TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60000 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (935ms).
 | – Problem 2 was processed with processor SubtermCriterion (1ms).
 | – Problem 3 was processed with processor SubtermCriterion (1ms).
 |    | – Problem 8 was processed with processor ReductionPairSAT (153ms).
 |    |    | – Problem 11 was processed with processor ReductionPairSAT (89ms).
 | – Problem 4 was processed with processor ReductionPairSAT (5951ms).
 |    | – Problem 10 was processed with processor ReductionPairSAT (3490ms).
 |    |    | – Problem 13 was processed with processor ReductionPairSAT (3729ms).
 |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (15ms).
 |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (18ms).
 |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (14ms).
 |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (17ms).
 |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (30ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (23ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (29ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (26ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (27ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (28ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (28ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 was processed with processor ForwardNarrowing (34ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 28 was processed with processor ForwardNarrowing (93ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 29 was processed with processor ForwardNarrowing (39ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 30 was processed with processor ForwardNarrowing (40ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 31 was processed with processor ForwardNarrowing (103ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 32 was processed with processor ForwardNarrowing (34ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 33 was processed with processor ForwardNarrowing (55ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 34 was processed with processor ForwardNarrowing (283ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 35 remains open; application of the following processors failed [ForwardNarrowing (139ms), ForwardNarrowing (365ms), ForwardNarrowing (263ms), ForwardNarrowing (257ms), ForwardNarrowing (343ms), ForwardNarrowing (354ms), ForwardNarrowing (258ms), ForwardNarrowing (336ms), ForwardNarrowing (165ms), ForwardNarrowing (291ms), ForwardNarrowing (388ms), ForwardNarrowing (458ms), ForwardNarrowing (437ms), ForwardNarrowing (461ms), ForwardNarrowing (292ms), ForwardNarrowing (433ms), ForwardNarrowing (446ms), ForwardNarrowing (489ms), ForwardNarrowing (577ms), ForwardNarrowing (timeout)].
 | – Problem 5 was processed with processor SubtermCriterion (0ms).
 | – Problem 6 was processed with processor SubtermCriterion (1ms).
 |    | – Problem 9 was processed with processor ReductionPairSAT (93ms).
 |    |    | – Problem 12 was processed with processor ReductionPairSAT (63ms).
 | – Problem 7 was processed with processor SubtermCriterion (0ms).

The following open problems remain:

Open Dependency Pair Problem 14

Dependency Pairs

active#(sel(0, cons(X, Y))) → mark#(X)mark#(g(X)) → mark#(X)
mark#(cons(X1, X2)) → mark#(X1)active#(g(s(X))) → mark#(s(s(g(X))))
mark#(f(X)) → mark#(X)mark#(sel(X1, X2)) → active#(sel(mark(X1), mark(X2)))
mark#(f(X)) → active#(f(mark(X)))active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))
mark#(sel(X1, X2)) → mark#(X2)mark#(g(X)) → active#(g(mark(X)))
mark#(s(X)) → mark#(X)mark#(sel(X1, X2)) → mark#(X1)
active#(f(X)) → mark#(cons(X, f(g(X))))active#(g(0)) → mark#(s(0))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

active#(f(X)) → f#(g(X))sel#(mark(X1), X2) → sel#(X1, X2)
mark#(cons(X1, X2)) → active#(cons(mark(X1), X2))active#(sel(0, cons(X, Y))) → mark#(X)
g#(mark(X)) → g#(X)cons#(mark(X1), X2) → cons#(X1, X2)
f#(active(X)) → f#(X)active#(f(X)) → g#(X)
active#(f(X)) → cons#(X, f(g(X)))mark#(s(X)) → s#(mark(X))
active#(g(0)) → s#(0)active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))
mark#(sel(X1, X2)) → mark#(X2)mark#(g(X)) → active#(g(mark(X)))
cons#(X1, mark(X2)) → cons#(X1, X2)mark#(s(X)) → mark#(X)
f#(mark(X)) → f#(X)mark#(sel(X1, X2)) → mark#(X1)
mark#(f(X)) → f#(mark(X))active#(g(0)) → mark#(s(0))
mark#(cons(X1, X2)) → cons#(mark(X1), X2)mark#(sel(X1, X2)) → sel#(mark(X1), mark(X2))
mark#(0) → active#(0)mark#(s(X)) → active#(s(mark(X)))
active#(sel(s(X), cons(Y, Z))) → sel#(X, Z)mark#(g(X)) → mark#(X)
mark#(g(X)) → g#(mark(X))mark#(cons(X1, X2)) → mark#(X1)
active#(g(s(X))) → mark#(s(s(g(X))))active#(g(s(X))) → s#(s(g(X)))
cons#(active(X1), X2) → cons#(X1, X2)mark#(f(X)) → mark#(X)
mark#(sel(X1, X2)) → active#(sel(mark(X1), mark(X2)))sel#(X1, mark(X2)) → sel#(X1, X2)
mark#(f(X)) → active#(f(mark(X)))g#(active(X)) → g#(X)
s#(mark(X)) → s#(X)sel#(active(X1), X2) → sel#(X1, X2)
cons#(X1, active(X2)) → cons#(X1, X2)sel#(X1, active(X2)) → sel#(X1, X2)
active#(g(s(X))) → s#(g(X))s#(active(X)) → s#(X)
active#(f(X)) → mark#(cons(X, f(g(X))))active#(g(s(X))) → g#(X)

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The following SCCs where found

f#(active(X)) → f#(X)f#(mark(X)) → f#(X)
s#(mark(X)) → s#(X)s#(active(X)) → s#(X)
cons#(X1, active(X2)) → cons#(X1, X2)cons#(mark(X1), X2) → cons#(X1, X2)
cons#(X1, mark(X2)) → cons#(X1, X2)cons#(active(X1), X2) → cons#(X1, X2)
sel#(active(X1), X2) → sel#(X1, X2)sel#(mark(X1), X2) → sel#(X1, X2)
sel#(X1, active(X2)) → sel#(X1, X2)sel#(X1, mark(X2)) → sel#(X1, X2)
g#(active(X)) → g#(X)g#(mark(X)) → g#(X)
mark#(cons(X1, X2)) → active#(cons(mark(X1), X2))mark#(0) → active#(0)
active#(sel(0, cons(X, Y))) → mark#(X)mark#(s(X)) → active#(s(mark(X)))
mark#(g(X)) → mark#(X)mark#(cons(X1, X2)) → mark#(X1)
active#(g(s(X))) → mark#(s(s(g(X))))mark#(sel(X1, X2)) → active#(sel(mark(X1), mark(X2)))
mark#(f(X)) → mark#(X)mark#(f(X)) → active#(f(mark(X)))
active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))mark#(sel(X1, X2)) → mark#(X2)
mark#(g(X)) → active#(g(mark(X)))mark#(s(X)) → mark#(X)
mark#(sel(X1, X2)) → mark#(X1)active#(f(X)) → mark#(cons(X, f(g(X))))
active#(g(0)) → mark#(s(0))

Problem 2: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

s#(mark(X)) → s#(X)s#(active(X)) → s#(X)

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

s#(mark(X)) → s#(X)s#(active(X)) → s#(X)

Problem 3: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

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

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

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

Problem 8: ReductionPairSAT

Dependency Pair Problem

Dependency Pairs

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

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

Function Precedence

mark < cons# < active < f = g = 0 = s = sel = cons

Argument Filtering

f: all arguments are removed from f
g: all arguments are removed from g
cons#: collapses to 2
0: all arguments are removed from 0
s: all arguments are removed from s
active: collapses to 1
mark: 1
sel: 1 2
cons: all arguments are removed from cons

Status

f: multiset
g: multiset
0: multiset
s: multiset
mark: multiset
sel: lexicographic with permutation 1 → 1 2 → 2
cons: multiset

Usable Rules

There are no usable rules.

The dependency pairs and usable rules are stronlgy conservative!

Eliminated dependency pairs

The following dependency pairs (at least) can be eliminated according to the given precedence.

cons#(X1, mark(X2)) → cons#(X1, X2)

Problem 11: ReductionPairSAT

Dependency Pair Problem

Dependency Pairs

cons#(X1, active(X2)) → cons#(X1, X2)

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

Function Precedence

cons# < active < f = g = 0 = s = mark = sel = cons

Argument Filtering

f: all arguments are removed from f
g: collapses to 1
cons#: collapses to 2
0: all arguments are removed from 0
s: 1
active: 1
mark: all arguments are removed from mark
sel: 1 2
cons: all arguments are removed from cons

Status

f: multiset
0: multiset
s: lexicographic with permutation 1 → 1
active: multiset
mark: multiset
sel: lexicographic with permutation 1 → 1 2 → 2
cons: multiset

Usable Rules

There are no usable rules.

The dependency pairs and usable rules are stronlgy conservative!

Eliminated dependency pairs

The following dependency pairs (at least) can be eliminated according to the given precedence.

cons#(X1, active(X2)) → cons#(X1, X2)

Problem 4: ReductionPairSAT

Dependency Pair Problem

Dependency Pairs

mark#(0) → active#(0)mark#(cons(X1, X2)) → active#(cons(mark(X1), X2))
mark#(s(X)) → active#(s(mark(X)))active#(sel(0, cons(X, Y))) → mark#(X)
mark#(g(X)) → mark#(X)mark#(cons(X1, X2)) → mark#(X1)
active#(g(s(X))) → mark#(s(s(g(X))))mark#(f(X)) → mark#(X)
mark#(sel(X1, X2)) → active#(sel(mark(X1), mark(X2)))mark#(f(X)) → active#(f(mark(X)))
active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))mark#(sel(X1, X2)) → mark#(X2)
mark#(g(X)) → active#(g(mark(X)))mark#(s(X)) → mark#(X)
mark#(sel(X1, X2)) → mark#(X1)active#(f(X)) → mark#(cons(X, f(g(X))))
active#(g(0)) → mark#(s(0))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

Function Precedence

active < f = g = 0 = s = mark = active# = sel = mark# = cons

Argument Filtering

f: all arguments are removed from f
g: all arguments are removed from g
0: all arguments are removed from 0
s: all arguments are removed from s
active: collapses to 1
mark: all arguments are removed from mark
active#: collapses to 1
sel: all arguments are removed from sel
mark#: all arguments are removed from mark#
cons: all arguments are removed from cons

Status

f: multiset
g: multiset
0: multiset
s: multiset
mark: multiset
sel: multiset
mark#: multiset
cons: multiset

Usable Rules

cons(active(X1), X2) → cons(X1, X2)sel(X1, mark(X2)) → sel(X1, X2)
mark(s(X)) → active(s(mark(X)))active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))
active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
cons(X1, mark(X2)) → cons(X1, X2)f(active(X)) → f(X)
active(sel(0, cons(X, Y))) → mark(X)g(mark(X)) → g(X)
f(mark(X)) → f(X)mark(f(X)) → active(f(mark(X)))
mark(0) → active(0)s(active(X)) → s(X)
cons(X1, active(X2)) → cons(X1, X2)g(active(X)) → g(X)
active(g(s(X))) → mark(s(s(g(X))))mark(g(X)) → active(g(mark(X)))
sel(X1, active(X2)) → sel(X1, X2)mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
s(mark(X)) → s(X)sel(active(X1), X2) → sel(X1, X2)
sel(mark(X1), X2) → sel(X1, X2)

The dependency pairs and usable rules are stronlgy conservative!

Eliminated dependency pairs

The following dependency pairs (at least) can be eliminated according to the given precedence.

mark#(0) → active#(0)

Problem 10: ReductionPairSAT

Dependency Pair Problem

Dependency Pairs

mark#(cons(X1, X2)) → active#(cons(mark(X1), X2))mark#(s(X)) → active#(s(mark(X)))
active#(sel(0, cons(X, Y))) → mark#(X)mark#(g(X)) → mark#(X)
mark#(cons(X1, X2)) → mark#(X1)active#(g(s(X))) → mark#(s(s(g(X))))
mark#(f(X)) → mark#(X)mark#(sel(X1, X2)) → active#(sel(mark(X1), mark(X2)))
mark#(f(X)) → active#(f(mark(X)))active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))
mark#(sel(X1, X2)) → mark#(X2)mark#(g(X)) → active#(g(mark(X)))
mark#(s(X)) → mark#(X)active#(f(X)) → mark#(cons(X, f(g(X))))
mark#(sel(X1, X2)) → mark#(X1)active#(g(0)) → mark#(s(0))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

Function Precedence

f = g = mark = active# = sel = mark# = cons < 0 = s = active

Argument Filtering

f: all arguments are removed from f
g: all arguments are removed from g
0: all arguments are removed from 0
s: all arguments are removed from s
active: collapses to 1
mark: all arguments are removed from mark
active#: collapses to 1
sel: all arguments are removed from sel
mark#: all arguments are removed from mark#
cons: all arguments are removed from cons

Status

f: multiset
g: multiset
0: multiset
s: multiset
mark: multiset
sel: multiset
mark#: multiset
cons: multiset

Usable Rules

cons(active(X1), X2) → cons(X1, X2)sel(X1, mark(X2)) → sel(X1, X2)
mark(s(X)) → active(s(mark(X)))active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))
active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
cons(X1, mark(X2)) → cons(X1, X2)f(active(X)) → f(X)
active(sel(0, cons(X, Y))) → mark(X)g(mark(X)) → g(X)
f(mark(X)) → f(X)mark(f(X)) → active(f(mark(X)))
mark(0) → active(0)s(active(X)) → s(X)
cons(X1, active(X2)) → cons(X1, X2)g(active(X)) → g(X)
active(g(s(X))) → mark(s(s(g(X))))mark(g(X)) → active(g(mark(X)))
sel(X1, active(X2)) → sel(X1, X2)mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
s(mark(X)) → s(X)sel(active(X1), X2) → sel(X1, X2)
sel(mark(X1), X2) → sel(X1, X2)

The dependency pairs and usable rules are stronlgy conservative!

Eliminated dependency pairs

The following dependency pairs (at least) can be eliminated according to the given precedence.

mark#(s(X)) → active#(s(mark(X)))

Problem 13: ReductionPairSAT

Dependency Pair Problem

Dependency Pairs

mark#(cons(X1, X2)) → active#(cons(mark(X1), X2))active#(sel(0, cons(X, Y))) → mark#(X)
mark#(g(X)) → mark#(X)mark#(cons(X1, X2)) → mark#(X1)
active#(g(s(X))) → mark#(s(s(g(X))))mark#(f(X)) → mark#(X)
mark#(sel(X1, X2)) → active#(sel(mark(X1), mark(X2)))mark#(f(X)) → active#(f(mark(X)))
active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))mark#(sel(X1, X2)) → mark#(X2)
mark#(g(X)) → active#(g(mark(X)))mark#(s(X)) → mark#(X)
mark#(sel(X1, X2)) → mark#(X1)active#(f(X)) → mark#(cons(X, f(g(X))))
active#(g(0)) → mark#(s(0))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

Function Precedence

active# < f = g = s = active = mark = sel = mark# < 0 = cons

Argument Filtering

f: all arguments are removed from f
g: all arguments are removed from g
0: all arguments are removed from 0
s: all arguments are removed from s
active: collapses to 1
mark: all arguments are removed from mark
active#: collapses to 1
sel: all arguments are removed from sel
mark#: all arguments are removed from mark#
cons: all arguments are removed from cons

Status

f: multiset
g: multiset
0: multiset
s: multiset
mark: multiset
sel: multiset
mark#: multiset
cons: multiset

Usable Rules

cons(active(X1), X2) → cons(X1, X2)sel(X1, mark(X2)) → sel(X1, X2)
mark(s(X)) → active(s(mark(X)))active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))
active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
cons(X1, mark(X2)) → cons(X1, X2)f(active(X)) → f(X)
active(sel(0, cons(X, Y))) → mark(X)g(mark(X)) → g(X)
f(mark(X)) → f(X)mark(f(X)) → active(f(mark(X)))
mark(0) → active(0)s(active(X)) → s(X)
cons(X1, active(X2)) → cons(X1, X2)g(active(X)) → g(X)
active(g(s(X))) → mark(s(s(g(X))))mark(g(X)) → active(g(mark(X)))
sel(X1, active(X2)) → sel(X1, X2)mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)mark(cons(X1, X2)) → active(cons(mark(X1), X2))
s(mark(X)) → s(X)sel(active(X1), X2) → sel(X1, X2)
sel(mark(X1), X2) → sel(X1, X2)

The dependency pairs and usable rules are stronlgy conservative!

Eliminated dependency pairs

The following dependency pairs (at least) can be eliminated according to the given precedence.

