TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60002 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (454ms).
 | – Problem 2 was processed with processor SubtermCriterion (2ms).
 | – Problem 3 was processed with processor SubtermCriterion (0ms).
 | – Problem 4 was processed with processor SubtermCriterion (1ms).
 | – Problem 5 was processed with processor ForwardNarrowing (5ms).
 |    | – Problem 9 was processed with processor ForwardNarrowing (5ms).
 |    |    | – Problem 10 was processed with processor ForwardNarrowing (3ms).
 |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (38ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (14ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (11ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 was processed with processor ForwardNarrowing (13ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 28 was processed with processor ForwardNarrowing (26ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 29 was processed with processor ForwardNarrowing (75ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 30 was processed with processor ForwardNarrowing (95ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 31 was processed with processor ForwardNarrowing (151ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 32 remains open; application of the following processors failed [ForwardNarrowing (47ms), ForwardNarrowing (142ms), ForwardNarrowing (57ms), ForwardNarrowing (58ms), ForwardNarrowing (69ms), ForwardNarrowing (43ms), ForwardNarrowing (43ms), ForwardNarrowing (50ms), ForwardNarrowing (57ms), ForwardNarrowing (57ms), ForwardNarrowing (56ms), ForwardNarrowing (59ms), ForwardNarrowing (82ms), ForwardNarrowing (91ms), ForwardNarrowing (45ms), ForwardNarrowing (147ms), ForwardNarrowing (51ms), ForwardNarrowing (53ms), ForwardNarrowing (52ms), ForwardNarrowing (74ms), ForwardNarrowing (59ms), ForwardNarrowing (72ms), ForwardNarrowing (48ms), ForwardNarrowing (131ms), ForwardNarrowing (46ms), ForwardNarrowing (53ms), ForwardNarrowing (46ms)].
 | – Problem 6 was processed with processor SubtermCriterion (0ms).
 | – Problem 7 was processed with processor SubtermCriterion (2ms).
 | – Problem 8 was processed with processor SubtermCriterion (2ms).

The following open problems remain:

Open Dependency Pair Problem 5

Dependency Pairs

top#(mark(X)) → top#(proper(X))top#(ok(X)) → top#(active(X))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, ok, mark, proper, top, cons

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

proper#(cons(X1, X2)) → proper#(X1)top#(ok(X)) → top#(active(X))
cons#(mark(X1), X2) → cons#(X1, X2)active#(f(s(0))) → f#(p(s(0)))
cons#(ok(X1), ok(X2)) → cons#(X1, X2)p#(mark(X)) → p#(X)
top#(ok(X)) → active#(X)proper#(p(X)) → proper#(X)
active#(cons(X1, X2)) → cons#(active(X1), X2)active#(p(X)) → p#(active(X))
proper#(p(X)) → p#(proper(X))f#(mark(X)) → f#(X)
top#(mark(X)) → proper#(X)f#(ok(X)) → f#(X)
active#(f(0)) → s#(0)proper#(f(X)) → f#(proper(X))
top#(mark(X)) → top#(proper(X))proper#(f(X)) → proper#(X)
active#(f(s(0))) → p#(s(0))proper#(cons(X1, X2)) → proper#(X2)
active#(p(X)) → active#(X)active#(s(X)) → s#(active(X))
s#(ok(X)) → s#(X)active#(f(s(0))) → s#(0)
s#(mark(X)) → s#(X)proper#(s(X)) → proper#(X)
active#(f(X)) → f#(active(X))active#(f(0)) → cons#(0, f(s(0)))
proper#(cons(X1, X2)) → cons#(proper(X1), proper(X2))active#(s(X)) → active#(X)
proper#(s(X)) → s#(proper(X))active#(f(0)) → f#(s(0))
p#(ok(X)) → p#(X)active#(f(X)) → active#(X)
active#(cons(X1, X2)) → active#(X1)

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

The following SCCs where found

f#(mark(X)) → f#(X)f#(ok(X)) → f#(X)
cons#(mark(X1), X2) → cons#(X1, X2)cons#(ok(X1), ok(X2)) → cons#(X1, X2)
p#(ok(X)) → p#(X)p#(mark(X)) → p#(X)
active#(s(X)) → active#(X)active#(p(X)) → active#(X)
active#(f(X)) → active#(X)active#(cons(X1, X2)) → active#(X1)
proper#(s(X)) → proper#(X)proper#(cons(X1, X2)) → proper#(X1)
proper#(f(X)) → proper#(X)proper#(cons(X1, X2)) → proper#(X2)
proper#(p(X)) → proper#(X)
top#(mark(X)) → top#(proper(X))top#(ok(X)) → top#(active(X))
s#(mark(X)) → s#(X)s#(ok(X)) → s#(X)

Problem 2: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

f#(mark(X)) → f#(X)f#(ok(X)) → f#(X)

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

f#(mark(X)) → f#(X)f#(ok(X)) → f#(X)

Problem 3: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

s#(mark(X)) → s#(X)s#(ok(X)) → s#(X)

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

s#(mark(X)) → s#(X)s#(ok(X)) → s#(X)

Problem 4: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

cons#(mark(X1), X2) → cons#(X1, X2)cons#(ok(X1), ok(X2)) → cons#(X1, X2)

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

cons#(mark(X1), X2) → cons#(X1, X2)cons#(ok(X1), ok(X2)) → cons#(X1, X2)

Problem 5: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(X)) → top#(proper(X))top#(ok(X)) → top#(active(X))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

The right-hand side of the rule top#(mark(X)) → top#(proper(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
top#(ok(0)) 
top#(f(proper(_x21))) 
top#(p(proper(_x21))) 
top#(cons(proper(_x21), proper(_x22))) 
top#(s(proper(_x21))) 
Thus, the rule top#(mark(X)) → top#(proper(X)) is replaced by the following rules:
top#(mark(0)) → top#(ok(0))top#(mark(f(_x21))) → top#(f(proper(_x21)))
top#(mark(s(_x21))) → top#(s(proper(_x21)))top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))
top#(mark(p(_x21))) → top#(p(proper(_x21)))

Problem 9: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(0)) → top#(ok(0))top#(ok(X)) → top#(active(X))
top#(mark(f(_x21))) → top#(f(proper(_x21)))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(mark(p(_x21))) → top#(p(proper(_x21)))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, ok, mark, proper, top, cons

Strategy

The right-hand side of the rule top#(ok(X)) → top#(active(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
top#(mark(0)) 
top#(s(active(_x21))) 
top#(p(active(_x21))) 
top#(cons(active(_x21), _x22)) 
top#(mark(f(p(s(0))))) 
top#(mark(cons(0, f(s(0))))) 
top#(f(active(_x21))) 
Thus, the rule top#(ok(X)) → top#(active(X)) is replaced by the following rules:
top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))
top#(ok(s(_x21))) → top#(s(active(_x21)))top#(ok(p(s(0)))) → top#(mark(0))
top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))top#(ok(p(_x21))) → top#(p(active(_x21)))
top#(ok(f(_x21))) → top#(f(active(_x21)))

Problem 10: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(mark(0)) → top#(ok(0))top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))
top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))top#(ok(s(_x21))) → top#(s(active(_x21)))
top#(ok(p(s(0)))) → top#(mark(0))top#(mark(f(_x21))) → top#(f(proper(_x21)))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))top#(mark(p(_x21))) → top#(p(proper(_x21)))
top#(ok(p(_x21))) → top#(p(active(_x21)))top#(ok(f(_x21))) → top#(f(active(_x21)))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

The right-hand side of the rule top#(mark(0)) → top#(ok(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 top#(mark(0)) → top#(ok(0)) is deleted.

Problem 11: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))
top#(ok(p(s(0)))) → top#(mark(0))top#(ok(s(_x21))) → top#(s(active(_x21)))
top#(mark(f(_x21))) → top#(f(proper(_x21)))top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))
top#(mark(s(_x21))) → top#(s(proper(_x21)))top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))
top#(ok(f(_x21))) → top#(f(active(_x21)))top#(ok(p(_x21))) → top#(p(active(_x21)))
top#(mark(p(_x21))) → top#(p(proper(_x21)))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, ok, mark, proper, top, cons

Strategy

The right-hand side of the rule top#(ok(s(_x21))) → top#(s(active(_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
top#(s(mark(cons(0, f(s(0)))))) 
top#(s(cons(active(_x41), _x42))) 
top#(s(mark(f(p(s(0)))))) 
top#(s(f(active(_x41)))) 
top#(s(mark(0))) 
top#(s(p(active(_x41)))) 
top#(s(s(active(_x41)))) 
Thus, the rule top#(ok(s(_x21))) → top#(s(active(_x21))) is replaced by the following rules:
top#(ok(s(p(s(0))))) → top#(s(mark(0)))top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))
top#(ok(s(f(0)))) → top#(s(mark(cons(0, f(s(0))))))top#(ok(s(f(_x41)))) → top#(s(f(active(_x41))))
top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))top#(ok(s(p(_x41)))) → top#(s(p(active(_x41))))
top#(ok(s(f(s(0))))) → top#(s(mark(f(p(s(0))))))

Problem 12: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(p(s(0))))) → top#(s(mark(0)))top#(ok(s(f(0)))) → top#(s(mark(cons(0, f(s(0))))))
top#(ok(s(f(_x41)))) → top#(s(f(active(_x41))))top#(ok(p(s(0)))) → top#(mark(0))
top#(ok(s(f(s(0))))) → top#(s(mark(f(p(s(0))))))top#(ok(s(p(_x41)))) → top#(s(p(active(_x41))))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(ok(p(_x21))) → top#(p(active(_x21)))top#(ok(f(_x21))) → top#(f(active(_x21)))
top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))
top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))
top#(mark(f(_x21))) → top#(f(proper(_x21)))top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))
top#(mark(p(_x21))) → top#(p(proper(_x21)))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

The right-hand side of the rule top#(ok(s(p(s(0))))) → top#(s(mark(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
top#(mark(s(0))) 
Thus, the rule top#(ok(s(p(s(0))))) → top#(s(mark(0))) is replaced by the following rules:
top#(ok(s(p(s(0))))) → top#(mark(s(0)))

Problem 13: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(p(s(0))))) → top#(mark(s(0)))top#(ok(s(f(0)))) → top#(s(mark(cons(0, f(s(0))))))
top#(ok(s(f(_x41)))) → top#(s(f(active(_x41))))top#(ok(p(s(0)))) → top#(mark(0))
top#(ok(s(f(s(0))))) → top#(s(mark(f(p(s(0))))))top#(ok(s(p(_x41)))) → top#(s(p(active(_x41))))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(ok(p(_x21))) → top#(p(active(_x21)))top#(ok(f(_x21))) → top#(f(active(_x21)))
top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))
top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))
top#(mark(f(_x21))) → top#(f(proper(_x21)))top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))
top#(mark(p(_x21))) → top#(p(proper(_x21)))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, ok, mark, proper, top, cons

Strategy

The right-hand side of the rule top#(ok(s(f(0)))) → top#(s(mark(cons(0, f(s(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
top#(mark(s(cons(0, f(s(0)))))) 
Thus, the rule top#(ok(s(f(0)))) → top#(s(mark(cons(0, f(s(0)))))) is replaced by the following rules:
top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))

Problem 14: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(p(s(0))))) → top#(mark(s(0)))top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))
top#(ok(s(f(_x41)))) → top#(s(f(active(_x41))))top#(ok(p(s(0)))) → top#(mark(0))
top#(ok(s(f(s(0))))) → top#(s(mark(f(p(s(0))))))top#(ok(s(p(_x41)))) → top#(s(p(active(_x41))))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(ok(p(_x21))) → top#(p(active(_x21)))top#(ok(f(_x21))) → top#(f(active(_x21)))
top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))
top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))
top#(mark(f(_x21))) → top#(f(proper(_x21)))top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))
top#(mark(p(_x21))) → top#(p(proper(_x21)))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

The right-hand side of the rule top#(ok(s(f(_x41)))) → top#(s(f(active(_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
top#(s(f(mark(0)))) 
top#(s(f(cons(active(_x51), _x52)))) 
top#(s(f(mark(cons(0, f(s(0))))))) 
top#(s(f(f(active(_x51))))) 
top#(s(f(p(active(_x51))))) 
top#(s(f(s(active(_x51))))) 
top#(s(f(mark(f(p(s(0))))))) 
Thus, the rule top#(ok(s(f(_x41)))) → top#(s(f(active(_x41)))) is replaced by the following rules:
top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))top#(ok(s(f(f(0))))) → top#(s(f(mark(cons(0, f(s(0)))))))
top#(ok(s(f(p(_x51))))) → top#(s(f(p(active(_x51)))))top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))
top#(ok(s(f(f(s(0)))))) → top#(s(f(mark(f(p(s(0)))))))top#(ok(s(f(p(s(0)))))) → top#(s(f(mark(0))))
top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))

Problem 15: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(p(s(0))))) → top#(mark(s(0)))top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))
top#(ok(p(s(0)))) → top#(mark(0))top#(ok(s(f(s(0))))) → top#(s(mark(f(p(s(0))))))
top#(ok(s(p(_x41)))) → top#(s(p(active(_x41))))top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))
top#(mark(s(_x21))) → top#(s(proper(_x21)))top#(ok(p(_x21))) → top#(p(active(_x21)))
top#(ok(f(_x21))) → top#(f(active(_x21)))top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))
top#(ok(s(f(p(s(0)))))) → top#(s(f(mark(0))))top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))
top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))
top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))
top#(ok(s(f(f(0))))) → top#(s(f(mark(cons(0, f(s(0)))))))top#(ok(s(f(p(_x51))))) → top#(s(f(p(active(_x51)))))
top#(mark(f(_x21))) → top#(f(proper(_x21)))top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))
top#(mark(p(_x21))) → top#(p(proper(_x21)))top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))
top#(ok(s(f(f(s(0)))))) → top#(s(f(mark(f(p(s(0)))))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, ok, mark, proper, top, cons

Strategy

The right-hand side of the rule top#(ok(p(s(0)))) → top#(mark(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 top#(ok(p(s(0)))) → top#(mark(0)) is deleted.

Problem 16: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(p(s(0))))) → top#(mark(s(0)))top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))
top#(ok(s(f(s(0))))) → top#(s(mark(f(p(s(0))))))top#(ok(s(p(_x41)))) → top#(s(p(active(_x41))))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(ok(p(_x21))) → top#(p(active(_x21)))top#(ok(f(_x21))) → top#(f(active(_x21)))
top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))top#(ok(s(f(p(s(0)))))) → top#(s(f(mark(0))))
top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))
top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))
top#(ok(s(f(p(_x51))))) → top#(s(f(p(active(_x51)))))top#(ok(s(f(f(0))))) → top#(s(f(mark(cons(0, f(s(0)))))))
top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))top#(mark(f(_x21))) → top#(f(proper(_x21)))
top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))top#(mark(p(_x21))) → top#(p(proper(_x21)))
top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))top#(ok(s(f(f(s(0)))))) → top#(s(f(mark(f(p(s(0)))))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

The right-hand side of the rule top#(ok(s(f(s(0))))) → top#(s(mark(f(p(s(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
top#(mark(s(f(p(s(0)))))) 
Thus, the rule top#(ok(s(f(s(0))))) → top#(s(mark(f(p(s(0)))))) is replaced by the following rules:
top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))

Problem 17: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(p(s(0))))) → top#(mark(s(0)))top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))
top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))top#(ok(s(p(_x41)))) → top#(s(p(active(_x41))))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(ok(p(_x21))) → top#(p(active(_x21)))top#(ok(f(_x21))) → top#(f(active(_x21)))
top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))top#(ok(s(f(p(s(0)))))) → top#(s(f(mark(0))))
top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))
top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))
top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))top#(ok(s(f(f(0))))) → top#(s(f(mark(cons(0, f(s(0)))))))
top#(ok(s(f(p(_x51))))) → top#(s(f(p(active(_x51)))))top#(mark(f(_x21))) → top#(f(proper(_x21)))
top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))top#(mark(p(_x21))) → top#(p(proper(_x21)))
top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))top#(ok(s(f(f(s(0)))))) → top#(s(f(mark(f(p(s(0)))))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, ok, mark, proper, top, cons

Strategy

The right-hand side of the rule top#(ok(s(p(_x41)))) → top#(s(p(active(_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
top#(s(p(cons(active(_x51), _x52)))) 
top#(s(p(s(active(_x51))))) 
top#(s(p(mark(cons(0, f(s(0))))))) 
top#(s(p(mark(f(p(s(0))))))) 
top#(s(p(f(active(_x51))))) 
top#(s(p(p(active(_x51))))) 
top#(s(p(mark(0)))) 
Thus, the rule top#(ok(s(p(_x41)))) → top#(s(p(active(_x41)))) is replaced by the following rules:
top#(ok(s(p(cons(_x51, _x52))))) → top#(s(p(cons(active(_x51), _x52))))top#(ok(s(p(p(_x51))))) → top#(s(p(p(active(_x51)))))
top#(ok(s(p(f(s(0)))))) → top#(s(p(mark(f(p(s(0)))))))top#(ok(s(p(f(_x51))))) → top#(s(p(f(active(_x51)))))
top#(ok(s(p(f(0))))) → top#(s(p(mark(cons(0, f(s(0)))))))top#(ok(s(p(s(_x51))))) → top#(s(p(s(active(_x51)))))
top#(ok(s(p(p(s(0)))))) → top#(s(p(mark(0))))

Problem 18: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(p(s(0))))) → top#(mark(s(0)))top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))
top#(ok(s(f(p(s(0)))))) → top#(s(f(mark(0))))top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))
top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))top#(ok(s(f(f(0))))) → top#(s(f(mark(cons(0, f(s(0)))))))
top#(ok(s(f(p(_x51))))) → top#(s(f(p(active(_x51)))))top#(mark(f(_x21))) → top#(f(proper(_x21)))
top#(ok(s(p(f(0))))) → top#(s(p(mark(cons(0, f(s(0)))))))top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))
top#(mark(p(_x21))) → top#(p(proper(_x21)))top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))
top#(ok(s(f(f(s(0)))))) → top#(s(f(mark(f(p(s(0)))))))top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))
top#(ok(s(p(p(_x51))))) → top#(s(p(p(active(_x51)))))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(ok(s(p(s(_x51))))) → top#(s(p(s(active(_x51)))))
top#(ok(f(_x21))) → top#(f(active(_x21)))top#(ok(p(_x21))) → top#(p(active(_x21)))
top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))
top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))top#(ok(s(p(cons(_x51, _x52))))) → top#(s(p(cons(active(_x51), _x52))))
top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))top#(ok(s(p(f(s(0)))))) → top#(s(p(mark(f(p(s(0)))))))
top#(ok(s(p(f(_x51))))) → top#(s(p(f(active(_x51)))))top#(ok(s(p(p(s(0)))))) → top#(s(p(mark(0))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

The right-hand side of the rule top#(ok(s(f(p(s(0)))))) → top#(s(f(mark(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
top#(s(mark(f(0)))) 
Thus, the rule top#(ok(s(f(p(s(0)))))) → top#(s(f(mark(0)))) is replaced by the following rules:
top#(ok(s(f(p(s(0)))))) → top#(s(mark(f(0))))

Problem 19: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(p(s(0))))) → top#(mark(s(0)))top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))
top#(ok(s(f(p(s(0)))))) → top#(s(mark(f(0))))top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))
top#(ok(s(f(p(_x51))))) → top#(s(f(p(active(_x51)))))top#(ok(s(f(f(0))))) → top#(s(f(mark(cons(0, f(s(0)))))))
top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))top#(mark(f(_x21))) → top#(f(proper(_x21)))
top#(ok(s(p(f(0))))) → top#(s(p(mark(cons(0, f(s(0)))))))top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))
top#(mark(p(_x21))) → top#(p(proper(_x21)))top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))
top#(ok(s(f(f(s(0)))))) → top#(s(f(mark(f(p(s(0)))))))top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))
top#(ok(s(p(p(_x51))))) → top#(s(p(p(active(_x51)))))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(ok(s(p(s(_x51))))) → top#(s(p(s(active(_x51)))))
top#(ok(f(_x21))) → top#(f(active(_x21)))top#(ok(p(_x21))) → top#(p(active(_x21)))
top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))
top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))top#(ok(s(p(cons(_x51, _x52))))) → top#(s(p(cons(active(_x51), _x52))))
top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))top#(ok(s(p(f(s(0)))))) → top#(s(p(mark(f(p(s(0)))))))
top#(ok(s(p(f(_x51))))) → top#(s(p(f(active(_x51)))))top#(ok(s(p(p(s(0)))))) → top#(s(p(mark(0))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, ok, mark, proper, top, cons

Strategy

The right-hand side of the rule top#(ok(s(f(p(s(0)))))) → top#(s(mark(f(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
top#(mark(s(f(0)))) 
Thus, the rule top#(ok(s(f(p(s(0)))))) → top#(s(mark(f(0)))) is replaced by the following rules:
top#(ok(s(f(p(s(0)))))) → top#(mark(s(f(0))))

Problem 20: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(p(s(0))))) → top#(mark(s(0)))top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))
top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))
top#(ok(s(f(f(0))))) → top#(s(f(mark(cons(0, f(s(0)))))))top#(ok(s(f(p(_x51))))) → top#(s(f(p(active(_x51)))))
top#(mark(f(_x21))) → top#(f(proper(_x21)))top#(ok(s(p(f(0))))) → top#(s(p(mark(cons(0, f(s(0)))))))
top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))top#(mark(p(_x21))) → top#(p(proper(_x21)))
top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))top#(ok(s(f(f(s(0)))))) → top#(s(f(mark(f(p(s(0)))))))
top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))top#(ok(s(p(p(_x51))))) → top#(s(p(p(active(_x51)))))
top#(mark(s(_x21))) → top#(s(proper(_x21)))top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))
top#(ok(s(p(s(_x51))))) → top#(s(p(s(active(_x51)))))top#(ok(f(_x21))) → top#(f(active(_x21)))
top#(ok(p(_x21))) → top#(p(active(_x21)))top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))
top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))
top#(ok(s(p(cons(_x51, _x52))))) → top#(s(p(cons(active(_x51), _x52))))top#(ok(s(f(p(s(0)))))) → top#(mark(s(f(0))))
top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))top#(ok(s(p(f(s(0)))))) → top#(s(p(mark(f(p(s(0)))))))
top#(ok(s(p(f(_x51))))) → top#(s(p(f(active(_x51)))))top#(ok(s(p(p(s(0)))))) → top#(s(p(mark(0))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

The right-hand side of the rule top#(ok(s(f(p(_x51))))) → top#(s(f(p(active(_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
top#(s(f(p(mark(cons(0, f(s(0)))))))) 
top#(s(f(p(s(active(_x61)))))) 
top#(s(f(p(cons(active(_x61), _x62))))) 
top#(s(f(p(p(active(_x61)))))) 
top#(s(f(p(mark(0))))) 
top#(s(f(p(f(active(_x61)))))) 
top#(s(f(p(mark(f(p(s(0)))))))) 
Thus, the rule top#(ok(s(f(p(_x51))))) → top#(s(f(p(active(_x51))))) is replaced by the following rules:
top#(ok(s(f(p(cons(_x61, _x62)))))) → top#(s(f(p(cons(active(_x61), _x62)))))top#(ok(s(f(p(f(_x61)))))) → top#(s(f(p(f(active(_x61))))))
top#(ok(s(f(p(f(s(0))))))) → top#(s(f(p(mark(f(p(s(0))))))))top#(ok(s(f(p(p(s(0))))))) → top#(s(f(p(mark(0)))))
top#(ok(s(f(p(p(_x61)))))) → top#(s(f(p(p(active(_x61))))))top#(ok(s(f(p(f(0)))))) → top#(s(f(p(mark(cons(0, f(s(0))))))))
top#(ok(s(f(p(s(_x61)))))) → top#(s(f(p(s(active(_x61))))))

Problem 21: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(p(s(0))))) → top#(mark(s(0)))top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))
top#(ok(s(f(p(p(_x61)))))) → top#(s(f(p(p(active(_x61))))))top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))
top#(ok(s(f(f(0))))) → top#(s(f(mark(cons(0, f(s(0)))))))top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))
top#(mark(f(_x21))) → top#(f(proper(_x21)))top#(ok(s(p(f(0))))) → top#(s(p(mark(cons(0, f(s(0)))))))
top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))top#(mark(p(_x21))) → top#(p(proper(_x21)))
top#(ok(s(f(p(p(s(0))))))) → top#(s(f(p(mark(0)))))top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))
top#(ok(s(f(f(s(0)))))) → top#(s(f(mark(f(p(s(0)))))))top#(ok(s(f(p(cons(_x61, _x62)))))) → top#(s(f(p(cons(active(_x61), _x62)))))
top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))top#(ok(s(p(p(_x51))))) → top#(s(p(p(active(_x51)))))
top#(ok(s(f(p(f(_x61)))))) → top#(s(f(p(f(active(_x61))))))top#(ok(s(f(p(f(s(0))))))) → top#(s(f(p(mark(f(p(s(0))))))))
top#(mark(s(_x21))) → top#(s(proper(_x21)))top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))
top#(ok(s(p(s(_x51))))) → top#(s(p(s(active(_x51)))))top#(ok(f(_x21))) → top#(f(active(_x21)))
top#(ok(p(_x21))) → top#(p(active(_x21)))top#(ok(s(f(p(f(0)))))) → top#(s(f(p(mark(cons(0, f(s(0))))))))
top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))
top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))top#(ok(s(p(cons(_x51, _x52))))) → top#(s(p(cons(active(_x51), _x52))))
top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))top#(ok(s(f(p(s(0)))))) → top#(mark(s(f(0))))
top#(ok(s(p(f(s(0)))))) → top#(s(p(mark(f(p(s(0)))))))top#(ok(s(p(f(_x51))))) → top#(s(p(f(active(_x51)))))
top#(ok(s(p(p(s(0)))))) → top#(s(p(mark(0))))top#(ok(s(f(p(s(_x61)))))) → top#(s(f(p(s(active(_x61))))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, ok, mark, proper, top, cons

Strategy

The right-hand side of the rule top#(ok(s(f(p(p(_x61)))))) → top#(s(f(p(p(active(_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
top#(s(f(p(p(p(active(_x71))))))) 
top#(s(f(p(p(mark(f(p(s(0))))))))) 
top#(s(f(p(p(mark(cons(0, f(s(0))))))))) 
top#(s(f(p(p(cons(active(_x71), _x72)))))) 
top#(s(f(p(p(s(active(_x71))))))) 
top#(s(f(p(p(f(active(_x71))))))) 
top#(s(f(p(p(mark(0)))))) 
Thus, the rule top#(ok(s(f(p(p(_x61)))))) → top#(s(f(p(p(active(_x61)))))) is replaced by the following rules:
top#(ok(s(f(p(p(f(0))))))) → top#(s(f(p(p(mark(cons(0, f(s(0)))))))))top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(f(p(p(mark(f(p(s(0)))))))))
top#(ok(s(f(p(p(p(s(0)))))))) → top#(s(f(p(p(mark(0))))))top#(ok(s(f(p(p(cons(_x71, _x72))))))) → top#(s(f(p(p(cons(active(_x71), _x72))))))
top#(ok(s(f(p(p(s(_x71))))))) → top#(s(f(p(p(s(active(_x71)))))))top#(ok(s(f(p(p(p(_x71))))))) → top#(s(f(p(p(p(active(_x71)))))))
top#(ok(s(f(p(p(f(_x71))))))) → top#(s(f(p(p(f(active(_x71)))))))

