112), _x102)))))))))

Rewrite Rules

a__incr(nil) → nila__incr(cons(X, L)) → cons(s(mark(X)), incr(L))
a__adx(nil) → nila__adx(cons(X, L)) → a__incr(cons(mark(X), adx(L)))
a__nats → a__adx(a__zeros)a__zeros → cons(0, zeros)
a__head(cons(X, L)) → mark(X)a__tail(cons(X, L)) → mark(L)
mark(incr(X)) → a__incr(mark(X))mark(adx(X)) → a__adx(mark(X))
mark(nats) → a__natsmark(zeros) → a__zeros
mark(head(X)) → a__head(mark(X))mark(tail(X)) → a__tail(mark(X))
mark(nil) → nilmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(0) → 0
a__incr(X) → incr(X)a__adx(X) → adx(X)
a__nats → natsa__zeros → zeros
a__head(X) → head(X)a__tail(X) → tail(X)

Original Signature

Termination of terms over the following signature is verified: a__zeros, mark, tail, a__nats, a__tail, nats, 0, a__incr, s, zeros, a__adx, adx, incr, a__head, head, cons, nil

Strategy

The right-hand side of the rule mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(_x121))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(mark(_x121)))), _x92)))))))) is 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
a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(cons(mark(_x131), _x132)))), _x92)))))))) 
a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(s(mark(_x131))))), _x92)))))))) 
a__incr#(head(s(a__head(adx(adx(head(cons(a__head(s(a__incr(mark(_x121)))), _x92)))))))) 
a__incr#(head(s(head(a__adx(adx(head(cons(a__head(s(a__incr(mark(_x121)))), _x92)))))))) 
a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(a__nats))), _x92)))))))) 
a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(nil))), _x92)))))))) 
a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(a__incr(mark(_x131))))), _x92)))))))) 
a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(a__tail(mark(_x131))))), _x92)))))))) 
a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(0))), _x92)))))))) 
a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(incr(mark(_x121)))), _x92)))))))) 
a__incr#(head(s(a__head(a__adx(adx(head(cons(head(s(a__incr(mark(_x121)))), _x92)))))))) 
a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(a__head(mark(_x131))))), _x92)))))))) 
a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(a__zeros))), _x92)))))))) 
a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(a__adx(mark(_x131))))), _x92)))))))) 
Thus, the rule mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(_x121))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(mark(_x121)))), _x92)))))))) is replaced by the following rules:
mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(head(_x131)))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(a__head(mark(_x131))))), _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(adx(_x131)))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(a__adx(mark(_x131))))), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(incr(_x131)))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(a__incr(mark(_x131))))), _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(0))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(0))), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(nats))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(a__nats))), _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(zeros))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(a__zeros))), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(_x121))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(head(s(a__incr(mark(_x121)))), _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(cons(_x131, _x132)))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(cons(mark(_x131), _x132)))), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(tail(_x131)))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(a__tail(mark(_x131))))), _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(nil))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(nil))), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(_x121))), _x92))))))))) → a__incr#(head(s(a__head(adx(adx(head(cons(a__head(s(a__incr(mark(_x121)))), _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(s(_x131)))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(a__incr(s(mark(_x131))))), _x92))))))))
mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(_x121))), _x92))))))))) → a__incr#(head(s(head(a__adx(adx(head(cons(a__head(s(a__incr(mark(_x121)))), _x92))))))))mark#(incr(head(s(head(adx(adx(head(cons(head(s(incr(_x121))), _x92))))))))) → a__incr#(head(s(a__head(a__adx(adx(head(cons(a__head(s(incr(mark(_x121)))), _x92))))))))