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

Problem 14: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

active#(sel(0, cons(X, Y))) → mark#(X)mark#(g(X)) → mark#(X)
mark#(cons(X1, X2)) → mark#(X1)active#(g(s(X))) → mark#(s(s(g(X))))
mark#(f(X)) → mark#(X)mark#(sel(X1, X2)) → active#(sel(mark(X1), mark(X2)))
mark#(f(X)) → active#(f(mark(X)))active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))
mark#(sel(X1, X2)) → mark#(X2)mark#(g(X)) → active#(g(mark(X)))
mark#(s(X)) → mark#(X)mark#(sel(X1, X2)) → mark#(X1)
active#(f(X)) → mark#(cons(X, f(g(X))))active#(g(0)) → mark#(s(0))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(X1, X2)) → active#(sel(mark(X1), mark(X2))) 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
active#(sel(active(s(mark(_x31))), mark(X2))) 
active#(sel(active(cons(mark(_x31), _x32)), mark(X2))) 
active#(sel(mark(X1), active(s(mark(_x41))))) 
active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42))))) 
active#(sel(_x21, mark(X2))) 
active#(sel(active(0), mark(X2))) 
active#(sel(active(g(mark(_x31))), mark(X2))) 
active#(sel(mark(X1), _x22)) 
active#(sel(mark(X1), active(g(mark(_x41))))) 
active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2))) 
active#(sel(active(f(mark(_x31))), mark(X2))) 
active#(sel(mark(X1), active(cons(mark(_x41), _x42)))) 
active#(sel(mark(X1), active(0))) 
active#(sel(mark(X1), active(f(mark(_x41))))) 
Thus, the rule mark#(sel(X1, X2)) → active#(sel(mark(X1), mark(X2))) is replaced by the following rules:
mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))mark#(sel(cons(_x31, _x32), X2)) → active#(sel(active(cons(mark(_x31), _x32)), mark(X2)))
mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))
mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))
mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))
mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))
mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))

Problem 15: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

active#(sel(0, cons(X, Y))) → mark#(X)mark#(sel(cons(_x31, _x32), X2)) → active#(sel(active(cons(mark(_x31), _x32)), mark(X2)))
mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))
active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))
mark#(sel(X1, X2)) → mark#(X2)mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))
mark#(g(X)) → active#(g(mark(X)))mark#(s(X)) → mark#(X)
mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))mark#(sel(X1, X2)) → mark#(X1)
active#(g(0)) → mark#(s(0))mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))
mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))mark#(g(X)) → mark#(X)
mark#(cons(X1, X2)) → mark#(X1)active#(g(s(X))) → mark#(s(s(g(X))))
mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))
mark#(f(X)) → mark#(X)mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))
mark#(f(X)) → active#(f(mark(X)))mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))
mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))
active#(f(X)) → mark#(cons(X, f(g(X))))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(cons(_x31, _x32), X2)) → active#(sel(active(cons(mark(_x31), _x32)), mark(X2))) 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
active#(sel(active(cons(mark(_x31), _x32)), active(0))) 
active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2))) 
active#(sel(active(cons(active(0), _x32)), mark(X2))) 
active#(sel(cons(mark(_x31), _x32), mark(X2))) 
active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2))) 
active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41))))) 
active#(sel(active(cons(mark(_x31), _x52)), mark(X2))) 
active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42))))) 
active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2))) 
active#(sel(active(cons(_x51, _x52)), mark(X2))) 
active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2))) 
active#(sel(active(cons(mark(_x31), _x32)), _x22)) 
active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(_x41))))) 
Thus, the rule mark#(sel(cons(_x31, _x32), X2)) → active#(sel(active(cons(mark(_x31), _x32)), mark(X2))) is replaced by the following rules:
mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))
mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))
mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))

Problem 16: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

active#(sel(0, cons(X, Y))) → mark#(X)mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(_x41)))))
mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))
active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))
mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))mark#(sel(X1, X2)) → mark#(X2)
mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))
mark#(g(X)) → active#(g(mark(X)))mark#(s(X)) → mark#(X)
mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))mark#(sel(X1, X2)) → mark#(X1)
active#(g(0)) → mark#(s(0))mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))
mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))
mark#(g(X)) → mark#(X)mark#(cons(X1, X2)) → mark#(X1)
mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))active#(g(s(X))) → mark#(s(s(g(X))))
mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))mark#(f(X)) → mark#(X)
mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))
mark#(f(X)) → active#(f(mark(X)))mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))
mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))
mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))
mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))active#(f(X)) → mark#(cons(X, f(g(X))))
mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x42)))) 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
active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42)))) 
active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42)))) 
active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42)))) 
active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42)))) 
active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42)))) 
active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62)))) 
active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62)))) 
active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42)))) 
active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x42)))) 
Thus, the rule mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x42)))) is replaced by the following rules:
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))
mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))
mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))

Problem 17: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))
mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))
mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))
mark#(s(X)) → mark#(X)mark#(sel(X1, X2)) → mark#(X1)
active#(g(0)) → mark#(s(0))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))
mark#(g(X)) → mark#(X)mark#(cons(X1, X2)) → mark#(X1)
mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))
mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))
mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))
mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))active#(f(X)) → mark#(cons(X, f(g(X))))
mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))
active#(sel(0, cons(X, Y))) → mark#(X)mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))
mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))
mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))
mark#(sel(X1, X2)) → mark#(X2)mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))
mark#(g(X)) → active#(g(mark(X)))mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))
mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
active#(g(s(X))) → mark#(s(s(g(X))))mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))
mark#(f(X)) → mark#(X)mark#(f(X)) → active#(f(mark(X)))
mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))
mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))
mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(_x41))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72)))))) 
active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41))))) 
active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41))))) 
active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(mark(_x41))))) 
active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41))))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72))))))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61)))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71))))))) 
active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41)))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71))))))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(active(0))))) 
active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41))))) 
active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41))))) 
active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41))))) 
active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41))))) 
Thus, the rule mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(_x41))))) is replaced by the following rules:
mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(0)))))
mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))

Problem 18: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))
mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))
mark#(s(X)) → mark#(X)mark#(sel(X1, X2)) → mark#(X1)
active#(g(0)) → mark#(s(0))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))
mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))
mark#(g(X)) → mark#(X)mark#(cons(X1, X2)) → mark#(X1)
mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))
mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))
mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))
active#(f(X)) → mark#(cons(X, f(g(X))))mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))
mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))active#(sel(0, cons(X, Y))) → mark#(X)
mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))
mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))
mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))
mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))
mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(X1, X2)) → mark#(X2)mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))
mark#(g(X)) → active#(g(mark(X)))mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))
mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))
mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))active#(g(s(X))) → mark#(s(s(g(X))))
mark#(f(X)) → mark#(X)mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))
mark#(f(X)) → active#(f(mark(X)))mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))
mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))
mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))
mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(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
active#(sel(active(cons(active(0), _x32)), active(g(active(0))))) 
active#(sel(cons(mark(_x31), _x32), active(g(active(0))))) 
active#(sel(active(cons(_x51, _x52)), active(g(active(0))))) 
active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0))))) 
active#(sel(active(cons(mark(_x31), _x32)), g(active(0)))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(0)))) 
active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0))))) 
active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0))))) 
active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0))))) 
active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0))))) 
Thus, the rule mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(0))))) is replaced by the following rules:
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))
mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))
mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))
mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))

Problem 19: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))
mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))
mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))
mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))
mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))
mark#(s(X)) → mark#(X)mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(X1, X2)) → mark#(X1)
active#(g(0)) → mark#(s(0))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))
mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))
mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))mark#(g(X)) → mark#(X)
mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))mark#(cons(X1, X2)) → mark#(X1)
mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))
mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))
active#(f(X)) → mark#(cons(X, f(g(X))))mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))
active#(sel(0, cons(X, Y))) → mark#(X)mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))
mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))
mark#(sel(X1, X2)) → mark#(X2)mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))mark#(g(X)) → active#(g(mark(X)))
mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))
mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))active#(g(s(X))) → mark#(s(s(g(X))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))
mark#(f(X)) → mark#(X)mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))
mark#(f(X)) → active#(f(mark(X)))mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))
mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))
mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(mark(_x71))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0))))))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91))))))))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71)))))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92)))))))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71))))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91))))))))) 
active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91))))))))) 
active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71)))))) 
active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92))))))))) 
active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71))))))) 
Thus, the rule mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(mark(_x71))))))) is replaced by the following rules:
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))
mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))

Problem 20: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))
mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))
mark#(s(X)) → mark#(X)mark#(sel(X1, X2)) → mark#(X1)
mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))
mark#(cons(X1, X2)) → mark#(X1)mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))active#(sel(0, cons(X, Y))) → mark#(X)
mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))
mark#(g(X)) → active#(g(mark(X)))mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))
mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))
mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
active#(g(s(X))) → mark#(s(s(g(X))))mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))
mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))
mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))
mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))active#(g(0)) → mark#(s(0))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))mark#(g(X)) → mark#(X)
mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))
mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))
mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))active#(f(X)) → mark#(cons(X, f(g(X))))
mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))
mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(X1, X2)) → mark#(X2)mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))
mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))mark#(f(X)) → mark#(X)
mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))mark#(f(X)) → active#(f(mark(X)))
mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))
mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(mark(_x71))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0))))))) 
active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91))))))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92))))))))) 
active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71))))))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91))))))))) 
active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71)))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91))))))))) 
active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71)))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92)))))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
Thus, the rule mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(mark(_x71))))))) is replaced by the following rules:
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(cons(sel(mark(_x71), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71)))))))

Problem 21: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(s(X)) → mark#(X)
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, X2)) → mark#(X1)
mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))
mark#(cons(X1, X2)) → mark#(X1)mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0)))))))mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
active#(sel(0, cons(X, Y))) → mark#(X)mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))
mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))
mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71)))))))
mark#(g(X)) → active#(g(mark(X)))mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))
mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
active#(g(s(X))) → mark#(s(s(g(X))))mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(_x61, _x82), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))
mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))
mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))
mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(mark(_x71), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))
active#(g(0)) → mark#(s(0))mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))
mark#(g(X)) → mark#(X)mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))
mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))
mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71)))))))active#(f(X)) → mark#(cons(X, f(g(X))))
mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(X1, X2)) → mark#(X2)mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))
mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))
mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))
mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))
mark#(f(X)) → mark#(X)mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))mark#(f(X)) → active#(f(mark(X)))
mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))
mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x81)))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71)))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61)))))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(_x81))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(_x81))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
Thus, the rule mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x81)))))) is replaced by the following rules:
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(_x81)))))mark#(sel(cons(sel(0, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(_x81)))))

Problem 22: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))
mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))
mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(s(X)) → mark#(X)mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(X1, X2)) → mark#(X1)mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))
mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))mark#(cons(X1, X2)) → mark#(X1)
mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0)))))))mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
active#(sel(0, cons(X, Y))) → mark#(X)mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71)))))))mark#(g(X)) → active#(g(mark(X)))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))
mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
active#(g(s(X))) → mark#(s(s(g(X))))mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(_x61, _x82), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))
mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))
mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(mark(_x71), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))
mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))active#(g(0)) → mark#(s(0))
mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))mark#(g(X)) → mark#(X)
mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))
mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71)))))))
active#(f(X)) → mark#(cons(X, f(g(X))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))
mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))mark#(sel(X1, X2)) → mark#(X2)
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))
mark#(f(X)) → mark#(X)mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))
mark#(f(X)) → active#(f(mark(X)))mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))
mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81)))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
active#(sel(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71)))))) 
active#(sel(active(cons(active(sel(f(mark(_x91)), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(active(f(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(active(0))), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(sel(active(f(mark(_x91))), mark(_x62)), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(active(g(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(active(s(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x91))), _x82)), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), g(active(f(_x81))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(cons(mark(_x91), f(g(mark(_x91))))), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61)))))))) 
active#(sel(active(cons(active(sel(active(f(active(sel(mark(_x121), mark(_x122))))), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(f(_x81))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(0))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(active(cons(mark(_x121), _x122)))), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
Thus, the rule mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81)))))) is replaced by the following rules:
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(sel(f(_x91), _x82), _x32), g(f(active(f(mark(_x91))))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), _x82)), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(sel(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(sel(mark(_x121), mark(_x122))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(f(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(f(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(sel(f(cons(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(cons(mark(_x121), _x122)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(mark(_x91), f(g(mark(_x91))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(cons(sel(f(0), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(0))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(g(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(g(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(f(_x81)))))mark#(sel(cons(sel(f(_x91), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(mark(_x91))), mark(_x62)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(f(_x91), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(s(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(s(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(f(mark(_x91)))))) → active#(sel(active(cons(active(sel(f(mark(_x91)), mark(_x62))), _x32)), active(g(active(f(_x81))))))

Problem 23: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(mark(_x91), f(g(mark(_x91))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(s(X)) → mark#(X)
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, X2)) → mark#(X1)
mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))mark#(cons(X1, X2)) → mark#(X1)
mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))
mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))
mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x82), _x32), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
active#(sel(0, cons(X, Y))) → mark#(X)mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))
mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x91), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71)))))))mark#(g(X)) → active#(g(mark(X)))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))
mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
active#(g(s(X))) → mark#(s(s(g(X))))mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(f(_x91), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))
mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))
mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))
mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(_x81)))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(cons(sel(mark(_x71), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))
mark#(sel(cons(sel(f(cons(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(cons(mark(_x121), _x122)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))
active#(g(0)) → mark#(s(0))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))
mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(g(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(g(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))
mark#(g(X)) → mark#(X)mark#(sel(cons(sel(f(_x91), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))
mark#(sel(cons(sel(f(_x91), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))
mark#(sel(cons(sel(f(_x91), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))active#(f(X)) → mark#(cons(X, f(g(X))))
mark#(sel(cons(sel(f(_x91), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(f(mark(_x91)))))) → active#(sel(active(cons(active(sel(f(mark(_x91)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x91), _x82), _x32), g(f(active(f(mark(_x91))))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), _x82)), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(sel(f(sel(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(sel(mark(_x121), mark(_x122))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(f(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(f(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, X2)) → mark#(X2)
mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))mark#(sel(cons(sel(f(_x91), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(f(0), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(0))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(mark(_x91))), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))
mark#(f(X)) → mark#(X)mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))mark#(f(X)) → active#(f(mark(X)))
mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(s(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(s(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32), active(g(active(f(_x81))))))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
active#(sel(active(cons(mark(_x31), _x52)), g(active(f(mark(_x71)))))) 
active#(sel(active(cons(active(cons(mark(_x71), _x72)), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(g(mark(_x71))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92))))))))) 
active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(g(mark(_x91))))))))) 
active#(sel(active(cons(active(s(mark(_x71))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(mark(_x31), _x52)), active(g(f(mark(_x71)))))) 
active#(sel(active(cons(active(0), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(f(mark(_x91))))))))) 
active#(sel(active(cons(_x61, _x62)), active(g(active(f(mark(_x71))))))) 
active#(sel(cons(mark(_x31), _x52), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(f(mark(_x71))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(s(mark(_x91))))))))) 
active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71))))))))) 
active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(cons(mark(_x91), _x92)))))))) 
active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(0))))))) 
active#(sel(active(cons(active(sel(mark(_x71), mark(_x72))), _x52)), active(g(active(f(mark(_x71))))))) 
Thus, the rule mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71))))))) is replaced by the following rules:
mark#(sel(cons(f(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(s(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(cons(sel(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x71), mark(_x72))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), g(active(f(mark(_x71))))))
mark#(sel(cons(g(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(mark(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(0, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(0), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(_x31, mark(_x52)), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(0)))))))
mark#(sel(cons(_x31, mark(active(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(f(mark(_x71))))))
mark#(sel(cons(cons(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x71), _x72)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x61, mark(_x62)), g(f(_x71)))) → active#(sel(active(cons(_x61, _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x52), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))