Problem 22: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(p(s(0))))) → top#(mark(s(0)))top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(f(p(p(mark(f(p(s(0)))))))))
top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))top#(ok(s(f(p(p(cons(_x71, _x72))))))) → top#(s(f(p(p(cons(active(_x71), _x72))))))
top#(ok(s(f(p(p(p(_x71))))))) → top#(s(f(p(p(p(active(_x71)))))))top#(ok(s(f(p(p(f(0))))))) → top#(s(f(p(p(mark(cons(0, f(s(0)))))))))
top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))top#(ok(s(f(p(p(p(s(0)))))))) → top#(s(f(p(p(mark(0))))))
top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))top#(ok(s(f(f(0))))) → top#(s(f(mark(cons(0, f(s(0)))))))
top#(mark(f(_x21))) → top#(f(proper(_x21)))top#(ok(s(p(f(0))))) → top#(s(p(mark(cons(0, f(s(0)))))))
top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))top#(mark(p(_x21))) → top#(p(proper(_x21)))
top#(ok(s(f(p(p(s(0))))))) → top#(s(f(p(mark(0)))))top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))
top#(ok(s(f(f(s(0)))))) → top#(s(f(mark(f(p(s(0)))))))top#(ok(s(f(p(cons(_x61, _x62)))))) → top#(s(f(p(cons(active(_x61), _x62)))))
top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))top#(ok(s(p(p(_x51))))) → top#(s(p(p(active(_x51)))))
top#(ok(s(f(p(f(_x61)))))) → top#(s(f(p(f(active(_x61))))))top#(ok(s(f(p(f(s(0))))))) → top#(s(f(p(mark(f(p(s(0))))))))
top#(ok(s(f(p(p(s(_x71))))))) → top#(s(f(p(p(s(active(_x71)))))))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(ok(p(_x21))) → top#(p(active(_x21)))
top#(ok(f(_x21))) → top#(f(active(_x21)))top#(ok(s(p(s(_x51))))) → top#(s(p(s(active(_x51)))))
top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))top#(ok(s(f(p(f(0)))))) → top#(s(f(p(mark(cons(0, f(s(0))))))))
top#(ok(s(f(p(p(f(_x71))))))) → top#(s(f(p(p(f(active(_x71)))))))top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))
top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))top#(ok(s(p(cons(_x51, _x52))))) → top#(s(p(cons(active(_x51), _x52))))
top#(ok(s(f(p(s(0)))))) → top#(mark(s(f(0))))top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))
top#(ok(s(p(f(s(0)))))) → top#(s(p(mark(f(p(s(0)))))))top#(ok(s(p(f(_x51))))) → top#(s(p(f(active(_x51)))))
top#(ok(s(p(p(s(0)))))) → top#(s(p(mark(0))))top#(ok(s(f(p(s(_x61)))))) → top#(s(f(p(s(active(_x61))))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

The right-hand side of the rule top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(f(p(p(mark(f(p(s(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
top#(s(f(p(mark(p(f(p(s(0))))))))) 
Thus, the rule top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(f(p(p(mark(f(p(s(0))))))))) is replaced by the following rules:
top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(f(p(mark(p(f(p(s(0)))))))))

Problem 23: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(p(s(0))))) → top#(mark(s(0)))top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))
top#(ok(s(f(p(p(cons(_x71, _x72))))))) → top#(s(f(p(p(cons(active(_x71), _x72))))))top#(ok(s(f(p(p(p(_x71))))))) → top#(s(f(p(p(p(active(_x71)))))))
top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(f(p(mark(p(f(p(s(0)))))))))top#(ok(s(f(p(p(f(0))))))) → top#(s(f(p(p(mark(cons(0, f(s(0)))))))))
top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))top#(ok(s(f(p(p(p(s(0)))))))) → top#(s(f(p(p(mark(0))))))
top#(ok(s(f(f(0))))) → top#(s(f(mark(cons(0, f(s(0)))))))top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))
top#(mark(f(_x21))) → top#(f(proper(_x21)))top#(ok(s(p(f(0))))) → top#(s(p(mark(cons(0, f(s(0)))))))
top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))top#(mark(p(_x21))) → top#(p(proper(_x21)))
top#(ok(s(f(p(p(s(0))))))) → top#(s(f(p(mark(0)))))top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))
top#(ok(s(f(f(s(0)))))) → top#(s(f(mark(f(p(s(0)))))))top#(ok(s(f(p(cons(_x61, _x62)))))) → top#(s(f(p(cons(active(_x61), _x62)))))
top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))top#(ok(s(p(p(_x51))))) → top#(s(p(p(active(_x51)))))
top#(ok(s(f(p(f(_x61)))))) → top#(s(f(p(f(active(_x61))))))top#(ok(s(f(p(f(s(0))))))) → top#(s(f(p(mark(f(p(s(0))))))))
top#(ok(s(f(p(p(s(_x71))))))) → top#(s(f(p(p(s(active(_x71)))))))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(ok(s(p(s(_x51))))) → top#(s(p(s(active(_x51)))))
top#(ok(f(_x21))) → top#(f(active(_x21)))top#(ok(p(_x21))) → top#(p(active(_x21)))
top#(ok(s(f(p(p(f(_x71))))))) → top#(s(f(p(p(f(active(_x71)))))))top#(ok(s(f(p(f(0)))))) → top#(s(f(p(mark(cons(0, f(s(0))))))))
top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))
top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))top#(ok(s(p(cons(_x51, _x52))))) → top#(s(p(cons(active(_x51), _x52))))
top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))top#(ok(s(f(p(s(0)))))) → top#(mark(s(f(0))))
top#(ok(s(p(f(s(0)))))) → top#(s(p(mark(f(p(s(0)))))))top#(ok(s(p(f(_x51))))) → top#(s(p(f(active(_x51)))))
top#(ok(s(p(p(s(0)))))) → top#(s(p(mark(0))))top#(ok(s(f(p(s(_x61)))))) → top#(s(f(p(s(active(_x61))))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, ok, mark, proper, top, cons

Strategy

The right-hand side of the rule top#(ok(s(f(p(p(cons(_x71, _x72))))))) → top#(s(f(p(p(cons(active(_x71), _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
top#(s(f(p(p(cons(cons(active(_x81), _x82), _x72)))))) 
top#(s(f(p(p(cons(f(active(_x81)), _x72)))))) 
top#(s(f(p(p(cons(mark(cons(0, f(s(0)))), _x72)))))) 
top#(s(f(p(p(cons(s(active(_x81)), _x72)))))) 
top#(s(f(p(p(cons(mark(f(p(s(0)))), _x72)))))) 
top#(s(f(p(p(cons(p(active(_x81)), _x72)))))) 
top#(s(f(p(p(cons(mark(0), _x72)))))) 
Thus, the rule top#(ok(s(f(p(p(cons(_x71, _x72))))))) → top#(s(f(p(p(cons(active(_x71), _x72)))))) is replaced by the following rules:
top#(ok(s(f(p(p(cons(p(_x81), _x72))))))) → top#(s(f(p(p(cons(p(active(_x81)), _x72))))))top#(ok(s(f(p(p(cons(f(_x81), _x72))))))) → top#(s(f(p(p(cons(f(active(_x81)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(0)), _x72))))))) → top#(s(f(p(p(cons(mark(0), _x72))))))top#(ok(s(f(p(p(cons(f(s(0)), _x72))))))) → top#(s(f(p(p(cons(mark(f(p(s(0)))), _x72))))))
top#(ok(s(f(p(p(cons(s(_x81), _x72))))))) → top#(s(f(p(p(cons(s(active(_x81)), _x72))))))top#(ok(s(f(p(p(cons(f(0), _x72))))))) → top#(s(f(p(p(cons(mark(cons(0, f(s(0)))), _x72))))))
top#(ok(s(f(p(p(cons(cons(_x81, _x82), _x72))))))) → top#(s(f(p(p(cons(cons(active(_x81), _x82), _x72))))))

Problem 24: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(f(p(p(cons(p(_x81), _x72))))))) → top#(s(f(p(p(cons(p(active(_x81)), _x72))))))top#(ok(s(p(s(0))))) → top#(mark(s(0)))
top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))top#(ok(s(f(p(p(cons(s(_x81), _x72))))))) → top#(s(f(p(p(cons(s(active(_x81)), _x72))))))
top#(ok(s(f(p(p(p(_x71))))))) → top#(s(f(p(p(p(active(_x71)))))))top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(f(p(mark(p(f(p(s(0)))))))))
top#(ok(s(f(p(p(f(0))))))) → top#(s(f(p(p(mark(cons(0, f(s(0)))))))))top#(ok(s(f(p(p(cons(f(_x81), _x72))))))) → top#(s(f(p(p(cons(f(active(_x81)), _x72))))))
top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))top#(ok(s(f(p(p(cons(p(s(0)), _x72))))))) → top#(s(f(p(p(cons(mark(0), _x72))))))
top#(ok(s(f(p(p(p(s(0)))))))) → top#(s(f(p(p(mark(0))))))top#(ok(s(f(p(p(cons(f(s(0)), _x72))))))) → top#(s(f(p(p(cons(mark(f(p(s(0)))), _x72))))))
top#(ok(s(f(f(0))))) → top#(s(f(mark(cons(0, f(s(0)))))))top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))
top#(mark(f(_x21))) → top#(f(proper(_x21)))top#(ok(s(p(f(0))))) → top#(s(p(mark(cons(0, f(s(0)))))))
top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))top#(mark(p(_x21))) → top#(p(proper(_x21)))
top#(ok(s(f(p(p(s(0))))))) → top#(s(f(p(mark(0)))))top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))
top#(ok(s(f(f(s(0)))))) → top#(s(f(mark(f(p(s(0)))))))top#(ok(s(f(p(p(cons(cons(_x81, _x82), _x72))))))) → top#(s(f(p(p(cons(cons(active(_x81), _x82), _x72))))))
top#(ok(s(f(p(cons(_x61, _x62)))))) → top#(s(f(p(cons(active(_x61), _x62)))))top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))
top#(ok(s(p(p(_x51))))) → top#(s(p(p(active(_x51)))))top#(ok(s(f(p(f(_x61)))))) → top#(s(f(p(f(active(_x61))))))
top#(ok(s(f(p(f(s(0))))))) → top#(s(f(p(mark(f(p(s(0))))))))top#(ok(s(f(p(p(s(_x71))))))) → top#(s(f(p(p(s(active(_x71)))))))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(ok(s(f(p(p(cons(f(0), _x72))))))) → top#(s(f(p(p(cons(mark(cons(0, f(s(0)))), _x72))))))top#(ok(p(_x21))) → top#(p(active(_x21)))
top#(ok(f(_x21))) → top#(f(active(_x21)))top#(ok(s(p(s(_x51))))) → top#(s(p(s(active(_x51)))))
top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))top#(ok(s(f(p(f(0)))))) → top#(s(f(p(mark(cons(0, f(s(0))))))))
top#(ok(s(f(p(p(f(_x71))))))) → top#(s(f(p(p(f(active(_x71)))))))top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))
top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))top#(ok(s(p(cons(_x51, _x52))))) → top#(s(p(cons(active(_x51), _x52))))
top#(ok(s(f(p(s(0)))))) → top#(mark(s(f(0))))top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))
top#(ok(s(p(f(s(0)))))) → top#(s(p(mark(f(p(s(0)))))))top#(ok(s(p(f(_x51))))) → top#(s(p(f(active(_x51)))))
top#(ok(s(p(p(s(0)))))) → top#(s(p(mark(0))))top#(ok(s(f(p(s(_x61)))))) → top#(s(f(p(s(active(_x61))))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

The right-hand side of the rule top#(ok(s(f(p(p(cons(p(_x81), _x72))))))) → top#(s(f(p(p(cons(p(active(_x81)), _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
top#(s(f(p(p(cons(p(cons(active(_x91), _x92)), _x72)))))) 
top#(s(f(p(p(cons(p(f(active(_x91))), _x72)))))) 
top#(s(f(p(p(cons(p(s(active(_x91))), _x72)))))) 
top#(s(f(p(p(cons(p(p(active(_x91))), _x72)))))) 
top#(s(f(p(p(cons(p(mark(cons(0, f(s(0))))), _x72)))))) 
top#(s(f(p(p(cons(p(mark(f(p(s(0))))), _x72)))))) 
top#(s(f(p(p(cons(p(mark(0)), _x72)))))) 
Thus, the rule top#(ok(s(f(p(p(cons(p(_x81), _x72))))))) → top#(s(f(p(p(cons(p(active(_x81)), _x72)))))) is replaced by the following rules:
top#(ok(s(f(p(p(cons(p(s(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(s(active(_x91))), _x72))))))top#(ok(s(f(p(p(cons(p(f(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(f(active(_x91))), _x72))))))
top#(ok(s(f(p(p(cons(p(p(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(p(active(_x91))), _x72))))))top#(ok(s(f(p(p(cons(p(f(s(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(f(p(s(0))))), _x72))))))
top#(ok(s(f(p(p(cons(p(cons(_x91, _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(active(_x91), _x92)), _x72))))))top#(ok(s(f(p(p(cons(p(p(s(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(0)), _x72))))))
top#(ok(s(f(p(p(cons(p(f(0)), _x72))))))) → top#(s(f(p(p(cons(p(mark(cons(0, f(s(0))))), _x72))))))

Problem 25: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(f(p(p(cons(p(s(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(s(active(_x91))), _x72))))))top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))
top#(ok(s(f(p(p(cons(p(cons(_x91, _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(active(_x91), _x92)), _x72))))))top#(ok(s(f(p(p(f(0))))))) → top#(s(f(p(p(mark(cons(0, f(s(0)))))))))
top#(ok(s(f(p(p(cons(f(_x81), _x72))))))) → top#(s(f(p(p(cons(f(active(_x81)), _x72))))))top#(ok(s(f(p(p(cons(p(s(0)), _x72))))))) → top#(s(f(p(p(cons(mark(0), _x72))))))
top#(ok(s(f(p(p(cons(f(s(0)), _x72))))))) → top#(s(f(p(p(cons(mark(f(p(s(0)))), _x72))))))top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))
top#(ok(s(f(f(0))))) → top#(s(f(mark(cons(0, f(s(0)))))))top#(mark(f(_x21))) → top#(f(proper(_x21)))
top#(ok(s(p(f(0))))) → top#(s(p(mark(cons(0, f(s(0)))))))top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))
top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))top#(ok(s(f(f(s(0)))))) → top#(s(f(mark(f(p(s(0)))))))
top#(ok(s(f(p(cons(_x61, _x62)))))) → top#(s(f(p(cons(active(_x61), _x62)))))top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))
top#(ok(s(p(p(_x51))))) → top#(s(p(p(active(_x51)))))top#(ok(s(f(p(f(_x61)))))) → top#(s(f(p(f(active(_x61))))))
top#(ok(s(f(p(p(s(_x71))))))) → top#(s(f(p(p(s(active(_x71)))))))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(ok(s(p(s(_x51))))) → top#(s(p(s(active(_x51)))))top#(ok(s(f(p(p(cons(p(p(s(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(0)), _x72))))))
top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))top#(ok(s(f(p(f(0)))))) → top#(s(f(p(mark(cons(0, f(s(0))))))))
top#(ok(s(f(p(p(f(_x71))))))) → top#(s(f(p(p(f(active(_x71)))))))top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))
top#(ok(s(p(cons(_x51, _x52))))) → top#(s(p(cons(active(_x51), _x52))))top#(ok(s(f(p(s(0)))))) → top#(mark(s(f(0))))
top#(ok(s(p(f(_x51))))) → top#(s(p(f(active(_x51)))))top#(ok(s(p(p(s(0)))))) → top#(s(p(mark(0))))
top#(ok(s(f(p(s(_x61)))))) → top#(s(f(p(s(active(_x61))))))top#(ok(s(p(s(0))))) → top#(mark(s(0)))
top#(ok(s(f(p(p(cons(s(_x81), _x72))))))) → top#(s(f(p(p(cons(s(active(_x81)), _x72))))))top#(ok(s(f(p(p(p(_x71))))))) → top#(s(f(p(p(p(active(_x71)))))))
top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(f(p(mark(p(f(p(s(0)))))))))top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))
top#(ok(s(f(p(p(p(s(0)))))))) → top#(s(f(p(p(mark(0))))))top#(ok(s(f(p(p(cons(p(f(s(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(f(p(s(0))))), _x72))))))
top#(ok(s(f(p(p(s(0))))))) → top#(s(f(p(mark(0)))))top#(mark(p(_x21))) → top#(p(proper(_x21)))
top#(ok(s(f(p(p(cons(cons(_x81, _x82), _x72))))))) → top#(s(f(p(p(cons(cons(active(_x81), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(f(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(f(active(_x91))), _x72))))))
top#(ok(s(f(p(f(s(0))))))) → top#(s(f(p(mark(f(p(s(0))))))))top#(ok(s(f(p(p(cons(f(0), _x72))))))) → top#(s(f(p(p(cons(mark(cons(0, f(s(0)))), _x72))))))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(ok(f(_x21))) → top#(f(active(_x21)))
top#(ok(p(_x21))) → top#(p(active(_x21)))top#(ok(s(f(p(p(cons(p(f(0)), _x72))))))) → top#(s(f(p(p(cons(p(mark(cons(0, f(s(0))))), _x72))))))
top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))top#(ok(s(f(p(p(cons(p(p(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(p(active(_x91))), _x72))))))
top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))top#(ok(s(p(f(s(0)))))) → top#(s(p(mark(f(p(s(0)))))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, ok, mark, proper, top, cons

Strategy

The right-hand side of the rule top#(ok(s(f(p(p(cons(p(s(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(s(active(_x91))), _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
top#(s(f(p(p(cons(p(s(mark(cons(0, f(s(0)))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(f(active(_x101)))), _x72)))))) 
top#(s(f(p(p(cons(p(s(mark(f(p(s(0)))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(p(active(_x101)))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(active(_x101)))), _x72)))))) 
top#(s(f(p(p(cons(p(s(mark(0))), _x72)))))) 
top#(s(f(p(p(cons(p(s(cons(active(_x101), _x102))), _x72)))))) 
Thus, the rule top#(ok(s(f(p(p(cons(p(s(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(s(active(_x91))), _x72)))))) is replaced by the following rules:
top#(ok(s(f(p(p(cons(p(s(f(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(f(active(_x101)))), _x72))))))top#(ok(s(f(p(p(cons(p(s(p(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(0))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(active(_x101)))), _x72))))))top#(ok(s(f(p(p(cons(p(s(p(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(p(active(_x101)))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(f(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(f(p(s(0)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(f(0))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(cons(0, f(s(0)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(cons(_x101, _x102))), _x72))))))) → top#(s(f(p(p(cons(p(s(cons(active(_x101), _x102))), _x72))))))

Problem 26: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(f(p(p(cons(p(s(s(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(active(_x101)))), _x72))))))top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))
top#(ok(s(f(p(p(cons(p(cons(_x91, _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(active(_x91), _x92)), _x72))))))top#(ok(s(f(p(p(f(0))))))) → top#(s(f(p(p(mark(cons(0, f(s(0)))))))))
top#(ok(s(f(p(p(cons(f(_x81), _x72))))))) → top#(s(f(p(p(cons(f(active(_x81)), _x72))))))top#(ok(s(f(p(p(cons(p(s(0)), _x72))))))) → top#(s(f(p(p(cons(mark(0), _x72))))))
top#(ok(s(f(p(p(cons(f(s(0)), _x72))))))) → top#(s(f(p(p(cons(mark(f(p(s(0)))), _x72))))))top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))
top#(ok(s(f(f(0))))) → top#(s(f(mark(cons(0, f(s(0)))))))top#(mark(f(_x21))) → top#(f(proper(_x21)))
top#(ok(s(p(f(0))))) → top#(s(p(mark(cons(0, f(s(0)))))))top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))
top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))top#(ok(s(f(f(s(0)))))) → top#(s(f(mark(f(p(s(0)))))))
top#(ok(s(f(p(cons(_x61, _x62)))))) → top#(s(f(p(cons(active(_x61), _x62)))))top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))
top#(ok(s(p(p(_x51))))) → top#(s(p(p(active(_x51)))))top#(ok(s(f(p(f(_x61)))))) → top#(s(f(p(f(active(_x61))))))
top#(ok(s(f(p(p(s(_x71))))))) → top#(s(f(p(p(s(active(_x71)))))))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(ok(s(f(p(p(cons(p(s(f(0))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(cons(0, f(s(0)))))), _x72))))))top#(ok(s(p(s(_x51))))) → top#(s(p(s(active(_x51)))))
top#(ok(s(f(p(p(cons(p(p(s(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(0)), _x72))))))top#(ok(s(f(p(f(0)))))) → top#(s(f(p(mark(cons(0, f(s(0))))))))
top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))top#(ok(s(f(p(p(f(_x71))))))) → top#(s(f(p(p(f(active(_x71)))))))
top#(ok(s(f(p(p(cons(p(s(f(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(f(active(_x101)))), _x72))))))top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))
top#(ok(s(p(cons(_x51, _x52))))) → top#(s(p(cons(active(_x51), _x52))))top#(ok(s(f(p(s(0)))))) → top#(mark(s(f(0))))
top#(ok(s(p(f(_x51))))) → top#(s(p(f(active(_x51)))))top#(ok(s(p(p(s(0)))))) → top#(s(p(mark(0))))
top#(ok(s(f(p(s(_x61)))))) → top#(s(f(p(s(active(_x61))))))top#(ok(s(p(s(0))))) → top#(mark(s(0)))
top#(ok(s(f(p(p(cons(p(s(p(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(0))), _x72))))))top#(ok(s(f(p(p(cons(s(_x81), _x72))))))) → top#(s(f(p(p(cons(s(active(_x81)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(f(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(f(p(s(0)))))), _x72))))))top#(ok(s(f(p(p(p(_x71))))))) → top#(s(f(p(p(p(active(_x71)))))))
top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(f(p(mark(p(f(p(s(0)))))))))top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))
top#(ok(s(f(p(p(p(s(0)))))))) → top#(s(f(p(p(mark(0))))))top#(ok(s(f(p(p(cons(p(f(s(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(f(p(s(0))))), _x72))))))
top#(ok(s(f(p(p(s(0))))))) → top#(s(f(p(mark(0)))))top#(mark(p(_x21))) → top#(p(proper(_x21)))
top#(ok(s(f(p(p(cons(cons(_x81, _x82), _x72))))))) → top#(s(f(p(p(cons(cons(active(_x81), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(f(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(f(active(_x91))), _x72))))))
top#(ok(s(f(p(f(s(0))))))) → top#(s(f(p(mark(f(p(s(0))))))))top#(ok(s(f(p(p(cons(p(s(p(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(p(active(_x101)))), _x72))))))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(ok(s(f(p(p(cons(f(0), _x72))))))) → top#(s(f(p(p(cons(mark(cons(0, f(s(0)))), _x72))))))
top#(ok(p(_x21))) → top#(p(active(_x21)))top#(ok(f(_x21))) → top#(f(active(_x21)))
top#(ok(s(f(p(p(cons(p(f(0)), _x72))))))) → top#(s(f(p(p(cons(p(mark(cons(0, f(s(0))))), _x72))))))top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))
top#(ok(s(f(p(p(cons(p(p(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(p(active(_x91))), _x72))))))top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))
top#(ok(s(p(f(s(0)))))) → top#(s(p(mark(f(p(s(0)))))))top#(ok(s(f(p(p(cons(p(s(cons(_x101, _x102))), _x72))))))) → top#(s(f(p(p(cons(p(s(cons(active(_x101), _x102))), _x72))))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

The right-hand side of the rule top#(ok(s(f(p(p(cons(p(s(s(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(active(_x101)))), _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
top#(s(f(p(p(cons(p(s(s(mark(f(p(s(0))))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(mark(cons(0, f(s(0))))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(s(active(_x111))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(f(active(_x111))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(cons(active(_x111), _x112)))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(mark(0)))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(p(active(_x111))))), _x72)))))) 
Thus, the rule top#(ok(s(f(p(p(cons(p(s(s(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(active(_x101)))), _x72)))))) is replaced by the following rules:
top#(ok(s(f(p(p(cons(p(s(s(f(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(cons(0, f(s(0))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(s(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(f(p(s(0))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(_x111)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(active(_x111))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(p(s(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(0)))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(_x111)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(active(_x111))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(p(_x111)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(p(active(_x111))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(cons(_x111, _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(active(_x111), _x112)))), _x72))))))

Problem 27: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))top#(ok(s(f(p(p(cons(p(s(s(f(_x111)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(active(_x111))))), _x72))))))
top#(ok(s(f(p(p(cons(p(cons(_x91, _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(active(_x91), _x92)), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(cons(_x111, _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(active(_x111), _x112)))), _x72))))))
top#(ok(s(f(p(p(f(0))))))) → top#(s(f(p(p(mark(cons(0, f(s(0)))))))))top#(ok(s(f(p(p(cons(f(_x81), _x72))))))) → top#(s(f(p(p(cons(f(active(_x81)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(_x111)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(active(_x111))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(0)), _x72))))))) → top#(s(f(p(p(cons(mark(0), _x72))))))
top#(ok(s(f(p(p(cons(f(s(0)), _x72))))))) → top#(s(f(p(p(cons(mark(f(p(s(0)))), _x72))))))top#(ok(s(s(_x41)))) → top#(s(s(active(_x41))))
top#(ok(s(f(f(0))))) → top#(s(f(mark(cons(0, f(s(0)))))))top#(mark(f(_x21))) → top#(f(proper(_x21)))
top#(ok(s(p(f(0))))) → top#(s(p(mark(cons(0, f(s(0)))))))top#(ok(cons(_x21, _x22))) → top#(cons(active(_x21), _x22))
top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))top#(ok(s(f(f(s(0)))))) → top#(s(f(mark(f(p(s(0)))))))
top#(ok(s(f(p(cons(_x61, _x62)))))) → top#(s(f(p(cons(active(_x61), _x62)))))top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))
top#(ok(s(p(p(_x51))))) → top#(s(p(p(active(_x51)))))top#(ok(s(f(p(f(_x61)))))) → top#(s(f(p(f(active(_x61))))))
top#(ok(s(f(p(p(s(_x71))))))) → top#(s(f(p(p(s(active(_x71)))))))top#(ok(s(f(p(p(cons(p(s(f(0))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(cons(0, f(s(0)))))), _x72))))))
top#(mark(s(_x21))) → top#(s(proper(_x21)))top#(ok(s(p(s(_x51))))) → top#(s(p(s(active(_x51)))))
top#(ok(s(f(p(p(cons(p(p(s(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(0)), _x72))))))top#(ok(s(f(p(f(0)))))) → top#(s(f(p(mark(cons(0, f(s(0))))))))
top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))top#(ok(s(f(p(p(f(_x71))))))) → top#(s(f(p(p(f(active(_x71)))))))
top#(ok(s(f(p(p(cons(p(s(f(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(f(active(_x101)))), _x72))))))top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))
top#(ok(s(p(cons(_x51, _x52))))) → top#(s(p(cons(active(_x51), _x52))))top#(ok(s(f(p(s(0)))))) → top#(mark(s(f(0))))
top#(ok(s(f(p(p(cons(p(s(s(p(s(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(0)))), _x72))))))top#(ok(s(p(f(_x51))))) → top#(s(p(f(active(_x51)))))
top#(ok(s(p(p(s(0)))))) → top#(s(p(mark(0))))top#(ok(s(f(p(s(_x61)))))) → top#(s(f(p(s(active(_x61))))))
top#(ok(s(p(s(0))))) → top#(mark(s(0)))top#(ok(s(f(p(p(cons(p(s(s(f(s(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(f(p(s(0))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(p(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(0))), _x72))))))top#(ok(s(f(p(p(cons(s(_x81), _x72))))))) → top#(s(f(p(p(cons(s(active(_x81)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(f(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(f(p(s(0)))))), _x72))))))top#(ok(s(f(p(p(p(_x71))))))) → top#(s(f(p(p(p(active(_x71)))))))
top#(ok(s(f(p(p(cons(p(s(s(p(_x111)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(p(active(_x111))))), _x72))))))top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(f(p(mark(p(f(p(s(0)))))))))
top#(ok(s(f(p(p(cons(p(s(s(f(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(cons(0, f(s(0))))))), _x72))))))top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))
top#(ok(s(f(p(p(p(s(0)))))))) → top#(s(f(p(p(mark(0))))))top#(ok(s(f(p(p(cons(p(f(s(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(f(p(s(0))))), _x72))))))
top#(mark(p(_x21))) → top#(p(proper(_x21)))top#(ok(s(f(p(p(s(0))))))) → top#(s(f(p(mark(0)))))
top#(ok(s(f(p(p(cons(cons(_x81, _x82), _x72))))))) → top#(s(f(p(p(cons(cons(active(_x81), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(f(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(f(active(_x91))), _x72))))))
top#(ok(s(f(p(f(s(0))))))) → top#(s(f(p(mark(f(p(s(0))))))))top#(ok(s(f(p(p(cons(p(s(p(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(p(active(_x101)))), _x72))))))
top#(ok(s(f(p(p(cons(f(0), _x72))))))) → top#(s(f(p(p(cons(mark(cons(0, f(s(0)))), _x72))))))top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))
top#(ok(f(_x21))) → top#(f(active(_x21)))top#(ok(p(_x21))) → top#(p(active(_x21)))
top#(ok(s(f(p(p(cons(p(f(0)), _x72))))))) → top#(s(f(p(p(cons(p(mark(cons(0, f(s(0))))), _x72))))))top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))
top#(ok(s(f(p(p(cons(p(p(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(p(active(_x91))), _x72))))))top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))
top#(ok(s(p(f(s(0)))))) → top#(s(p(mark(f(p(s(0)))))))top#(ok(s(f(p(p(cons(p(s(cons(_x101, _x102))), _x72))))))) → top#(s(f(p(p(cons(p(s(cons(active(_x101), _x102))), _x72))))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, ok, mark, proper, top, cons