Problem 24: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(s(X)) → mark#(X)
mark#(sel(X1, X2)) → mark#(X1)mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))
mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x82), _x32), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
active#(sel(0, cons(X, Y))) → mark#(X)mark#(sel(cons(f(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(s(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))
mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))
mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(0, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))
mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(_x81)))))mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))
mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))mark#(sel(cons(sel(f(cons(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(cons(mark(_x121), _x122)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
active#(g(0)) → mark#(s(0))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))
mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(g(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(g(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))mark#(g(X)) → mark#(X)
mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(mark(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))active#(f(X)) → mark#(cons(X, f(g(X))))
mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))
mark#(sel(cons(sel(f(_x91), _x82), _x32), g(f(active(f(mark(_x91))))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(_x81))))))active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))
mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))mark#(sel(X1, X2)) → mark#(X2)
mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(0)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(sel(f(_x91), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(mark(_x91))), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))mark#(sel(cons(0, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(0), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x52), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71))))))
mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(mark(_x91), f(g(mark(_x91))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))
mark#(cons(X1, X2)) → mark#(X1)mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0)))))))mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x61, mark(_x62)), g(f(_x71)))) → active#(sel(active(cons(_x61, _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(g(X)) → active#(g(mark(X)))mark#(sel(cons(cons(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x71), _x72)), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(f(_x81)))))active#(g(s(X))) → mark#(s(s(g(X))))
mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(sel(f(_x91), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))
mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))
mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(cons(sel(mark(_x71), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))
mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(sel(f(_x91), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))mark#(sel(cons(sel(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x71), mark(_x72))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(f(_x91), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(f(mark(_x91)))))) → active#(sel(active(cons(active(sel(f(mark(_x91)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))mark#(sel(cons(sel(f(sel(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(sel(mark(_x121), mark(_x122))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(sel(f(f(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(f(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(g(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))
mark#(sel(cons(sel(f(_x91), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(0), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(0))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(f(X)) → mark#(X)
mark#(f(X)) → active#(f(mark(X)))mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(s(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(s(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(active(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(f(mark(_x71))))))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81)))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(_x81))))) 
active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61)))))))) 
active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71)))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(_x81))))) 
Thus, the rule mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81)))))) is replaced by the following rules:
mark#(sel(cons(sel(s(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(_x81))))))mark#(sel(cons(sel(cons(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(sel(f(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(g(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(sel(_x61, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(_x81)))))
mark#(sel(cons(sel(_x61, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(_x81)))))mark#(sel(cons(sel(_x71, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(sel(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))

Problem 25: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(s(X)) → mark#(X)
mark#(sel(X1, X2)) → mark#(X1)mark#(sel(cons(sel(s(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))
mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(_x81)))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x82), _x32), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91)))))))))active#(sel(0, cons(X, Y))) → mark#(X)
mark#(sel(cons(f(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))
mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))mark#(sel(cons(s(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))
mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))
mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(cons(sel(_x61, _x82), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))
mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))
mark#(sel(cons(sel(f(cons(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(cons(mark(_x121), _x122)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))active#(g(0)) → mark#(s(0))
mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))
mark#(sel(cons(sel(f(_x91), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(g(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(g(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(g(X)) → mark#(X)
mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(_x31, mark(mark(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
active#(f(X)) → mark#(cons(X, f(g(X))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x71, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(f(_x91), _x82), _x32), g(f(active(f(mark(_x91))))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))
mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(_x81))))))
active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))
mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(X1, X2)) → mark#(X2)mark#(sel(cons(_x31, mark(_x52)), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(0)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(_x61, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(mark(_x91))), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(g(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))
mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))
mark#(sel(cons(0, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(0), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x52), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(_x61, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(mark(_x91), f(g(mark(_x91))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))mark#(cons(X1, X2)) → mark#(X1)
mark#(sel(cons(sel(f(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0)))))))mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x61, mark(_x62)), g(f(_x71)))) → active#(sel(active(cons(_x61, _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(_x81)))))mark#(g(X)) → active#(g(mark(X)))
mark#(sel(cons(cons(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x71), _x72)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(f(_x81)))))active#(g(s(X))) → mark#(s(s(g(X))))
mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(sel(f(_x91), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))mark#(sel(cons(sel(_x61, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(_x81)))))
mark#(sel(cons(sel(mark(_x71), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(sel(cons(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))mark#(sel(cons(sel(_x61, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(_x81))))))
mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(sel(f(_x91), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))mark#(sel(cons(sel(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x71), mark(_x72))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(f(_x91), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(sel(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(f(mark(_x91)))))) → active#(sel(active(cons(active(sel(f(mark(_x91)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))
mark#(sel(cons(sel(f(sel(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(sel(mark(_x121), mark(_x122))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(sel(f(f(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(f(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71))))))
mark#(sel(cons(g(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))mark#(sel(cons(sel(f(_x91), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(0), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(0))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))
mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(f(X)) → mark#(X)mark#(sel(cons(sel(_x61, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))
mark#(f(X)) → active#(f(mark(X)))mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(s(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(s(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(f(mark(_x71))))))mark#(sel(cons(_x31, mark(active(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(mark(_x41))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(cons(mark(_x71), _x72)))))) 
active#(sel(active(cons(active(f(active(s(mark(_x91))))), _x32)), active(g(mark(_x41))))) 
active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(_x61)))) 
active#(sel(cons(active(f(mark(_x61))), _x32), active(g(mark(_x41))))) 
active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(g(mark(_x71))))))) 
active#(sel(active(cons(active(f(active(g(mark(_x91))))), _x32)), active(g(mark(_x41))))) 
active#(sel(active(cons(active(f(mark(_x61))), _x32)), g(mark(_x41)))) 
active#(sel(active(cons(active(f(_x81)), _x32)), active(g(mark(_x41))))) 
active#(sel(active(cons(active(f(active(f(mark(_x91))))), _x32)), active(g(mark(_x41))))) 
active#(sel(active(cons(active(f(active(0))), _x32)), active(g(mark(_x41))))) 
active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(f(active(cons(mark(_x91), _x92)))), _x32)), active(g(mark(_x41))))) 
active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(s(mark(_x71))))))) 
active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0))))) 
active#(sel(active(cons(f(mark(_x61)), _x52)), active(g(mark(_x41))))) 
active#(sel(active(cons(active(f(active(sel(mark(_x91), mark(_x92))))), _x32)), active(g(mark(_x41))))) 
active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(sel(mark(_x71), mark(_x72))))))) 
active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41))))) 
active#(sel(active(cons(mark(cons(mark(_x61), f(g(mark(_x61))))), _x32)), active(g(mark(_x41))))) 
Thus, the rule mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(mark(_x41))))) is replaced by the following rules:
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), g(mark(_x41))))mark#(sel(cons(f(s(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(s(mark(_x91))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(f(_x61), _x32), g(_x61))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(_x61))))
mark#(sel(cons(f(f(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(f(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(f(sel(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(sel(mark(_x91), mark(_x92))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(f(cons(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(cons(mark(_x91), _x92)))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(f(_x61), mark(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))
mark#(sel(cons(f(_x61), _x52), g(_x41))) → active#(sel(active(cons(f(mark(_x61)), _x52)), active(g(mark(_x41)))))mark#(sel(cons(f(0), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(0))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(f(_x61), _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(cons(mark(_x71), _x72))))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(cons(active(f(mark(_x61))), _x32), active(g(mark(_x41)))))
mark#(sel(cons(f(_x61), _x32), g(g(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(g(mark(_x71)))))))mark#(sel(cons(f(g(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(g(mark(_x91))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(f(_x61), active(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))mark#(sel(cons(f(_x61), _x32), g(s(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(s(mark(_x71)))))))
mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(f(_x81), _x32), g(_x41))) → active#(sel(active(cons(active(f(_x81)), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(f(_x61), _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(mark(cons(mark(_x61), f(g(mark(_x61))))), _x32)), active(g(mark(_x41)))))

Problem 26: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(s(X)) → mark#(X)mark#(sel(X1, X2)) → mark#(X1)
mark#(sel(cons(sel(s(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))
mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(_x81)))))mark#(sel(cons(f(_x61), active(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))mark#(sel(cons(f(_x61), _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x82), _x32), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
active#(sel(0, cons(X, Y))) → mark#(X)mark#(sel(cons(f(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(s(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), g(active(f(_x81)))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))
mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(0, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))
mark#(sel(cons(f(g(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(g(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(cons(f(s(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(s(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))
mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))mark#(sel(cons(sel(f(cons(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(cons(mark(_x121), _x122)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
active#(g(0)) → mark#(s(0))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))
mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(g(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(g(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))
mark#(g(X)) → mark#(X)mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))
mark#(sel(cons(f(sel(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(sel(mark(_x91), mark(_x92))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(mark(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))active#(f(X)) → mark#(cons(X, f(g(X))))
mark#(sel(cons(sel(_x71, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(mark(cons(mark(_x61), f(g(mark(_x61))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))
mark#(sel(cons(sel(f(_x91), _x82), _x32), g(f(active(f(mark(_x91))))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x52), g(_x41))) → active#(sel(active(cons(f(mark(_x61)), _x52)), active(g(mark(_x41)))))
active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))
mark#(sel(X1, X2)) → mark#(X2)mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(0)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(_x61, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(mark(_x91))), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(f(f(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(f(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(sel(_x61, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(g(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(f(cons(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(cons(mark(_x91), _x92)))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))
mark#(sel(cons(0, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(0), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x52), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(_x61, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(mark(_x91), f(g(mark(_x91))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(f(_x81), _x32), g(_x41))) → active#(sel(active(cons(active(f(_x81)), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))
mark#(cons(X1, X2)) → mark#(X1)mark#(sel(cons(sel(f(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(_x31, mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(f(_x61), mark(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0)))))))mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x61, mark(_x62)), g(f(_x71)))) → active#(sel(active(cons(_x61, _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(_x61))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(_x61))))
mark#(sel(cons(sel(f(_x91), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(f(0), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(0))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(_x81)))))mark#(g(X)) → active#(g(mark(X)))
mark#(sel(cons(cons(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x71), _x72)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(f(_x81)))))active#(g(s(X))) → mark#(s(s(g(X))))
mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(cons(active(f(mark(_x61))), _x32), active(g(mark(_x41)))))mark#(sel(cons(f(_x61), _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(cons(mark(_x71), _x72))))))
mark#(sel(cons(sel(f(_x91), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))mark#(sel(cons(sel(_x61, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(_x81)))))
mark#(sel(cons(sel(mark(_x71), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(sel(cons(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))mark#(sel(cons(sel(_x61, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(_x81))))))
mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(f(_x61), _x32), g(g(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(g(mark(_x71)))))))
mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(sel(f(_x91), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))mark#(sel(cons(sel(f(_x91), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x71), mark(_x72))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(sel(f(_x91), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(sel(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(f(mark(_x91)))))) → active#(sel(active(cons(active(sel(f(mark(_x91)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), g(mark(_x41))))
mark#(sel(cons(sel(f(sel(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(sel(mark(_x121), mark(_x122))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(sel(f(f(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(f(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71))))))
mark#(sel(cons(g(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))
mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))mark#(sel(cons(sel(f(_x91), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(s(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(s(mark(_x71)))))))mark#(sel(cons(sel(f(0), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(0))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))
mark#(f(X)) → mark#(X)mark#(f(X)) → active#(f(mark(X)))
mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(s(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(s(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(active(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(f(mark(_x71))))))mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x42)))) 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
active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(_x61, _x62)))) 
active#(sel(active(cons(active(s(active(g(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(f(mark(_x71))), _x42)))) 
active#(sel(active(cons(active(s(active(sel(mark(_x91), mark(_x92))))), _x32)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(g(mark(_x71))), _x42)))) 
active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42)))) 
active#(sel(active(cons(active(s(active(s(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(s(mark(_x61)), _x52)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(active(s(active(cons(mark(_x91), _x92)))), _x32)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(active(s(mark(_x61))), _x32)), cons(mark(_x41), _x42))) 
active#(sel(active(cons(active(s(active(0))), _x32)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(0), _x42)))) 
active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(s(mark(_x71))), _x42)))) 
active#(sel(active(cons(active(s(active(f(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62)))) 
active#(sel(cons(active(s(mark(_x61))), _x32), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(active(s(_x81)), _x32)), active(cons(mark(_x41), _x42)))) 
active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42)))) 
Thus, the rule mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x42)))) is replaced by the following rules:
mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(cons(active(s(mark(_x61))), _x32), active(cons(mark(_x41), _x42))))mark#(sel(cons(s(_x61), _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(f(mark(_x71))), _x42))))
mark#(sel(cons(s(_x61), _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(cons(s(0), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(0))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(s(_x61), _x32), cons(_x61, _x62))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(_x61, _x62))))mark#(sel(cons(s(_x61), _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(s(mark(_x71))), _x42))))
mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), cons(mark(_x41), _x42)))mark#(sel(cons(s(_x61), _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(s(_x61), _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(s(g(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(g(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(s(_x61), _x32), cons(0, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(0), _x42))))mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(s(f(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(f(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(s(sel(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(sel(mark(_x91), mark(_x92))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(s(_x81), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(_x81)), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(s(cons(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(cons(mark(_x91), _x92)))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(s(_x61), _x52), cons(_x41, _x42))) → active#(sel(active(cons(s(mark(_x61)), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(s(s(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(s(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(s(_x61), mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(s(_x61), active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))

Problem 27: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(s(X)) → mark#(X)
mark#(sel(X1, X2)) → mark#(X1)mark#(sel(cons(sel(s(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(_x81)))))
mark#(sel(cons(f(_x61), active(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))mark#(sel(cons(s(_x61), _x52), cons(_x41, _x42))) → active#(sel(active(cons(s(mark(_x61)), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))mark#(sel(cons(f(_x61), _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
active#(sel(0, cons(X, Y))) → mark#(X)mark#(sel(cons(f(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(s(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(s(_x61), _x32), cons(0, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(0), _x42))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), g(active(f(_x81)))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))
mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(0, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(f(g(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(g(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(f(s(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(s(mark(_x91))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(_x81)))))mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))
mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))mark#(sel(cons(sel(f(cons(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(cons(mark(_x121), _x122)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
active#(g(0)) → mark#(s(0))mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))mark#(sel(cons(s(_x61), mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(_x91), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(g(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(g(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(g(X)) → mark#(X)
mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))mark#(sel(cons(f(sel(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(sel(mark(_x91), mark(_x92))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), g(active(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(_x31, mark(mark(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))active#(f(X)) → mark#(cons(X, f(g(X))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x71, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(mark(cons(mark(_x61), f(g(mark(_x61))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(f(_x91), _x82), _x32), g(f(active(f(mark(_x91))))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))
mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x52), g(_x41))) → active#(sel(active(cons(f(mark(_x61)), _x52)), active(g(mark(_x41)))))active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))
mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(X1, X2)) → mark#(X2)mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(0)))))))mark#(sel(cons(s(s(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(s(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(_x61, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(mark(_x91))), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), cons(mark(_x41), _x42)))
mark#(sel(cons(s(_x61), _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(f(f(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(f(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(sel(_x61, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(g(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(f(cons(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(cons(mark(_x91), _x92)))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))
mark#(sel(cons(0, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(0), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(s(_x81), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(_x81)), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x52), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(_x61, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(mark(_x91), f(g(mark(_x91))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(f(_x81), _x32), g(_x41))) → active#(sel(active(cons(active(f(_x81)), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))
mark#(sel(cons(s(_x61), _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))mark#(cons(X1, X2)) → mark#(X1)
mark#(sel(cons(sel(f(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(s(g(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(g(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(f(_x61), mark(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0)))))))mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x61, mark(_x62)), g(f(_x71)))) → active#(sel(active(cons(_x61, _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(cons(active(s(mark(_x61))), _x32), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(_x61))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(_x61))))mark#(sel(cons(sel(f(_x91), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(f(0), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(0))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(_x31, mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(_x81)))))
mark#(g(X)) → active#(g(mark(X)))mark#(sel(cons(cons(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x71), _x72)), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(cons(s(_x61), _x32), cons(_x61, _x62))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(_x61, _x62))))active#(g(s(X))) → mark#(s(s(g(X))))
mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(cons(active(f(mark(_x61))), _x32), active(g(mark(_x41)))))mark#(sel(cons(f(_x61), _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(cons(mark(_x71), _x72))))))
mark#(sel(cons(sel(f(_x91), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))mark#(sel(cons(sel(_x61, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(mark(_x71), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(sel(cons(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))
mark#(sel(cons(sel(_x61, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(_x81))))))mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(f(_x61), _x32), g(g(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(g(mark(_x71)))))))mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(sel(f(_x91), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))mark#(sel(cons(sel(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x71), mark(_x72))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(f(_x91), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(f(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(f(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(sel(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(f(mark(_x91)))))) → active#(sel(active(cons(active(sel(f(mark(_x91)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), g(mark(_x41))))
mark#(sel(cons(sel(f(sel(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(sel(mark(_x121), mark(_x122))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(0), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(0))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(sel(f(f(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(f(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(g(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(sel(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(sel(mark(_x91), mark(_x92))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))mark#(sel(cons(sel(f(_x91), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(s(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(s(mark(_x71)))))))mark#(sel(cons(s(cons(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(cons(mark(_x91), _x92)))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(0), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(0))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))
mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(_x61), _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(s(mark(_x71))), _x42))))mark#(f(X)) → mark#(X)
mark#(sel(cons(sel(_x61, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(f(X)) → active#(f(mark(X)))
mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(s(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(s(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(f(mark(_x71))))))
mark#(sel(cons(_x31, mark(active(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x81)))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
active#(sel(active(cons(active(sel(active(0), active(0))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71)))))) 
active#(sel(active(cons(active(sel(active(0), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), g(active(f(_x81))))) 
active#(sel(active(cons(active(sel(active(0), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(0, mark(_x62))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(0), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(0), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(f(_x81))))) 
active#(sel(active(cons(active(sel(active(0), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(sel(active(0), mark(_x62)), _x42)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61)))))))) 
active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(0), _x72)), _x52)), active(g(active(f(_x81)))))) 
active#(sel(cons(active(sel(active(0), mark(_x62))), _x52), active(g(active(f(_x81)))))) 
Thus, the rule mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x81)))))) is replaced by the following rules:
mark#(sel(cons(sel(0, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(f(_x81)))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(sel(0, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(active(0), mark(_x62))), _x52), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), g(active(f(_x81)))))mark#(sel(cons(sel(0, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(active(0), mark(_x62)), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(0, mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), _x72)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(sel(0, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(0))), _x52)), active(g(active(f(_x81))))))

Problem 28: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(s(X)) → mark#(X)mark#(sel(X1, X2)) → mark#(X1)
mark#(sel(cons(sel(s(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))
mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(f(_x81)))))mark#(sel(cons(sel(0, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(_x81)))))mark#(sel(cons(f(_x61), active(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))
mark#(sel(cons(sel(0, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), _x72)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), _x52), cons(_x41, _x42))) → active#(sel(active(cons(s(mark(_x61)), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))mark#(sel(cons(f(_x61), _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
active#(sel(0, cons(X, Y))) → mark#(X)mark#(sel(cons(f(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(s(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(s(_x61), _x32), cons(0, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(0), _x42))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), g(active(f(_x81)))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))
mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(0, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))
mark#(sel(cons(f(g(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(g(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(cons(f(s(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(s(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))
mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))mark#(sel(cons(sel(f(cons(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(cons(mark(_x121), _x122)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
active#(g(0)) → mark#(s(0))mark#(sel(cons(s(_x61), mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(g(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(g(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))mark#(g(X)) → mark#(X)
mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))mark#(sel(cons(f(sel(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(sel(mark(_x91), mark(_x92))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), g(active(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(mark(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), g(active(f(_x81)))))mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))active#(f(X)) → mark#(cons(X, f(g(X))))
mark#(sel(cons(sel(_x71, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(mark(cons(mark(_x61), f(g(mark(_x61))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(sel(0, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x91), _x82), _x32), g(f(active(f(mark(_x91))))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), _x82)), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x52), g(_x41))) → active#(sel(active(cons(f(mark(_x61)), _x52)), active(g(mark(_x41)))))active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))
mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(X1, X2)) → mark#(X2)mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(0)))))))mark#(sel(cons(s(s(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(s(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(_x61, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(mark(_x91))), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), cons(mark(_x41), _x42)))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(sel(cons(s(_x61), _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(f(f(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(f(mark(_x91))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(active(0), mark(_x62))), _x52), active(g(active(f(_x81))))))mark#(sel(cons(sel(g(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(f(cons(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(cons(mark(_x91), _x92)))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))
mark#(sel(cons(0, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(0), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(s(_x81), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(_x81)), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))
mark#(sel(cons(sel(0, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(0))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x52), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))
mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))mark#(sel(cons(sel(0, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(0, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(mark(_x91), f(g(mark(_x91))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(f(_x81), _x32), g(_x41))) → active#(sel(active(cons(active(f(_x81)), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))mark#(sel(cons(s(_x61), _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(f(mark(_x71))), _x42))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))
mark#(cons(X1, X2)) → mark#(X1)mark#(sel(cons(sel(f(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(_x31, mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(s(g(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(g(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(f(_x61), mark(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x61, mark(_x62)), g(f(_x71)))) → active#(sel(active(cons(_x61, _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(cons(active(s(mark(_x61))), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(0, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(_x61))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(_x61))))mark#(sel(cons(sel(f(_x91), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))mark#(sel(cons(sel(0, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(f(0), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(0))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(_x31, mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(_x81)))))mark#(g(X)) → active#(g(mark(X)))
mark#(sel(cons(cons(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x71), _x72)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(f(_x81)))))mark#(sel(cons(s(_x61), _x32), cons(_x61, _x62))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(_x61, _x62))))
active#(g(s(X))) → mark#(s(s(g(X))))mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))mark#(sel(cons(sel(f(_x91), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(cons(mark(_x71), _x72))))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(cons(active(f(mark(_x61))), _x32), active(g(mark(_x41)))))
mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))
mark#(sel(cons(sel(0, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(active(0), mark(_x62)), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(0, mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))
mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(sel(_x61, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(cons(sel(mark(_x71), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(s(_x61), _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(cons(sel(cons(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))mark#(sel(cons(sel(_x61, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(_x81))))))
mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(f(_x61), _x32), g(g(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(g(mark(_x71)))))))
mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(sel(f(_x91), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))mark#(sel(cons(sel(f(_x91), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x71), mark(_x72))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(sel(f(_x91), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(s(f(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(f(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(sel(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(f(mark(_x91)))))) → active#(sel(active(cons(active(sel(f(mark(_x91)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), g(mark(_x41))))
mark#(sel(cons(sel(f(sel(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(sel(mark(_x121), mark(_x122))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(0), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(0))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(sel(f(f(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(f(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(g(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(sel(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(sel(mark(_x91), mark(_x92))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))
mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))mark#(sel(cons(sel(f(_x91), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(cons(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(cons(mark(_x91), _x92)))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(f(_x61), _x32), g(s(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(s(mark(_x71)))))))
mark#(sel(cons(sel(f(0), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(0))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))
mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(s(_x61), _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(s(mark(_x71))), _x42))))
mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))
mark#(f(X)) → mark#(X)mark#(f(X)) → active#(f(mark(X)))
mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(s(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(s(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(active(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(f(mark(_x71))))))mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x81)))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
active#(sel(cons(active(sel(active(f(_x111)), mark(_x62))), _x32), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), g(active(f(_x81))))) 
active#(sel(active(cons(active(sel(active(f(_x111)), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(_x111)), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(_x111)), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(_x111)), _x82)), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(cons(_x91, f(g(_x91)))), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(_x111)), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(_x111)), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(_x111)), active(0))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(_x101)), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x71)))))) 
active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(f(_x81))))) 
active#(sel(active(cons(active(sel(f(_x111), mark(_x62))), _x32)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61)))))))) 
active#(sel(active(cons(sel(active(f(_x111)), mark(_x62)), _x52)), active(g(active(f(_x81)))))) 
Thus, the rule mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x81)))))) is replaced by the following rules:
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(f(_x111))))) → active#(sel(active(cons(active(sel(f(_x111), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), g(active(f(_x81)))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(_x91, f(g(_x91)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(mark(_x101)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x101)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x111), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(_x111)), mark(_x62)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(cons(sel(f(_x111), _x82), _x32), g(f(active(f(_x111)))))) → active#(sel(active(cons(active(sel(active(f(_x111)), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(_x111)), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x111), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(sel(f(_x111), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(active(_x101)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x101)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x111), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(0))), _x32)), active(g(active(f(_x81))))))

Problem 29: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(s(X)) → mark#(X)
mark#(sel(X1, X2)) → mark#(X1)mark#(sel(cons(sel(s(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(f(_x81)))))
mark#(sel(cons(sel(f(_x111), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(_x81)))))mark#(sel(cons(sel(0, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), _x72)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), active(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))mark#(sel(cons(s(_x61), _x52), cons(_x41, _x42))) → active#(sel(active(cons(s(mark(_x61)), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))mark#(sel(cons(f(_x61), _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
active#(sel(0, cons(X, Y))) → mark#(X)mark#(sel(cons(f(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(s(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(s(_x61), _x32), cons(0, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(0), _x42))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), g(active(f(_x81)))))
mark#(sel(cons(sel(f(_x111), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))
mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(cons(sel(_x61, _x82), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))
mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(f(g(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(g(mark(_x91))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(cons(f(s(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(s(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(cons(sel(f(_x111), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))
mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))mark#(sel(cons(sel(f(cons(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(cons(mark(_x121), _x122)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
active#(g(0)) → mark#(s(0))mark#(sel(cons(sel(f(active(_x101)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x101)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))
mark#(sel(cons(s(_x61), mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(f(_x91), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(g(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(g(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(g(X)) → mark#(X)mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))
mark#(sel(cons(f(sel(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(sel(mark(_x91), mark(_x92))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(_x31, mark(mark(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), g(active(f(_x81)))))
mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))active#(f(X)) → mark#(cons(X, f(g(X))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x71, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(mark(cons(mark(_x61), f(g(mark(_x61))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(0, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))
mark#(sel(cons(sel(f(_x91), _x82), _x32), g(f(active(f(mark(_x91))))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x52), g(_x41))) → active#(sel(active(cons(f(mark(_x61)), _x52)), active(g(mark(_x41)))))
active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))
mark#(sel(cons(sel(f(_x111), _x82), _x32), g(f(active(f(_x111)))))) → active#(sel(active(cons(active(sel(active(f(_x111)), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(X1, X2)) → mark#(X2)mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(0)))))))mark#(sel(cons(s(s(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(s(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(_x61, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(mark(_x91))), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), cons(mark(_x41), _x42)))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(sel(cons(s(_x61), _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(f(f(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(f(mark(_x91))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(active(0), mark(_x62))), _x52), active(g(active(f(_x81))))))mark#(sel(cons(sel(g(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(f(cons(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(cons(mark(_x91), _x92)))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))
mark#(sel(cons(0, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(0), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(s(_x81), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(_x81)), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))
mark#(sel(cons(sel(0, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(0))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x52), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))
mark#(sel(cons(sel(0, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))
mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(sel(0, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(mark(_x91), f(g(mark(_x91))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(f(_x81), _x32), g(_x41))) → active#(sel(active(cons(active(f(_x81)), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(f(_x111), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x111), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))mark#(cons(X1, X2)) → mark#(X1)
mark#(sel(cons(sel(f(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(s(g(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(g(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(f(_x61), mark(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0)))))))mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x61, mark(_x62)), g(f(_x71)))) → active#(sel(active(cons(_x61, _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(cons(active(s(mark(_x61))), _x32), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(0, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(_x91, f(g(_x91)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(_x61))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(_x61))))mark#(sel(cons(sel(f(_x91), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))mark#(sel(cons(sel(0, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(f(0), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(0))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(f(_x81)))))mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(_x31, mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))
mark#(g(X)) → active#(g(mark(X)))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(_x81)))))
mark#(sel(cons(cons(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x71), _x72)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(f(_x81)))))mark#(sel(cons(s(_x61), _x32), cons(_x61, _x62))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(_x61, _x62))))
active#(g(s(X))) → mark#(s(s(g(X))))mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(cons(active(f(mark(_x61))), _x32), active(g(mark(_x41)))))
mark#(sel(cons(f(_x61), _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(cons(mark(_x71), _x72))))))mark#(sel(cons(sel(f(_x91), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(0, mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(active(0), mark(_x62)), _x42)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))
mark#(sel(cons(sel(_x61, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(mark(_x71), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(sel(cons(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))
mark#(sel(cons(sel(_x61, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(_x111)), mark(_x62)), _x52)), active(g(active(f(_x81))))))
mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(f(_x61), _x32), g(g(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(g(mark(_x71)))))))
mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), g(active(f(_x81)))))
mark#(sel(cons(sel(f(_x91), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))mark#(sel(cons(sel(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x71), mark(_x72))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(f(_x91), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(f(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(f(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(_x111)), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x111), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(sel(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(f(mark(_x91)))))) → active#(sel(active(cons(active(sel(f(mark(_x91)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(f(_x111))))) → active#(sel(active(cons(active(sel(f(_x111), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), g(mark(_x41))))
mark#(sel(cons(sel(f(sel(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(sel(mark(_x121), mark(_x122))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(0), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(0))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(_x111), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(sel(f(mark(_x101)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x101)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(f(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(f(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(g(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(sel(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(sel(mark(_x91), mark(_x92))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))mark#(sel(cons(sel(f(_x91), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(s(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(s(mark(_x71)))))))mark#(sel(cons(s(cons(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(cons(mark(_x91), _x92)))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(0), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(0))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(s(_x61), _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(s(mark(_x71))), _x42))))
mark#(f(X)) → mark#(X)mark#(sel(cons(sel(_x61, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))
mark#(f(X)) → active#(f(mark(X)))mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(s(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(s(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(f(mark(_x71))))))mark#(sel(cons(_x31, mark(active(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(g(mark(_x91))))))))) 
active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(mark(_x71))))))) 
active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(0))))))) 
active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71))))))))) 
active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81)))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(mark(_x71)))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(mark(_x71)))))) 
active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(f(mark(_x91))))))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(cons(mark(_x91), _x92)))))))) 
active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(mark(_x71))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(s(mark(_x91))))))))) 
active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92))))))))) 
Thus, the rule mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71))))))) is replaced by the following rules:
mark#(sel(cons(sel(0, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, s(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(f(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(sel(_x61, _x62), mark(active(_x42))), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(cons(_x81, _x82), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(mark(_x71), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(sel(g(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, cons(_x91, _x92)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), mark(_x42)), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, sel(_x91, _x92)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x71, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(sel(_x61, _x62), mark(mark(_x42))), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x72), mark(_x52)), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, 0), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, g(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(s(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(sel(_x81, _x82), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, f(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(0)))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))