Strategy

The right-hand side of the rule top#(ok(s(f(p(p(cons(p(s(s(f(_x111)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(active(_x111))))), _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
top#(s(f(p(p(cons(p(s(s(f(f(active(_x121)))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(f(mark(f(p(s(0)))))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(f(mark(cons(0, f(s(0)))))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(f(p(active(_x121)))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(f(mark(0))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(f(cons(active(_x121), _x122))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(f(s(active(_x121)))))), _x72)))))) 
Thus, the rule top#(ok(s(f(p(p(cons(p(s(s(f(_x111)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(active(_x111))))), _x72)))))) is replaced by the following rules:
top#(ok(s(f(p(p(cons(p(s(s(f(f(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(mark(cons(0, f(s(0)))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(s(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(s(active(_x121)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(p(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(p(active(_x121)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(active(_x121)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(mark(f(p(s(0)))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(cons(_x121, _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(active(_x121), _x122))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(p(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(mark(0))))), _x72))))))

Problem 28: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(cons(f(0), _x32))) → top#(mark(cons(cons(0, f(s(0))), _x32)))top#(ok(s(f(f(s(0)))))) → top#(mark(s(f(f(p(s(0)))))))
top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))top#(ok(s(f(p(f(cons(f(_x81), _x72))))))) → top#(s(f(p(f(cons(f(active(_x81)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(active(_x131))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(cons(_x131, _x132)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(cons(active(_x131), _x132)))))), _x72))))))
top#(ok(s(f(p(p(s(_x71))))))) → top#(s(f(p(p(s(active(_x71)))))))top#(ok(s(f(p(p(cons(p(s(f(0))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(cons(0, f(s(0)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(_x91)), _x72))))))) → top#(s(f(p(p(cons(f(f(active(_x91))), _x72))))))top#(ok(cons(s(_x41), _x22))) → top#(cons(s(active(_x41)), _x22))
top#(ok(s(p(p(p(s(0))))))) → top#(s(p(p(mark(0)))))top#(ok(s(f(p(p(cons(p(p(s(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(0)), _x72))))))
top#(ok(s(f(p(f(f(s(0)))))))) → top#(s(f(p(f(mark(f(p(s(0)))))))))top#(ok(s(f(p(p(f(_x71))))))) → top#(s(f(p(p(f(active(_x71)))))))
top#(ok(s(cons(_x41, _x42)))) → top#(s(cons(active(_x41), _x42)))top#(ok(s(f(p(p(cons(p(cons(cons(_x101, _x102), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(cons(active(_x101), _x102), _x92)), _x72))))))
top#(ok(s(f(p(p(cons(f(s(_x91)), _x72))))))) → top#(s(f(p(p(cons(f(s(active(_x91))), _x72))))))top#(ok(s(f(p(s(0)))))) → top#(mark(s(f(0))))
top#(ok(s(f(p(p(cons(p(s(s(p(s(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(0)))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(active(_x121)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(f(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(mark(cons(0, f(s(0)))))))), _x72))))))top#(ok(s(s(cons(p(_x61), _x52))))) → top#(s(s(cons(p(active(_x61)), _x52))))
top#(ok(s(f(p(p(cons(p(s(s(f(cons(_x121, _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(active(_x121), _x122))))), _x72))))))top#(ok(s(f(p(s(_x61)))))) → top#(s(f(p(s(active(_x61))))))
top#(ok(cons(cons(_x41, _x42), _x22))) → top#(cons(cons(active(_x41), _x42), _x22))top#(ok(s(f(p(f(cons(p(_x81), _x72))))))) → top#(s(f(p(f(cons(p(active(_x81)), _x72))))))
top#(ok(s(p(s(0))))) → top#(mark(s(0)))top#(ok(s(f(p(p(cons(p(s(s(s(s(f(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(mark(cons(0, f(s(0))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(s(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(f(p(s(0))))))), _x72))))))top#(ok(s(p(p(p(f(cons(f(0), _x82)))))))) → top#(s(p(p(p(f(cons(mark(cons(0, f(s(0)))), _x82)))))))
top#(ok(s(p(p(p(p(_x71))))))) → top#(s(p(p(p(p(active(_x71)))))))top#(ok(s(p(p(f(0)))))) → top#(s(p(p(mark(cons(0, f(s(0))))))))
top#(ok(s(f(p(p(cons(s(_x81), _x72))))))) → top#(s(f(p(p(cons(s(active(_x81)), _x72))))))top#(ok(s(f(p(f(f(0))))))) → top#(s(f(p(f(mark(cons(0, f(s(0)))))))))
top#(ok(s(s(cons(s(_x61), _x52))))) → top#(s(s(cons(s(active(_x61)), _x52))))top#(ok(s(f(p(p(cons(p(s(s(cons(p(s(0)), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(mark(0), _x112)))), _x72))))))
top#(ok(s(f(p(cons(s(_x71), _x62)))))) → top#(s(f(p(cons(s(active(_x71)), _x62)))))top#(ok(s(f(p(p(cons(f(f(0)), _x72))))))) → top#(s(f(p(p(cons(f(mark(cons(0, f(s(0))))), _x72))))))
top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(f(p(mark(p(f(p(s(0)))))))))top#(ok(s(f(p(p(cons(p(s(s(f(p(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(mark(0))))), _x72))))))
top#(ok(s(f(p(f(cons(s(_x81), _x72))))))) → top#(s(f(p(f(cons(s(active(_x81)), _x72))))))top#(ok(s(f(p(p(cons(f(p(_x91)), _x72))))))) → top#(s(f(p(p(cons(f(p(active(_x91))), _x72))))))
top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))top#(ok(cons(f(_x41), _x22))) → top#(cons(f(active(_x41)), _x22))
top#(ok(s(f(p(p(cons(p(s(s(cons(p(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(p(active(_x121)), _x112)))), _x72))))))top#(ok(s(f(p(p(p(s(0)))))))) → top#(s(f(p(p(mark(0))))))
top#(ok(s(f(p(p(cons(p(f(s(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(f(p(s(0))))), _x72))))))top#(ok(s(s(cons(p(s(0)), _x52))))) → top#(s(s(cons(mark(0), _x52))))
top#(ok(s(p(p(p(f(cons(p(s(0)), _x72)))))))) → top#(s(p(p(p(f(mark(cons(0, _x72))))))))top#(ok(s(f(p(p(cons(cons(_x81, _x82), _x72))))))) → top#(s(f(p(p(cons(cons(active(_x81), _x82), _x72))))))
top#(ok(s(p(p(p(s(s(_x81)))))))) → top#(s(p(p(p(s(s(active(_x81))))))))top#(ok(s(s(f(0))))) → top#(s(s(mark(cons(0, f(s(0)))))))
top#(ok(s(f(p(p(cons(p(f(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(f(active(_x91))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(p(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(mark(0))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(cons(s(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(s(active(_x121)), _x112)))), _x72))))))top#(ok(s(s(p(_x51))))) → top#(s(s(p(active(_x51)))))
top#(ok(p(_x21))) → top#(p(active(_x21)))top#(ok(f(_x21))) → top#(f(active(_x21)))
top#(ok(s(p(p(p(f(cons(s(_x91), _x82)))))))) → top#(s(p(p(p(f(cons(s(active(_x91)), _x82)))))))top#(ok(s(f(p(p(cons(p(cons(f(s(0)), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(mark(f(p(s(0)))), _x92)), _x72))))))
top#(ok(s(f(p(cons(f(_x71), _x62)))))) → top#(s(f(p(cons(f(active(_x71)), _x62)))))top#(ok(s(f(p(p(cons(p(f(0)), _x72))))))) → top#(s(f(p(p(cons(p(mark(cons(0, f(s(0))))), _x72))))))
top#(ok(s(p(p(p(f(p(s(0))))))))) → top#(s(p(p(p(f(mark(0)))))))top#(ok(s(p(p(p(s(f(s(0))))))))) → top#(s(p(p(p(s(mark(f(p(s(0))))))))))
top#(ok(s(p(p(p(f(f(_x81)))))))) → top#(s(p(p(p(f(f(active(_x81))))))))top#(ok(s(p(p(p(s(f(_x81)))))))) → top#(s(p(p(p(s(f(active(_x81))))))))
top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))top#(ok(s(p(f(s(0)))))) → top#(s(p(mark(f(p(s(0)))))))
top#(ok(s(f(p(f(f(_x71))))))) → top#(s(f(p(f(f(active(_x71)))))))top#(ok(s(p(p(p(f(cons(cons(_x91, _x92), _x82)))))))) → top#(s(p(p(p(f(cons(cons(active(_x91), _x92), _x82)))))))
top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))top#(ok(s(p(p(p(f(cons(p(_x91), _x82)))))))) → top#(s(p(p(p(f(cons(p(active(_x91)), _x82)))))))
top#(ok(s(f(p(cons(p(_x71), _x62)))))) → top#(s(f(p(cons(p(active(_x71)), _x62)))))top#(ok(s(f(f(0))))) → top#(s(mark(f(cons(0, f(s(0)))))))
top#(mark(f(cons(_x41, _x42)))) → top#(f(cons(proper(_x41), proper(_x42))))top#(ok(s(f(p(p(cons(p(s(s(s(cons(_x121, _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(cons(active(_x121), _x122))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(f(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(f(active(_x131))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(p(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(p(active(_x121)))))), _x72))))))
top#(ok(s(p(p(p(s(f(0)))))))) → top#(s(p(p(p(mark(s(cons(0, f(s(0))))))))))top#(ok(s(s(cons(cons(_x61, _x62), _x52))))) → top#(s(s(cons(cons(active(_x61), _x62), _x52))))
top#(mark(f(0))) → top#(f(ok(0)))top#(ok(s(p(p(p(s(p(s(0))))))))) → top#(s(p(p(p(s(mark(0)))))))
top#(ok(s(f(p(p(cons(p(s(0)), _x72))))))) → top#(s(f(p(p(cons(mark(0), _x72))))))top#(ok(s(f(p(p(cons(f(s(0)), _x62))))))) → top#(s(f(p(p(mark(cons(f(p(s(0))), _x62)))))))
top#(ok(s(f(p(p(cons(p(s(s(f(s(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(s(active(_x121)))))), _x72))))))top#(ok(s(f(p(p(cons(p(cons(s(_x101), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(s(active(_x101)), _x92)), _x72))))))
top#(ok(s(s(cons(f(_x61), _x52))))) → top#(s(s(cons(f(active(_x61)), _x52))))top#(ok(s(f(p(p(cons(p(cons(f(0), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(mark(cons(0, f(s(0)))), _x92)), _x72))))))
top#(ok(s(p(f(0))))) → top#(s(p(mark(cons(0, f(s(0)))))))top#(ok(s(f(p(f(p(_x71))))))) → top#(s(f(p(f(p(active(_x71)))))))
top#(ok(s(s(s(_x51))))) → top#(s(s(s(active(_x51)))))top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))
top#(ok(s(f(p(p(cons(p(s(s(cons(f(s(0)), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(mark(f(p(s(0)))), _x112)))), _x72))))))top#(ok(s(p(p(p(s(p(_x81)))))))) → top#(s(p(p(p(s(p(active(_x81))))))))
top#(ok(cons(p(_x41), _x22))) → top#(cons(p(active(_x41)), _x22))top#(ok(s(f(p(p(f(0))))))) → top#(s(f(p(mark(p(cons(0, f(s(0)))))))))
top#(ok(s(p(p(p(f(f(s(0))))))))) → top#(s(p(p(p(f(mark(f(p(s(0))))))))))top#(ok(s(f(p(f(cons(cons(_x81, _x82), _x72))))))) → top#(s(f(p(f(cons(cons(active(_x81), _x82), _x72))))))
top#(ok(s(p(p(p(f(s(_x81)))))))) → top#(s(p(p(p(f(s(active(_x81))))))))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(ok(s(p(s(_x51))))) → top#(s(p(s(active(_x51)))))top#(ok(s(f(p(f(cons(f(0), _x72))))))) → top#(s(f(p(f(cons(mark(cons(0, f(s(0)))), _x72))))))
top#(ok(s(f(p(f(0)))))) → top#(s(f(p(mark(cons(0, f(s(0))))))))top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))
top#(ok(s(s(f(_x51))))) → top#(s(s(f(active(_x51)))))top#(ok(s(f(p(p(cons(p(s(f(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(f(active(_x101)))), _x72))))))
top#(ok(s(p(p(f(s(0))))))) → top#(s(p(p(mark(f(p(s(0))))))))top#(ok(s(p(cons(_x51, _x52))))) → top#(s(p(cons(active(_x51), _x52))))
top#(ok(s(p(p(p(f(p(_x81)))))))) → top#(s(p(p(p(f(p(active(_x81))))))))top#(ok(s(p(f(_x51))))) → top#(s(p(f(active(_x51)))))
top#(mark(f(p(_x41)))) → top#(f(p(proper(_x41))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(mark(f(p(s(0)))))))), _x72))))))
top#(ok(s(p(p(p(f(0))))))) → top#(s(p(p(p(mark(cons(0, f(s(0)))))))))top#(ok(s(p(p(s(0)))))) → top#(s(p(mark(0))))
top#(mark(f(f(_x41)))) → top#(f(f(proper(_x41))))top#(ok(s(s(f(s(0)))))) → top#(s(mark(s(f(p(s(0)))))))
top#(ok(s(f(p(p(cons(f(cons(_x91, _x92)), _x72))))))) → top#(s(f(p(p(cons(f(cons(active(_x91), _x92)), _x72))))))top#(ok(s(f(p(p(cons(p(s(p(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(0))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(cons(f(0), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(mark(cons(0, f(s(0)))), _x112)))), _x72))))))top#(mark(f(s(_x41)))) → top#(f(s(proper(_x41))))
top#(ok(s(f(p(p(cons(p(s(f(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(f(p(s(0)))))), _x72))))))top#(ok(s(f(p(f(cons(p(s(0)), _x72))))))) → top#(s(f(p(f(cons(mark(0), _x72))))))
top#(ok(cons(f(s(0)), _x22))) → top#(cons(mark(f(p(s(0)))), _x22))top#(ok(s(f(p(p(p(_x71))))))) → top#(s(f(p(p(p(active(_x71)))))))
top#(ok(s(f(p(p(cons(p(s(s(p(_x111)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(p(active(_x111))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(cons(cons(_x121, _x122), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(cons(active(_x121), _x122), _x112)))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(f(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(mark(f(p(s(0))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(cons(0, f(s(0))))))), _x72))))))
top#(ok(s(f(p(cons(f(0), _x62)))))) → top#(s(f(p(cons(mark(cons(0, f(s(0)))), _x62)))))top#(ok(s(p(p(p(f(s(0)))))))) → top#(s(p(p(mark(p(f(p(s(0)))))))))
top#(ok(s(f(p(p(cons(p(s(s(s(f(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(mark(f(p(s(0)))))))), _x72))))))top#(ok(s(f(p(p(cons(f(p(s(0))), _x72))))))) → top#(s(f(p(p(cons(f(mark(0)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(cons(f(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(f(active(_x121)), _x112)))), _x72))))))top#(ok(s(s(cons(f(s(0)), _x52))))) → top#(s(s(cons(mark(f(p(s(0)))), _x52))))
top#(ok(s(f(p(cons(p(s(0)), _x62)))))) → top#(s(f(p(cons(mark(0), _x62)))))top#(ok(s(f(p(p(cons(f(f(s(0))), _x72))))))) → top#(s(f(p(p(cons(f(mark(f(p(s(0))))), _x72))))))
top#(ok(s(p(p(f(_x61)))))) → top#(s(p(p(f(active(_x61))))))top#(mark(p(_x21))) → top#(p(proper(_x21)))
top#(ok(s(f(p(p(s(0))))))) → top#(s(f(p(mark(0)))))top#(ok(s(f(p(cons(f(s(0)), _x62)))))) → top#(s(f(p(cons(mark(f(p(s(0)))), _x62)))))
top#(ok(s(f(p(p(cons(p(cons(f(_x101), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(f(active(_x101)), _x92)), _x72))))))top#(ok(s(p(p(p(f(cons(f(s(0)), _x72)))))))) → top#(s(p(p(mark(p(f(cons(f(p(s(0))), _x72))))))))
top#(ok(s(f(p(p(cons(p(cons(p(_x101), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(p(active(_x101)), _x92)), _x72))))))top#(ok(s(p(p(s(_x61)))))) → top#(s(p(p(s(active(_x61))))))
top#(ok(s(p(p(p(f(f(0)))))))) → top#(s(p(p(p(f(mark(cons(0, f(s(0))))))))))top#(ok(s(f(p(p(cons(p(cons(p(s(0)), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(mark(0), _x92)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(p(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(p(active(_x121)))))), _x72))))))top#(ok(s(f(p(f(s(0))))))) → top#(s(f(p(mark(f(p(s(0))))))))
top#(ok(s(f(p(p(cons(p(s(p(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(p(active(_x101)))), _x72))))))top#(ok(s(f(p(cons(cons(_x71, _x72), _x62)))))) → top#(s(f(p(cons(cons(active(_x71), _x72), _x62)))))
top#(ok(s(f(p(p(cons(f(0), _x72))))))) → top#(s(f(p(p(cons(mark(cons(0, f(s(0)))), _x72))))))top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))
top#(ok(s(f(p(f(cons(f(s(0)), _x72))))))) → top#(s(f(p(f(cons(mark(f(p(s(0)))), _x72))))))top#(ok(s(p(p(p(s(cons(_x81, _x82)))))))) → top#(s(p(p(p(s(cons(active(_x81), _x82)))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(mark(cons(0, f(s(0)))))))), _x72))))))top#(ok(s(p(p(p(f(cons(f(_x91), _x82)))))))) → top#(s(p(p(p(f(cons(f(active(_x91)), _x82)))))))
top#(ok(s(p(p(cons(_x61, _x62)))))) → top#(s(p(p(cons(active(_x61), _x62)))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(mark(0)))))), _x72))))))
top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))top#(ok(cons(p(s(0)), _x22))) → top#(cons(mark(0), _x22))
top#(ok(s(f(p(f(p(s(0)))))))) → top#(s(f(p(f(mark(0))))))top#(ok(s(f(p(p(cons(p(p(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(p(active(_x91))), _x72))))))
top#(ok(s(s(p(s(0)))))) → top#(s(s(mark(0))))top#(ok(s(s(cons(f(0), _x52))))) → top#(s(s(cons(mark(cons(0, f(s(0)))), _x52))))
top#(ok(s(f(p(p(cons(p(s(cons(_x101, _x102))), _x72))))))) → top#(s(f(p(p(cons(p(s(cons(active(_x101), _x102))), _x72))))))top#(ok(s(p(p(p(p(s(0)))))))) → top#(s(p(p(p(mark(0))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(s(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(s(active(_x131))))))), _x72))))))top#(ok(s(p(p(p(cons(_x71, _x72))))))) → top#(s(p(p(p(cons(active(_x71), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(f(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(f(active(_x121)))))), _x72))))))top#(ok(s(f(p(f(s(_x71))))))) → top#(s(f(p(f(s(active(_x71)))))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

The right-hand side of the rule top#(ok(s(f(p(p(cons(p(s(s(s(s(p(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(active(_x131))))))), _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
top#(s(f(p(p(cons(p(s(s(s(s(p(f(active(_x141)))))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(s(s(p(mark(0))))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(s(s(p(s(active(_x141)))))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(s(s(p(p(active(_x141)))))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(s(s(p(mark(cons(0, f(s(0)))))))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(s(s(p(mark(f(p(s(0)))))))))), _x72)))))) 
top#(s(f(p(p(cons(p(s(s(s(s(p(cons(active(_x141), _x142))))))), _x72)))))) 
Thus, the rule top#(ok(s(f(p(p(cons(p(s(s(s(s(p(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(active(_x131))))))), _x72)))))) is replaced by the following rules:
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(s(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(s(active(_x141)))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(cons(0, f(s(0)))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(active(_x141)))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(p(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(0))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(f(p(s(0)))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(p(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(p(active(_x141)))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(_x141, _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(active(_x141), _x142))))))), _x72))))))

Problem 29: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))top#(ok(s(p(s(0))))) → top#(mark(s(0)))
top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(f(p(mark(p(f(p(s(0)))))))))top#(ok(s(f(p(f(cons(s(_x81), _x72))))))) → top#(s(f(p(f(cons(s(active(_x81)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(active(_x151))))))))), _x72))))))top#(ok(s(f(p(cons(s(f(_x81)), _x62)))))) → top#(s(f(p(cons(s(f(active(_x81))), _x62)))))
top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))top#(ok(s(f(p(p(p(s(0)))))))) → top#(s(f(p(p(mark(0))))))
top#(ok(s(f(p(cons(s(s(_x81)), _x62)))))) → top#(s(f(p(cons(s(s(active(_x81))), _x62)))))top#(ok(s(f(p(p(cons(p(f(s(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(f(p(s(0))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(0)), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(mark(f(p(s(0)))), _x132)))))), _x72))))))top#(ok(s(s(cons(p(s(0)), _x52))))) → top#(s(s(cons(mark(0), _x52))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(_x151)), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(active(_x151))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(_x161), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(active(_x161)), _x152)))))))), _x72))))))
top#(ok(s(p(p(p(f(cons(p(s(0)), _x72)))))))) → top#(s(p(p(p(f(mark(cons(0, _x72))))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(_x161))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(active(_x161)))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(cons(_x81, _x82), _x72))))))) → top#(s(f(p(p(cons(cons(active(_x81), _x82), _x72))))))top#(ok(s(s(f(0))))) → top#(s(s(mark(cons(0, f(s(0)))))))
top#(ok(s(p(p(p(s(s(_x81)))))))) → top#(s(p(p(p(s(s(active(_x81))))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(f(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(mark(cons(0, f(s(0)))))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(f(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(f(active(_x91))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(p(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(mark(0))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(p(s(0)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(mark(0))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(s(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(s(active(_x161)))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(p(active(_x141)))))))), _x72))))))top#(ok(s(s(p(_x51))))) → top#(s(s(p(active(_x51)))))
top#(ok(s(cons(cons(cons(_x61, _x62), _x52), _x42)))) → top#(s(cons(cons(cons(active(_x61), _x62), _x52), _x42)))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(mark(f(p(s(0)))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(cons(_x111, _x112)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(cons(active(_x111), _x112)))), _x72))))))top#(ok(f(_x21))) → top#(f(active(_x21)))
top#(ok(p(_x21))) → top#(p(active(_x21)))top#(ok(s(f(p(p(cons(p(cons(f(s(0)), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(mark(f(p(s(0)))), _x92)), _x72))))))
top#(ok(s(f(p(p(cons(p(f(0)), _x72))))))) → top#(s(f(p(p(cons(p(mark(cons(0, f(s(0))))), _x72))))))top#(ok(s(f(p(cons(f(_x71), _x62)))))) → top#(s(f(p(cons(f(active(_x71)), _x62)))))
top#(ok(s(p(p(p(f(p(s(0))))))))) → top#(s(p(p(p(f(mark(0)))))))top#(ok(s(f(p(p(cons(p(s(s(f(cons(f(0), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(mark(cons(0, f(s(0)))), _x122))))), _x72))))))
top#(ok(s(f(f(_x51))))) → top#(s(f(f(active(_x51)))))top#(ok(s(f(p(p(cons(p(s(s(f(cons(p(_x131), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(p(active(_x131)), _x122))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(cons(_x131, _x132)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(cons(active(_x131), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(mark(cons(0, f(s(0)))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(0), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(mark(cons(0, f(s(0)))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(_x141, _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(active(_x141), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(s(p(s(0))), _x72))))))) → top#(s(f(p(p(cons(s(mark(0)), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(p(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(p(active(_x151))))))))), _x72))))))
top#(ok(s(s(cons(p(s(_x71)), _x52))))) → top#(s(s(cons(p(s(active(_x71))), _x52))))top#(ok(s(f(p(p(cons(f(f(f(0))), _x72))))))) → top#(s(f(p(p(cons(f(f(mark(cons(0, f(s(0)))))), _x72))))))
top#(ok(s(p(p(p(f(cons(cons(_x91, _x92), _x82)))))))) → top#(s(p(p(p(f(cons(cons(active(_x91), _x92), _x82)))))))top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))
top#(ok(s(s(cons(p(p(s(0))), _x52))))) → top#(s(s(cons(p(mark(0)), _x52))))top#(ok(s(p(p(p(f(cons(p(_x91), _x82)))))))) → top#(s(p(p(p(f(cons(p(active(_x91)), _x82)))))))
top#(ok(s(f(p(cons(p(_x71), _x62)))))) → top#(s(f(p(cons(p(active(_x71)), _x62)))))top#(ok(s(f(p(p(cons(p(s(s(s(cons(_x121, _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(cons(active(_x121), _x122))))), _x72))))))
top#(mark(f(cons(_x41, _x42)))) → top#(f(cons(proper(_x41), proper(_x42))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(mark(f(p(s(0))))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(p(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(p(active(_x121)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(mark(cons(0, f(s(0))))))))))), _x72))))))
top#(ok(s(s(cons(cons(_x61, _x62), _x52))))) → top#(s(s(cons(cons(active(_x61), _x62), _x52))))top#(mark(f(0))) → top#(f(ok(0)))
top#(ok(s(p(p(p(s(p(s(0))))))))) → top#(s(p(p(p(s(mark(0)))))))top#(ok(s(f(p(p(cons(p(s(0)), _x72))))))) → top#(s(f(p(p(cons(mark(0), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(p(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(p(active(_x131))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(p(s(0))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(mark(0)))), _x72))))))
top#(ok(s(f(p(p(cons(p(cons(f(0), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(mark(cons(0, f(s(0)))), _x92)), _x72))))))top#(ok(s(p(f(0))))) → top#(s(p(mark(cons(0, f(s(0)))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(p(_x161))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(p(active(_x161)))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(p(s(0)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(mark(0), _x152)))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(cons(_x151, _x152)), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(cons(active(_x151), _x152)), _x132)))))), _x72))))))top#(ok(s(s(s(_x51))))) → top#(s(s(s(active(_x51)))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(f(s(0)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(mark(f(p(s(0)))), _x152)))))))), _x72))))))top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))
top#(ok(s(f(p(p(cons(p(s(s(cons(f(s(0)), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(mark(f(p(s(0)))), _x112)))), _x72))))))top#(ok(s(f(p(cons(s(f(s(0))), _x62)))))) → top#(s(f(p(cons(s(mark(f(p(s(0))))), _x62)))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(cons(_x161, _x162), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(cons(active(_x161), _x162), _x152)))))))), _x72))))))top#(ok(cons(p(_x41), _x22))) → top#(cons(p(active(_x41)), _x22))
top#(ok(s(f(p(p(cons(p(s(s(f(cons(s(_x131), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(s(active(_x131)), _x122))))), _x72))))))top#(ok(s(f(p(f(cons(cons(_x81, _x82), _x72))))))) → top#(s(f(p(f(cons(cons(active(_x81), _x82), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(f(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(s(cons(0, f(s(0)))))))), _x72))))))top#(ok(s(f(p(p(cons(s(f(_x91)), _x72))))))) → top#(s(f(p(p(cons(s(f(active(_x91))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(p(_x151), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(p(active(_x151)), _x142))))))), _x72))))))top#(mark(s(_x21))) → top#(s(proper(_x21)))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(cons(_x151, _x152), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(cons(active(_x151), _x152), _x142))))))), _x72))))))top#(ok(s(p(s(_x51))))) → top#(s(p(s(active(_x51)))))
top#(ok(s(cons(cons(f(_x61), _x52), _x42)))) → top#(s(cons(cons(f(active(_x61)), _x52), _x42)))top#(ok(s(f(p(f(cons(f(0), _x72))))))) → top#(s(f(p(f(cons(mark(cons(0, f(s(0)))), _x72))))))
top#(ok(s(f(p(f(0)))))) → top#(s(f(p(mark(cons(0, f(s(0))))))))top#(ok(s(p(p(f(s(0))))))) → top#(s(p(p(mark(f(p(s(0))))))))
top#(ok(s(f(p(p(cons(f(f(p(s(0)))), _x72))))))) → top#(s(f(p(p(cons(f(mark(f(0))), _x72))))))top#(ok(s(p(p(p(f(p(_x81)))))))) → top#(s(p(p(p(f(p(active(_x81))))))))
top#(mark(f(p(_x41)))) → top#(f(p(proper(_x41))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(mark(f(p(s(0)))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(p(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(mark(0)))))), _x72))))))top#(ok(s(p(p(s(0)))))) → top#(s(p(mark(0))))
top#(mark(f(f(_x41)))) → top#(f(f(proper(_x41))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(p(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(mark(0)))))))), _x72))))))
top#(mark(f(s(_x41)))) → top#(f(s(proper(_x41))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(f(_x161), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(f(active(_x161)), _x152)))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(p(s(0)), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(mark(0), _x132)))))), _x72))))))top#(ok(cons(f(s(0)), _x22))) → top#(cons(mark(f(p(s(0)))), _x22))
top#(ok(s(f(p(s(f(_x71))))))) → top#(s(f(p(s(f(active(_x71)))))))top#(ok(s(cons(cons(f(s(0)), _x52), _x42)))) → top#(s(cons(cons(mark(f(p(s(0)))), _x52), _x42)))
top#(ok(s(f(p(p(cons(p(s(s(s(s(f(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(mark(f(p(s(0))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(f(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(mark(cons(0, f(s(0)))))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(p(s(0))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(mark(0)), _x132)))))), _x72))))))top#(ok(s(f(p(cons(f(0), _x62)))))) → top#(s(f(p(cons(mark(cons(0, f(s(0)))), _x62)))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(p(s(0)), _x152)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(s(cons(0, _x152))), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(cons(_x141, _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(cons(active(_x141), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(s(s(_x91)), _x72))))))) → top#(s(f(p(p(cons(s(s(active(_x91))), _x72))))))top#(ok(s(f(p(p(cons(f(f(f(_x101))), _x72))))))) → top#(s(f(p(p(cons(f(f(f(active(_x101)))), _x72))))))
top#(ok(s(p(p(p(f(s(0)))))))) → top#(s(p(p(mark(p(f(p(s(0)))))))))top#(ok(s(f(p(p(cons(p(s(s(s(f(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(mark(f(p(s(0)))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(cons(f(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(f(active(_x121)), _x112)))), _x72))))))top#(ok(s(f(p(cons(p(s(0)), _x62)))))) → top#(s(f(p(cons(mark(0), _x62)))))
top#(mark(p(_x21))) → top#(p(proper(_x21)))top#(ok(s(p(p(f(_x61)))))) → top#(s(p(p(f(active(_x61))))))
top#(ok(s(f(p(p(cons(p(cons(p(_x101), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(p(active(_x101)), _x92)), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(f(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(f(active(_x151))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(s(0))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(mark(f(p(s(0))))), _x132)))))), _x72))))))top#(ok(s(p(p(p(f(f(0)))))))) → top#(s(p(p(p(f(mark(cons(0, f(s(0))))))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(s(_x161)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(s(active(_x161))), _x142))))))), _x72))))))top#(ok(s(s(cons(p(f(s(0))), _x52))))) → top#(s(s(cons(mark(p(f(p(s(0))))), _x52))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(p(_x161), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(p(active(_x161)), _x152)))))))), _x72))))))top#(ok(s(f(p(p(cons(p(cons(p(s(0)), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(mark(0), _x92)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(f(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(mark(f(p(s(0))))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(cons(_x161, _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(cons(active(_x161), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(p(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(p(active(_x101)))), _x72))))))top#(ok(s(f(p(cons(cons(_x71, _x72), _x62)))))) → top#(s(f(p(cons(cons(active(_x71), _x72), _x62)))))
top#(ok(s(f(p(p(cons(f(f(p(f(0)))), _x72))))))) → top#(s(f(p(p(cons(f(mark(f(p(cons(0, f(s(0))))))), _x72))))))top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(f(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(f(active(_x161)))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(f(s(0))), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(s(f(p(s(0))))), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(mark(cons(0, f(s(0)))))))), _x72))))))top#(ok(s(p(p(cons(_x61, _x62)))))) → top#(s(p(p(cons(active(_x61), _x62)))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(mark(0)))))), _x72))))))top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))
top#(ok(cons(p(s(0)), _x22))) → top#(cons(mark(0), _x22))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(f(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(mark(f(p(s(0)))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(mark(0))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(cons(_x101, _x102))), _x72))))))) → top#(s(f(p(p(cons(p(s(cons(active(_x101), _x102))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(f(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(mark(cons(0, f(s(0))))))))), _x72))))))top#(ok(s(cons(f(_x51), _x42)))) → top#(s(cons(f(active(_x51)), _x42)))
top#(ok(s(f(p(s(cons(_x71, _x72))))))) → top#(s(f(p(s(cons(active(_x71), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(cons(_x141, _x142), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(cons(active(_x141), _x142), _x132)))))), _x72))))))
top#(ok(s(cons(cons(f(0), _x52), _x42)))) → top#(s(cons(cons(mark(cons(0, f(s(0)))), _x52), _x42)))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(0)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(mark(cons(0, f(s(0))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(p(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(p(active(_x161)))))))))), _x72))))))top#(ok(cons(f(0), _x32))) → top#(mark(cons(cons(0, f(s(0))), _x32)))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(s(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(s(active(_x141)))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(p(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(mark(0))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(f(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(mark(f(p(s(0)))))))))))), _x72))))))top#(ok(s(cons(f(0), _x42)))) → top#(s(cons(mark(cons(0, f(s(0)))), _x42)))
top#(ok(s(cons(f(s(0)), _x42)))) → top#(s(cons(mark(f(p(s(0)))), _x42)))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(f(_x171), _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(f(active(_x171)), _x162)), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(s(p(_x91)), _x72))))))) → top#(s(f(p(p(cons(s(p(active(_x91))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(s(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(s(active(_x141)))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(f(0))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(mark(f(cons(0, f(s(0)))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(s(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(s(active(_x151))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(p(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(p(active(_x141)))))))), _x72))))))top#(ok(s(f(f(s(0)))))) → top#(mark(s(f(f(p(s(0)))))))
top#(ok(s(f(p(p(cons(f(f(s(_x101))), _x72))))))) → top#(s(f(p(p(cons(f(f(s(active(_x101)))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(p(_x121))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(p(active(_x121)))))), _x72))))))
top#(ok(s(f(p(f(cons(f(_x81), _x72))))))) → top#(s(f(p(f(cons(f(active(_x81)), _x72))))))top#(ok(s(f(p(p(s(_x71))))))) → top#(s(f(p(p(s(active(_x71)))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(cons(_x131, _x132)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(cons(active(_x131), _x132)))))), _x72))))))top#(ok(cons(s(_x41), _x22))) → top#(cons(s(active(_x41)), _x22))
top#(ok(s(p(p(p(s(0))))))) → top#(s(p(p(mark(0)))))top#(ok(s(f(p(p(cons(p(p(s(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(0)), _x72))))))
top#(ok(s(f(p(p(f(_x71))))))) → top#(s(f(p(p(f(active(_x71)))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(p(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(p(active(_x131))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(0))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(mark(cons(0, f(s(0)))))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(s(_x91)), _x72))))))) → top#(s(f(p(p(cons(f(s(active(_x91))), _x72))))))
top#(ok(s(f(p(p(cons(p(cons(cons(_x101, _x102), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(cons(active(_x101), _x102), _x92)), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(0)), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(mark(cons(0, f(s(0))))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(s(_x171), _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(s(active(_x171)), _x162)), _x142))))))), _x72))))))top#(ok(s(f(p(s(0)))))) → top#(mark(s(f(0))))
top#(ok(s(f(p(p(cons(p(s(s(p(s(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(0)))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(p(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(mark(0))))), _x72))))))
top#(ok(s(f(p(p(cons(s(cons(_x91, _x92)), _x72))))))) → top#(s(f(p(p(cons(s(cons(active(_x91), _x92)), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(f(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(f(f(p(s(0))))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(p(s(0)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(0), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(cons(_x101, _x102))), _x72))))))) → top#(s(f(p(p(cons(f(f(cons(active(_x101), _x102))), _x72))))))
top#(ok(cons(cons(_x41, _x42), _x22))) → top#(cons(cons(active(_x41), _x42), _x22))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(s(0)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(mark(f(p(s(0)))))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(p(_x141), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(p(active(_x141)), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(f(_x121))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(f(active(_x121)))))), _x72))))))
top#(ok(s(f(p(f(cons(p(_x81), _x72))))))) → top#(s(f(p(f(cons(p(active(_x81)), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(f(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(mark(cons(0, f(s(0))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(f(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(s(cons(0, f(s(0)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(s(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(f(p(s(0))))))), _x72))))))
top#(ok(s(p(p(p(f(cons(f(0), _x82)))))))) → top#(s(p(p(p(f(cons(mark(cons(0, f(s(0)))), _x82)))))))top#(ok(s(p(p(p(p(_x71))))))) → top#(s(p(p(p(p(active(_x71)))))))
top#(ok(s(f(p(p(cons(s(f(0)), _x72))))))) → top#(s(f(p(p(cons(s(mark(cons(0, f(s(0))))), _x72))))))top#(ok(s(p(p(f(0)))))) → top#(s(p(p(mark(cons(0, f(s(0))))))))
top#(ok(s(f(p(f(f(0))))))) → top#(s(f(p(f(mark(cons(0, f(s(0)))))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(f(p(s(0)))))))))), _x72))))))
top#(ok(s(s(cons(s(_x61), _x52))))) → top#(s(s(cons(s(active(_x61)), _x52))))top#(ok(s(f(p(p(cons(p(s(s(f(cons(cons(_x131, _x132), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(cons(active(_x131), _x132), _x122))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(f(0), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(mark(cons(0, f(s(0)))), _x152)))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(p(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(p(active(_x141)))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(0)), _x72))))))) → top#(s(f(p(p(cons(f(mark(cons(0, f(s(0))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(p(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(p(active(_x161)))))))))), _x72))))))
top#(ok(s(cons(cons(s(_x61), _x52), _x42)))) → top#(s(cons(cons(s(active(_x61)), _x52), _x42)))top#(ok(s(f(p(p(cons(p(s(s(f(p(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(mark(0))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(p(_x151)), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(p(active(_x151))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(p(_x91)), _x72))))))) → top#(s(f(p(p(cons(f(p(active(_x91))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(cons(p(s(0)), _x102)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(cons(0, _x102))))), _x72))))))top#(ok(cons(f(_x41), _x22))) → top#(cons(f(active(_x41)), _x22))
top#(ok(s(f(p(p(cons(p(s(s(cons(p(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(p(active(_x121)), _x112)))), _x72))))))top#(ok(s(f(p(p(cons(f(f(f(s(0)))), _x72))))))) → top#(s(f(p(p(cons(mark(f(f(f(p(s(0)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(s(_x141), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(s(active(_x141)), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(cons(_x161, _x162))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(cons(active(_x161), _x162))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(p(_x161)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(p(active(_x161))), _x142))))))), _x72))))))top#(ok(s(f(p(cons(s(f(0)), _x62)))))) → top#(s(f(p(cons(s(mark(cons(0, f(s(0))))), _x62)))))
top#(ok(s(f(p(p(cons(p(s(s(cons(s(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(s(active(_x121)), _x112)))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(p(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(mark(0))))))), _x72))))))
top#(ok(s(cons(p(_x51), _x42)))) → top#(s(cons(p(active(_x51)), _x42)))top#(ok(s(p(p(p(f(cons(s(_x91), _x82)))))))) → top#(s(p(p(p(f(cons(s(active(_x91)), _x82)))))))
top#(ok(s(cons(p(s(0)), _x42)))) → top#(s(cons(mark(0), _x42)))top#(ok(s(f(p(p(cons(f(f(p(f(_x111)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(f(active(_x111))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(f(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(f(active(_x131))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(f(0)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(s(cons(0, f(s(0))))), _x142))))))), _x72))))))
top#(ok(s(p(p(p(s(f(s(0))))))))) → top#(s(p(p(p(s(mark(f(p(s(0))))))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(mark(0)))))))), _x72))))))
top#(ok(s(p(p(p(f(f(_x81)))))))) → top#(s(p(p(p(f(f(active(_x81))))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(s(_x161))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(s(active(_x161)))), _x132)))))), _x72))))))
top#(ok(s(p(p(p(s(f(_x81)))))))) → top#(s(p(p(p(s(f(active(_x81))))))))top#(ok(s(s(cons(p(f(_x71)), _x52))))) → top#(s(s(cons(p(f(active(_x71))), _x52))))
top#(ok(s(p(f(s(0)))))) → top#(s(p(mark(f(p(s(0)))))))top#(ok(s(f(p(f(f(_x71))))))) → top#(s(f(p(f(f(active(_x71)))))))
top#(ok(s(f(p(p(cons(f(f(p(f(s(0))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(mark(f(p(s(0))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(cons(_x151, _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(cons(active(_x151), _x152)))))))), _x72))))))
top#(ok(s(s(cons(p(cons(_x71, _x72)), _x52))))) → top#(s(s(cons(p(cons(active(_x71), _x72)), _x52))))top#(ok(s(f(f(0))))) → top#(s(mark(f(cons(0, f(s(0)))))))
top#(ok(s(f(p(cons(s(cons(_x81, _x82)), _x62)))))) → top#(s(f(p(cons(s(cons(active(_x81), _x82)), _x62)))))top#(ok(s(f(p(s(p(_x71))))))) → top#(s(f(p(s(p(active(_x71)))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(f(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(f(active(_x131))))))), _x72))))))top#(ok(s(p(p(p(s(f(0)))))))) → top#(s(p(p(p(mark(s(cons(0, f(s(0))))))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(mark(f(p(s(0))))))))), _x72))))))top#(ok(s(s(cons(p(p(_x71)), _x52))))) → top#(s(s(cons(p(p(active(_x71))), _x52))))
top#(ok(s(f(p(p(cons(f(s(0)), _x62))))))) → top#(s(f(p(p(mark(cons(f(p(s(0))), _x62)))))))top#(ok(s(f(p(p(cons(p(cons(s(_x101), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(s(active(_x101)), _x92)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(s(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(s(active(_x121)))))), _x72))))))top#(ok(s(s(cons(f(_x61), _x52))))) → top#(s(s(cons(f(active(_x61)), _x52))))
top#(ok(s(f(p(f(p(_x71))))))) → top#(s(f(p(f(p(active(_x71)))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(f(_x151), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(f(active(_x151)), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(f(0), _x132))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(cons(cons(0, f(s(0))), _x132)))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(p(_x171), _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(p(active(_x171)), _x162)), _x142))))))), _x72))))))
top#(ok(s(p(p(p(s(p(_x81)))))))) → top#(s(p(p(p(s(p(active(_x81))))))))top#(ok(s(f(p(p(cons(p(s(s(f(cons(f(s(0)), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(mark(f(p(s(0)))), _x122))))), _x72))))))
top#(ok(s(f(p(p(f(0))))))) → top#(s(f(p(mark(p(cons(0, f(s(0)))))))))top#(ok(s(f(p(p(cons(f(f(p(s(f(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(mark(f(p(s(0)))))))), _x72))))))
top#(ok(s(p(p(p(f(f(s(0))))))))) → top#(s(p(p(p(f(mark(f(p(s(0))))))))))top#(ok(s(p(p(p(f(s(_x81)))))))) → top#(s(p(p(p(f(s(active(_x81))))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(p(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(mark(0))))))))), _x72))))))top#(ok(s(s(cons(p(f(0)), _x52))))) → top#(s(s(cons(p(mark(cons(0, f(s(0))))), _x52))))
top#(ok(s(f(p(p(cons(f(f(p(p(_x111)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(p(active(_x111))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(cons(p(s(0)), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(mark(0), _x122))))), _x72))))))
top#(ok(s(s(f(_x51))))) → top#(s(s(f(active(_x51)))))top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))
top#(ok(s(f(p(p(cons(p(s(f(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(f(active(_x101)))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(p(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(mark(0)))))), _x72))))))
top#(ok(s(p(cons(_x51, _x52))))) → top#(s(p(cons(active(_x51), _x52))))top#(ok(s(f(p(p(cons(f(f(p(s(f(0))))), _x72))))))) → top#(s(f(p(p(cons(f(f(mark(p(s(cons(0, f(s(0)))))))), _x72))))))
top#(ok(s(p(f(_x51))))) → top#(s(p(f(active(_x51)))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(f(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(f(active(_x161)))))))))), _x72))))))
top#(ok(s(p(p(p(f(0))))))) → top#(s(p(p(p(mark(cons(0, f(s(0)))))))))top#(ok(s(f(p(s(f(s(0)))))))) → top#(s(f(p(mark(s(f(p(s(0)))))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(f(_x161)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(f(active(_x161))), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(f(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(mark(f(p(s(0)))))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(cons(_x161, _x162))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(cons(active(_x161), _x162))))))))), _x72))))))top#(ok(s(f(p(f(f(s(0)))))))) → top#(s(f(mark(p(f(f(p(s(0)))))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(f(0), _x152)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(mark(cons(cons(0, f(s(0))), _x152))), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(cons(0, f(s(0)))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(cons(_x91, _x92)), _x72))))))) → top#(s(f(p(p(cons(f(cons(active(_x91), _x92)), _x72))))))top#(ok(s(s(f(s(0)))))) → top#(s(mark(s(f(p(s(0)))))))
top#(ok(s(f(p(p(cons(p(s(p(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(0))), _x72))))))top#(ok(s(f(p(p(cons(s(f(s(0))), _x72))))))) → top#(s(f(p(p(cons(s(mark(f(p(s(0))))), _x72))))))
top#(ok(s(f(p(s(p(s(0)))))))) → top#(s(f(p(s(mark(0))))))top#(ok(s(f(p(p(cons(p(s(s(cons(f(0), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(mark(cons(0, f(s(0)))), _x112)))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(f(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(mark(cons(0, f(s(0))))))))))), _x72))))))top#(ok(s(f(p(s(f(0))))))) → top#(s(f(p(s(mark(cons(0, f(s(0)))))))))
top#(ok(s(f(p(cons(s(p(_x81)), _x62)))))) → top#(s(f(p(cons(s(p(active(_x81))), _x62)))))top#(ok(s(cons(s(_x51), _x42)))) → top#(s(cons(s(active(_x51)), _x42)))
top#(ok(s(f(p(p(cons(p(s(f(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(f(p(s(0)))))), _x72))))))top#(ok(s(f(p(f(cons(p(s(0)), _x72))))))) → top#(s(f(p(f(cons(mark(0), _x72))))))
top#(ok(s(f(p(p(p(_x71))))))) → top#(s(f(p(p(p(active(_x71)))))))top#(ok(s(f(p(p(cons(p(s(s(p(_x111)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(p(active(_x111))))), _x72))))))
top#(ok(s(cons(cons(p(s(0)), _x52), _x42)))) → top#(s(cons(cons(mark(0), _x52), _x42)))top#(ok(s(f(p(p(cons(p(s(s(cons(cons(_x121, _x122), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(cons(active(_x121), _x122), _x112)))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(cons(0, f(s(0))))))), _x72))))))top#(ok(s(f(p(cons(s(p(s(0))), _x62)))))) → top#(s(f(p(cons(mark(s(0)), _x62)))))
top#(ok(s(s(cons(f(s(0)), _x52))))) → top#(s(s(cons(mark(f(p(s(0)))), _x52))))top#(ok(s(f(p(p(cons(f(p(s(0))), _x72))))))) → top#(s(f(p(p(cons(f(mark(0)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(p(s(0))), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(s(0)), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(cons(f(_x131), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(f(active(_x131)), _x122))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(s(0))), _x72))))))) → top#(s(f(p(p(cons(f(mark(f(p(s(0))))), _x72))))))top#(ok(s(f(p(p(s(0))))))) → top#(s(f(p(mark(0)))))
top#(ok(s(f(p(cons(f(s(0)), _x62)))))) → top#(s(f(p(cons(mark(f(p(s(0)))), _x62)))))top#(ok(s(f(p(s(s(_x71))))))) → top#(s(f(p(s(s(active(_x71)))))))
top#(ok(s(f(p(p(cons(p(cons(f(_x101), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(f(active(_x101)), _x92)), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(s(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(s(active(_x141)))))))), _x72))))))
top#(ok(s(p(p(p(f(cons(f(s(0)), _x72)))))))) → top#(s(p(p(mark(p(f(cons(f(p(s(0))), _x72))))))))top#(ok(s(f(p(p(cons(f(f(p(s(cons(_x121, _x122))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(cons(active(_x121), _x122))))), _x72))))))
top#(ok(s(p(p(s(_x61)))))) → top#(s(p(p(s(active(_x61))))))top#(ok(s(f(p(p(cons(p(s(s(f(p(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(p(active(_x121)))))), _x72))))))
top#(ok(s(f(p(f(s(0))))))) → top#(s(f(p(mark(f(p(s(0))))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(f(s(0)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(f(p(s(0)))), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(0), _x72))))))) → top#(s(f(p(p(cons(mark(cons(0, f(s(0)))), _x72))))))top#(ok(s(f(p(f(cons(f(s(0)), _x72))))))) → top#(s(f(p(f(cons(mark(f(p(s(0)))), _x72))))))
top#(ok(s(p(p(p(s(cons(_x81, _x82)))))))) → top#(s(p(p(p(s(cons(active(_x81), _x82)))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(f(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(f(active(_x141)))))))), _x72))))))
top#(ok(s(p(p(p(f(cons(f(_x91), _x82)))))))) → top#(s(p(p(p(f(cons(f(active(_x91)), _x82)))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(cons(_x171, _x172), _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(cons(active(_x171), _x172), _x162)), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(f(s(0)), _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(mark(f(p(s(0)))), _x162)), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(s(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(s(active(_x131))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(p(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(0))))))), _x72))))))top#(ok(s(f(p(f(p(s(0)))))))) → top#(s(f(p(f(mark(0))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(s(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(s(active(_x161)))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(p(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(p(active(_x91))), _x72))))))
top#(ok(s(cons(cons(p(_x61), _x52), _x42)))) → top#(s(cons(cons(p(active(_x61)), _x52), _x42)))top#(ok(s(s(p(s(0)))))) → top#(s(s(mark(0))))
top#(ok(s(s(cons(f(0), _x52))))) → top#(s(s(cons(mark(cons(0, f(s(0)))), _x52))))top#(ok(s(p(p(p(p(s(0)))))))) → top#(s(p(p(p(mark(0))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(s(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(s(active(_x131))))))), _x72))))))top#(ok(s(p(p(p(cons(_x71, _x72))))))) → top#(s(p(p(p(cons(active(_x71), _x72))))))
top#(ok(s(f(p(f(s(_x71))))))) → top#(s(f(p(f(s(active(_x71)))))))top#(ok(s(f(p(p(cons(p(s(s(s(f(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(f(active(_x121)))))), _x72))))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

The right-hand side of the rule top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(f(p(mark(p(f(p(s(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
top#(s(f(mark(p(p(f(p(s(0))))))))) 
Thus, the rule top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(f(p(mark(p(f(p(s(0))))))))) is replaced by the following rules:
top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(f(mark(p(p(f(p(s(0)))))))))