Problem 30: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(s(X)) → mark#(X)mark#(sel(X1, X2)) → mark#(X1)
mark#(sel(cons(sel(s(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2)))
mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(f(_x81)))))mark#(sel(cons(sel(f(_x111), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(_x81)))))
mark#(sel(cons(f(_x61), active(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))mark#(sel(cons(sel(0, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), _x72)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x52), cons(_x41, _x42))) → active#(sel(active(cons(s(mark(_x61)), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))mark#(sel(cons(f(_x61), _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
active#(sel(0, cons(X, Y))) → mark#(X)mark#(sel(cons(f(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(s(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(s(_x61), _x32), cons(0, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(0), _x42))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), g(active(f(_x81)))))
mark#(sel(cons(sel(_x61, _x62), mark(_x42)), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(_x111), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))
mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(0, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(cons(sel(_x61, _x82), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))
mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))mark#(sel(cons(f(g(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(g(mark(_x91))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(_x81)))))mark#(sel(cons(f(s(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(s(mark(_x91))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(f(_x111), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))
mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))mark#(sel(cons(sel(f(cons(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(cons(mark(_x121), _x122)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(cons(sel(_x61, cons(_x91, _x92)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(mark(_x71)))))))active#(g(0)) → mark#(s(0))
mark#(sel(cons(sel(f(active(_x101)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x101)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(g(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(g(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))mark#(g(X)) → mark#(X)
mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), mark(mark(_x42))), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(f(sel(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(sel(mark(_x91), mark(_x92))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(mark(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), g(active(f(_x81)))))
mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))
active#(f(X)) → mark#(cons(X, f(g(X))))mark#(sel(cons(sel(_x71, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(mark(cons(mark(_x61), f(g(mark(_x61))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(0, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))
mark#(sel(cons(sel(f(_x91), _x82), _x32), g(f(active(f(mark(_x91))))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(f(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(f(_x61), _x52), g(_x41))) → active#(sel(active(cons(f(mark(_x61)), _x52)), active(g(mark(_x41)))))
active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))
mark#(sel(cons(sel(f(_x111), _x82), _x32), g(f(active(f(_x111)))))) → active#(sel(active(cons(active(sel(active(f(_x111)), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(X1, X2)) → mark#(X2)mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(g(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(0)))))))
mark#(sel(cons(s(s(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(s(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(sel(_x61, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(mark(_x91))), mark(_x62)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), cons(mark(_x41), _x42)))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(sel(cons(s(_x61), _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(f(f(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(f(mark(_x91))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(active(0), mark(_x62))), _x52), active(g(active(f(_x81))))))mark#(sel(cons(sel(g(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(f(cons(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(cons(mark(_x91), _x92)))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))
mark#(sel(cons(0, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(0), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(s(_x81), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(_x81)), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))
mark#(sel(cons(sel(0, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(0))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x52), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))
mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))mark#(sel(cons(sel(0, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(0, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(mark(_x91), f(g(mark(_x91))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(f(_x81), _x32), g(_x41))) → active#(sel(active(cons(active(f(_x81)), _x32)), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x111), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))
mark#(sel(cons(sel(f(_x111), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(f(mark(_x71))), _x42))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(mark(_x71))))))mark#(cons(X1, X2)) → mark#(X1)
mark#(sel(cons(sel(f(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(s(g(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(g(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(f(_x61), mark(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0)))))))mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(0)))))))
mark#(sel(cons(_x61, mark(_x62)), g(f(_x71)))) → active#(sel(active(cons(_x61, _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(cons(active(s(mark(_x61))), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(0, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(_x91, f(g(_x91)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(_x61))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(_x61))))
mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(0, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(f(0), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(0))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(_x31, mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(sel(mark(_x71), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(_x81)))))mark#(g(X)) → active#(g(mark(X)))
mark#(sel(cons(cons(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x71), _x72)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(f(_x81)))))mark#(sel(cons(sel(_x71, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(_x61), _x32), cons(_x61, _x62))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(_x61, _x62))))active#(g(s(X))) → mark#(s(s(g(X))))
mark#(sel(cons(sel(_x61, g(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))mark#(sel(cons(sel(f(_x91), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(cons(mark(_x71), _x72))))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(cons(active(f(mark(_x61))), _x32), active(g(mark(_x41)))))
mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))
mark#(sel(cons(sel(0, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(active(0), mark(_x62)), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(0, mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(s(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(sel(_x61, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(cons(sel(0, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, s(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(mark(_x71), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(s(_x61), _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(cons(sel(cons(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))mark#(sel(cons(sel(f(_x111), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(_x111)), mark(_x62)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(_x81))))))mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))
mark#(sel(cons(sel(_x61, _x62), mark(active(_x42))), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(f(_x61), _x32), g(g(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(g(mark(_x71)))))))
mark#(sel(cons(sel(cons(_x81, _x82), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, sel(_x91, _x92)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), g(active(f(_x81)))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(sel(f(_x91), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))mark#(sel(cons(sel(f(_x91), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x72), mark(_x52)), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x71), mark(_x72))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(_x61, 0), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(s(f(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(f(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x111), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(_x111)), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(sel(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(f(mark(_x91)))))) → active#(sel(active(cons(active(sel(f(mark(_x91)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(f(_x111))))) → active#(sel(active(cons(active(sel(f(_x111), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), g(mark(_x41))))mark#(sel(cons(sel(f(sel(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(sel(mark(_x121), mark(_x122))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(0), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(0))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(f(_x111), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(sel(f(mark(_x101)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x101)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(sel(f(f(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(f(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(g(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(sel(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(sel(mark(_x91), mark(_x92))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))
mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))mark#(sel(cons(sel(f(_x91), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(cons(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(cons(mark(_x91), _x92)))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(f(_x61), _x32), g(s(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(s(mark(_x71)))))))
mark#(sel(cons(sel(f(_x111), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(0), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(0))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(s(_x61), _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(s(mark(_x71))), _x42))))mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(f(X)) → mark#(X)
mark#(f(X)) → active#(f(mark(X)))mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(s(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(s(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(sel(_x81, _x82), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, f(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(active(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(f(mark(_x71))))))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2))) 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
active#(sel(active(f(active(g(mark(_x61))))), mark(X2))) 
active#(sel(active(f(active(sel(mark(_x61), mark(_x62))))), mark(X2))) 
active#(sel(active(f(mark(_x31))), _x22)) 
active#(sel(active(f(active(f(mark(_x61))))), mark(X2))) 
active#(sel(active(f(mark(_x31))), active(sel(mark(_x41), mark(_x42))))) 
active#(sel(active(f(active(s(mark(_x61))))), mark(X2))) 
active#(sel(active(f(mark(_x31))), active(0))) 
active#(sel(active(f(mark(_x31))), active(f(mark(_x41))))) 
active#(sel(active(f(_x51)), mark(X2))) 
active#(sel(active(f(mark(_x31))), active(cons(mark(_x41), _x42)))) 
active#(sel(active(f(active(0))), mark(X2))) 
active#(sel(mark(cons(mark(_x31), f(g(mark(_x31))))), mark(X2))) 
active#(sel(f(mark(_x31)), mark(X2))) 
active#(sel(active(f(mark(_x31))), active(s(mark(_x41))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), mark(X2))) 
active#(sel(active(f(mark(_x31))), active(g(mark(_x41))))) 
Thus, the rule mark#(sel(f(_x31), X2)) → active#(sel(active(f(mark(_x31))), mark(X2))) is replaced by the following rules:
mark#(sel(f(g(_x61)), X2)) → active#(sel(active(f(active(g(mark(_x61))))), mark(X2)))mark#(sel(f(_x31), s(_x41))) → active#(sel(active(f(mark(_x31))), active(s(mark(_x41)))))
mark#(sel(f(sel(_x61, _x62)), X2)) → active#(sel(active(f(active(sel(mark(_x61), mark(_x62))))), mark(X2)))mark#(sel(f(_x51), X2)) → active#(sel(active(f(_x51)), mark(X2)))
mark#(sel(f(_x31), g(_x41))) → active#(sel(active(f(mark(_x31))), active(g(mark(_x41)))))mark#(sel(f(_x31), 0)) → active#(sel(active(f(mark(_x31))), active(0)))
mark#(sel(f(s(_x61)), X2)) → active#(sel(active(f(active(s(mark(_x61))))), mark(X2)))mark#(sel(f(_x31), cons(_x41, _x42))) → active#(sel(active(f(mark(_x31))), active(cons(mark(_x41), _x42))))
mark#(sel(f(_x31), sel(_x41, _x42))) → active#(sel(active(f(mark(_x31))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(_x31), f(_x41))) → active#(sel(active(f(mark(_x31))), active(f(mark(_x41)))))
mark#(sel(f(f(_x61)), X2)) → active#(sel(active(f(active(f(mark(_x61))))), mark(X2)))mark#(sel(f(_x31), X2)) → active#(sel(mark(cons(mark(_x31), f(g(mark(_x31))))), mark(X2)))
mark#(sel(f(_x31), X2)) → active#(sel(f(mark(_x31)), mark(X2)))mark#(sel(f(0), X2)) → active#(sel(active(f(active(0))), mark(X2)))
mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), mark(X2)))mark#(sel(f(_x31), _x22)) → active#(sel(active(f(mark(_x31))), _x22))

Problem 31: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(s(X)) → mark#(X)mark#(sel(X1, X2)) → mark#(X1)
mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), mark(X2)))mark#(sel(f(g(_x61)), X2)) → active#(sel(active(f(active(g(mark(_x61))))), mark(X2)))
mark#(sel(f(sel(_x61, _x62)), X2)) → active#(sel(active(f(active(sel(mark(_x61), mark(_x62))))), mark(X2)))mark#(sel(cons(sel(s(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))mark#(sel(f(_x31), g(_x41))) → active#(sel(active(f(mark(_x31))), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(f(s(_x61)), X2)) → active#(sel(active(f(active(s(mark(_x61))))), mark(X2)))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(f(_x81)))))mark#(sel(cons(sel(f(_x111), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))
mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(_x81)))))
mark#(sel(cons(sel(0, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), _x72)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), active(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(s(_x61), _x52), cons(_x41, _x42))) → active#(sel(active(cons(s(mark(_x61)), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))mark#(sel(cons(f(_x61), _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
active#(sel(0, cons(X, Y))) → mark#(X)mark#(sel(cons(f(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(s(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(s(_x61), _x32), cons(0, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(0), _x42))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), g(active(f(_x81)))))
mark#(sel(cons(sel(f(_x111), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), mark(_x42)), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(mark(_x71)))))))
mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))
mark#(sel(f(_x31), s(_x41))) → active#(sel(active(f(mark(_x31))), active(s(mark(_x41)))))mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(cons(_x31, mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(f(g(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(g(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(f(_x31), _x22)) → active#(sel(active(f(mark(_x31))), _x22))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(cons(f(s(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(s(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(cons(sel(f(_x111), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))
mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))mark#(sel(cons(sel(f(cons(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(cons(mark(_x121), _x122)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(_x31), X2)) → active#(sel(mark(cons(mark(_x31), f(g(mark(_x31))))), mark(X2)))
mark#(sel(cons(sel(_x61, cons(_x91, _x92)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
active#(g(0)) → mark#(s(0))mark#(sel(cons(sel(f(active(_x101)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x101)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))
mark#(sel(cons(s(_x61), mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(f(_x91), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(g(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(g(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(g(X)) → mark#(X)mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), mark(mark(_x42))), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(f(sel(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(sel(mark(_x91), mark(_x92))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), g(active(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(mark(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), g(active(f(_x81)))))mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))active#(f(X)) → mark#(cons(X, f(g(X))))
mark#(sel(cons(sel(_x71, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(mark(cons(mark(_x61), f(g(mark(_x61))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(sel(0, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x91), _x82), _x32), g(f(active(f(mark(_x91))))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), _x82)), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(_x51), X2)) → active#(sel(active(f(_x51)), mark(X2)))mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(f(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(f(_x31), sel(_x41, _x42))) → active#(sel(active(f(mark(_x31))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(f(_x61), _x52), g(_x41))) → active#(sel(active(cons(f(mark(_x61)), _x52)), active(g(mark(_x41)))))active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))
mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))mark#(sel(cons(sel(f(_x111), _x82), _x32), g(f(active(f(_x111)))))) → active#(sel(active(cons(active(sel(active(f(_x111)), _x82)), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))mark#(sel(X1, X2)) → mark#(X2)
mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(g(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(0)))))))mark#(sel(f(0), X2)) → active#(sel(active(f(active(0))), mark(X2)))
mark#(sel(cons(s(s(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(s(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(sel(_x61, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(mark(_x91))), mark(_x62)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), cons(mark(_x41), _x42)))
mark#(sel(f(_x31), cons(_x41, _x42))) → active#(sel(active(f(mark(_x31))), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(s(_x61), _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(f(f(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(f(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(sel(_x61, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(active(0), mark(_x62))), _x52), active(g(active(f(_x81))))))
mark#(sel(cons(sel(g(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))
mark#(sel(cons(f(cons(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(cons(mark(_x91), _x92)))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))mark#(sel(cons(0, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(0), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))mark#(sel(cons(s(_x81), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(_x81)), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))mark#(sel(cons(sel(0, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(0))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x52), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(f(_x31), 0)) → active#(sel(active(f(mark(_x31))), active(0)))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))
mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))mark#(sel(cons(sel(0, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(0, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(mark(_x91), f(g(mark(_x91))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(cons(f(_x81), _x32), g(_x41))) → active#(sel(active(cons(active(f(_x81)), _x32)), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x111), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))
mark#(sel(cons(sel(f(_x111), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(f(mark(_x71))), _x42))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(mark(_x71))))))mark#(cons(X1, X2)) → mark#(X1)
mark#(sel(cons(sel(f(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(f(_x61), mark(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))
mark#(sel(cons(s(g(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(g(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(0)))))))
mark#(sel(cons(_x61, mark(_x62)), g(f(_x71)))) → active#(sel(active(cons(_x61, _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(cons(active(s(mark(_x61))), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(0, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(_x91, f(g(_x91)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(_x61))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(_x61))))
mark#(sel(cons(sel(f(_x91), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))
mark#(sel(cons(sel(0, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(f(0), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(0))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(mark(_x71), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))
mark#(g(X)) → active#(g(mark(X)))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(_x81)))))
mark#(sel(cons(cons(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x71), _x72)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(f(_x81)))))mark#(sel(cons(sel(_x71, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(_x61), _x32), cons(_x61, _x62))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(_x61, _x62))))active#(g(s(X))) → mark#(s(s(g(X))))
mark#(sel(cons(sel(_x61, g(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(cons(active(f(mark(_x61))), _x32), active(g(mark(_x41)))))
mark#(sel(cons(f(_x61), _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(cons(mark(_x71), _x72))))))mark#(sel(cons(sel(f(_x91), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(0, mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(active(0), mark(_x62)), _x42)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(s(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))mark#(sel(cons(sel(_x61, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))
mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(_x81)))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(0, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, s(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(mark(_x71), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(sel(cons(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))mark#(sel(cons(sel(_x61, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x111), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(_x111)), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))
mark#(sel(cons(sel(_x61, _x62), mark(active(_x42))), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(cons(_x81, _x82), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(f(_x61), _x32), g(g(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(g(mark(_x71)))))))mark#(sel(f(_x31), X2)) → active#(sel(f(mark(_x31)), mark(X2)))
mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(sel(_x61, sel(_x91, _x92)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(sel(f(_x91), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))mark#(sel(cons(sel(_x61, _x72), mark(_x52)), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x71), mark(_x72))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, 0), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(f(_x91), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(f(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(f(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(_x111)), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x111), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(f(f(_x61)), X2)) → active#(sel(active(f(active(f(mark(_x61))))), mark(X2)))
mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(sel(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(f(mark(_x91)))))) → active#(sel(active(cons(active(sel(f(mark(_x91)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(f(_x111))))) → active#(sel(active(cons(active(sel(f(_x111), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), g(mark(_x41))))mark#(sel(cons(sel(f(sel(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(sel(mark(_x121), mark(_x122))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(0), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(0))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(sel(f(_x111), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(sel(f(mark(_x101)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x101)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(f(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(f(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(g(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(f(_x31), f(_x41))) → active#(sel(active(f(mark(_x31))), active(f(mark(_x41)))))mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(s(sel(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(sel(mark(_x91), mark(_x92))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))
mark#(sel(cons(sel(f(_x91), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(s(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(s(mark(_x71)))))))
mark#(sel(cons(s(cons(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(cons(mark(_x91), _x92)))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(f(0), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(0))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x111), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))
mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(_x61), _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(s(mark(_x71))), _x42))))mark#(f(X)) → mark#(X)
mark#(sel(cons(sel(_x61, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(f(X)) → active#(f(mark(X)))
mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(s(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(s(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(sel(_x81, _x82), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, f(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(f(mark(_x71))))))
mark#(sel(cons(_x31, mark(active(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), mark(X2))) 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
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), mark(_x42))))) 
active#(sel(active(f(active(cons(_x71, _x72)))), mark(X2))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), _x22)) 
active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), mark(X2))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(g(mark(_x41))))) 
active#(sel(active(f(active(cons(mark(_x61), _x72)))), mark(X2))) 
active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), mark(X2))) 
active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), mark(X2))) 
active#(sel(f(active(cons(mark(_x61), _x62))), mark(X2))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(cons(mark(_x41), _x42)))) 
active#(sel(active(f(cons(mark(_x61), _x62))), mark(X2))) 
active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), mark(X2))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(s(mark(_x41))))) 
active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), mark(X2))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(mark(_x41))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(0))) 
active#(sel(active(f(active(cons(active(0), _x62)))), mark(X2))) 
active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), mark(X2))) 
Thus, the rule mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), mark(X2))) is replaced by the following rules:
mark#(sel(f(cons(g(_x81), _x62)), X2)) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), mark(X2)))mark#(sel(f(cons(_x61, _x62)), _x22)) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), _x22))
mark#(sel(f(cons(_x61, active(_x72))), X2)) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), mark(X2)))mark#(sel(f(cons(_x61, _x62)), 0)) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(0)))
mark#(sel(f(cons(_x61, _x62)), cons(_x41, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(cons(mark(_x41), _x42))))mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), g(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(g(mark(_x41)))))mark#(sel(f(cons(_x71, _x72)), X2)) → active#(sel(active(f(active(cons(_x71, _x72)))), mark(X2)))
mark#(sel(f(cons(_x61, _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(s(_x81), _x62)), X2)) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), mark(X2)))
mark#(sel(f(cons(cons(_x81, _x82), _x62)), X2)) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), mark(X2)))mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(active(f(cons(mark(_x61), _x62))), mark(X2)))
mark#(sel(f(cons(_x61, _x62)), s(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(s(mark(_x41)))))mark#(sel(f(cons(f(_x81), _x62)), X2)) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), mark(X2)))
mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(f(active(cons(mark(_x61), _x62))), mark(X2)))mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), mark(X2)))
mark#(sel(f(cons(0, _x62)), X2)) → active#(sel(active(f(active(cons(active(0), _x62)))), mark(X2)))mark#(sel(f(cons(_x61, mark(_x72))), X2)) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), mark(X2)))
mark#(sel(f(cons(sel(_x81, _x82), _x62)), X2)) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), mark(X2)))