Problem 30: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(f(f(f(0)))))) → top#(s(f(f(mark(cons(0, f(s(0))))))))top#(ok(s(p(s(0))))) → top#(mark(s(0)))
top#(ok(s(s(p(f(cons(cons(_x81, _x82), _x72))))))) → top#(s(s(p(f(cons(cons(active(_x81), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(cons(_x131, _x132)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(cons(active(_x131), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(_x141, _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(active(_x141), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(s(p(s(0))), _x72))))))) → top#(s(f(p(p(cons(s(mark(0)), _x72))))))
top#(ok(s(f(p(p(cons(f(f(f(0))), _x72))))))) → top#(s(f(p(p(cons(f(f(mark(cons(0, f(s(0)))))), _x72))))))top#(ok(s(s(cons(p(s(_x71)), _x52))))) → top#(s(s(cons(p(s(active(_x71))), _x52))))
top#(ok(s(s(p(cons(_x61, _x62)))))) → top#(s(s(p(cons(active(_x61), _x62)))))top#(ok(s(f(p(p(cons(cons(cons(_x91, _x92), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(cons(active(_x91), _x92), _x82), _x72))))))
top#(ok(s(p(p(p(f(cons(p(_x91), _x82)))))))) → top#(s(p(p(p(f(cons(p(active(_x91)), _x82)))))))top#(mark(f(cons(_x41, _x42)))) → top#(f(cons(proper(_x41), proper(_x42))))
top#(ok(s(f(p(p(cons(p(s(s(s(cons(_x121, _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(cons(active(_x121), _x122))))), _x72))))))top#(ok(s(f(p(cons(s(f(f(s(0)))), _x62)))))) → top#(s(f(p(cons(s(f(mark(f(p(s(0)))))), _x62)))))
top#(ok(s(f(p(p(cons(p(s(s(s(p(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(p(active(_x121)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(s(_x201)))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(s(active(_x201))))), _x162))), _x132)))))), _x72))))))
top#(ok(f(f(f(0))))) → top#(f(f(mark(cons(0, f(s(0)))))))top#(ok(s(f(p(p(cons(f(f(p(p(s(0))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(mark(0)))), _x72))))))
top#(ok(s(f(p(p(cons(cons(s(_x91), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(s(active(_x91)), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(p(_x161))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(p(active(_x161)))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(cons(f(0), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(mark(cons(0, f(s(0)))), _x92)), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(p(s(0))), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(mark(0)), _x152)))))))), _x72))))))
top#(ok(s(f(p(cons(s(f(p(s(0)))), _x62)))))) → top#(s(f(p(cons(s(mark(f(0))), _x62)))))top#(ok(s(s(s(_x51))))) → top#(s(s(s(active(_x51)))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(f(s(0)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(mark(f(p(s(0)))), _x152)))))))), _x72))))))top#(ok(s(f(f(p(s(0))))))) → top#(s(f(f(mark(0)))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(s(_x171)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(s(active(_x171))))), _x132)))))), _x72))))))top#(ok(s(s(p(p(s(0))))))) → top#(s(s(p(mark(0)))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(f(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(f(active(_x161)))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(cons(f(s(0)), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(mark(f(p(s(0)))), _x112)))), _x72))))))
top#(ok(cons(p(_x41), _x22))) → top#(cons(p(active(_x41)), _x22))top#(ok(s(f(p(cons(s(s(cons(_x91, _x92))), _x62)))))) → top#(s(f(p(cons(s(s(cons(active(_x91), _x92))), _x62)))))
top#(ok(s(f(p(p(cons(cons(f(0), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(mark(cons(0, f(s(0)))), _x82), _x72))))))top#(ok(s(f(p(cons(s(s(f(s(0)))), _x62)))))) → top#(s(f(p(cons(s(s(mark(f(p(s(0)))))), _x62)))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(p(_x171), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(p(active(_x171)), _x162))), _x132)))))), _x72))))))top#(ok(s(f(p(f(cons(cons(_x81, _x82), _x72))))))) → top#(s(f(p(f(cons(cons(active(_x81), _x82), _x72))))))
top#(ok(f(s(_x41)))) → top#(f(s(active(_x41))))top#(ok(s(f(p(p(cons(s(f(_x91)), _x72))))))) → top#(s(f(p(p(cons(s(f(active(_x91))), _x72))))))
top#(mark(s(_x21))) → top#(s(proper(_x21)))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(cons(_x151, _x152), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(cons(active(_x151), _x152), _x142))))))), _x72))))))
top#(ok(s(cons(cons(f(_x61), _x52), _x42)))) → top#(s(cons(cons(f(active(_x61)), _x52), _x42)))top#(ok(s(f(p(f(0)))))) → top#(s(f(p(mark(cons(0, f(s(0))))))))
top#(ok(s(s(p(f(f(_x71))))))) → top#(s(s(p(f(f(active(_x71)))))))top#(mark(f(p(_x41)))) → top#(f(p(proper(_x41))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(mark(f(p(s(0)))))))), _x72))))))top#(ok(s(s(p(f(f(0))))))) → top#(s(s(p(f(mark(cons(0, f(s(0)))))))))
top#(ok(p(cons(_x41, _x42)))) → top#(p(cons(active(_x41), _x42)))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(p(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(p(p(active(_x151))))))))), _x72))))))
top#(mark(f(s(_x41)))) → top#(f(s(proper(_x41))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(p(s(0)), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(mark(0), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(cons(p(s(0)), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(mark(0), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(s(_x171)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(s(active(_x171))))), _x132)))))), _x72))))))
top#(ok(s(f(p(s(f(_x71))))))) → top#(s(f(p(s(f(active(_x71)))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(0)), _x122)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(mark(cons(f(p(s(0))), _x122))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(p(s(0))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(mark(0)), _x132)))))), _x72))))))top#(ok(s(f(p(cons(f(0), _x62)))))) → top#(s(f(p(cons(mark(cons(0, f(s(0)))), _x62)))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(cons(_x141, _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(cons(active(_x141), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(f(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(mark(f(p(s(0)))))))), _x72))))))
top#(ok(s(p(p(p(f(s(0)))))))) → top#(s(p(p(mark(p(f(p(s(0)))))))))top#(ok(s(f(p(p(cons(f(f(f(_x101))), _x72))))))) → top#(s(f(p(p(cons(f(f(f(active(_x101)))), _x72))))))
top#(ok(s(f(p(p(cons(s(s(_x91)), _x72))))))) → top#(s(f(p(p(cons(s(s(active(_x91))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(cons(f(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(f(active(_x121)), _x112)))), _x72))))))
top#(ok(s(p(p(f(_x61)))))) → top#(s(p(p(f(active(_x61))))))top#(ok(s(f(p(p(cons(p(cons(p(_x101), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(p(active(_x101)), _x92)), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(p(_x171)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(p(active(_x171))))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(p(s(0)), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(mark(0), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(f(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(f(active(_x151))))))))), _x72))))))top#(ok(s(p(p(p(f(cons(p(s(0)), _x72)))))))) → top#(s(p(p(p(mark(f(cons(0, _x72))))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(s(0))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(mark(f(p(s(0))))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(s(_x161)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(s(active(_x161))), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(cons(p(s(0)), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(mark(0), _x92)), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(p(_x161), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(p(active(_x161)), _x152)))))))), _x72))))))
top#(ok(s(f(p(cons(s(f(s(f(0)))), _x62)))))) → top#(s(f(p(cons(s(f(s(mark(cons(0, f(s(0))))))), _x62)))))top#(ok(s(f(p(p(cons(p(s(s(f(f(f(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(mark(f(p(s(0))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(f(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(p(mark(f(p(s(0))))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(f(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(f(active(_x161)))))))))), _x72))))))
top#(ok(s(p(p(cons(_x61, _x62)))))) → top#(s(p(p(cons(active(_x61), _x62)))))top#(ok(s(f(p(p(cons(cons(p(_x91), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(p(active(_x91)), _x82), _x72))))))
top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(mark(0)))))), _x72))))))
top#(ok(cons(p(s(0)), _x22))) → top#(cons(mark(0), _x22))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(f(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(mark(f(p(s(0)))))))))), _x72))))))
top#(ok(s(s(p(f(cons(s(_x81), _x72))))))) → top#(s(s(p(f(cons(s(active(_x81)), _x72))))))top#(ok(s(f(p(p(cons(p(s(cons(_x101, _x102))), _x72))))))) → top#(s(f(p(p(cons(p(s(cons(active(_x101), _x102))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(s(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(p(s(active(_x151))))))))), _x72))))))top#(ok(s(cons(f(_x51), _x42)))) → top#(s(cons(f(active(_x51)), _x42)))
top#(ok(s(f(p(s(cons(_x71, _x72))))))) → top#(s(f(p(s(cons(active(_x71), _x72))))))top#(ok(s(s(p(f(p(s(0)))))))) → top#(s(s(p(f(mark(0))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(p(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(p(active(_x161)))))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(s(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(s(active(_x141)))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(f(s(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(f(s(active(_x101)))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(f(s(0))), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(mark(f(p(s(0))))), _x152)))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(p(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(p(mark(0)))))))), _x72))))))top#(ok(s(f(p(f(cons(s(p(s(0))), _x72))))))) → top#(s(f(p(f(cons(s(mark(0)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(p(s(0))))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(mark(0)))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(s(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(s(active(_x151))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(p(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(p(active(_x141)))))))), _x72))))))top#(ok(f(p(_x41)))) → top#(f(p(active(_x41))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(f(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(mark(cons(0, f(s(0)))))))))))), _x72))))))top#(ok(s(f(f(s(0)))))) → top#(mark(s(f(f(p(s(0)))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(f(s(0))))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(mark(f(f(p(s(0))))))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(p(_x121))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(p(active(_x121)))))), _x72))))))
top#(ok(s(f(p(f(cons(f(_x81), _x72))))))) → top#(s(f(p(f(cons(f(active(_x81)), _x72))))))top#(ok(s(f(p(f(cons(s(f(s(0))), _x72))))))) → top#(s(f(p(f(cons(s(mark(f(p(s(0))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(f(0)))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(mark(cons(0, f(s(0))))))), _x162))), _x132)))))), _x72))))))top#(ok(s(s(p(f(s(0))))))) → top#(s(s(p(mark(f(p(s(0))))))))
top#(ok(f(f(f(_x51))))) → top#(f(f(f(active(_x51)))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(0))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(mark(cons(0, f(s(0)))))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(s(_x91)), _x72))))))) → top#(s(f(p(p(cons(f(s(active(_x91))), _x72))))))top#(ok(s(f(p(p(cons(p(cons(cons(_x101, _x102), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(cons(active(_x101), _x102), _x92)), _x72))))))
top#(ok(s(f(p(s(0)))))) → top#(mark(s(f(0))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(cons(_x171, _x172), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(cons(active(_x171), _x172), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(s(cons(_x91, _x92)), _x72))))))) → top#(s(f(p(p(cons(s(cons(active(_x91), _x92)), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(f(0)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(mark(cons(0, f(s(0))))))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(p(s(0)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(0), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(cons(_x101, _x102))), _x72))))))) → top#(s(f(p(p(cons(f(f(cons(active(_x101), _x102))), _x72))))))
top#(ok(cons(cons(_x41, _x42), _x22))) → top#(cons(cons(active(_x41), _x42), _x22))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(f(0))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(mark(cons(0, f(s(0)))))), _x132)))))), _x72))))))
top#(ok(s(f(p(f(cons(p(_x81), _x72))))))) → top#(s(f(p(f(cons(p(active(_x81)), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(f(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(mark(cons(0, f(s(0))))))))), _x72))))))
top#(ok(s(p(p(p(p(_x71))))))) → top#(s(p(p(p(p(active(_x71)))))))top#(ok(s(p(p(f(0)))))) → top#(s(p(p(mark(cons(0, f(s(0))))))))
top#(ok(s(f(p(f(f(0))))))) → top#(s(f(p(f(mark(cons(0, f(s(0)))))))))top#(ok(s(s(cons(s(_x61), _x52))))) → top#(s(s(cons(s(active(_x61)), _x52))))
top#(ok(s(f(p(p(cons(p(s(s(f(cons(cons(_x131, _x132), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(cons(active(_x131), _x132), _x122))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(f(_x181)), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(f(active(_x181))), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(0)), _x72))))))) → top#(s(f(p(p(cons(f(mark(cons(0, f(s(0))))), _x72))))))top#(ok(s(f(p(p(cons(p(f(f(0))), _x72))))))) → top#(s(f(p(p(cons(p(f(mark(cons(0, f(s(0)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(s(_x161))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(s(active(_x161)))), _x132)))))), _x72))))))top#(ok(s(cons(cons(s(_x61), _x52), _x42)))) → top#(s(cons(cons(s(active(_x61)), _x52), _x42)))
top#(ok(s(f(p(p(cons(f(f(p(cons(f(s(0)), _x112)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(cons(mark(f(p(s(0)))), _x112)))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(p(_x151)), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(p(active(_x151))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(f(s(0)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(mark(f(p(s(0)))))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(cons(p(s(0)), _x102)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(cons(0, _x102))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(cons(p(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(p(active(_x121)), _x112)))), _x72))))))top#(ok(p(f(0)))) → top#(p(mark(cons(0, f(s(0))))))
top#(ok(s(cons(cons(cons(p(_x71), _x62), _x52), _x42)))) → top#(s(cons(cons(cons(p(active(_x71)), _x62), _x52), _x42)))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(s(0)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(mark(0))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(mark(s(f(p(s(0)))))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(cons(_x181, _x182)), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(cons(active(_x181), _x182)), _x162))), _x132)))))), _x72))))))
top#(ok(f(f(f(s(0)))))) → top#(f(f(mark(f(p(s(0)))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(s(_x141), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(s(active(_x141)), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(p(_x161)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(p(active(_x161))), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(cons(s(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(s(active(_x121)), _x112)))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(f(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(p(f(active(_x151))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(f(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(f(active(_x131))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(f(0)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(s(cons(0, f(s(0))))), _x142))))))), _x72))))))top#(ok(s(p(p(p(s(f(_x81)))))))) → top#(s(p(p(p(s(f(active(_x81))))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(p(s(0)), _x162)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(mark(cons(0, _x162))))), _x132)))))), _x72))))))top#(ok(s(s(cons(p(f(_x71)), _x52))))) → top#(s(s(cons(p(f(active(_x71))), _x52))))
top#(ok(s(f(p(p(cons(p(f(p(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(f(p(active(_x101)))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(cons(_x151, _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(cons(active(_x151), _x152)))))))), _x72))))))
top#(ok(s(f(f(f(s(0))))))) → top#(s(f(f(mark(f(p(s(0))))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(cons(_x171, _x172)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(cons(active(_x171), _x172)))))))))), _x72))))))
top#(ok(s(f(f(0))))) → top#(s(mark(f(cons(0, f(s(0)))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(f(s(0))))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(mark(f(p(s(0))))))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(s(_x191))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(s(active(_x191)))), _x162))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(f(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(f(active(_x131))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(f(0), _x172)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(mark(cons(0, f(s(0)))), _x172)))), _x132)))))), _x72))))))top#(ok(s(f(p(cons(s(f(f(0))), _x62)))))) → top#(s(f(p(cons(s(f(mark(cons(0, f(s(0)))))), _x62)))))
top#(ok(s(s(cons(p(p(_x71)), _x52))))) → top#(s(s(cons(p(p(active(_x71))), _x52))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(mark(f(p(s(0))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(s(0)), _x62))))))) → top#(s(f(p(p(mark(cons(f(p(s(0))), _x62)))))))top#(ok(s(f(p(p(cons(p(s(s(f(s(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(s(active(_x121)))))), _x72))))))
top#(ok(s(s(cons(f(_x61), _x52))))) → top#(s(s(cons(f(active(_x61)), _x52))))top#(ok(s(f(p(p(p(s(0)))))))) → top#(s(f(p(mark(p(0))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(f(_x151), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(f(active(_x151)), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(p(_x171), _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(p(active(_x171)), _x162)), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(f(0), _x132))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(cons(cons(0, f(s(0))), _x132)))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(s(_x171), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(s(active(_x171)), _x162))), _x132)))))), _x72))))))
top#(ok(s(cons(cons(cons(s(_x71), _x62), _x52), _x42)))) → top#(s(cons(cons(cons(s(active(_x71)), _x62), _x52), _x42)))top#(ok(s(f(p(f(cons(s(cons(_x91, _x92)), _x72))))))) → top#(s(f(p(f(cons(s(cons(active(_x91), _x92)), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(f(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(mark(f(p(s(0)))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(s(_x181)), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(s(active(_x181))), _x162))), _x132)))))), _x72))))))
top#(ok(s(p(p(p(f(f(s(0))))))))) → top#(s(p(p(p(f(mark(f(p(s(0))))))))))top#(ok(s(p(p(p(f(s(_x81)))))))) → top#(s(p(p(p(f(s(active(_x81))))))))
top#(ok(s(f(p(cons(s(s(f(_x91))), _x62)))))) → top#(s(f(p(cons(s(s(f(active(_x91)))), _x62)))))top#(ok(s(f(p(cons(s(s(f(0))), _x62)))))) → top#(s(f(p(cons(s(s(mark(cons(0, f(s(0)))))), _x62)))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(f(_x171)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(f(active(_x171))))))))))), _x72))))))top#(ok(s(s(cons(p(f(0)), _x52))))) → top#(s(s(cons(p(mark(cons(0, f(s(0))))), _x52))))
top#(ok(s(s(p(s(_x61)))))) → top#(s(s(p(s(active(_x61))))))top#(ok(s(f(p(p(cons(p(s(s(f(cons(p(s(0)), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(mark(0), _x122))))), _x72))))))
top#(ok(s(s(f(_x51))))) → top#(s(s(f(active(_x51)))))top#(ok(s(f(p(f(cons(s(f(0)), _x72))))))) → top#(s(f(p(f(cons(s(mark(cons(0, f(s(0))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(p(s(0)))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(mark(0))), _x162))), _x132)))))), _x72))))))top#(ok(s(p(cons(_x51, _x52))))) → top#(s(p(cons(active(_x51), _x52))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(p(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(mark(0)))))), _x72))))))top#(ok(s(cons(cons(cons(f(0), _x62), _x52), _x42)))) → top#(s(cons(cons(cons(mark(cons(0, f(s(0)))), _x62), _x52), _x42)))
top#(ok(s(f(p(p(cons(f(f(p(s(f(0))))), _x72))))))) → top#(s(f(p(p(cons(f(f(mark(p(s(cons(0, f(s(0)))))))), _x72))))))top#(ok(s(p(f(_x51))))) → top#(s(p(f(active(_x51)))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(f(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(f(active(_x161)))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(f(_x161)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(f(active(_x161))), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(cons(_x161, _x162))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(cons(active(_x161), _x162))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(cons(0, f(s(0)))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(f(0), _x152)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(mark(cons(cons(0, f(s(0))), _x152))), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(f(cons(_x91, _x92)), _x72))))))) → top#(s(f(p(p(cons(f(cons(active(_x91), _x92)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(p(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(0))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(f(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(mark(cons(0, f(s(0))))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(cons(f(0), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(mark(cons(0, f(s(0)))), _x112)))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(s(_x181), _x172)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(s(active(_x181)), _x172)))), _x132)))))), _x72))))))
top#(ok(s(f(p(cons(f(s(_x81)), _x62)))))) → top#(s(f(p(cons(f(s(active(_x81))), _x62)))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(cons(_x191, _x192))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(cons(active(_x191), _x192))), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(p(s(0))))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(mark(0)))), _x162))), _x132)))))), _x72))))))top#(ok(s(f(p(cons(s(f(cons(_x91, _x92))), _x62)))))) → top#(s(f(p(cons(s(f(cons(active(_x91), _x92))), _x62)))))
top#(ok(s(f(p(cons(s(p(_x81)), _x62)))))) → top#(s(f(p(cons(s(p(active(_x81))), _x62)))))top#(ok(s(f(p(f(cons(p(s(0)), _x72))))))) → top#(s(f(p(f(cons(mark(0), _x72))))))
top#(ok(p(p(_x41)))) → top#(p(p(active(_x41))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(p(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(mark(p(0))))))))), _x72))))))
top#(ok(s(cons(cons(p(s(0)), _x52), _x42)))) → top#(s(cons(cons(mark(0), _x52), _x42)))top#(ok(s(f(p(p(cons(p(s(s(p(_x111)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(p(active(_x111))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(f(_x181), _x172)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(f(active(_x181)), _x172)))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(cons(f(_x131), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(f(active(_x131)), _x122))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(s(0))), _x72))))))) → top#(s(f(p(p(cons(f(mark(f(p(s(0))))), _x72))))))top#(ok(s(f(p(cons(f(s(0)), _x62)))))) → top#(s(f(p(cons(mark(f(p(s(0)))), _x62)))))
top#(ok(s(f(p(p(s(0))))))) → top#(s(f(p(mark(0)))))top#(ok(s(f(p(p(cons(f(f(p(cons(p(s(0)), _x112)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(cons(mark(0), _x112)))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(cons(_x121, _x122))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(cons(active(_x121), _x122))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(0), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(mark(cons(0, f(s(0)))), _x162))), _x132)))))), _x72))))))
top#(ok(s(p(p(p(f(cons(f(s(0)), _x72)))))))) → top#(s(p(p(mark(p(f(cons(f(p(s(0))), _x72))))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(s(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(s(active(_x141)))))))), _x72))))))
top#(ok(s(f(p(cons(s(f(p(_x91))), _x62)))))) → top#(s(f(p(cons(s(f(p(active(_x91)))), _x62)))))top#(ok(s(f(p(p(cons(p(s(s(f(p(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(p(active(_x121)))))), _x72))))))
top#(ok(s(f(p(f(s(0))))))) → top#(s(f(p(mark(f(p(s(0))))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(f(s(0)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(f(p(s(0)))), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(cons(_x161, _x162))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(cons(active(_x161), _x162))))))))), _x72))))))top#(ok(s(f(p(f(cons(f(s(0)), _x72))))))) → top#(s(f(p(f(cons(mark(f(p(s(0)))), _x72))))))
top#(ok(f(f(s(0))))) → top#(f(mark(f(p(s(0))))))top#(ok(s(p(p(p(s(cons(_x81, _x82)))))))) → top#(s(p(p(p(s(cons(active(_x81), _x82)))))))
top#(ok(s(p(p(p(f(cons(f(_x91), _x82)))))))) → top#(s(p(p(p(f(cons(f(active(_x91)), _x82)))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(f(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(f(active(_x141)))))))), _x72))))))
top#(ok(s(f(p(f(p(s(0)))))))) → top#(s(f(p(f(mark(0))))))top#(ok(s(f(p(p(cons(p(p(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(p(active(_x91))), _x72))))))
top#(ok(s(s(p(s(0)))))) → top#(s(s(mark(0))))top#(ok(s(s(cons(f(0), _x52))))) → top#(s(s(cons(mark(cons(0, f(s(0)))), _x52))))
top#(ok(s(f(p(p(cons(p(s(s(s(f(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(f(active(_x121)))))), _x72))))))top#(ok(s(f(p(f(s(_x71))))))) → top#(s(f(p(f(s(active(_x71)))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(f(s(0))))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(mark(f(p(s(0))))))))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(f(_x171)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(f(active(_x171))))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(f(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(p(mark(cons(0, f(s(0))))))))))), _x72))))))top#(ok(s(cons(cons(cons(f(_x71), _x62), _x52), _x42)))) → top#(s(cons(cons(cons(f(active(_x71)), _x62), _x52), _x42)))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(s(0)))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(mark(f(p(s(0)))))), _x162))), _x132)))))), _x72))))))top#(ok(s(s(p(f(cons(f(s(0)), _x72))))))) → top#(s(s(p(f(cons(mark(f(p(s(0)))), _x72))))))
top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))top#(ok(f(f(p(_x51))))) → top#(f(f(p(active(_x51)))))
top#(ok(p(s(_x41)))) → top#(p(s(active(_x41))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(p(_x171)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(p(active(_x171))), _x152)))))))), _x72))))))
top#(ok(s(f(p(cons(f(p(_x81)), _x62)))))) → top#(s(f(p(cons(f(p(active(_x81))), _x62)))))top#(ok(s(s(p(p(_x61)))))) → top#(s(s(p(p(active(_x61))))))
top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(cons(_x181, _x182), _x172)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(cons(active(_x181), _x182), _x172)))), _x132)))))), _x72))))))
top#(ok(f(f(cons(_x51, _x52))))) → top#(f(f(cons(active(_x51), _x52))))top#(ok(s(f(p(cons(s(f(s(f(_x101)))), _x62)))))) → top#(s(f(p(cons(s(f(s(f(active(_x101))))), _x62)))))
top#(ok(s(s(p(f(cons(f(0), _x72))))))) → top#(s(s(p(f(cons(mark(cons(0, f(s(0)))), _x72))))))top#(ok(s(s(f(0))))) → top#(s(s(mark(cons(0, f(s(0)))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(s(0))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(mark(0)), _x162))), _x132)))))), _x72))))))top#(ok(s(p(p(p(s(s(_x81)))))))) → top#(s(p(p(p(s(s(active(_x81))))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(f(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(mark(cons(0, f(s(0)))))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(p(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(mark(0))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(p(s(0)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(mark(0))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(s(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(s(active(_x161)))))))))), _x72))))))
top#(ok(s(p(p(p(f(p(s(0))))))))) → top#(s(p(p(p(f(mark(0)))))))top#(ok(s(s(p(f(0)))))) → top#(s(s(p(mark(cons(0, f(s(0))))))))
top#(ok(f(p(s(0))))) → top#(f(mark(0)))top#(ok(s(f(p(p(cons(p(s(s(f(cons(f(0), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(mark(cons(0, f(s(0)))), _x122))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(cons(p(_x131), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(p(active(_x131)), _x122))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(0), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(mark(cons(0, f(s(0)))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(mark(cons(0, f(s(0)))))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(cons(cons(_x121, _x122), _x112)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(cons(cons(active(_x121), _x122), _x112)))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(p(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(p(active(_x151))))))))), _x72))))))top#(ok(s(f(f(f(_x61)))))) → top#(s(f(f(f(active(_x61))))))
top#(ok(s(s(p(f(cons(p(s(0)), _x72))))))) → top#(s(s(p(f(cons(mark(0), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(0))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(mark(p(cons(0, f(s(0)))))), _x162))), _x132)))))), _x72))))))
top#(ok(s(p(p(p(f(cons(cons(_x91, _x92), _x82)))))))) → top#(s(p(p(p(f(cons(cons(active(_x91), _x92), _x82)))))))top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))
top#(ok(s(s(cons(p(p(s(0))), _x52))))) → top#(s(s(cons(p(mark(0)), _x52))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(p(_x191))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(p(active(_x191)))), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(cons(f(_x91), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(f(active(_x91)), _x82), _x72))))))top#(ok(s(f(p(cons(p(_x71), _x62)))))) → top#(s(f(p(cons(p(active(_x71)), _x62)))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(mark(f(p(s(0))))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(mark(cons(0, f(s(0))))))))))), _x72))))))
top#(mark(f(0))) → top#(f(ok(0)))top#(ok(s(s(cons(cons(_x61, _x62), _x52))))) → top#(s(s(cons(cons(active(_x61), _x62), _x52))))
top#(ok(s(f(p(p(cons(p(s(0)), _x72))))))) → top#(s(f(p(p(cons(mark(0), _x72))))))top#(ok(s(p(p(p(s(p(s(0))))))))) → top#(s(p(p(p(s(mark(0)))))))
top#(ok(s(s(p(f(cons(p(_x81), _x72))))))) → top#(s(s(p(f(cons(p(active(_x81)), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(p(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(p(active(_x131))))))), _x72))))))
top#(ok(p(f(_x41)))) → top#(p(f(active(_x41))))top#(ok(s(p(f(0))))) → top#(s(p(mark(cons(0, f(s(0)))))))
top#(ok(s(f(p(cons(f(f(s(0))), _x62)))))) → top#(s(f(p(cons(mark(f(f(p(s(0))))), _x62)))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(cons(_x151, _x152)), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(cons(active(_x151), _x152)), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(p(s(0)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(mark(0), _x152)))))))), _x72))))))top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))
top#(ok(s(f(p(cons(f(cons(_x81, _x82)), _x62)))))) → top#(s(f(p(cons(f(cons(active(_x81), _x82)), _x62)))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(cons(_x161, _x162), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(cons(active(_x161), _x162), _x152)))))))), _x72))))))
top#(ok(s(f(p(cons(s(f(s(0))), _x62)))))) → top#(s(f(p(cons(s(mark(f(p(s(0))))), _x62)))))top#(ok(s(f(p(p(cons(p(s(s(f(cons(s(_x131), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(s(active(_x131)), _x122))))), _x72))))))
top#(ok(s(f(p(f(cons(s(s(_x91)), _x72))))))) → top#(s(f(p(f(cons(s(s(active(_x91))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(p(s(0))))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(mark(0)))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(cons(_x171, _x172)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(cons(active(_x171), _x172)), _x152)))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(f(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(s(cons(0, f(s(0)))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(p(_x151), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(p(active(_x151)), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(cons(f(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(cons(f(active(_x121)), _x112)))), _x72))))))
top#(ok(s(p(s(_x51))))) → top#(s(p(s(active(_x51)))))top#(ok(s(f(p(f(cons(f(0), _x72))))))) → top#(s(f(p(f(cons(mark(cons(0, f(s(0)))), _x72))))))
top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(mark(f(p(p(f(p(s(0)))))))))top#(ok(s(p(p(f(s(0))))))) → top#(s(p(p(mark(f(p(s(0))))))))
top#(ok(s(f(p(p(cons(p(f(f(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(f(f(active(_x101)))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(0)))), _x72))))))) → top#(s(f(p(p(cons(f(mark(f(0))), _x72))))))
top#(ok(s(p(p(p(f(p(_x81)))))))) → top#(s(p(p(p(f(p(active(_x81))))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(f(s(0))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(mark(f(p(s(0))))), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(p(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(mark(0)))))), _x72))))))top#(ok(s(f(p(p(cons(p(f(cons(_x101, _x102))), _x72))))))) → top#(s(f(p(p(cons(p(f(cons(active(_x101), _x102))), _x72))))))
top#(ok(s(p(p(s(0)))))) → top#(s(p(mark(0))))top#(mark(f(f(_x41)))) → top#(f(f(proper(_x41))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(p(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(mark(0)))))))), _x72))))))top#(ok(s(f(p(cons(s(s(p(s(0)))), _x62)))))) → top#(s(f(p(cons(s(s(mark(0))), _x62)))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(f(_x201)))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(f(active(_x201))))), _x162))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(f(_x161), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(f(active(_x161)), _x152)))))))), _x72))))))
top#(ok(s(f(p(cons(s(f(s(cons(_x101, _x102)))), _x62)))))) → top#(s(f(p(cons(s(f(s(cons(active(_x101), _x102)))), _x62)))))top#(ok(s(f(p(p(cons(p(cons(f(s(0)), _x82)), _x72))))))) → top#(s(f(p(p(cons(p(mark(cons(f(p(s(0))), _x82))), _x72))))))
top#(ok(f(f(0)))) → top#(f(mark(cons(0, f(s(0))))))top#(ok(cons(f(s(0)), _x22))) → top#(cons(mark(f(p(s(0)))), _x22))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(f(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(mark(cons(0, f(s(0)))))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(f(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(mark(f(p(s(0))))))))), _x72))))))
top#(ok(s(cons(cons(f(s(0)), _x52), _x42)))) → top#(s(cons(cons(mark(f(p(s(0)))), _x52), _x42)))top#(ok(s(f(p(p(cons(f(f(p(cons(f(0), _x112)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(cons(mark(cons(0, f(s(0)))), _x112)))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(p(s(0)), _x152)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(s(cons(0, _x152))), _x142))))))), _x72))))))top#(ok(s(f(p(cons(p(s(0)), _x62)))))) → top#(s(f(p(cons(mark(0), _x62)))))
top#(mark(p(_x21))) → top#(p(proper(_x21)))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(f(s(0)), _x172)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(mark(f(p(s(0)))), _x172)))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(p(_x171)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(p(active(_x171))))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(f(_x171)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(f(active(_x171))))), _x132)))))), _x72))))))
top#(ok(s(p(p(p(f(f(0)))))))) → top#(s(p(p(p(f(mark(cons(0, f(s(0))))))))))top#(ok(s(s(cons(p(f(s(0))), _x52))))) → top#(s(s(cons(mark(p(f(p(s(0))))), _x52))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(cons(_x161, _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(cons(active(_x161), _x162))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(f(0)))), _x72))))))) → top#(s(f(p(p(cons(f(mark(f(p(cons(0, f(s(0))))))), _x72))))))
top#(ok(s(f(p(cons(cons(_x71, _x72), _x62)))))) → top#(s(f(p(cons(cons(active(_x71), _x72), _x62)))))top#(ok(s(f(p(p(cons(p(s(p(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(p(active(_x101)))), _x72))))))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(f(s(0))), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(s(f(p(s(0))))), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(mark(cons(0, f(s(0)))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(f(_x171)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(f(active(_x171))), _x152)))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(mark(0))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(p(_x171)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(p(active(_x171))))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(f(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(mark(cons(0, f(s(0))))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(cons(_x201, _x202)))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(cons(active(_x201), _x202)))), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(cons(s(f(f(_x91))), _x62)))))) → top#(s(f(p(cons(s(f(f(active(_x91)))), _x62)))))top#(ok(s(s(p(f(s(_x71))))))) → top#(s(s(p(f(s(active(_x71)))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(cons(_x141, _x142), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(cons(active(_x141), _x142), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(0)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(mark(cons(0, f(s(0))))))))), _x72))))))
top#(ok(s(cons(cons(f(0), _x52), _x42)))) → top#(s(cons(cons(mark(cons(0, f(s(0)))), _x52), _x42)))top#(ok(cons(f(0), _x32))) → top#(mark(cons(cons(0, f(s(0))), _x32)))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(f(0)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(mark(cons(0, f(s(0))))))), _x132)))))), _x72))))))top#(ok(s(s(p(f(p(_x71))))))) → top#(s(s(p(f(p(active(_x71)))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(p(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(mark(0))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(f(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(mark(f(p(s(0)))))))))))), _x72))))))
top#(ok(s(cons(f(s(0)), _x42)))) → top#(s(cons(mark(f(p(s(0)))), _x42)))top#(ok(s(cons(f(0), _x42)))) → top#(s(cons(mark(cons(0, f(s(0)))), _x42)))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(f(_x171), _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(f(active(_x171)), _x162)), _x142))))))), _x72))))))top#(ok(s(s(p(f(cons(f(_x81), _x72))))))) → top#(s(s(p(f(cons(f(active(_x81)), _x72))))))
top#(ok(s(f(p(p(cons(s(p(_x91)), _x72))))))) → top#(s(f(p(p(cons(s(p(active(_x91))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(p(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(p(active(_x161)))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(s(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(s(active(_x141)))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(f(0))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(mark(f(cons(0, f(s(0)))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(f(_x161))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(f(active(_x161)))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(f(f(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(f(mark(f(p(s(0)))))), _x72))))))
top#(ok(s(f(p(p(cons(cons(f(s(0)), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(mark(f(p(s(0)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(s(_x101))), _x72))))))) → top#(s(f(p(p(cons(f(f(s(active(_x101)))), _x72))))))
top#(ok(s(f(p(p(cons(p(f(p(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(mark(f(0))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(cons(_x131, _x132)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(cons(active(_x131), _x132)))))), _x72))))))
top#(ok(s(f(p(p(s(_x71))))))) → top#(s(f(p(p(s(active(_x71)))))))top#(ok(cons(s(_x41), _x22))) → top#(cons(s(active(_x41)), _x22))
top#(ok(p(p(s(0))))) → top#(mark(p(0)))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(cons(_x171, _x172)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(cons(active(_x171), _x172)))), _x132)))))), _x72))))))
top#(ok(s(p(p(p(s(0))))))) → top#(s(p(p(mark(0)))))top#(ok(s(f(p(f(cons(s(f(_x91)), _x72))))))) → top#(s(f(p(f(cons(s(f(active(_x91))), _x72))))))
top#(ok(s(f(p(p(cons(p(p(s(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(0)), _x72))))))top#(ok(s(f(p(p(f(_x71))))))) → top#(s(f(p(p(f(active(_x71)))))))
top#(ok(s(f(p(cons(s(f(s(f(s(0))))), _x62)))))) → top#(s(f(p(cons(s(f(s(mark(f(p(s(0))))))), _x62)))))top#(ok(s(f(p(p(cons(p(s(s(f(f(p(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(p(active(_x131))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(0)), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(mark(cons(0, f(s(0))))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(s(_x171), _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(s(active(_x171)), _x162)), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(p(s(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(0)))), _x72))))))top#(ok(s(f(f(p(_x61)))))) → top#(s(f(f(p(active(_x61))))))
top#(ok(s(f(p(p(cons(f(f(p(s(p(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(mark(0))))), _x72))))))top#(ok(s(f(p(cons(s(s(p(_x91))), _x62)))))) → top#(s(f(p(cons(s(s(p(active(_x91)))), _x62)))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(f(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(f(f(p(s(0))))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(f(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(mark(s(cons(0, f(s(0))))))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(f(_x121))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(f(active(_x121)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(s(0)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(mark(f(p(s(0)))))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(p(_x141), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(p(active(_x141)), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(s(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(f(p(s(0))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(f(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(s(cons(0, f(s(0)))))), _x72))))))top#(ok(s(p(p(p(f(cons(f(0), _x82)))))))) → top#(s(p(p(p(f(cons(mark(cons(0, f(s(0)))), _x82)))))))
top#(ok(s(f(p(p(cons(s(f(0)), _x72))))))) → top#(s(f(p(p(cons(s(mark(cons(0, f(s(0))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(f(p(s(0)))))))))), _x72))))))
top#(ok(s(cons(cons(cons(cons(_x71, _x72), _x62), _x52), _x42)))) → top#(s(cons(cons(cons(cons(active(_x71), _x72), _x62), _x52), _x42)))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(p(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(p(active(_x141)))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(f(0), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(mark(cons(0, f(s(0)))), _x152)))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(p(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(p(active(_x161)))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(f(0)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(mark(cons(0, f(s(0))))), _x152)))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(p(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(mark(0))))), _x72))))))
top#(ok(s(f(p(p(cons(f(p(_x91)), _x72))))))) → top#(s(f(p(p(cons(f(p(active(_x91))), _x72))))))top#(ok(cons(f(_x41), _x22))) → top#(cons(f(active(_x41)), _x22))
top#(ok(s(f(p(cons(f(f(0)), _x62)))))) → top#(s(f(p(cons(f(mark(cons(0, f(s(0))))), _x62)))))top#(ok(s(f(p(p(cons(f(f(p(cons(s(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(cons(s(active(_x121)), _x112)))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(p(_x201)))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(p(active(_x201))))), _x162))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(f(s(0)))), _x72))))))) → top#(s(f(p(p(cons(mark(f(f(f(p(s(0)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(cons(_x161, _x162))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(cons(active(_x161), _x162))))))))), _x72))))))top#(ok(s(cons(cons(cons(f(s(0)), _x62), _x52), _x42)))) → top#(s(cons(cons(cons(mark(f(p(s(0)))), _x62), _x52), _x42)))
top#(ok(s(f(p(cons(s(f(0)), _x62)))))) → top#(s(f(p(cons(s(mark(cons(0, f(s(0))))), _x62)))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(p(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(mark(0))))))), _x72))))))
top#(ok(s(cons(p(_x51), _x42)))) → top#(s(cons(p(active(_x51)), _x42)))top#(ok(s(p(p(p(f(cons(s(_x91), _x82)))))))) → top#(s(p(p(p(f(cons(s(active(_x91)), _x82)))))))
top#(ok(s(f(p(p(cons(f(f(p(f(_x111)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(f(active(_x111))))), _x72))))))top#(ok(s(cons(p(s(0)), _x42)))) → top#(s(cons(mark(0), _x42)))
top#(ok(s(p(p(p(s(f(s(0))))))))) → top#(s(p(p(p(s(mark(f(p(s(0))))))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(mark(0)))))))), _x72))))))
top#(ok(s(f(f(cons(_x61, _x62)))))) → top#(s(f(f(cons(active(_x61), _x62)))))top#(ok(f(f(s(_x51))))) → top#(f(f(s(active(_x51)))))
top#(ok(s(p(p(p(f(f(_x81)))))))) → top#(s(p(p(p(f(f(active(_x81))))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(s(_x161))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(s(active(_x161)))), _x132)))))), _x72))))))
top#(ok(s(p(f(s(0)))))) → top#(s(p(mark(f(p(s(0)))))))top#(ok(s(f(p(p(cons(f(f(p(f(s(0))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(mark(f(p(s(0))))))), _x72))))))
top#(ok(s(f(p(f(f(_x71))))))) → top#(s(f(p(f(f(active(_x71)))))))top#(ok(s(s(cons(p(cons(_x71, _x72)), _x52))))) → top#(s(s(cons(p(cons(active(_x71), _x72)), _x52))))
top#(ok(s(cons(cons(cons(p(s(0)), _x62), _x52), _x42)))) → top#(s(cons(cons(cons(mark(0), _x62), _x52), _x42)))top#(ok(s(f(p(cons(s(cons(_x81, _x82)), _x62)))))) → top#(s(f(p(cons(s(cons(active(_x81), _x82)), _x62)))))
top#(ok(s(s(p(f(f(s(0)))))))) → top#(s(s(p(f(mark(f(p(s(0)))))))))top#(ok(s(f(p(s(p(_x71))))))) → top#(s(f(p(s(p(active(_x71)))))))
top#(ok(s(p(p(p(s(f(0)))))))) → top#(s(p(p(p(mark(s(cons(0, f(s(0))))))))))top#(ok(s(f(p(p(cons(p(cons(s(_x101), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(s(active(_x101)), _x92)), _x72))))))
top#(ok(s(f(p(f(p(_x71))))))) → top#(s(f(p(f(p(active(_x71)))))))top#(ok(s(f(p(p(cons(p(f(0)), _x62))))))) → top#(s(f(p(p(mark(cons(p(cons(0, f(s(0)))), _x62)))))))
top#(ok(s(p(p(p(s(p(_x81)))))))) → top#(s(p(p(p(s(p(active(_x81))))))))top#(ok(s(f(p(p(cons(p(s(s(f(cons(f(s(0)), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(mark(f(p(s(0)))), _x122))))), _x72))))))
top#(ok(f(cons(_x41, _x42)))) → top#(f(cons(active(_x41), _x42)))top#(ok(s(f(p(p(f(0))))))) → top#(s(f(p(mark(p(cons(0, f(s(0)))))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(f(0)), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(mark(cons(0, f(s(0))))), _x162))), _x132)))))), _x72))))))top#(ok(s(f(p(cons(s(f(s(p(_x101)))), _x62)))))) → top#(s(f(p(cons(s(f(s(p(active(_x101))))), _x62)))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(p(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(mark(0))))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(f(s(0))))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(mark(f(f(p(s(0))))))), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(s(_x171)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(s(active(_x171))))))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(p(s(0))))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(mark(0)))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(p(_x111)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(p(active(_x111))))), _x72))))))top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))
top#(ok(s(f(p(p(cons(p(f(s(0))), _x72))))))) → top#(s(f(p(p(cons(mark(p(f(p(s(0))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(s(_x171)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(s(active(_x171))), _x152)))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(f(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(f(active(_x101)))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(cons(_x151, _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(p(cons(active(_x151), _x152)))))))), _x72))))))
top#(ok(s(p(p(p(f(0))))))) → top#(s(p(p(p(mark(cons(0, f(s(0)))))))))top#(ok(s(f(p(s(f(s(0)))))))) → top#(s(f(p(mark(s(f(p(s(0)))))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(f(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(mark(f(p(s(0)))))))))))), _x72))))))top#(ok(s(f(p(f(f(s(0)))))))) → top#(s(f(mark(p(f(f(p(s(0)))))))))
top#(ok(s(s(f(s(0)))))) → top#(s(mark(s(f(p(s(0)))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(p(_x181), _x172)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(p(active(_x181)), _x172)))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(s(f(s(0))), _x72))))))) → top#(s(f(p(p(cons(s(mark(f(p(s(0))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(s(0)), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(mark(f(p(s(0)))), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(s(p(s(0)))))))) → top#(s(f(p(s(mark(0))))))top#(ok(s(f(p(s(f(0))))))) → top#(s(f(p(s(mark(cons(0, f(s(0)))))))))
top#(ok(s(cons(s(_x51), _x42)))) → top#(s(cons(s(active(_x51)), _x42)))top#(ok(s(f(p(p(cons(p(s(f(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(f(p(s(0)))))), _x72))))))
top#(ok(s(f(p(cons(f(f(_x81)), _x62)))))) → top#(s(f(p(cons(f(f(active(_x81))), _x62)))))top#(ok(f(f(p(s(0)))))) → top#(f(f(mark(0))))
top#(ok(s(f(p(p(p(_x71))))))) → top#(s(f(p(p(p(active(_x71)))))))top#(ok(s(f(p(p(cons(p(s(s(cons(cons(_x121, _x122), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(cons(active(_x121), _x122), _x112)))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(cons(0, f(s(0))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(f(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(mark(f(p(s(0)))))))))))), _x72))))))
top#(ok(s(f(p(cons(s(p(s(0))), _x62)))))) → top#(s(f(p(cons(mark(s(0)), _x62)))))top#(ok(s(f(p(p(cons(f(p(s(0))), _x72))))))) → top#(s(f(p(p(cons(f(mark(0)), _x72))))))
top#(ok(s(s(cons(f(s(0)), _x52))))) → top#(s(s(cons(mark(f(p(s(0)))), _x52))))top#(ok(p(f(s(0))))) → top#(p(mark(f(p(s(0))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(p(s(0))), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(s(0)), _x142))))))), _x72))))))top#(ok(s(f(f(s(_x61)))))) → top#(s(f(f(s(active(_x61))))))
top#(ok(s(f(p(cons(s(f(s(p(s(0))))), _x62)))))) → top#(s(f(p(cons(s(f(mark(s(0)))), _x62)))))top#(ok(s(f(p(s(s(_x71))))))) → top#(s(f(p(s(s(active(_x71)))))))
top#(ok(s(f(p(p(cons(p(cons(f(_x101), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(f(active(_x101)), _x92)), _x72))))))top#(ok(s(f(p(cons(s(s(s(_x91))), _x62)))))) → top#(s(f(p(cons(s(s(s(active(_x91)))), _x62)))))
top#(ok(s(f(p(cons(s(f(s(s(_x101)))), _x62)))))) → top#(s(f(p(cons(s(f(s(s(active(_x101))))), _x62)))))top#(ok(s(p(p(s(_x61)))))) → top#(s(p(p(s(active(_x61))))))
top#(ok(s(f(p(p(cons(f(f(p(cons(p(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(cons(p(active(_x121)), _x112)))), _x72))))))top#(ok(s(f(p(p(cons(f(0), _x72))))))) → top#(s(f(p(p(cons(mark(cons(0, f(s(0)))), _x72))))))
top#(ok(s(s(cons(p(s(0)), _x42))))) → top#(s(s(mark(cons(0, _x42)))))top#(ok(s(f(p(f(cons(s(p(_x91)), _x72))))))) → top#(s(f(p(f(cons(s(p(active(_x91))), _x72))))))
top#(ok(s(f(p(cons(f(p(s(0))), _x62)))))) → top#(s(f(p(cons(f(mark(0)), _x62)))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(cons(_x171, _x172), _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(cons(active(_x171), _x172), _x162)), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(f(s(0)), _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(mark(f(p(s(0)))), _x162)), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(s(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(s(active(_x131))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(p(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(0))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(s(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(s(active(_x161)))))))))), _x72))))))
top#(ok(s(cons(cons(p(_x61), _x52), _x42)))) → top#(s(cons(cons(p(active(_x61)), _x52), _x42)))top#(ok(s(p(p(p(p(s(0)))))))) → top#(s(p(p(p(mark(0))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(s(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(s(active(_x131))))))), _x72))))))top#(ok(s(p(p(p(cons(_x71, _x72))))))) → top#(s(p(p(p(cons(active(_x71), _x72))))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