Problem 32: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(mark(_x41)))))mark#(sel(f(cons(_x61, _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(s(X)) → mark#(X)mark#(sel(X1, X2)) → mark#(X1)
mark#(sel(f(cons(g(_x81), _x62)), X2)) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), mark(X2)))mark#(sel(f(g(_x61)), X2)) → active#(sel(active(f(active(g(mark(_x61))))), mark(X2)))
mark#(sel(f(sel(_x61, _x62)), X2)) → active#(sel(active(f(active(sel(mark(_x61), mark(_x62))))), mark(X2)))mark#(sel(cons(sel(s(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))mark#(sel(f(_x31), g(_x41))) → active#(sel(active(f(mark(_x31))), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(f(s(_x61)), X2)) → active#(sel(active(f(active(s(mark(_x61))))), mark(X2)))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(f(_x81)))))mark#(sel(cons(sel(f(_x111), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(active(f(cons(mark(_x61), _x62))), mark(X2)))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(_x81)))))mark#(sel(cons(f(_x61), active(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))
mark#(sel(cons(sel(0, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), _x72)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(s(_x61), _x52), cons(_x41, _x42))) → active#(sel(active(cons(s(mark(_x61)), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))
mark#(sel(cons(f(_x61), _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x82), _x32), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91)))))))))active#(sel(0, cons(X, Y))) → mark#(X)
mark#(sel(cons(f(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))
mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))mark#(sel(cons(s(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(g(mark(_x71))), _x42))))
mark#(sel(cons(s(_x61), _x32), cons(0, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(0), _x42))))mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))
mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(cons(sel(_x61, _x62), mark(_x42)), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x111), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))
mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))mark#(sel(f(_x31), s(_x41))) → active#(sel(active(f(mark(_x31))), active(s(mark(_x41)))))
mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(0, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(cons(sel(_x61, _x82), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))
mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))mark#(sel(cons(f(g(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(g(mark(_x91))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(f(_x31), _x22)) → active#(sel(active(f(mark(_x31))), _x22))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(cons(f(s(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(s(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x111), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))mark#(sel(f(cons(_x71, _x72)), X2)) → active#(sel(active(f(active(cons(_x71, _x72)))), mark(X2)))
mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))mark#(sel(cons(sel(f(cons(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(cons(mark(_x121), _x122)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(cons(cons(_x81, _x82), _x62)), X2)) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), mark(X2)))mark#(sel(f(_x31), X2)) → active#(sel(mark(cons(mark(_x31), f(g(mark(_x31))))), mark(X2)))
mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(cons(sel(_x61, cons(_x91, _x92)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(mark(_x71)))))))active#(g(0)) → mark#(s(0))
mark#(sel(cons(sel(f(active(_x101)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x101)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(cons(_x61, mark(_x72))), X2)) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), mark(X2)))mark#(sel(cons(sel(f(g(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(g(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(f(cons(sel(_x81, _x82), _x62)), X2)) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), mark(X2)))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))mark#(g(X)) → mark#(X)
mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), mark(mark(_x42))), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(f(sel(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(sel(mark(_x91), mark(_x92))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(mark(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), g(active(f(_x81)))))
mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))
active#(f(X)) → mark#(cons(X, f(g(X))))mark#(sel(cons(sel(_x71, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(mark(cons(mark(_x61), f(g(mark(_x61))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(sel(0, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(f(cons(_x61, active(_x72))), X2)) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), mark(X2)))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x91), _x82), _x32), g(f(active(f(mark(_x91))))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), _x82)), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(_x51), X2)) → active#(sel(active(f(_x51)), mark(X2)))mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), 0)) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(0)))mark#(sel(cons(_x31, mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(mark(_x71))))))mark#(sel(cons(sel(f(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(_x31), sel(_x41, _x42))) → active#(sel(active(f(mark(_x31))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(f(_x61), _x52), g(_x41))) → active#(sel(active(cons(f(mark(_x61)), _x52)), active(g(mark(_x41)))))
active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))
mark#(sel(cons(sel(f(_x111), _x82), _x32), g(f(active(f(_x111)))))) → active#(sel(active(cons(active(sel(active(f(_x111)), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(X1, X2)) → mark#(X2)mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(g(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(0)))))))
mark#(sel(f(0), X2)) → active#(sel(active(f(active(0))), mark(X2)))mark#(sel(cons(s(s(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(s(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(_x61, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(mark(_x91))), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))
mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), cons(mark(_x41), _x42)))mark#(sel(f(_x31), cons(_x41, _x42))) → active#(sel(active(f(mark(_x31))), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(sel(cons(s(_x61), _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(f(f(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(f(mark(_x91))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(active(0), mark(_x62))), _x52), active(g(active(f(_x81))))))mark#(sel(cons(sel(g(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(f(cons(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(cons(mark(_x91), _x92)))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(f(cons(s(_x81), _x62)), X2)) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), mark(X2)))mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))mark#(sel(cons(0, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(0), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))mark#(sel(f(cons(f(_x81), _x62)), X2)) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), mark(X2)))
mark#(sel(cons(s(_x81), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(_x81)), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))
mark#(sel(cons(sel(0, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(0))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x52), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(f(_x31), 0)) → active#(sel(active(f(mark(_x31))), active(0)))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))
mark#(sel(cons(sel(0, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))
mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(sel(0, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(mark(_x91), f(g(mark(_x91))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(f(_x81), _x32), g(_x41))) → active#(sel(active(cons(active(f(_x81)), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(f(_x111), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x111), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(f(cons(_x61, _x62)), cons(_x41, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))
mark#(cons(X1, X2)) → mark#(X1)mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(mark(_x71))))))
mark#(sel(f(cons(_x61, _x62)), g(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(_x31, mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(s(g(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(g(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(f(_x61), mark(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(f(active(cons(mark(_x61), _x62))), mark(X2)))mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(0)))))))mark#(sel(cons(_x61, mark(_x62)), g(f(_x71)))) → active#(sel(active(cons(_x61, _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(cons(active(s(mark(_x61))), _x32), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(0, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(_x91, f(g(_x91)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(_x61))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(_x61))))mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(sel(0, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(f(0), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(0))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(f(_x81)))))mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(_x31, mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(sel(mark(_x71), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(_x81)))))
mark#(g(X)) → active#(g(mark(X)))mark#(sel(cons(cons(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x71), _x72)), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(cons(sel(_x71, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(s(_x61), _x32), cons(_x61, _x62))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(_x61, _x62))))
active#(g(s(X))) → mark#(s(s(g(X))))mark#(sel(cons(sel(_x61, g(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(sel(f(_x91), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(cons(mark(_x71), _x72))))))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(cons(active(f(mark(_x61))), _x32), active(g(mark(_x41)))))mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))mark#(sel(cons(sel(0, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(active(0), mark(_x62)), _x42)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(0, mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(s(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(f(cons(_x61, _x62)), s(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(s(mark(_x41)))))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(sel(_x61, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(cons(sel(0, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, s(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(mark(_x71), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(s(_x61), _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(cons(sel(cons(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))mark#(sel(cons(sel(f(_x111), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(_x111)), mark(_x62)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(_x81))))))mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))
mark#(sel(cons(sel(_x61, _x62), mark(active(_x42))), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(f(_x61), _x32), g(g(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(g(mark(_x71)))))))
mark#(sel(cons(sel(cons(_x81, _x82), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(f(_x31), X2)) → active#(sel(f(mark(_x31)), mark(X2)))
mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, sel(_x91, _x92)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(sel(f(_x91), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))
mark#(sel(cons(sel(f(_x91), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x72), mark(_x52)), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x71), mark(_x72))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(sel(_x61, 0), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(cons(s(f(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(f(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(_x111), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(_x111)), mark(_x62))), _x32), active(g(active(f(_x81))))))mark#(sel(f(f(_x61)), X2)) → active#(sel(active(f(active(f(mark(_x61))))), mark(X2)))
mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(sel(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(f(mark(_x91)))))) → active#(sel(active(cons(active(sel(f(mark(_x91)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(f(_x111))))) → active#(sel(active(cons(active(sel(f(_x111), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), g(mark(_x41))))mark#(sel(f(cons(_x61, _x62)), _x22)) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), _x22))
mark#(sel(cons(sel(f(sel(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(sel(mark(_x121), mark(_x122))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(0), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(0))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(_x111), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(sel(f(mark(_x101)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x101)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(sel(f(f(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(f(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71))))))
mark#(sel(cons(g(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(f(_x31), f(_x41))) → active#(sel(active(f(mark(_x31))), active(f(mark(_x41)))))
mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(s(sel(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(sel(mark(_x91), mark(_x92))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))
mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))mark#(sel(cons(sel(f(_x91), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(cons(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(cons(mark(_x91), _x92)))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(f(_x61), _x32), g(s(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(s(mark(_x71)))))))
mark#(sel(cons(sel(f(_x111), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(0), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(0))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(s(_x61), _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(s(mark(_x71))), _x42))))mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(f(X)) → mark#(X)
mark#(f(X)) → active#(f(mark(X)))mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(s(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(s(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(sel(_x81, _x82), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, f(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(active(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(f(mark(_x71))))))
mark#(sel(f(cons(0, _x62)), X2)) → active#(sel(active(f(active(cons(active(0), _x62)))), mark(X2)))mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(mark(_x41))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(f(mark(_x41))))) 
active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(f(mark(_x41))))) 
active#(sel(f(active(cons(mark(_x61), _x62))), active(f(mark(_x41))))) 
active#(sel(active(f(cons(mark(_x61), _x62))), active(f(mark(_x41))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(_x61)))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(f(mark(_x71))))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(0))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(sel(mark(_x71), mark(_x72))))))) 
active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(f(mark(_x41))))) 
active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(f(mark(_x41))))) 
active#(sel(active(f(active(cons(_x71, _x72)))), active(f(mark(_x41))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(g(mark(_x71))))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), f(mark(_x41)))) 
active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(f(mark(_x41))))) 
active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(f(mark(_x41))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(cons(mark(_x71), _x72)))))) 
active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(f(mark(_x41))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), mark(cons(mark(_x41), f(g(mark(_x41))))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(s(mark(_x71))))))) 
active#(sel(active(f(active(cons(active(0), _x62)))), active(f(mark(_x41))))) 
Thus, the rule mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(mark(_x41))))) is replaced by the following rules:
mark#(sel(f(cons(_x61, _x62)), f(_x61))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(_x61))))mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(f(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), f(mark(_x41))))mark#(sel(f(cons(cons(_x81, _x82), _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(f(mark(_x41)))))
mark#(sel(f(cons(_x61, mark(_x72))), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(f(mark(_x41)))))mark#(sel(f(cons(_x61, _x62)), f(0))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(0)))))
mark#(sel(f(cons(_x61, _x62)), f(cons(mark(_x61), _x62)))) → active#(sel(active(f(cons(mark(_x61), _x62))), active(f(mark(_x41)))))mark#(sel(f(cons(_x71, _x72)), f(_x41))) → active#(sel(active(f(active(cons(_x71, _x72)))), active(f(mark(_x41)))))
mark#(sel(f(cons(sel(_x81, _x82), _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(f(mark(_x41)))))mark#(sel(f(cons(s(_x81), _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(f(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), f(f(_x71)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(f(mark(_x71)))))))mark#(sel(f(cons(f(_x81), _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(f(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), mark(cons(mark(_x41), f(g(mark(_x41)))))))mark#(sel(f(cons(_x61, active(_x72))), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(f(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), f(cons(_x71, _x72)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(cons(mark(_x71), _x72))))))mark#(sel(f(cons(g(_x81), _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(f(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), f(sel(_x71, _x72)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(sel(mark(_x71), mark(_x72)))))))mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(f(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), f(g(_x71)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(g(mark(_x71)))))))mark#(sel(f(cons(_x61, _x62)), f(s(_x71)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(s(mark(_x71)))))))
mark#(sel(f(cons(0, _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(0), _x62)))), active(f(mark(_x41)))))