The right-hand side of the rule top#(ok(s(f(f(f(0)))))) → top#(s(f(f(mark(cons(0, f(s(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
top#(s(f(mark(f(cons(0, f(s(0)))))))) 
Thus, the rule top#(ok(s(f(f(f(0)))))) → top#(s(f(f(mark(cons(0, f(s(0)))))))) is replaced by the following rules:
top#(ok(s(f(f(f(0)))))) → top#(s(f(mark(f(cons(0, f(s(0))))))))

Problem 31: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

top#(ok(s(p(s(0))))) → top#(mark(s(0)))top#(ok(s(f(p(p(cons(cons(cons(_x91, _x92), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(cons(active(_x91), _x92), _x82), _x72))))))
top#(ok(s(p(p(p(f(cons(p(_x91), _x82)))))))) → top#(s(p(p(p(f(cons(p(active(_x91)), _x82)))))))top#(mark(f(cons(_x41, _x42)))) → top#(f(cons(proper(_x41), proper(_x42))))
top#(ok(s(f(p(p(cons(p(s(s(s(cons(_x121, _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(cons(active(_x121), _x122))))), _x72))))))top#(ok(s(f(p(cons(s(f(f(s(0)))), _x62)))))) → top#(s(f(p(cons(s(f(mark(f(p(s(0)))))), _x62)))))
top#(ok(s(f(p(p(cons(p(s(s(s(p(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(p(active(_x121)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(s(_x201)))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(s(active(_x201))))), _x162))), _x132)))))), _x72))))))
top#(ok(f(f(f(0))))) → top#(f(f(mark(cons(0, f(s(0)))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(s(f(s(0))), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(mark(s(f(p(s(0))))), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(p(s(0))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(mark(0)))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(p(_x161))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(p(active(_x161)))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(cons(s(_x91), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(s(active(_x91)), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(cons(f(0), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(mark(cons(0, f(s(0)))), _x92)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(p(s(0))), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(mark(0)), _x152)))))))), _x72))))))top#(ok(s(f(p(cons(s(f(p(s(0)))), _x62)))))) → top#(s(f(p(cons(s(mark(f(0))), _x62)))))
top#(ok(s(s(s(_x51))))) → top#(s(s(s(active(_x51)))))top#(ok(s(f(f(p(s(0))))))) → top#(s(f(f(mark(0)))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(f(s(0)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(mark(f(p(s(0)))), _x152)))))))), _x72))))))top#(ok(s(s(p(p(s(0))))))) → top#(s(s(p(mark(0)))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(s(_x171)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(s(active(_x171))))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(f(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(f(active(_x161)))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(cons(f(s(0)), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(mark(f(p(s(0)))), _x112)))), _x72))))))top#(ok(cons(p(_x41), _x22))) → top#(cons(p(active(_x41)), _x22))
top#(ok(s(f(p(cons(s(s(cons(_x91, _x92))), _x62)))))) → top#(s(f(p(cons(s(s(cons(active(_x91), _x92))), _x62)))))top#(ok(s(f(p(p(cons(cons(f(0), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(mark(cons(0, f(s(0)))), _x82), _x72))))))
top#(ok(s(f(p(cons(s(s(f(s(0)))), _x62)))))) → top#(s(f(p(cons(s(s(mark(f(p(s(0)))))), _x62)))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(cons(f(_x271), _x262)))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(cons(f(active(_x271)), _x262)))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(p(_x171), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(p(active(_x171)), _x162))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(s(s(p(s(0)))), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(s(s(mark(0))), _x142))))))), _x72))))))
top#(ok(s(f(p(f(cons(cons(_x81, _x82), _x72))))))) → top#(s(f(p(f(cons(cons(active(_x81), _x82), _x72))))))top#(ok(f(s(_x41)))) → top#(f(s(active(_x41))))
top#(ok(s(s(cons(p(s(f(p(_x91)))), _x52))))) → top#(s(s(cons(p(s(f(p(active(_x91))))), _x52))))top#(ok(s(f(p(p(cons(s(f(_x91)), _x72))))))) → top#(s(f(p(p(cons(s(f(active(_x91))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(f(p(s(0))), _x202))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(f(mark(0)), _x202))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(s(p(f(cons(cons(s(_x91), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(s(active(_x91)), _x82), _x72))))))
top#(mark(s(_x21))) → top#(s(proper(_x21)))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(cons(_x151, _x152), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(cons(active(_x151), _x152), _x142))))))), _x72))))))
top#(ok(s(cons(cons(f(_x61), _x52), _x42)))) → top#(s(cons(cons(f(active(_x61)), _x52), _x42)))top#(ok(s(f(p(f(0)))))) → top#(s(f(p(mark(cons(0, f(s(0))))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(f(0), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(mark(cons(0, f(s(0)))), _x142))))))), _x72))))))top#(ok(s(s(p(f(f(_x71))))))) → top#(s(s(p(f(f(active(_x71)))))))
top#(mark(f(p(_x41)))) → top#(f(p(proper(_x41))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(mark(f(p(s(0)))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(p(f(_x161)))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(p(f(active(_x161))))), _x122)))), _x82), _x72))))))top#(ok(s(s(p(f(f(0))))))) → top#(s(s(p(f(mark(cons(0, f(s(0)))))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(s(_x191)))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(s(active(_x191))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(s(cons(p(s(s(_x81))), _x52))))) → top#(s(s(cons(p(s(s(active(_x81)))), _x52))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(s(s(f(0))), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(s(s(mark(cons(0, f(s(0)))))), _x142))))))), _x72))))))top#(ok(p(cons(_x41, _x42)))) → top#(p(cons(active(_x41), _x42)))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(p(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(p(p(active(_x151))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(cons(p(s(0)), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(cons(mark(0), _x132)))))), _x72))))))
top#(mark(f(s(_x41)))) → top#(f(s(proper(_x41))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(p(s(0)), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(mark(0), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(cons(p(s(0)), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(mark(0), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(s(_x171)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(s(active(_x171))))), _x132)))))), _x72))))))
top#(ok(s(f(p(s(f(_x71))))))) → top#(s(f(p(s(f(active(_x71)))))))top#(ok(s(s(p(cons(cons(f(_x81), _x72), _x62)))))) → top#(s(s(p(cons(cons(f(active(_x81)), _x72), _x62)))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(0)), _x122)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(mark(cons(f(p(s(0))), _x122))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(p(s(0))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(mark(0)), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(s(f(_x161)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(s(f(active(_x161))), _x142))))))), _x72))))))top#(ok(s(f(p(cons(f(0), _x62)))))) → top#(s(f(p(cons(mark(cons(0, f(s(0)))), _x62)))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(cons(_x141, _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(cons(active(_x141), _x142))))))), _x72))))))top#(ok(s(s(p(cons(cons(cons(_x81, _x82), _x72), _x62)))))) → top#(s(s(p(cons(cons(cons(active(_x81), _x82), _x72), _x62)))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(p(s(0)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(mark(0), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(f(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(mark(f(p(s(0)))))))), _x72))))))
top#(ok(s(p(p(p(f(s(0)))))))) → top#(s(p(p(mark(p(f(p(s(0)))))))))top#(ok(s(f(p(p(cons(f(f(f(_x101))), _x72))))))) → top#(s(f(p(p(cons(f(f(f(active(_x101)))), _x72))))))
top#(ok(s(f(p(p(cons(s(s(_x91)), _x72))))))) → top#(s(f(p(p(cons(s(s(active(_x91))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(cons(f(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(f(active(_x121)), _x112)))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(cons(_x161, _x162), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(cons(active(_x161), _x162), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(s(cons(p(s(cons(_x81, _x82))), _x52))))) → top#(s(s(cons(p(s(cons(active(_x81), _x82))), _x52))))
top#(ok(s(p(p(f(_x61)))))) → top#(s(p(p(f(active(_x61))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(p(s(0))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(mark(0)))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(p(cons(p(_x101), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(p(active(_x101)), _x92)), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(p(_x171)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(p(active(_x171))))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(p(s(0)), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(mark(0), _x162))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(s(s(f(_x171))), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(s(s(f(active(_x171)))), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(f(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(f(active(_x151))))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(s(_x261), _x202))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(s(active(_x261)), _x202))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(p(p(p(f(cons(p(s(0)), _x72)))))))) → top#(s(p(p(p(mark(f(cons(0, _x72))))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(s(0))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(mark(f(p(s(0))))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(s(_x161)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(s(active(_x161))), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(p(cons(p(s(0)), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(mark(0), _x92)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(p(_x161), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(p(active(_x161)), _x152)))))))), _x72))))))top#(ok(s(f(p(cons(s(f(s(f(0)))), _x62)))))) → top#(s(f(p(cons(s(f(s(mark(cons(0, f(s(0))))))), _x62)))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(f(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(mark(f(p(s(0))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(f(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(p(mark(f(p(s(0))))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(f(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(f(active(_x161)))))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(p(_x191)))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(p(active(_x191))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(f(p(p(s(0))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(f(mark(p(0)))), _x82), _x72))))))top#(ok(s(p(p(cons(_x61, _x62)))))) → top#(s(p(p(cons(active(_x61), _x62)))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(cons(s(_x271), _x262)))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(cons(s(active(_x271)), _x262)))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(cons(p(_x91), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(p(active(_x91)), _x82), _x72))))))
top#(ok(f(s(0)))) → top#(mark(f(p(s(0)))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(mark(0)))))), _x72))))))
top#(ok(cons(p(s(0)), _x22))) → top#(cons(mark(0), _x22))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(f(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(mark(f(p(s(0)))))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(p(_x261)))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(p(active(_x261))))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(s(p(cons(cons(p(s(0)), _x72), _x62)))))) → top#(s(s(p(cons(cons(mark(0), _x72), _x62)))))
top#(ok(s(s(p(f(cons(s(_x81), _x72))))))) → top#(s(s(p(f(cons(s(active(_x81)), _x72))))))top#(ok(s(f(p(p(cons(p(s(cons(_x101, _x102))), _x72))))))) → top#(s(f(p(p(cons(p(s(cons(active(_x101), _x102))), _x72))))))
top#(ok(s(cons(f(_x51), _x42)))) → top#(s(cons(f(active(_x51)), _x42)))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(s(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(p(s(active(_x151))))))))), _x72))))))
top#(ok(s(f(p(s(cons(_x71, _x72))))))) → top#(s(f(p(s(cons(active(_x71), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(cons(f(0), _x262)))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(cons(mark(cons(0, f(s(0)))), _x262)))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(s(p(f(p(s(0)))))))) → top#(s(s(p(f(mark(0))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(p(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(p(active(_x161)))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(cons(f(s(0)), _x152), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(cons(mark(f(p(s(0)))), _x152), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(s(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(s(active(_x141)))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(f(s(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(f(s(active(_x101)))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(f(s(0))), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(mark(f(p(s(0))))), _x152)))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(f(0), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(mark(cons(0, f(s(0)))), _x82), _x72))))))top#(ok(s(s(cons(p(s(p(s(0)))), _x52))))) → top#(s(s(cons(p(s(mark(0))), _x52))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(p(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(p(mark(0)))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(f(p(cons(_x121, _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(f(p(cons(active(_x121), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(f(cons(s(p(s(0))), _x72))))))) → top#(s(f(p(f(cons(s(mark(0)), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(p(s(0))))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(mark(0)))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(s(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(s(active(_x151))))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(p(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(p(active(_x141)))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(f(f(_x281)), _x202))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(f(f(active(_x281))), _x202))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(f(p(_x41)))) → top#(f(p(active(_x41))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(f(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(mark(cons(0, f(s(0)))))))))))), _x72))))))top#(ok(s(f(f(s(0)))))) → top#(mark(s(f(f(p(s(0)))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(f(s(0))))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(mark(f(f(p(s(0))))))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(s(p(s(0))), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(s(mark(0)), _x142))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(f(f(s(0))), _x202))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(f(mark(f(p(s(0))))), _x202))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(p(_x121))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(p(active(_x121)))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(s(0)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(mark(f(p(s(0)))))), _x82), _x72))))))top#(ok(s(f(p(f(cons(f(_x81), _x72))))))) → top#(s(f(p(f(cons(f(active(_x81)), _x72))))))
top#(ok(s(f(p(f(cons(s(f(s(0))), _x72))))))) → top#(s(f(p(f(cons(s(mark(f(p(s(0))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(f(0)))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(mark(cons(0, f(s(0))))))), _x162))), _x132)))))), _x72))))))
top#(ok(s(s(p(f(s(0))))))) → top#(s(s(p(mark(f(p(s(0))))))))top#(ok(s(s(p(f(cons(cons(p(f(0)), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(mark(cons(0, f(s(0))))), _x82), _x72))))))
top#(ok(f(f(f(_x51))))) → top#(f(f(f(active(_x51)))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(0))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(mark(cons(0, f(s(0)))))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(s(_x91)), _x72))))))) → top#(s(f(p(p(cons(f(s(active(_x91))), _x72))))))top#(ok(s(f(p(p(cons(p(cons(cons(_x101, _x102), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(cons(active(_x101), _x102), _x92)), _x72))))))
top#(ok(s(f(p(s(0)))))) → top#(mark(s(f(0))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(cons(_x171, _x172), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(cons(active(_x171), _x172), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(s(cons(_x91, _x92)), _x72))))))) → top#(s(f(p(p(cons(s(cons(active(_x91), _x92)), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(f(_x151), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(f(active(_x151)), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(f(0)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(mark(cons(0, f(s(0))))))), _x132)))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(p(f(0)))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(p(mark(cons(0, f(s(0))))))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(p(s(0)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(0), _x142))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(f(_x151))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(f(active(_x151)))), _x122)))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(p(p(_x131))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(p(p(active(_x131)))))), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(cons(_x101, _x102))), _x72))))))) → top#(s(f(p(p(cons(f(f(cons(active(_x101), _x102))), _x72))))))
top#(ok(s(s(p(f(cons(cons(f(s(0)), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(mark(f(p(s(0)))), _x82), _x72))))))top#(ok(cons(cons(_x41, _x42), _x22))) → top#(cons(cons(active(_x41), _x42), _x22))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(f(0))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(mark(cons(0, f(s(0)))))), _x132)))))), _x72))))))top#(ok(s(f(p(f(cons(p(_x81), _x72))))))) → top#(s(f(p(f(cons(p(active(_x81)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(f(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(mark(cons(0, f(s(0))))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(p(_x201))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(p(active(_x201)))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(p(p(p(p(_x71))))))) → top#(s(p(p(p(p(active(_x71)))))))top#(ok(s(p(p(f(0)))))) → top#(s(p(p(mark(cons(0, f(s(0))))))))
top#(ok(s(f(p(f(f(0))))))) → top#(s(f(p(f(mark(cons(0, f(s(0)))))))))top#(ok(s(s(cons(s(_x61), _x52))))) → top#(s(s(cons(s(active(_x61)), _x52))))
top#(ok(s(f(p(p(cons(p(s(s(f(cons(cons(_x131, _x132), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(cons(active(_x131), _x132), _x122))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(s(s(f(s(0)))), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(s(mark(s(f(p(s(0)))))), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(f(_x181)), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(f(active(_x181))), _x162))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(0)), _x72))))))) → top#(s(f(p(p(cons(f(mark(cons(0, f(s(0))))), _x72))))))
top#(ok(s(f(p(p(cons(p(f(f(0))), _x72))))))) → top#(s(f(p(p(cons(p(f(mark(cons(0, f(s(0)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(s(_x161))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(s(active(_x161)))), _x132)))))), _x72))))))
top#(ok(s(cons(cons(s(_x61), _x52), _x42)))) → top#(s(cons(cons(s(active(_x61)), _x52), _x42)))top#(ok(s(f(p(p(cons(f(f(p(cons(f(s(0)), _x112)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(cons(mark(f(p(s(0)))), _x112)))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(p(_x151)), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(p(active(_x151))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(f(s(0)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(mark(f(p(s(0)))))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(s(s(cons(_x171, _x172))), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(s(s(cons(active(_x171), _x172))), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(cons(p(s(0)), _x102)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(cons(0, _x102))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(cons(p(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(p(active(_x121)), _x112)))), _x72))))))top#(ok(p(f(0)))) → top#(p(mark(cons(0, f(s(0))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(cons(_x181, _x182))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(cons(active(_x181), _x182))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(p(cons(f(s(0)), _x132))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(p(cons(mark(f(p(s(0)))), _x132))))), _x82), _x72))))))
top#(ok(s(cons(cons(cons(p(_x71), _x62), _x52), _x42)))) → top#(s(cons(cons(cons(p(active(_x71)), _x62), _x52), _x42)))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(s(0)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(mark(0))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(mark(s(f(p(s(0)))))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(f(f(_x111))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(f(f(active(_x111)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(cons(_x181, _x182)), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(cons(active(_x181), _x182)), _x162))), _x132)))))), _x72))))))top#(ok(f(f(f(s(0)))))) → top#(f(f(mark(f(p(s(0)))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(s(_x141), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(s(active(_x141)), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(p(_x161)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(p(active(_x161))), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(cons(s(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(s(active(_x121)), _x112)))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(p(_x131), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(p(active(_x131)), _x122)))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(s(_x201))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(s(active(_x201)))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(f(s(_x281)), _x202))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(f(s(active(_x281))), _x202))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(f(f(s(0)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(f(mark(f(p(s(0)))))), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(f(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(p(f(active(_x151))))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(f(0)))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(mark(p(cons(0, f(s(0))))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(s(p(f(cons(cons(p(cons(_x101, _x102)), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(cons(active(_x101), _x102)), _x82), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(f(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(f(active(_x131))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(f(0)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(s(cons(0, f(s(0))))), _x142))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(f(_x201))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(f(active(_x201)))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(p(p(p(s(f(_x81)))))))) → top#(s(p(p(p(s(f(active(_x81))))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(p(s(0)), _x162)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(mark(cons(0, _x162))))), _x132)))))), _x72))))))top#(ok(s(s(cons(p(f(_x71)), _x52))))) → top#(s(s(cons(p(f(active(_x71))), _x52))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(p(s(0)))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(mark(0))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(cons(f(s(0)), _x122)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(mark(cons(f(p(s(0))), _x122))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(f(p(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(f(p(active(_x101)))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(s(0)), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(mark(0), _x82), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(cons(f(_x161), _x152), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(cons(f(active(_x161)), _x152), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(cons(_x151, _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(cons(active(_x151), _x152)))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(s(_x121)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(s(active(_x121))))), _x82), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(s(_x181))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(s(active(_x181)))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(f(f(f(s(0))))))) → top#(s(f(f(mark(f(p(s(0))))))))top#(ok(s(s(p(f(cons(cons(p(s(_x101)), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(s(active(_x101))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(cons(_x171, _x172)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(cons(active(_x171), _x172)))))))))), _x72))))))top#(ok(s(f(f(0))))) → top#(s(mark(f(cons(0, f(s(0)))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(s(cons(_x161, _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(s(cons(active(_x161), _x162)), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(f(s(0))))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(mark(f(p(s(0))))))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(s(_x191))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(s(active(_x191)))), _x162))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(f(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(f(active(_x131))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(f(0), _x172)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(mark(cons(0, f(s(0)))), _x172)))), _x132)))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(f(s(0)), _x202))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(mark(f(p(s(0)))), _x202))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(cons(s(f(f(0))), _x62)))))) → top#(s(f(p(cons(s(f(mark(cons(0, f(s(0)))))), _x62)))))top#(ok(s(s(cons(p(p(_x71)), _x52))))) → top#(s(s(cons(p(p(active(_x71))), _x52))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(mark(f(p(s(0))))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(p(s(0))))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(mark(0)))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(cons(_x191, _x192)))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(cons(active(_x191), _x192)))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(s(0)), _x62))))))) → top#(s(f(p(p(mark(cons(f(p(s(0))), _x62)))))))
top#(ok(s(f(p(p(cons(p(s(s(f(s(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(s(active(_x121)))))), _x72))))))top#(ok(s(s(cons(f(_x61), _x52))))) → top#(s(s(cons(f(active(_x61)), _x52))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(f(_x151), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(f(active(_x151)), _x142))))))), _x72))))))top#(ok(s(f(p(p(p(s(0)))))))) → top#(s(f(p(mark(p(0))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(p(_x171), _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(p(active(_x171)), _x162)), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(f(0), _x132))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(cons(cons(0, f(s(0))), _x132)))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(s(_x171), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(s(active(_x171)), _x162))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(cons(f(0), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(cons(mark(cons(0, f(s(0)))), _x132)))))), _x72))))))
top#(ok(s(f(p(f(cons(s(cons(_x91, _x92)), _x72))))))) → top#(s(f(p(f(cons(s(cons(active(_x91), _x92)), _x72))))))top#(ok(s(cons(cons(cons(s(_x71), _x62), _x52), _x42)))) → top#(s(cons(cons(cons(s(active(_x71)), _x62), _x52), _x42)))
top#(ok(s(f(p(p(cons(f(f(p(s(f(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(mark(f(p(s(0)))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(s(_x181)), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(s(active(_x181))), _x162))), _x132)))))), _x72))))))
top#(ok(s(p(p(p(f(f(s(0))))))))) → top#(s(p(p(p(f(mark(f(p(s(0))))))))))top#(ok(s(s(p(f(cons(cons(p(f(s(_x111))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(f(s(active(_x111)))), _x82), _x72))))))
top#(ok(s(p(p(p(f(s(_x81)))))))) → top#(s(p(p(p(f(s(active(_x81))))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(cons(p(s(0)), _x142), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(mark(cons(0, _x142)), _x142))))))), _x72))))))
top#(ok(s(f(p(cons(s(s(f(_x91))), _x62)))))) → top#(s(f(p(cons(s(s(f(active(_x91)))), _x62)))))top#(ok(s(f(p(cons(s(s(f(0))), _x62)))))) → top#(s(f(p(cons(s(s(mark(cons(0, f(s(0)))))), _x62)))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(f(_x171)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(f(active(_x171))))))))))), _x72))))))top#(ok(s(s(cons(p(f(0)), _x52))))) → top#(s(s(cons(p(mark(cons(0, f(s(0))))), _x52))))
top#(ok(s(s(p(s(_x61)))))) → top#(s(s(p(s(active(_x61))))))top#(ok(s(f(p(p(cons(p(s(s(f(cons(p(s(0)), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(mark(0), _x122))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(f(s(0)))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(mark(f(p(s(0)))))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(cons(_x191, _x192)))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(cons(active(_x191), _x192)))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(p(cons(cons(_x141, _x142), _x132))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(p(cons(cons(active(_x141), _x142), _x132))))), _x82), _x72))))))top#(ok(s(s(f(_x51))))) → top#(s(s(f(active(_x51)))))
top#(ok(s(f(p(f(cons(s(f(0)), _x72))))))) → top#(s(f(p(f(cons(s(mark(cons(0, f(s(0))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(p(s(0)))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(mark(0))), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(p(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(mark(0)))))), _x72))))))top#(ok(s(p(cons(_x51, _x52))))) → top#(s(p(cons(active(_x51), _x52))))
top#(ok(s(cons(cons(cons(f(0), _x62), _x52), _x42)))) → top#(s(cons(cons(cons(mark(cons(0, f(s(0)))), _x62), _x52), _x42)))top#(ok(s(f(p(p(cons(f(f(p(s(f(0))))), _x72))))))) → top#(s(f(p(p(cons(f(f(mark(p(s(cons(0, f(s(0)))))))), _x72))))))
top#(ok(s(p(f(_x51))))) → top#(s(p(f(active(_x51)))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(f(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(f(active(_x161)))))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(p(cons(p(s(0)), _x132))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(p(cons(mark(0), _x132))))), _x82), _x72))))))top#(ok(s(f(f(f(0)))))) → top#(s(mark(f(f(cons(0, f(s(0))))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(f(_x161)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(f(active(_x161))), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(cons(_x161, _x162))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(cons(active(_x161), _x162))))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(s(_x111))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(s(active(_x111)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(cons(0, f(s(0)))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(f(0), _x152)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(mark(cons(cons(0, f(s(0))), _x152))), _x142))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(s(_x141)), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(s(active(_x141))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(f(cons(_x91, _x92)), _x72))))))) → top#(s(f(p(p(cons(f(cons(active(_x91), _x92)), _x72))))))top#(ok(s(f(p(p(cons(p(s(p(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(0))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(f(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(mark(cons(0, f(s(0))))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(cons(f(0), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(mark(cons(0, f(s(0)))), _x112)))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(s(_x181), _x172)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(s(active(_x181)), _x172)))), _x132)))))), _x72))))))top#(ok(s(f(p(cons(f(s(_x81)), _x62)))))) → top#(s(f(p(cons(f(s(active(_x81))), _x62)))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(cons(_x191, _x192))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(cons(active(_x191), _x192))), _x162))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(p(s(0))))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(mark(0)))), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(cons(s(f(cons(_x91, _x92))), _x62)))))) → top#(s(f(p(cons(s(f(cons(active(_x91), _x92))), _x62)))))top#(ok(s(f(p(cons(s(p(_x81)), _x62)))))) → top#(s(f(p(cons(s(p(active(_x81))), _x62)))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(p(_x201))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(p(active(_x201)))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(f(cons(p(s(0)), _x72))))))) → top#(s(f(p(f(cons(mark(0), _x72))))))
top#(ok(p(p(_x41)))) → top#(p(p(active(_x41))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(p(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(mark(p(0))))))))), _x72))))))
top#(ok(s(cons(cons(p(s(0)), _x52), _x42)))) → top#(s(cons(cons(mark(0), _x52), _x42)))top#(ok(s(f(p(p(cons(p(s(s(p(_x111)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(p(active(_x111))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(s(_x171)), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(s(active(_x171))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(f(_x181), _x172)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(f(active(_x181)), _x172)))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(cons(f(_x131), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(f(active(_x131)), _x122))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(f(f(0)), _x202))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(mark(f(cons(0, f(s(0))))), _x202))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(f(f(s(0))), _x72))))))) → top#(s(f(p(p(cons(f(mark(f(p(s(0))))), _x72))))))top#(ok(s(f(p(cons(f(s(0)), _x62)))))) → top#(s(f(p(cons(mark(f(p(s(0)))), _x62)))))
top#(ok(s(f(p(p(s(0))))))) → top#(s(f(p(mark(0)))))top#(ok(s(s(p(f(cons(cons(p(p(f(p(f(_x131))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(p(f(active(_x131)))))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(cons(p(s(0)), _x112)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(cons(mark(0), _x112)))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(cons(_x121, _x122))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(cons(active(_x121), _x122))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(0), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(mark(cons(0, f(s(0)))), _x162))), _x132)))))), _x72))))))top#(ok(s(p(p(p(f(cons(f(s(0)), _x72)))))))) → top#(s(p(p(mark(p(f(cons(f(p(s(0))), _x72))))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(s(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(s(active(_x141)))))))), _x72))))))top#(ok(s(f(p(cons(s(f(p(_x91))), _x62)))))) → top#(s(f(p(cons(s(f(p(active(_x91)))), _x62)))))
top#(ok(s(f(p(p(cons(p(s(s(f(p(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(p(active(_x121)))))), _x72))))))top#(ok(s(f(p(f(s(0))))))) → top#(s(f(p(mark(f(p(s(0))))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(f(s(0)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(f(p(s(0)))), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(cons(_x161, _x162))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(cons(active(_x161), _x162))))))))), _x72))))))
top#(ok(s(f(p(f(cons(f(s(0)), _x72))))))) → top#(s(f(p(f(cons(mark(f(p(s(0)))), _x72))))))top#(ok(f(f(s(0))))) → top#(f(mark(f(p(s(0))))))
top#(ok(s(p(p(p(s(cons(_x81, _x82)))))))) → top#(s(p(p(p(s(cons(active(_x81), _x82)))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(f(s(0)), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(mark(f(p(s(0)))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(p(p(p(f(cons(f(_x91), _x82)))))))) → top#(s(p(p(p(f(cons(f(active(_x91)), _x82)))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(f(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(f(active(_x141)))))))), _x72))))))
top#(ok(s(f(p(f(p(s(0)))))))) → top#(s(f(p(f(mark(0))))))top#(ok(s(f(p(p(cons(p(p(_x91)), _x72))))))) → top#(s(f(p(p(cons(p(p(active(_x91))), _x72))))))
top#(ok(s(s(p(s(0)))))) → top#(s(s(mark(0))))top#(ok(s(s(cons(f(0), _x52))))) → top#(s(s(cons(mark(cons(0, f(s(0)))), _x52))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(f(cons(_x281, _x282)), _x202))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(f(cons(active(_x281), _x282)), _x202))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(f(s(0)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(mark(f(p(s(0)))), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(f(_x121))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(f(active(_x121)))))), _x72))))))top#(ok(s(f(p(f(s(_x71))))))) → top#(s(f(p(f(s(active(_x71)))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(f(0)))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(mark(cons(0, f(s(0))))))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(cons(s(_x161), _x152), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(cons(s(active(_x161)), _x152), _x142))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(p(p(_x161)))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(p(p(active(_x161))))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(f(s(0))))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(mark(f(p(s(0))))))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(f(_x171)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(f(active(_x171))))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(f(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(p(mark(cons(0, f(s(0))))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(cons(f(0), _x152), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(cons(mark(cons(0, f(s(0)))), _x152), _x142))))))), _x72))))))top#(ok(s(cons(cons(cons(f(_x71), _x62), _x52), _x42)))) → top#(s(cons(cons(cons(f(active(_x71)), _x62), _x52), _x42)))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(s(0)))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(mark(f(p(s(0)))))), _x162))), _x132)))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(p(cons(f(_x141), _x132))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(p(cons(f(active(_x141)), _x132))))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(f(s(0)))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(mark(f(p(s(0)))))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(s(p(f(cons(f(s(0)), _x72))))))) → top#(s(s(p(f(cons(mark(f(p(s(0)))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(0)))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(mark(cons(0, f(s(0))))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(s(0))))) → top#(mark(s(f(p(s(0))))))
top#(ok(f(f(p(_x51))))) → top#(f(f(p(active(_x51)))))top#(ok(s(s(p(f(cons(cons(p(p(f(p(s(0))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(mark(0)))), _x82), _x72))))))
top#(ok(s(s(p(cons(cons(s(_x81), _x72), _x62)))))) → top#(s(s(p(cons(cons(s(active(_x81)), _x72), _x62)))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(cons(p(_x271), _x262)))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(cons(p(active(_x271)), _x262)))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(s(_x151))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(s(active(_x151)))), _x122)))), _x82), _x72))))))top#(ok(p(s(_x41)))) → top#(p(s(active(_x41))))
top#(ok(s(s(p(cons(f(s(0)), _x62)))))) → top#(s(s(p(cons(mark(f(p(s(0)))), _x62)))))top#(ok(s(s(cons(p(s(f(f(s(0))))), _x52))))) → top#(s(s(cons(p(s(f(mark(f(p(s(0))))))), _x52))))
top#(ok(s(s(cons(p(s(f(f(0)))), _x52))))) → top#(s(s(cons(p(s(f(mark(cons(0, f(s(0))))))), _x52))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(p(_x171)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(p(active(_x171))), _x152)))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(f(0)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(mark(cons(0, f(s(0))))))), _x82), _x72))))))top#(ok(s(s(p(f(cons(cons(p(f(p(f(0)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(f(p(mark(cons(0, f(s(0))))))), _x82), _x72))))))