Problem 33: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(f(mark(_x41)))))mark#(sel(f(cons(_x61, _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(s(X)) → mark#(X)mark#(sel(X1, X2)) → mark#(X1)
mark#(sel(f(cons(g(_x81), _x62)), X2)) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), mark(X2)))mark#(sel(f(g(_x61)), X2)) → active#(sel(active(f(active(g(mark(_x61))))), mark(X2)))
mark#(sel(f(sel(_x61, _x62)), X2)) → active#(sel(active(f(active(sel(mark(_x61), mark(_x62))))), mark(X2)))mark#(sel(cons(sel(s(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))mark#(sel(f(_x31), g(_x41))) → active#(sel(active(f(mark(_x31))), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(f(s(_x61)), X2)) → active#(sel(active(f(active(s(mark(_x61))))), mark(X2)))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(f(_x81)))))mark#(sel(cons(sel(f(_x111), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(active(f(cons(mark(_x61), _x62))), mark(X2)))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(_x81)))))mark#(sel(cons(sel(0, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), _x72)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), active(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(s(_x61), _x52), cons(_x41, _x42))) → active#(sel(active(cons(s(mark(_x61)), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))
mark#(sel(cons(f(_x61), _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x82), _x32), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), f(mark(_x41))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91)))))))))
active#(sel(0, cons(X, Y))) → mark#(X)mark#(sel(cons(f(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(s(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(f(cons(sel(_x81, _x82), _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(f(mark(_x41)))))
mark#(sel(cons(s(_x61), _x32), cons(0, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(0), _x42))))mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))
mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(cons(sel(f(_x111), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x42)), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(mark(_x71)))))))mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))
mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))mark#(sel(f(_x31), s(_x41))) → active#(sel(active(f(mark(_x31))), active(s(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), f(_x61))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(_x61))))mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(f(cons(_x61, mark(_x72))), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(f(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(cons(sel(_x61, _x82), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))
mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))mark#(sel(cons(f(g(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(g(mark(_x91))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(f(cons(_x61, _x62)), f(cons(_x71, _x72)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(cons(mark(_x71), _x72))))))
mark#(sel(f(_x31), _x22)) → active#(sel(active(f(mark(_x31))), _x22))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(cons(f(s(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(s(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(f(cons(cons(_x81, _x82), _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(f(mark(_x41)))))mark#(sel(cons(sel(f(_x111), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))mark#(sel(f(cons(_x71, _x72)), X2)) → active#(sel(active(f(active(cons(_x71, _x72)))), mark(X2)))
mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))mark#(sel(f(cons(cons(_x81, _x82), _x62)), X2)) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), mark(X2)))
mark#(sel(cons(sel(f(cons(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(cons(mark(_x121), _x122)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(_x31), X2)) → active#(sel(mark(cons(mark(_x31), f(g(mark(_x31))))), mark(X2)))mark#(sel(cons(sel(_x61, cons(_x91, _x92)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(f(cons(g(_x81), _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(f(mark(_x41)))))
active#(g(0)) → mark#(s(0))mark#(sel(cons(sel(f(active(_x101)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x101)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))
mark#(sel(cons(s(_x61), mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(f(cons(_x61, mark(_x72))), X2)) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), mark(X2)))
mark#(sel(cons(sel(f(g(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(g(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(f(cons(sel(_x81, _x82), _x62)), X2)) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), mark(X2)))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))
mark#(g(X)) → mark#(X)mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), mark(mark(_x42))), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(f(sel(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(sel(mark(_x91), mark(_x92))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), g(active(f(mark(_x71))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(mark(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), g(active(f(_x81)))))mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))active#(f(X)) → mark#(cons(X, f(g(X))))
mark#(sel(cons(sel(_x71, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(mark(cons(mark(_x61), f(g(mark(_x61))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))mark#(sel(f(cons(0, _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(0), _x62)))), active(f(mark(_x41)))))
mark#(sel(cons(sel(0, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(f(cons(_x61, active(_x72))), X2)) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), mark(X2)))
mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x91), _x82), _x32), g(f(active(f(mark(_x91))))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), _x82)), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(_x51), X2)) → active#(sel(active(f(_x51)), mark(X2)))mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), 0)) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(0)))mark#(sel(cons(_x31, mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(mark(_x71))))))mark#(sel(cons(sel(f(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(_x31), sel(_x41, _x42))) → active#(sel(active(f(mark(_x31))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(f(_x61), _x52), g(_x41))) → active#(sel(active(cons(f(mark(_x61)), _x52)), active(g(mark(_x41)))))
active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))
mark#(sel(cons(sel(f(_x111), _x82), _x32), g(f(active(f(_x111)))))) → active#(sel(active(cons(active(sel(active(f(_x111)), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(X1, X2)) → mark#(X2)mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(g(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(0)))))))
mark#(sel(f(0), X2)) → active#(sel(active(f(active(0))), mark(X2)))mark#(sel(cons(s(s(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(s(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(_x61, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(mark(_x91))), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))
mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), cons(mark(_x41), _x42)))mark#(sel(f(_x31), cons(_x41, _x42))) → active#(sel(active(f(mark(_x31))), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(sel(cons(s(_x61), _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))
mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(f(f(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(f(mark(_x91))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(_x61, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(active(0), mark(_x62))), _x52), active(g(active(f(_x81))))))mark#(sel(cons(sel(g(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(f(cons(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(cons(mark(_x91), _x92)))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(f(cons(s(_x81), _x62)), X2)) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), mark(X2)))mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))mark#(sel(cons(0, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(0), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))mark#(sel(f(cons(_x61, active(_x72))), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(f(mark(_x41)))))
mark#(sel(f(cons(f(_x81), _x62)), X2)) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), mark(X2)))mark#(sel(cons(s(_x81), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(_x81)), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))mark#(sel(f(cons(_x61, _x62)), f(g(_x71)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(g(mark(_x71)))))))
mark#(sel(cons(sel(0, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(0))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x52), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32), active(g(active(f(_x81))))))mark#(sel(cons(s(_x61), active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(f(_x31), 0)) → active#(sel(active(f(mark(_x31))), active(0)))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(f(cons(_x61, _x62)), f(cons(mark(_x61), _x62)))) → active#(sel(active(f(cons(mark(_x61), _x62))), active(f(mark(_x41)))))mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))
mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(cons(sel(0, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))mark#(sel(f(cons(f(_x81), _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(f(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(mark(_x91), f(g(mark(_x91))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x81), _x32), g(_x41))) → active#(sel(active(cons(active(f(_x81)), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(f(_x111), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x111), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(f(cons(_x61, _x62)), cons(_x41, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(mark(_x71))))))mark#(cons(X1, X2)) → mark#(X1)
mark#(sel(f(cons(_x61, _x62)), g(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(_x31, mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(f(_x61), mark(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))mark#(sel(cons(s(g(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(g(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), mark(cons(mark(_x41), f(g(mark(_x41)))))))
mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0)))))))
mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), mark(X2)))mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(f(active(cons(mark(_x61), _x62))), mark(X2)))
mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(0)))))))
mark#(sel(cons(_x61, mark(_x62)), g(f(_x71)))) → active#(sel(active(cons(_x61, _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(cons(active(s(mark(_x61))), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(0, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(_x91, f(g(_x91)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(_x61))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(_x61))))
mark#(sel(cons(sel(f(_x91), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))
mark#(sel(cons(sel(0, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(f(0), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(0))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(f(_x81)))))
mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(mark(_x71), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))
mark#(g(X)) → active#(g(mark(X)))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(_x81)))))
mark#(sel(cons(cons(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x71), _x72)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(f(_x81)))))mark#(sel(cons(sel(_x71, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(_x61), _x32), cons(_x61, _x62))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(_x61, _x62))))active#(g(s(X))) → mark#(s(s(g(X))))
mark#(sel(cons(sel(_x61, g(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))
mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(cons(active(f(mark(_x61))), _x32), active(g(mark(_x41)))))
mark#(sel(cons(f(_x61), _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(cons(mark(_x71), _x72))))))mark#(sel(cons(sel(f(_x91), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(0, mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(active(0), mark(_x62)), _x42)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(s(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(f(cons(_x61, _x62)), s(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(s(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))
mark#(sel(cons(sel(_x61, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(0, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, s(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(mark(_x71), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(sel(cons(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))mark#(sel(f(cons(_x61, _x62)), f(0))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(0)))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))mark#(sel(cons(sel(_x61, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x111), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(_x111)), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(f(cons(_x71, _x72)), f(_x41))) → active#(sel(active(f(active(cons(_x71, _x72)))), active(f(mark(_x41)))))
mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))mark#(sel(cons(sel(_x61, _x62), mark(active(_x42))), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(_x81))))))mark#(sel(cons(sel(0, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(cons(_x81, _x82), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(f(_x61), _x32), g(g(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(g(mark(_x71)))))))
mark#(sel(f(_x31), X2)) → active#(sel(f(mark(_x31)), mark(X2)))mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(_x61, sel(_x91, _x92)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), g(active(f(_x81)))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(sel(f(_x91), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))
mark#(sel(cons(sel(_x61, _x72), mark(_x52)), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x71), mark(_x72))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, 0), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))
mark#(sel(cons(sel(f(_x91), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(s(f(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(f(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(_x111)), mark(_x62))), _x32), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(f(_x61)), X2)) → active#(sel(active(f(active(f(mark(_x61))))), mark(X2)))mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(f(cons(_x61, _x62)), f(sel(_x71, _x72)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(sel(mark(_x71), mark(_x72)))))))mark#(sel(cons(sel(0, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(sel(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(f(mark(_x41)))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(f(mark(_x91)))))) → active#(sel(active(cons(active(sel(f(mark(_x91)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(f(_x111))))) → active#(sel(active(cons(active(sel(f(_x111), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(f(cons(_x61, _x62)), _x22)) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), _x22))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), g(mark(_x41))))mark#(sel(cons(sel(f(sel(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(sel(mark(_x121), mark(_x122))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(0), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(0))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(cons(sel(f(_x111), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(sel(f(mark(_x101)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x101)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(f(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(f(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71))))))mark#(sel(cons(g(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(f(_x31), f(_x41))) → active#(sel(active(f(mark(_x31))), active(f(mark(_x41)))))mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(s(sel(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(sel(mark(_x91), mark(_x92))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))
mark#(sel(cons(sel(f(_x91), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(f(_x61), _x32), g(s(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(s(mark(_x71)))))))
mark#(sel(cons(s(cons(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(cons(mark(_x91), _x92)))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(f(0), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(0))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x111), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(f(cons(_x61, _x62)), f(s(_x71)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(s(mark(_x71)))))))
mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(s(_x61), _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(s(mark(_x71))), _x42))))
mark#(f(X)) → mark#(X)mark#(sel(cons(sel(_x61, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))
mark#(f(X)) → active#(f(mark(X)))mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(s(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(s(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(f(cons(s(_x81), _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(f(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), f(f(_x71)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(f(mark(_x71)))))))mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(sel(_x81, _x82), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, f(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(f(mark(_x71))))))mark#(sel(cons(_x31, mark(active(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(cons(0, _x62)), X2)) → active#(sel(active(f(active(cons(active(0), _x62)))), mark(X2)))mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(f(cons(_x61, _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), mark(_x42))))) 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
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(s(mark(_x81))))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(f(mark(_x81))))))) 
active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(mark(_x41), mark(_x42))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(_x61, mark(_x42))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(f(mark(_x71))), mark(_x42))))) 
active#(sel(active(f(cons(mark(_x61), _x62))), active(sel(mark(_x41), mark(_x42))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(cons(mark(_x71), _x72)), mark(_x42))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), sel(mark(_x41), mark(_x42)))) 
active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(mark(_x41), mark(_x42))))) 
active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(sel(mark(_x41), mark(_x42))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(0), mark(_x42))))) 
active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(mark(_x41), mark(_x42))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(sel(mark(_x71), mark(_x72))), mark(_x42))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(sel(mark(_x81), mark(_x82))))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(g(mark(_x81))))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(0))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(s(mark(_x71))), mark(_x42))))) 
active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(sel(mark(_x41), mark(_x42))))) 
active#(sel(active(f(active(cons(_x71, _x72)))), active(sel(mark(_x41), mark(_x42))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(mark(_x71))), mark(_x42))))) 
active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(mark(_x41), mark(_x42))))) 
active#(sel(active(f(active(cons(active(0), _x62)))), active(sel(mark(_x41), mark(_x42))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), _x62)))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(cons(mark(_x81), _x82)))))) 
active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(sel(mark(_x41), mark(_x42))))) 
active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(sel(mark(_x41), mark(_x42))))) 
Thus, the rule mark#(sel(f(cons(_x61, _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), mark(_x42))))) is replaced by the following rules:
mark#(sel(f(cons(_x61, mark(_x42))), sel(_x61, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(_x61, mark(_x42)))))mark#(sel(f(cons(_x61, _x62)), sel(_x41, g(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(g(mark(_x81)))))))
mark#(sel(f(cons(_x61, _x62)), sel(_x41, _x42))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(_x61, _x62)), sel(_x41, _x42))) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(f(_x81), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(_x61, _x62)), sel(_x41, f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(f(mark(_x81)))))))
mark#(sel(f(cons(_x71, _x72)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(_x71, _x72)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(_x61, _x62)), sel(_x41, cons(_x81, _x82)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(cons(mark(_x81), _x82))))))
mark#(sel(f(cons(_x61, _x62)), sel(cons(_x71, _x72), _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(cons(mark(_x71), _x72)), mark(_x42)))))mark#(sel(f(cons(_x61, active(_x72))), sel(_x41, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(_x61, _x62)), sel(_x41, 0))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(0)))))mark#(sel(f(cons(mark(_x41), _x62)), sel(_x41, _x62))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), _x62))))
mark#(sel(f(cons(_x61, _x62)), sel(f(_x71), _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(f(mark(_x71))), mark(_x42)))))mark#(sel(f(cons(_x61, _x62)), sel(cons(mark(_x61), _x62), _x42))) → active#(sel(active(f(cons(mark(_x61), _x62))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(_x61, _x62)), sel(s(_x71), _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(s(mark(_x71))), mark(_x42)))))
mark#(sel(f(cons(s(_x81), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(_x61, _x62)), sel(0, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(0), mark(_x42)))))
mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(mark(_x71))), mark(_x42)))))mark#(sel(f(cons(cons(_x81, _x82), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(_x61, _x62)), sel(_x41, s(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(s(mark(_x81)))))))mark#(sel(f(cons(_x61, _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), sel(mark(_x41), mark(_x42))))
mark#(sel(f(cons(_x61, mark(_x72))), sel(_x41, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(_x61, _x62)), sel(_x41, sel(_x81, _x82)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(sel(mark(_x81), mark(_x82)))))))
mark#(sel(f(cons(g(_x81), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(_x61, _x62)), sel(sel(_x71, _x72), _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(sel(mark(_x71), mark(_x72))), mark(_x42)))))
mark#(sel(f(cons(0, _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(0), _x62)))), active(sel(mark(_x41), mark(_x42)))))