top#(ok(s(f(p(cons(f(p(_x81)), _x62)))))) → top#(s(f(p(cons(f(p(active(_x81))), _x62)))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(cons(_x131, _x132), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(cons(active(_x131), _x132), _x122)))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(f(_x91), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(f(active(_x91)), _x82), _x72))))))top#(ok(s(s(p(p(_x61)))))) → top#(s(s(p(p(active(_x61))))))
top#(ok(s(s(cons(p(s(f(f(_x91)))), _x52))))) → top#(s(s(cons(p(s(f(f(active(_x91))))), _x52))))top#(ok(f(0))) → top#(mark(cons(0, f(s(0)))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(cons(_x181, _x182), _x172)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(cons(active(_x181), _x182), _x172)))), _x132)))))), _x72))))))top#(ok(f(f(cons(_x51, _x52))))) → top#(f(f(cons(active(_x51), _x52))))
top#(ok(s(f(p(cons(s(f(s(f(_x101)))), _x62)))))) → top#(s(f(p(cons(s(f(s(f(active(_x101))))), _x62)))))top#(ok(s(s(p(f(cons(f(0), _x72))))))) → top#(s(s(p(f(cons(mark(cons(0, f(s(0)))), _x72))))))
top#(ok(s(s(f(0))))) → top#(s(s(mark(cons(0, f(s(0)))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(s(0))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(mark(0)), _x162))), _x132)))))), _x72))))))
top#(ok(s(p(p(p(s(s(_x81)))))))) → top#(s(p(p(p(s(s(active(_x81))))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(f(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(mark(cons(0, f(s(0)))))))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(p(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(mark(0))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(p(s(0)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(mark(0))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(s(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(s(active(_x161)))))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(p(s(0))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(mark(0)), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(p(p(p(f(p(s(0))))))))) → top#(s(p(p(p(f(mark(0)))))))top#(ok(s(s(p(f(0)))))) → top#(s(s(p(mark(cons(0, f(s(0))))))))
top#(ok(f(p(s(0))))) → top#(f(mark(0)))top#(ok(s(f(p(p(cons(p(s(s(f(cons(f(0), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(mark(cons(0, f(s(0)))), _x122))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(f(p(s(_x121)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(f(p(s(active(_x121))))), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(cons(p(_x131), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(p(active(_x131)), _x122))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(0), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(mark(cons(0, f(s(0)))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(mark(cons(0, f(s(0)))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(cons(cons(_x121, _x122), _x112)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(cons(cons(active(_x121), _x122), _x112)))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(p(_x151)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(p(active(_x151))))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(f(_x201))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(f(active(_x201)))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(f(f(_x61)))))) → top#(s(f(f(f(active(_x61))))))
top#(ok(s(s(p(f(cons(p(s(0)), _x72))))))) → top#(s(s(p(f(cons(mark(0), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(0))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(mark(p(cons(0, f(s(0)))))), _x162))), _x132)))))), _x72))))))
top#(ok(s(p(p(p(f(cons(cons(_x91, _x92), _x82)))))))) → top#(s(p(p(p(f(cons(cons(active(_x91), _x92), _x82)))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(s(0)), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(mark(0), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(f(0)))) → top#(mark(s(cons(0, f(s(0))))))top#(ok(s(s(p(f(cons(cons(p(p(f(p(f(s(0)))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(p(mark(f(p(s(0)))))))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(f(s(0))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(mark(f(p(s(0))))), _x82), _x72))))))top#(ok(s(s(cons(p(p(s(0))), _x52))))) → top#(s(s(cons(p(mark(0)), _x52))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(p(_x191))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(p(active(_x191)))), _x162))), _x132)))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(p(_x111))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(p(active(_x111)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(cons(f(_x91), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(f(active(_x91)), _x82), _x72))))))top#(ok(s(f(p(cons(p(_x71), _x62)))))) → top#(s(f(p(cons(p(active(_x71)), _x62)))))
top#(ok(s(s(p(cons(cons(f(0), _x72), _x62)))))) → top#(s(s(p(cons(cons(mark(cons(0, f(s(0)))), _x72), _x62)))))top#(ok(s(s(p(f(cons(cons(p(p(f(p(cons(s(_x141), _x132))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(p(cons(s(active(_x141)), _x132))))), _x82), _x72))))))
top#(ok(s(s(p(cons(p(_x71), _x62)))))) → top#(s(s(p(cons(p(active(_x71)), _x62)))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(p(_x151), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(p(active(_x151)), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(mark(f(p(s(0))))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(mark(cons(0, f(s(0))))))))))), _x72))))))
top#(ok(s(s(cons(cons(_x61, _x62), _x52))))) → top#(s(s(cons(cons(active(_x61), _x62), _x52))))top#(mark(f(0))) → top#(f(ok(0)))
top#(ok(s(f(p(p(cons(p(s(0)), _x72))))))) → top#(s(f(p(p(cons(mark(0), _x72))))))top#(ok(s(p(p(p(s(p(s(0))))))))) → top#(s(p(p(p(s(mark(0)))))))
top#(ok(s(s(p(f(cons(p(_x81), _x72))))))) → top#(s(s(p(f(cons(p(active(_x81)), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(p(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(p(active(_x131))))))), _x72))))))
top#(ok(s(p(f(0))))) → top#(s(p(mark(cons(0, f(s(0)))))))top#(ok(p(f(_x41)))) → top#(p(f(active(_x41))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(s(_x161), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(s(active(_x161)), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(p(s(0)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(mark(0), _x152)))))))), _x72))))))
top#(ok(s(f(p(cons(f(f(s(0))), _x62)))))) → top#(s(f(p(cons(mark(f(f(p(s(0))))), _x62)))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(cons(_x151, _x152)), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(cons(active(_x151), _x152)), _x132)))))), _x72))))))
top#(ok(s(f(cons(_x51, _x52))))) → top#(s(f(cons(active(_x51), _x52))))top#(ok(s(f(p(p(cons(p(s(s(f(f(cons(cons(_x141, _x142), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(cons(cons(active(_x141), _x142), _x132)))))), _x72))))))
top#(ok(s(f(p(cons(f(cons(_x81, _x82)), _x62)))))) → top#(s(f(p(cons(f(cons(active(_x81), _x82)), _x62)))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(cons(_x161, _x162), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(cons(active(_x161), _x162), _x152)))))))), _x72))))))
top#(ok(s(f(p(cons(s(f(s(0))), _x62)))))) → top#(s(f(p(cons(s(mark(f(p(s(0))))), _x62)))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(p(s(0))))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(mark(0)))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(cons(s(_x131), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(s(active(_x131)), _x122))))), _x72))))))top#(ok(s(f(p(f(cons(s(s(_x91)), _x72))))))) → top#(s(f(p(f(cons(s(s(active(_x91))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(cons(_x171, _x172)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(cons(active(_x171), _x172)), _x152)))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(cons(f(s(0)), _x262)))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(cons(mark(f(p(s(0)))), _x262)))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(f(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(s(cons(0, f(s(0)))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(p(_x151), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(p(active(_x151)), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(cons(f(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(cons(f(active(_x121)), _x112)))), _x72))))))top#(ok(s(p(s(_x51))))) → top#(s(p(s(active(_x51)))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(s(_x131), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(s(active(_x131)), _x122)))), _x82), _x72))))))top#(ok(s(f(p(f(cons(f(0), _x72))))))) → top#(s(f(p(f(cons(mark(cons(0, f(s(0)))), _x72))))))
top#(ok(s(f(p(p(f(s(0)))))))) → top#(s(mark(f(p(p(f(p(s(0)))))))))top#(ok(s(s(p(f(cons(cons(p(p(f(p(f(0))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(p(mark(cons(0, f(s(0)))))))), _x82), _x72))))))
top#(ok(s(p(p(f(s(0))))))) → top#(s(p(p(mark(f(p(s(0))))))))top#(ok(s(f(p(p(cons(p(f(f(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(f(f(active(_x101)))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(0)))), _x72))))))) → top#(s(f(p(p(cons(f(mark(f(0))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(f(0), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(mark(cons(0, f(s(0)))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(p(p(p(f(p(_x81)))))))) → top#(s(p(p(p(f(p(active(_x81))))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(f(s(0))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(mark(f(p(s(0))))), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(p(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(mark(0)))))), _x72))))))top#(ok(s(f(p(p(cons(p(f(cons(_x101, _x102))), _x72))))))) → top#(s(f(p(p(cons(p(f(cons(active(_x101), _x102))), _x72))))))
top#(ok(s(p(p(s(0)))))) → top#(s(p(mark(0))))top#(mark(f(f(_x41)))) → top#(f(f(proper(_x41))))
top#(ok(s(s(p(f(cons(cons(p(f(p(p(_x121)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(f(p(p(active(_x121))))), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(f(0))), _x72))))))) → top#(s(f(p(p(cons(f(mark(f(cons(0, f(s(0)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(p(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(mark(0)))))))), _x72))))))top#(ok(s(s(p(cons(cons(f(s(0)), _x72), _x62)))))) → top#(s(s(p(cons(cons(mark(f(p(s(0)))), _x72), _x62)))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(f(0))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(mark(cons(0, f(s(0)))))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(s(p(f(cons(cons(p(f(p(f(_x121)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(f(p(f(active(_x121))))), _x82), _x72))))))
top#(ok(s(f(p(cons(s(s(p(s(0)))), _x62)))))) → top#(s(f(p(cons(s(s(mark(0))), _x62)))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(f(_x201)))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(f(active(_x201))))), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(f(_x161), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(f(active(_x161)), _x152)))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(0))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(mark(f(f(p(s(0))))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(cons(s(f(s(cons(_x101, _x102)))), _x62)))))) → top#(s(f(p(cons(s(f(s(cons(active(_x101), _x102)))), _x62)))))top#(ok(cons(f(s(0)), _x22))) → top#(cons(mark(f(p(s(0)))), _x22))
top#(ok(s(s(p(f(cons(cons(p(p(s(0))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(mark(0)), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(cons(f(s(0)), _x82)), _x72))))))) → top#(s(f(p(p(cons(p(mark(cons(f(p(s(0))), _x82))), _x72))))))
top#(ok(f(f(0)))) → top#(f(mark(cons(0, f(s(0))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(f(s(0))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(mark(f(p(s(0))))))))), _x72))))))
top#(ok(s(cons(cons(f(s(0)), _x52), _x42)))) → top#(s(cons(cons(mark(f(p(s(0)))), _x52), _x42)))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(f(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(mark(cons(0, f(s(0)))))))))))), _x72))))))
top#(ok(s(s(cons(p(s(f(p(s(0))))), _x52))))) → top#(s(s(cons(p(s(f(mark(0)))), _x52))))top#(ok(s(f(p(p(cons(f(f(p(cons(f(0), _x112)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(cons(mark(cons(0, f(s(0)))), _x112)))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(p(s(0)), _x152)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(s(cons(0, _x152))), _x142))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(f(_x261)))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(f(active(_x261))))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(cons(p(s(0)), _x62)))))) → top#(s(f(p(cons(mark(0), _x62)))))top#(mark(p(_x21))) → top#(p(proper(_x21)))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(f(s(0)), _x172)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(mark(f(p(s(0)))), _x172)))), _x132)))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(p(s(_x161)))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(p(s(active(_x161))))), _x122)))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(p(_x141)), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(p(active(_x141))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(f(_x171)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(f(active(_x171))))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(p(_x171)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(p(active(_x171))))), _x132)))))), _x72))))))top#(ok(s(p(p(p(f(f(0)))))))) → top#(s(p(p(p(f(mark(cons(0, f(s(0))))))))))
top#(ok(s(s(cons(p(f(s(0))), _x52))))) → top#(s(s(cons(mark(p(f(p(s(0))))), _x52))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(0)), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(mark(cons(0, f(s(0))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(cons(_x161, _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(cons(active(_x161), _x162))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(p(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(p(active(_x101)))), _x72))))))
top#(ok(s(f(p(cons(cons(_x71, _x72), _x62)))))) → top#(s(f(p(cons(cons(active(_x71), _x72), _x62)))))top#(ok(s(f(p(p(cons(f(f(p(f(0)))), _x72))))))) → top#(s(f(p(p(cons(f(mark(f(p(cons(0, f(s(0))))))), _x72))))))
top#(mark(cons(_x21, _x22))) → top#(cons(proper(_x21), proper(_x22)))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(cons(p(s(0)), _x262)))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(cons(mark(0), _x262)))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(s(0)), _x112)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(mark(cons(f(p(s(0))), _x112))))), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(f(s(0))), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(s(f(p(s(0))))), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(mark(cons(0, f(s(0)))))))), _x72))))))top#(ok(s(s(cons(p(s(p(_x81))), _x52))))) → top#(s(s(cons(p(s(p(active(_x81)))), _x52))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(f(_x171)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(f(active(_x171))), _x152)))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(mark(0))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(p(_x171)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(p(active(_x171))))))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(p(f(s(0))))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(p(mark(f(p(s(0))))))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(f(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(mark(cons(0, f(s(0))))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(p(s(0)), _x252))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(mark(cons(0, _x252)))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(cons(s(f(f(_x91))), _x62)))))) → top#(s(f(p(cons(s(f(f(active(_x91)))), _x62)))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(cons(_x201, _x202)))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(cons(active(_x201), _x202)))), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(cons(_x141, _x142), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(cons(active(_x141), _x142), _x132)))))), _x72))))))top#(ok(s(s(p(f(s(_x71))))))) → top#(s(s(p(f(s(active(_x71)))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(0)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(mark(cons(0, f(s(0))))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(cons(_x111, _x112))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(cons(active(_x111), _x112))), _x82), _x72))))))
top#(ok(s(cons(cons(f(0), _x52), _x42)))) → top#(s(cons(cons(mark(cons(0, f(s(0)))), _x52), _x42)))top#(ok(cons(f(0), _x32))) → top#(mark(cons(cons(0, f(s(0))), _x32)))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(f(0)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(mark(cons(0, f(s(0))))))), _x132)))))), _x72))))))top#(ok(s(s(p(cons(cons(p(_x81), _x72), _x62)))))) → top#(s(s(p(cons(cons(p(active(_x81)), _x72), _x62)))))
top#(ok(s(s(p(f(p(_x71))))))) → top#(s(s(p(f(p(active(_x71)))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(s(0))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(mark(f(p(s(0))))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(p(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(mark(0))))))))), _x72))))))top#(ok(s(f(p(p(cons(s(p(s(0))), _x72))))))) → top#(s(f(p(p(cons(mark(s(0)), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(f(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(mark(f(p(s(0)))))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(cons(f(_x141), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(cons(f(active(_x141)), _x132)))))), _x72))))))
top#(ok(s(cons(f(0), _x42)))) → top#(s(cons(mark(cons(0, f(s(0)))), _x42)))top#(ok(s(cons(f(s(0)), _x42)))) → top#(s(cons(mark(f(p(s(0)))), _x42)))
top#(ok(s(s(p(f(cons(cons(p(p(f(f(s(0))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(mark(f(f(p(s(0))))))), _x82), _x72))))))top#(ok(s(s(p(f(cons(cons(p(f(p(s(0)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(f(mark(0))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(f(_x171), _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(f(active(_x171)), _x162)), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(s(p(_x91)), _x72))))))) → top#(s(f(p(p(cons(s(p(active(_x91))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(p(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(p(active(_x161)))))))))), _x72))))))top#(ok(s(s(p(f(cons(f(_x81), _x72))))))) → top#(s(s(p(f(cons(f(active(_x81)), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(s(0)))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(mark(f(p(s(0)))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(s(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(s(active(_x141)))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(f(0))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(mark(f(cons(0, f(s(0)))))))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(f(_x161))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(f(active(_x161)))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(f(f(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(f(mark(f(p(s(0)))))), _x72))))))top#(ok(s(f(p(p(cons(cons(f(s(0)), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(mark(f(p(s(0)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(cons(p(_x161), _x152), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(cons(p(active(_x161)), _x152), _x142))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(cons(_x141, _x142)), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(cons(active(_x141), _x142)), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(f(f(s(_x101))), _x72))))))) → top#(s(f(p(p(cons(f(f(s(active(_x101)))), _x72))))))top#(ok(s(f(p(p(cons(p(f(p(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(mark(f(0))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(0)))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(mark(0))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(cons(_x131, _x132)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(cons(active(_x131), _x132)))))), _x72))))))
top#(ok(s(f(p(p(s(_x71))))))) → top#(s(f(p(p(s(active(_x71)))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(p(s(0))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(mark(0)))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(cons(s(_x41), _x22))) → top#(cons(s(active(_x41)), _x22))top#(ok(s(s(p(cons(p(s(0)), _x52)))))) → top#(s(s(p(mark(cons(0, _x52))))))
top#(ok(s(f(p(f(cons(s(f(_x91)), _x72))))))) → top#(s(f(p(f(cons(s(f(active(_x91))), _x72))))))top#(ok(s(p(p(p(s(0))))))) → top#(s(p(p(mark(0)))))
top#(ok(p(p(s(0))))) → top#(mark(p(0)))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(cons(_x171, _x172)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(cons(active(_x171), _x172)))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(p(p(s(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(0)), _x72))))))top#(ok(s(f(p(cons(s(f(s(f(s(0))))), _x62)))))) → top#(s(f(p(cons(s(f(s(mark(f(p(s(0))))))), _x62)))))
top#(ok(s(f(p(p(f(_x71))))))) → top#(s(f(p(p(f(active(_x71)))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(p(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(p(active(_x131))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(0)), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(mark(cons(0, f(s(0))))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(s(_x171), _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(s(active(_x171)), _x162)), _x142))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(p(cons(p(_x141), _x132))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(p(cons(p(active(_x141)), _x132))))), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(p(s(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(0)))), _x72))))))
top#(ok(s(f(f(p(_x61)))))) → top#(s(f(f(p(active(_x61))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(0), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(mark(cons(0, f(s(0)))), _x122)))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(f(s(0))))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(mark(f(p(s(0))))))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(p(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(mark(0))))), _x72))))))
top#(ok(s(f(p(cons(s(s(p(_x91))), _x62)))))) → top#(s(f(p(cons(s(s(p(active(_x91)))), _x62)))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(f(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(f(f(p(s(0))))))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(p(s(_x131))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(p(s(active(_x131)))))), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(f(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(mark(s(cons(0, f(s(0))))))))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(f(f(0))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(f(mark(cons(0, f(s(0)))))), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(f(_x121))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(f(active(_x121)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(s(0)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(mark(f(p(s(0)))))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(p(_x141), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(p(active(_x141)), _x132)))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(f(_x161), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(f(active(_x161)), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(s(0))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(f(p(s(0))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(f(0))), _x72))))))) → top#(s(f(p(p(cons(p(mark(s(cons(0, f(s(0)))))), _x72))))))top#(ok(s(p(p(p(f(cons(f(0), _x82)))))))) → top#(s(p(p(p(f(cons(mark(cons(0, f(s(0)))), _x82)))))))
top#(ok(s(f(p(p(cons(s(f(0)), _x72))))))) → top#(s(f(p(p(cons(s(mark(cons(0, f(s(0))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(f(p(s(0)))))))))), _x72))))))
top#(ok(s(cons(cons(cons(cons(_x71, _x72), _x62), _x52), _x42)))) → top#(s(cons(cons(cons(cons(active(_x71), _x72), _x62), _x52), _x42)))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(p(_x141))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(p(active(_x141)))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(f(0), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(mark(cons(0, f(s(0)))), _x152)))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(p(_x171)), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(p(active(_x171))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(p(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(p(active(_x161)))))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(f(0)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(mark(cons(0, f(s(0))))), _x152)))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(p(s(0)))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(mark(0))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(p(s(0)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(mark(0))))), _x72))))))
top#(ok(s(f(p(p(cons(f(p(_x91)), _x72))))))) → top#(s(f(p(p(cons(f(p(active(_x91))), _x72))))))top#(ok(cons(f(_x41), _x22))) → top#(cons(f(active(_x41)), _x22))
top#(ok(s(s(p(f(cons(cons(cons(_x91, _x92), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(cons(active(_x91), _x92), _x82), _x72))))))top#(ok(s(f(p(cons(f(f(0)), _x62)))))) → top#(s(f(p(cons(f(mark(cons(0, f(s(0))))), _x62)))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(cons(cons(_x161, _x162), _x152), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(cons(cons(active(_x161), _x162), _x152), _x142))))))), _x72))))))top#(ok(s(s(cons(p(s(f(s(_x91)))), _x52))))) → top#(s(s(cons(p(s(f(s(active(_x91))))), _x52))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(f(0), _x202))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(mark(cons(0, f(s(0)))), _x202))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(cons(s(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(cons(s(active(_x121)), _x112)))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(f(_x191)))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(f(active(_x191))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(p(_x201)))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(p(active(_x201))))), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(f(s(0)))), _x72))))))) → top#(s(f(p(p(cons(mark(f(f(f(p(s(0)))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(cons(_x201, _x202))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(cons(active(_x201), _x202))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(f(cons(_x161, _x162))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(f(cons(active(_x161), _x162))))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(f(0))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(mark(cons(0, f(s(0)))))), _x122)))), _x82), _x72))))))
top#(ok(s(cons(cons(cons(f(s(0)), _x62), _x52), _x42)))) → top#(s(cons(cons(cons(mark(f(p(s(0)))), _x62), _x52), _x42)))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(cons(cons(_x271, _x272), _x262)))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(cons(cons(active(_x271), _x272), _x262)))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(cons(s(f(0)), _x62)))))) → top#(s(f(p(cons(s(mark(cons(0, f(s(0))))), _x62)))))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(p(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(mark(0))))))), _x72))))))
top#(ok(s(cons(p(_x51), _x42)))) → top#(s(cons(p(active(_x51)), _x42)))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(s(p(_x161)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(s(p(active(_x161))), _x142))))))), _x72))))))
top#(ok(s(p(p(p(f(cons(s(_x91), _x82)))))))) → top#(s(p(p(p(f(cons(s(active(_x91)), _x82)))))))top#(ok(s(f(p(p(cons(f(f(p(f(_x111)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(f(active(_x111))))), _x72))))))
top#(ok(s(cons(p(s(0)), _x42)))) → top#(s(cons(mark(0), _x42)))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(s(s(s(_x171))), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(s(s(s(active(_x171)))), _x142))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(s(0))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(mark(f(p(s(0))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(p(p(p(s(f(s(0))))))))) → top#(s(p(p(p(s(mark(f(p(s(0))))))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(0))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(mark(0)))))))), _x72))))))top#(ok(s(f(f(cons(_x61, _x62)))))) → top#(s(f(f(cons(active(_x61), _x62)))))
top#(ok(f(f(s(_x51))))) → top#(f(f(s(active(_x51)))))top#(ok(s(p(p(p(f(f(_x81)))))))) → top#(s(p(p(p(f(f(active(_x81))))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(cons(s(_x141), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(cons(s(active(_x141)), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(s(_x161))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(s(active(_x161)))), _x132)))))), _x72))))))
top#(ok(s(p(f(s(0)))))) → top#(s(p(mark(f(p(s(0)))))))top#(ok(s(s(p(f(cons(cons(p(p(f(0))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(mark(cons(0, f(s(0)))))), _x82), _x72))))))
top#(ok(s(s(p(cons(f(_x71), _x62)))))) → top#(s(s(p(cons(f(active(_x71)), _x62)))))top#(ok(s(s(cons(p(s(f(cons(_x91, _x92)))), _x52))))) → top#(s(s(cons(p(s(f(cons(active(_x91), _x92)))), _x52))))
top#(ok(s(f(p(p(cons(f(f(p(f(s(0))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(mark(f(p(s(0))))))), _x72))))))top#(ok(s(f(p(f(f(_x71))))))) → top#(s(f(p(f(f(active(_x71)))))))
top#(ok(s(s(p(f(cons(cons(p(p(p(s(0)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(mark(0))), _x82), _x72))))))top#(ok(s(s(cons(p(cons(_x71, _x72)), _x52))))) → top#(s(s(cons(p(cons(active(_x71), _x72)), _x52))))
top#(ok(s(s(cons(p(s(f(0))), _x52))))) → top#(s(s(cons(p(s(mark(cons(0, f(s(0)))))), _x52))))top#(ok(s(cons(cons(cons(p(s(0)), _x62), _x52), _x42)))) → top#(s(cons(cons(cons(mark(0), _x62), _x52), _x42)))
top#(ok(s(f(p(cons(s(cons(_x81, _x82)), _x62)))))) → top#(s(f(p(cons(s(cons(active(_x81), _x82)), _x62)))))top#(ok(s(s(p(f(f(s(0)))))))) → top#(s(s(p(f(mark(f(p(s(0)))))))))
top#(ok(s(f(p(s(p(_x71))))))) → top#(s(f(p(s(p(active(_x71)))))))top#(ok(s(s(p(f(cons(cons(p(p(f(p(cons(f(0), _x132))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(p(cons(mark(cons(0, f(s(0)))), _x132))))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(0))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(mark(cons(0, f(s(0)))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(f(p(_x281)), _x202))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(f(p(active(_x281))), _x202))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(f(s(0))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(mark(f(p(s(0))))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(p(p(p(s(f(0)))))))) → top#(s(p(p(p(mark(s(cons(0, f(s(0))))))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(cons(p(_x141), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(cons(p(active(_x141)), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(cons(s(_x101), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(s(active(_x101)), _x92)), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(s(_x261)))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(f(s(s(active(_x261))))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(f(p(_x71))))))) → top#(s(f(p(f(p(active(_x71)))))))
top#(ok(s(f(p(p(cons(p(f(0)), _x62))))))) → top#(s(f(p(p(mark(cons(p(cons(0, f(s(0)))), _x62)))))))top#(ok(s(p(p(p(s(p(_x81)))))))) → top#(s(p(p(p(s(p(active(_x81))))))))
top#(ok(s(f(p(p(cons(p(s(s(f(cons(f(s(0)), _x122))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(cons(mark(f(p(s(0)))), _x122))))), _x72))))))top#(ok(f(cons(_x41, _x42)))) → top#(f(cons(active(_x41), _x42)))
top#(ok(s(f(p(p(f(0))))))) → top#(s(f(p(mark(p(cons(0, f(s(0)))))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(f(0)), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(mark(cons(0, f(s(0))))), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(cons(s(f(s(p(_x101)))), _x62)))))) → top#(s(f(p(cons(s(f(s(p(active(_x101))))), _x62)))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(p(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(mark(0))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(f(f(s(0))))), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(p(mark(f(f(p(s(0))))))), _x162))), _x132)))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(s(_x171)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(s(s(active(_x171))))))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(p(s(0))))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(s(f(mark(0)))), _x132)))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(f(s(0)))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(mark(f(p(s(0)))))), _x122)))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(p(_x111)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(p(active(_x111))))), _x72))))))top#(ok(s(f(s(_x51))))) → top#(s(f(s(active(_x51)))))
top#(ok(s(f(p(p(cons(p(f(s(0))), _x72))))))) → top#(s(f(p(p(cons(mark(p(f(p(s(0))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(s(_x171)), _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(cons(s(s(active(_x171))), _x152)))))))), _x72))))))
top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(s(f(0)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(s(mark(cons(0, f(s(0))))), _x142))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(f(_x101))), _x72))))))) → top#(s(f(p(p(cons(p(s(f(active(_x101)))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(f(s(p(cons(_x151, _x152)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(p(cons(active(_x151), _x152)))))))), _x72))))))top#(ok(s(p(p(p(f(0))))))) → top#(s(p(p(p(mark(cons(0, f(s(0)))))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(p(p(s(0))))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(p(mark(0)))), _x122)))), _x82), _x72))))))top#(ok(s(s(cons(p(s(f(s(0)))), _x52))))) → top#(s(s(cons(p(s(mark(f(p(s(0)))))), _x52))))
top#(ok(s(f(p(s(f(s(0)))))))) → top#(s(f(p(mark(s(f(p(s(0)))))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(f(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(mark(f(p(s(0)))))))))))), _x72))))))
top#(ok(s(f(p(f(f(s(0)))))))) → top#(s(f(mark(p(f(f(p(s(0)))))))))top#(ok(s(s(f(s(0)))))) → top#(s(mark(s(f(p(s(0)))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(p(s(0)))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(mark(s(0))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(p(_x181), _x172)))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(p(cons(p(active(_x181)), _x172)))), _x132)))))), _x72))))))
top#(ok(s(f(p(p(cons(s(f(s(0))), _x72))))))) → top#(s(f(p(p(cons(s(mark(f(p(s(0))))), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(f(s(0)), _x162))), _x132)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(cons(f(f(cons(mark(f(p(s(0)))), _x162))), _x132)))))), _x72))))))
top#(ok(s(f(p(s(p(s(0)))))))) → top#(s(f(p(s(mark(0))))))top#(ok(s(f(p(s(f(0))))))) → top#(s(f(p(s(mark(cons(0, f(s(0)))))))))
top#(ok(s(cons(s(_x51), _x42)))) → top#(s(cons(s(active(_x51)), _x42)))top#(ok(s(f(p(p(cons(p(s(f(s(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(mark(f(p(s(0)))))), _x72))))))
top#(ok(s(f(p(cons(f(f(_x81)), _x62)))))) → top#(s(f(p(cons(f(f(active(_x81))), _x62)))))top#(ok(f(f(p(s(0)))))) → top#(f(f(mark(0))))
top#(ok(s(s(p(f(cons(cons(p(p(f(p(p(s(0)))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(p(mark(0))))), _x82), _x72))))))top#(ok(s(f(p(p(p(_x71))))))) → top#(s(f(p(p(p(active(_x71)))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(0)), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(mark(cons(0, f(s(0))))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(cons(cons(_x121, _x122), _x112)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(cons(cons(active(_x121), _x122), _x112)))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(f(0)))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(mark(cons(0, f(s(0))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(f(p(f(s(0)))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(f(p(mark(f(p(s(0)))))))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(p(_x261), _x202))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(p(active(_x261)), _x202))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(cons(s(p(s(0))), _x62)))))) → top#(s(f(p(cons(mark(s(0)), _x62)))))
top#(ok(s(s(p(f(cons(cons(p(p(f(f(_x121)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(f(active(_x121))))), _x82), _x72))))))top#(ok(s(s(p(f(cons(cons(p(f(p(f(s(0))))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(f(p(mark(f(p(s(0))))))), _x82), _x72))))))
top#(ok(s(f(p(p(cons(f(p(s(0))), _x72))))))) → top#(s(f(p(p(cons(f(mark(0)), _x72))))))top#(ok(s(s(cons(f(s(0)), _x52))))) → top#(s(s(cons(mark(f(p(s(0)))), _x52))))
top#(ok(p(f(s(0))))) → top#(p(mark(f(p(s(0))))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(p(s(0))), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(mark(s(0)), _x142))))))), _x72))))))
top#(ok(s(f(f(s(_x61)))))) → top#(s(f(f(s(active(_x61))))))top#(ok(s(f(p(cons(s(f(s(p(s(0))))), _x62)))))) → top#(s(f(p(cons(s(f(mark(s(0)))), _x62)))))
top#(ok(s(f(p(s(s(_x71))))))) → top#(s(f(p(s(s(active(_x71)))))))top#(ok(s(f(p(p(cons(p(cons(f(_x101), _x92)), _x72))))))) → top#(s(f(p(p(cons(p(cons(f(active(_x101)), _x92)), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(p(s(0)), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(mark(0), _x122)))), _x82), _x72))))))top#(ok(s(s(p(cons(f(0), _x52)))))) → top#(s(s(p(mark(cons(cons(0, f(s(0))), _x52))))))
top#(ok(s(f(p(cons(s(s(s(_x91))), _x62)))))) → top#(s(f(p(cons(s(s(s(active(_x91)))), _x62)))))top#(ok(s(f(p(cons(s(f(s(s(_x101)))), _x62)))))) → top#(s(f(p(cons(s(f(s(s(active(_x101))))), _x62)))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(f(0))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(mark(cons(0, f(s(0)))))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(p(s(0))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(mark(0)), _x122)))), _x82), _x72))))))
top#(ok(s(p(p(s(_x61)))))) → top#(s(p(p(s(active(_x61))))))top#(ok(s(f(p(p(cons(f(f(p(cons(p(_x121), _x112)))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(cons(p(active(_x121)), _x112)))), _x72))))))
top#(ok(s(s(p(cons(s(_x71), _x62)))))) → top#(s(s(p(cons(s(active(_x71)), _x62)))))top#(ok(s(f(p(p(cons(f(0), _x72))))))) → top#(s(f(p(p(cons(mark(cons(0, f(s(0)))), _x72))))))
top#(ok(s(s(cons(p(s(0)), _x42))))) → top#(s(s(mark(cons(0, _x42)))))top#(ok(s(s(p(f(cons(cons(p(f(cons(_x111, _x112))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(f(cons(active(_x111), _x112))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(p(cons(_x161, _x162)))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(p(cons(active(_x161), _x162)))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(f(cons(s(p(_x91)), _x72))))))) → top#(s(f(p(f(cons(s(p(active(_x91))), _x72))))))
top#(ok(s(f(p(cons(f(p(s(0))), _x62)))))) → top#(s(f(p(cons(f(mark(0)), _x62)))))top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(cons(_x171, _x172), _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(cons(active(_x171), _x172), _x162)), _x142))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(f(s(0)), _x162)), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(cons(s(cons(mark(f(p(s(0)))), _x162)), _x142))))))), _x72))))))top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(cons(_x261, _x262), _x202))))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(p(s(cons(cons(active(_x261), _x262), _x202))))), _x152))), _x122)))), _x82), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(cons(_x171, _x172)), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(cons(active(_x171), _x172)), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(f(p(p(cons(f(f(p(s(s(s(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(s(active(_x131))))))), _x72))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(p(p(s(0)))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(p(mark(0))))))), _x72))))))top#(ok(s(f(p(p(cons(p(s(s(f(f(s(f(s(s(_x161))))))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(f(f(s(f(s(s(active(_x161)))))))))), _x72))))))
top#(ok(s(cons(cons(p(_x61), _x52), _x42)))) → top#(s(cons(cons(p(active(_x61)), _x52), _x42)))top#(ok(s(f(p(p(cons(f(f(p(s(s(f(cons(s(s(p(_x171))), _x142))))))), _x72))))))) → top#(s(f(p(p(cons(f(f(p(s(s(f(cons(s(s(p(active(_x171)))), _x142))))))), _x72))))))
top#(ok(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(p(_x191)))), _x152))), _x122)))), _x82), _x72))))))) → top#(s(s(p(f(cons(cons(p(p(f(cons(f(f(cons(p(f(f(p(active(_x191))))), _x152))), _x122)))), _x82), _x72))))))top#(ok(s(p(p(p(p(s(0)))))))) → top#(s(p(p(p(mark(0))))))
top#(ok(s(f(p(p(cons(p(s(s(s(s(s(_x131)))))), _x72))))))) → top#(s(f(p(p(cons(p(s(s(s(s(s(active(_x131))))))), _x72))))))top#(ok(s(p(p(p(cons(_x71, _x72))))))) → top#(s(p(p(p(cons(active(_x71), _x72))))))

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

The right-hand side of the rule top#(ok(s(f(p(p(cons(cons(cons(_x91, _x92), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(cons(active(_x91), _x92), _x82), _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
top#(s(f(p(p(cons(cons(cons(f(active(_x101)), _x92), _x82), _x72)))))) 
top#(s(f(p(p(cons(cons(cons(mark(f(p(s(0)))), _x92), _x82), _x72)))))) 
top#(s(f(p(p(cons(cons(cons(mark(0), _x92), _x82), _x72)))))) 
top#(s(f(p(p(cons(cons(cons(mark(cons(0, f(s(0)))), _x92), _x82), _x72)))))) 
top#(s(f(p(p(cons(cons(cons(p(active(_x101)), _x92), _x82), _x72)))))) 
top#(s(f(p(p(cons(cons(cons(s(active(_x101)), _x92), _x82), _x72)))))) 
top#(s(f(p(p(cons(cons(cons(cons(active(_x101), _x102), _x92), _x82), _x72)))))) 
Thus, the rule top#(ok(s(f(p(p(cons(cons(cons(_x91, _x92), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(cons(active(_x91), _x92), _x82), _x72)))))) is replaced by the following rules:
top#(ok(s(f(p(p(cons(cons(cons(f(_x101), _x92), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(cons(f(active(_x101)), _x92), _x82), _x72))))))top#(ok(s(f(p(p(cons(cons(cons(p(s(0)), _x92), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(cons(mark(0), _x92), _x82), _x72))))))
top#(ok(s(f(p(p(cons(cons(cons(p(_x101), _x92), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(cons(p(active(_x101)), _x92), _x82), _x72))))))top#(ok(s(f(p(p(cons(cons(cons(s(_x101), _x92), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(cons(s(active(_x101)), _x92), _x82), _x72))))))
top#(ok(s(f(p(p(cons(cons(cons(f(s(0)), _x92), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(cons(mark(f(p(s(0)))), _x92), _x82), _x72))))))top#(ok(s(f(p(p(cons(cons(cons(f(0), _x92), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(cons(mark(cons(0, f(s(0)))), _x92), _x82), _x72))))))
top#(ok(s(f(p(p(cons(cons(cons(cons(_x101, _x102), _x92), _x82), _x72))))))) → top#(s(f(p(p(cons(cons(cons(cons(active(_x101), _x102), _x92), _x82), _x72))))))

Problem 6: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

p#(ok(X)) → p#(X)p#(mark(X)) → p#(X)

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

p#(ok(X)) → p#(X)p#(mark(X)) → p#(X)

Problem 7: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

active#(s(X)) → active#(X)active#(p(X)) → active#(X)
active#(f(X)) → active#(X)active#(cons(X1, X2)) → active#(X1)

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

active#(p(X)) → active#(X)active#(s(X)) → active#(X)
active#(f(X)) → active#(X)active#(cons(X1, X2)) → active#(X1)

Problem 8: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

proper#(s(X)) → proper#(X)proper#(cons(X1, X2)) → proper#(X1)
proper#(f(X)) → proper#(X)proper#(cons(X1, X2)) → proper#(X2)
proper#(p(X)) → proper#(X)

Rewrite Rules

active(f(0)) → mark(cons(0, f(s(0))))active(f(s(0))) → mark(f(p(s(0))))
active(p(s(0))) → mark(0)active(f(X)) → f(active(X))
active(cons(X1, X2)) → cons(active(X1), X2)active(s(X)) → s(active(X))
active(p(X)) → p(active(X))f(mark(X)) → mark(f(X))
cons(mark(X1), X2) → mark(cons(X1, X2))s(mark(X)) → mark(s(X))
p(mark(X)) → mark(p(X))proper(f(X)) → f(proper(X))
proper(0) → ok(0)proper(cons(X1, X2)) → cons(proper(X1), proper(X2))
proper(s(X)) → s(proper(X))proper(p(X)) → p(proper(X))
f(ok(X)) → ok(f(X))cons(ok(X1), ok(X2)) → ok(cons(X1, X2))
s(ok(X)) → ok(s(X))p(ok(X)) → ok(p(X))
top(mark(X)) → top(proper(X))top(ok(X)) → top(active(X))

Original Signature

Termination of terms over the following signature is verified: f, 0, s, p, active, mark, ok, proper, cons, top

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

proper#(s(X)) → proper#(X)proper#(cons(X1, X2)) → proper#(X1)
proper#(f(X)) → proper#(X)proper#(cons(X1, X2)) → proper#(X2)
proper#(p(X)) → proper#(X)