Problem 34: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

mark#(sel(f(cons(s(_x81), _x62)), sel(_x41, _x62))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(mark(_x41), _x62))))mark#(sel(f(cons(_x61, _x62)), sel(g(_x81), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(_x81)), active(f(mark(_x81)))))))
mark#(s(X)) → mark#(X)mark#(sel(f(sel(g(_x91), f(g(_x91)))), _x32)) → active#(sel(f(active(sel(active(g(mark(_x91))), active(f(active(g(mark(_x91)))))))), _x32))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81))))))mark#(sel(f(cons(f(_x81), _x62)), sel(_x41, f(_x81)))) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(sel(mark(_x41), active(f(mark(_x81)))))))
mark#(sel(f(sel(g(_x91), f(f(_x91)))), _x32)) → active#(sel(f(active(sel(active(g(mark(_x91))), active(f(active(f(mark(_x91)))))))), _x32))mark#(sel(f(sel(_x71, _x62)), s(_x41))) → active#(sel(active(f(active(sel(_x71, mark(_x62))))), active(s(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(0)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(0)))))))mark#(sel(cons(sel(0, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), _x72)), _x52)), active(g(active(f(_x81))))))
mark#(sel(f(cons(_x81, mark(_x82))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(_x81, _x82)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(s(_x61)), f(_x41))) → active#(sel(active(f(active(s(mark(_x61))))), active(f(mark(_x41)))))
mark#(sel(f(cons(_x61, active(_x72))), sel(g(mark(_x61)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(mark(_x71))), active(f(mark(_x81)))))))mark#(sel(f(sel(_x61, s(_x91))), X2)) → active#(sel(active(f(active(sel(mark(_x61), active(s(mark(_x91))))))), mark(X2)))
mark#(sel(cons(s(_x61), _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(f(cons(_x61, _x62)), sel(g(s(_x91)), f(_x91)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(s(mark(_x91))))), active(f(_x91))))))
mark#(sel(f(cons(s(_x81), active(_x72))), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x72)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(f(_x101))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(f(mark(_x101)))))))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(f(cons(0, _x62)), sel(g(_x71), f(_x81)))) → active#(sel(active(f(active(cons(active(0), _x62)))), active(sel(active(g(mark(_x71))), active(f(mark(_x81)))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, f(_x131)))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(f(mark(_x131)))))))))))mark#(sel(cons(sel(_x61, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(X1, s(_x41))) → active#(sel(mark(X1), active(s(mark(_x41)))))mark#(sel(f(s(sel(_x81, _x82))), cons(cons(_x71, _x72), _x42))) → active#(sel(active(f(active(s(active(sel(mark(_x81), mark(_x82))))))), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(f(g(g(f(_x101)))), X2)) → active#(sel(active(f(active(g(active(g(active(f(mark(_x101))))))))), mark(X2)))mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(f(cons(0, _x62)), sel(_x41, f(_x81)))) → active#(sel(active(f(active(cons(active(0), _x62)))), active(sel(mark(_x41), active(f(mark(_x81)))))))
mark#(sel(f(sel(_x61, f(_x91))), X2)) → active#(sel(active(f(active(sel(mark(_x61), active(f(mark(_x91))))))), mark(X2)))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, cons(_x131, _x132)))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(cons(mark(_x131), _x132))))))))))
mark#(sel(f(cons(_x61, mark(_x72))), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(mark(_x81)))))))mark#(sel(cons(s(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(cons(_x61, mark(_x72))), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(f(mark(_x41)))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), mark(cons(active(sel(mark(_x101), mark(_x102))), f(g(active(sel(mark(_x101), mark(_x102)))))))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(f(sel(_x61, _x82)), _x22)) → active#(sel(active(f(active(sel(mark(_x61), _x82)))), _x22))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(f(cons(_x71, _x72)), sel(g(_x71), f(_x81)))) → active#(sel(active(f(active(cons(_x71, _x72)))), active(sel(active(g(mark(_x71))), active(f(mark(_x81)))))))
mark#(sel(cons(_x31, _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(s(mark(_x71))), _x42))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, 0))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(0)))))))))
mark#(sel(f(g(g(_x81))), f(_x41))) → active#(sel(active(f(active(g(active(g(mark(_x81))))))), active(f(mark(_x41)))))mark#(sel(f(cons(sel(0, _x82), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(active(0), mark(_x82))), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(_x31), g(_x41))) → active#(sel(active(f(mark(_x31))), g(mark(_x41))))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(mark(_x81)))))))
mark#(sel(f(sel(cons(_x81, _x82), _x62)), X2)) → active#(sel(active(f(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))))), mark(X2)))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(s(_x71), _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(active(s(mark(_x71))), mark(_x42)))))
mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(f(_x101))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(mark(_x71))), active(f(active(f(mark(_x101)))))))))mark#(sel(f(cons(_x61, _x62)), sel(_x41, 0))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(0)))))
mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(sel(_x121, _x122), _x102))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(active(sel(active(sel(mark(_x121), mark(_x122))), mark(_x102)))))))))
mark#(sel(f(s(0)), cons(_x41, _x42))) → active#(sel(active(f(active(s(active(0))))), active(cons(mark(_x41), _x42))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), f(active(sel(mark(_x101), mark(_x102))))))))
mark#(sel(cons(sel(_x61, _x62), mark(mark(_x42))), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(mark(_x71)))))))mark#(sel(f(cons(cons(_x81, _x82), _x62)), sel(_x41, f(_x81)))) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(sel(mark(_x41), active(f(mark(_x81)))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(_x81)))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(mark(_x71))), active(f(mark(_x81)))))))mark#(sel(f(sel(_x61, g(g(_x131)))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(g(active(g(mark(_x131))))))))), _x22))
mark#(sel(f(sel(_x61, _x62)), f(_x41))) → active#(sel(active(f(active(sel(mark(_x61), mark(_x62))))), active(f(mark(_x41)))))mark#(sel(f(sel(0, f(0))), _x22)) → active#(sel(active(f(active(sel(active(0), mark(cons(active(0), f(g(active(0))))))))), _x22))
mark#(sel(f(sel(g(_x91), f(_x101))), _x32)) → active#(sel(f(sel(active(g(mark(_x91))), active(f(mark(_x101))))), _x32))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(g(active(0)), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(f(sel(g(cons(_x81, _x82)), f(_x101))), _x32)) → active#(sel(f(active(sel(active(g(active(cons(mark(_x81), _x82)))), active(f(mark(_x101)))))), _x32))active#(f(X)) → mark#(cons(X, f(g(X))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x71, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(mark(cons(mark(_x61), f(g(mark(_x61))))), _x32)), active(g(mark(_x41)))))mark#(sel(f(sel(g(0), f(_x101))), _x22)) → active#(sel(active(f(active(sel(active(g(active(0))), active(f(mark(_x101))))))), _x22))
mark#(sel(f(cons(_x61, _x62)), sel(_x41, f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), mark(cons(mark(_x81), f(g(mark(_x81)))))))))mark#(sel(cons(f(_x61), _x52), g(_x41))) → active#(sel(active(cons(f(mark(_x61)), _x52)), active(g(mark(_x41)))))
mark#(sel(f(sel(g(g(_x111)), f(_x101))), _x22)) → active#(sel(active(f(active(sel(active(g(active(g(mark(_x111))))), active(f(mark(_x101))))))), _x22))mark#(sel(f(s(active(cons(mark(_x71), _x72)))), cons(cons(_x71, _x72), mark(_x62)))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(cons(mark(_x71), _x72)), _x62))))
mark#(sel(f(sel(_x61, sel(_x101, _x102))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))))), _x22))mark#(sel(f(g(_x61)), s(_x41))) → active#(sel(active(f(active(g(mark(_x61))))), active(s(mark(_x41)))))
mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(f(g(g(_x81))), X2)) → active#(sel(f(active(g(active(g(mark(_x81)))))), mark(X2)))
mark#(sel(f(sel(_x61, _x62)), _x22)) → active#(sel(mark(cons(active(sel(mark(_x61), mark(_x62))), f(g(active(sel(mark(_x61), mark(_x62))))))), _x22))mark#(sel(cons(f(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(f(cons(_x61, _x62)), sel(g(f(_x91)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(f(mark(_x91))))), active(f(mark(_x81)))))))mark#(sel(cons(f(f(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(f(mark(_x91))))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(active(0), mark(_x62))), _x52), active(g(active(f(_x81))))))mark#(sel(cons(0, _x32), g(f(_x71)))) → active#(sel(active(cons(active(0), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(cons(s(_x81), _x62)), X2)) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), mark(X2)))mark#(sel(cons(g(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, mark(_x102))), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x102)))), active(f(mark(_x81)))))))mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(s(_x101))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(mark(_x71))), active(f(active(s(mark(_x101)))))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(f(s(_x71)), cons(cons(_x71, _x72), _x42))) → active#(sel(active(f(active(s(_x71)))), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(cons(0, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(0), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x112))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), _x112))))))))
mark#(sel(cons(_x31, _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))mark#(sel(cons(sel(_x61, s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(sel(_x71, _x62)), f(_x41))) → active#(sel(active(f(active(sel(_x71, mark(_x62))))), active(f(mark(_x41)))))mark#(sel(f(cons(_x61, _x62)), sel(_x41, f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), sel(mark(_x41), active(f(mark(_x81))))))
mark#(sel(cons(s(_x61), active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(f(cons(0, _x62)), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(0), _x62)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(mark(_x81)))))))
mark#(sel(f(s(_x61)), cons(_x41, _x42))) → active#(sel(mark(cons(active(s(mark(_x61))), f(g(active(s(mark(_x61))))))), active(cons(mark(_x41), _x42))))mark#(sel(f(cons(s(_x81), _x62)), sel(_x41, _x42))) → active#(sel(mark(cons(active(cons(active(s(mark(_x81))), _x62)), f(g(active(cons(active(s(mark(_x81))), _x62)))))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(_x61, _x62)), sel(0, f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(0), active(f(mark(_x81)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(g(_x101))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(g(mark(_x101)))))))))
mark#(sel(cons(f(_x61), _x32), X2)) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), mark(X2)))mark#(sel(f(cons(_x71, _x72)), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(_x71, _x72)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(mark(_x81)))))))
mark#(sel(f(g(g(_x81))), X2)) → active#(sel(active(f(g(active(g(mark(_x81)))))), mark(X2)))mark#(sel(f(g(_x61)), X2)) → active#(sel(f(active(g(mark(_x61)))), mark(X2)))
mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(_x41, _x42))) → active#(sel(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(sel(_x71, g(_x101))), X2)) → active#(sel(active(f(active(sel(_x71, active(g(mark(_x101))))))), mark(X2)))
mark#(sel(f(_x31), g(sel(_x71, _x72)))) → active#(sel(active(f(mark(_x31))), active(g(active(sel(mark(_x71), mark(_x72)))))))mark#(sel(f(g(g(_x91))), X2)) → active#(sel(active(f(active(g(active(g(_x91)))))), mark(X2)))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(cons(_x111, _x112), _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(active(cons(mark(_x111), _x112)), mark(_x92))))), active(f(mark(_x81)))))))mark#(sel(cons(f(_x81), _x32), g(_x41))) → active#(sel(active(cons(active(f(_x81)), _x32)), active(g(mark(_x41)))))
mark#(sel(f(sel(g(f(_x111)), f(_x101))), _x22)) → active#(sel(active(f(active(sel(active(g(active(f(mark(_x111))))), active(f(mark(_x101))))))), _x22))mark#(sel(cons(sel(f(_x111), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(cons(g(_x81), _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(mark(_x81)))))))mark#(sel(cons(sel(f(_x111), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(f(sel(_x61, f(_x101))), _x32)) → active#(sel(f(active(sel(mark(_x61), active(f(mark(_x101)))))), _x32))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(mark(_x71))))))mark#(cons(X1, X2)) → mark#(X1)
mark#(sel(f(cons(_x61, _x62)), g(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(g(mark(_x41)))))mark#(sel(f(g(sel(_x81, _x82))), X2)) → active#(sel(active(f(active(g(active(sel(mark(_x81), mark(_x82))))))), mark(X2)))
mark#(sel(X1, sel(_x41, _x42))) → active#(sel(mark(X1), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(sel(_x61, f(g(_x131)))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(f(active(g(mark(_x131))))))))), _x22))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(cons(mark(_x91), _x92))), active(f(mark(_x81)))))))mark#(sel(cons(s(g(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(g(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(f(sel(0, f(0))), _x22)) → active#(sel(active(f(active(sel(active(0), active(f(0)))))), _x22))mark#(sel(f(sel(g(_x91), f(0))), _x32)) → active#(sel(f(active(sel(active(g(mark(_x91))), active(f(active(0)))))), _x32))
mark#(sel(f(g(_x61)), f(_x41))) → active#(sel(active(f(active(g(mark(_x61))))), active(f(mark(_x41)))))mark#(sel(f(s(_x71)), 0)) → active#(sel(active(f(s(_x71))), active(0)))
mark#(sel(cons(_x31, _x32), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), sel(active(g(active(cons(mark(_x91), _x92)))), active(f(mark(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(mark(_x81)))))))mark#(sel(f(_x31), g(_x41))) → active#(sel(f(mark(_x31)), active(g(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), sel(_x41, f(cons(_x111, _x112))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(f(active(cons(mark(_x111), _x112))))))))mark#(sel(f(sel(_x71, _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(sel(_x71, mark(_x62))))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(sel(0, f(_x101))), _x22)) → active#(sel(active(f(active(sel(active(0), active(f(mark(_x101))))))), _x22))mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(0)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(mark(_x71))), active(f(active(0)))))))
mark#(sel(cons(sel(0, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(f(s(_x61)), cons(cons(cons(_x101, _x102), _x72), _x42))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(cons(active(cons(mark(_x101), _x102)), _x72)), _x42))))
mark#(sel(f(cons(sel(_x101, _x82), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(_x101, mark(_x82))), _x62)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(g(_x71), _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(active(g(mark(_x71))), _x62))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(f(_x81)))))mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))
mark#(sel(f(cons(_x61, active(_x52))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(mark(_x61), _x52))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(cons(s(mark(_x41)), _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(mark(_x41), _x62))))
mark#(g(X)) → active#(g(mark(X)))mark#(sel(f(cons(g(_x81), _x62)), sel(g(_x71), f(_x91)))) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(sel(active(g(mark(_x71))), active(f(_x91))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(f(_x81)))))mark#(sel(f(cons(_x61, _x62)), sel(g(sel(sel(_x111, _x112), _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(active(sel(mark(_x111), mark(_x112))), mark(_x92))))), active(f(mark(_x81)))))))
mark#(sel(f(cons(_x71, _x72)), sel(_x41, f(_x81)))) → active#(sel(active(f(active(cons(_x71, _x72)))), active(sel(mark(_x41), active(f(mark(_x81)))))))mark#(sel(f(cons(s(_x81), _x62)), sel(s(_x71), _x42))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(active(s(mark(_x71))), mark(_x42)))))
mark#(sel(cons(sel(_x61, g(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(f(s(_x71)), 0)) → active#(sel(f(active(s(_x71))), active(0)))
mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), cons(mark(_x41), _x42)))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(_x41, _x42))) → active#(sel(mark(cons(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)), f(g(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(sel(0, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(active(0), mark(_x62)), _x42)), active(g(active(f(_x81))))))mark#(sel(f(cons(_x61, _x62)), sel(f(_x71), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(f(mark(_x71))), active(f(mark(_x81)))))))
mark#(sel(cons(_x31, active(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))mark#(sel(cons(_x31, _x32), X2)) → active#(sel(cons(mark(_x31), _x32), mark(X2)))
mark#(sel(cons(sel(cons(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(f(s(_x61)), cons(_x41, _x42))) → active#(sel(f(active(s(mark(_x61)))), active(cons(mark(_x41), _x42))))
mark#(sel(f(cons(s(_x81), mark(_x72))), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x72)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(sel(_x91, _x92), mark(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(active(sel(mark(_x91), mark(_x92))), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(f(s(cons(mark(_x71), _x72))), cons(cons(_x71, _x72), _x62))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(cons(mark(_x71), _x72), _x62))))mark#(sel(f(cons(_x61, _x62)), f(0))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(0)))))
mark#(sel(cons(sel(_x61, _x62), active(_x42)), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(_x81))))))mark#(sel(f(sel(f(_x91), f(_x101))), _x22)) → active#(sel(active(f(active(sel(active(f(mark(_x91))), active(f(mark(_x101))))))), _x22))
mark#(sel(f(cons(g(_x81), _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), f(mark(_x81))))))
mark#(sel(cons(sel(_x61, _x62), mark(active(_x42))), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(cons(sel(cons(_x81, _x82), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x81), _x82)), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(f(sel(_x61, _x62)), mark(_x32))) → active#(sel(active(f(active(sel(mark(_x61), mark(_x62))))), _x32))
mark#(sel(f(sel(_x61, f(_x101))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), f(mark(_x101)))))), _x22))mark#(sel(f(sel(_x61, f(f(_x131)))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(f(active(f(mark(_x131))))))))), _x22))
mark#(sel(f(sel(0, f(0))), mark(_x32))) → active#(sel(active(f(active(sel(active(0), active(f(active(0))))))), _x32))mark#(sel(cons(_x31, _x32), cons(_x61, _x62))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(_x61, _x62))))
mark#(sel(cons(s(_x61), _x32), g(0))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(f(cons(s(f(_x111)), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(s(active(f(mark(_x111))))), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(sel(_x61, _x62)), 0)) → active#(sel(active(f(active(sel(mark(_x61), mark(_x62))))), active(0)))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, cons(_x131, _x132)))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(cons(mark(_x131), _x132))))))))))
mark#(sel(f(sel(_x61, _x62)), g(_x41))) → active#(sel(active(f(active(sel(mark(_x61), mark(_x62))))), active(g(mark(_x41)))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(cons(mark(_x61), _x62)), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(f(sel(_x71, _x62)), X2)) → active#(sel(active(f(sel(_x71, mark(_x62)))), mark(X2)))mark#(sel(cons(sel(f(_x111), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x32), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(0, g(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(g(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(s(0), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(0))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(f(s(0)), cons(cons(_x71, _x72), _x42))) → active#(sel(active(f(active(s(active(0))))), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(f(s(_x71)), X2)) → active#(sel(mark(cons(active(s(_x71)), f(g(active(s(_x71)))))), mark(X2)))
mark#(sel(cons(sel(f(mark(_x101)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x101)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(f(s(_x61)), s(_x41))) → active#(sel(active(f(active(s(mark(_x61))))), active(s(mark(_x41)))))
mark#(sel(f(_x31), g(_x61))) → active#(sel(active(f(mark(_x31))), active(g(_x61))))mark#(sel(cons(g(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(cons(_x61, active(_x72))), sel(g(0), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(mark(_x81)))))))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), f(active(sel(mark(_x101), mark(_x102))))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(f(cons(_x61, _x62)), sel(cons(_x71, _x72), _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(cons(mark(_x71), _x72)), mark(_x42)))))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(f(mark(_x71))))))mark#(sel(f(s(cons(_x81, _x82))), X2)) → active#(sel(active(f(active(s(active(cons(mark(_x81), _x82)))))), mark(X2)))
mark#(sel(f(sel(_x61, _x62)), X2)) → active#(sel(active(f(sel(mark(_x61), mark(_x62)))), mark(X2)))mark#(sel(f(sel(_x71, _x62)), g(_x41))) → active#(sel(active(f(active(sel(_x71, mark(_x62))))), active(g(mark(_x41)))))
mark#(sel(f(sel(f(_x91), 0)), _x22)) → active#(sel(active(f(active(sel(active(f(mark(_x91))), active(0))))), _x22))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), mark(cons(mark(_x81), f(g(mark(_x81)))))))))
mark#(sel(f(sel(mark(_x81), _x62)), X2)) → active#(sel(active(f(active(sel(_x81, mark(_x62))))), mark(X2)))mark#(sel(f(cons(f(_x81), _x62)), sel(g(_x71), f(_x91)))) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(sel(active(g(mark(_x71))), active(f(_x91))))))
mark#(sel(cons(_x31, _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(f(s(_x61)), cons(cons(_x71, _x72), _x42))) → active#(sel(mark(cons(active(s(mark(_x61))), f(g(active(s(mark(_x61))))))), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(f(cons(0, _x62)), sel(g(0), f(_x81)))) → active#(sel(active(f(active(cons(active(0), _x62)))), active(sel(active(g(active(0))), active(f(mark(_x81)))))))mark#(sel(cons(sel(_x61, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))
mark#(f(X)) → mark#(X)mark#(sel(f(sel(_x61, s(_x101))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(s(mark(_x101))))))), _x22))
mark#(sel(f(cons(s(_x81), _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(f(mark(_x41)))))mark#(sel(f(s(sel(_x81, _x82))), cons(_x41, _x42))) → active#(sel(active(f(active(s(active(sel(mark(_x81), mark(_x82))))))), active(cons(mark(_x41), _x42))))
mark#(sel(f(cons(sel(f(_x111), _x82), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(active(f(mark(_x111))), mark(_x82))), _x62)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, g(_x131)))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(g(mark(_x131)))))))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x92)), f(0)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(active(0)))))))mark#(sel(f(cons(cons(_x81, _x82), _x62)), sel(g(0), f(_x81)))) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(sel(active(g(active(0))), active(f(mark(_x81)))))))
mark#(sel(cons(sel(_x61, f(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(active(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(cons(0, _x62)), X2)) → active#(sel(active(f(active(cons(active(0), _x62)))), mark(X2)))mark#(sel(f(cons(_x71, _x72)), sel(g(0), f(_x81)))) → active#(sel(active(f(active(cons(_x71, _x72)))), active(sel(active(g(active(0))), active(f(mark(_x81)))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(_x91)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(_x91))))))mark#(sel(f(cons(s(sel(_x111, _x112)), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(s(active(sel(mark(_x111), mark(_x112))))), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(X1, X2)) → mark#(X1)mark#(sel(f(cons(s(_x81), _x62)), sel(_x41, cons(_x81, _x82)))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(mark(_x41), active(cons(mark(_x81), _x82))))))
mark#(sel(f(cons(g(_x81), _x62)), X2)) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), mark(X2)))mark#(sel(f(cons(f(_x91), mark(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(active(f(mark(_x91))), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(cons(sel(s(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(mark(_x81))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(mark(_x71))), active(f(_x81))))))
mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(f(_x71), _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(active(f(mark(_x71))), mark(_x42)))))mark#(sel(f(g(g(_x81))), _x22)) → active#(sel(active(f(active(g(active(g(mark(_x81))))))), _x22))
mark#(sel(f(s(_x61)), cons(_x61, _x62))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(_x61, _x62))))mark#(sel(f(cons(s(_x81), _x62)), sel(_x41, sel(_x81, _x82)))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(mark(_x41), active(sel(mark(_x81), mark(_x82)))))))
mark#(sel(f(sel(_x61, f(sel(_x131, _x132)))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(f(active(sel(mark(_x131), mark(_x132))))))))), _x22))mark#(sel(cons(sel(0, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(f(sel(s(_x91), f(0))), _x22)) → active#(sel(active(f(active(sel(active(s(mark(_x91))), active(f(active(0))))))), _x22))mark#(sel(f(sel(g(_x71), f(_x101))), _x32)) → active#(sel(f(active(sel(active(g(_x71)), active(f(mark(_x101)))))), _x32))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(f(sel(_x61, g(0))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(g(active(0))))))), _x22))
mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x32), active(g(active(f(mark(_x71)))))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(g(_x121), _x102))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(active(sel(active(g(mark(_x121))), mark(_x102)))))))))
mark#(sel(cons(f(_x61), active(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))mark#(sel(cons(s(_x61), _x52), cons(_x41, _x42))) → active#(sel(active(cons(s(mark(_x61)), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(_x91)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), sel(active(g(mark(_x71))), active(f(_x91)))))mark#(sel(f(cons(s(s(_x111)), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(s(active(s(mark(_x111))))), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(f(_x61), _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))mark#(sel(f(g(g(s(_x101)))), X2)) → active#(sel(active(f(active(g(active(g(active(s(mark(_x101))))))))), mark(X2)))
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(f(mark(_x71))))))
mark#(sel(f(cons(sel(_x81, _x102), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), _x102)), _x62)))), active(sel(mark(_x41), mark(_x42)))))active#(sel(0, cons(X, Y))) → mark#(X)
mark#(sel(f(sel(_x61, f(cons(_x131, _x132)))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(f(active(cons(mark(_x131), _x132)))))))), _x22))mark#(sel(cons(f(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(g(_x61)), cons(_x41, _x42))) → active#(sel(active(f(active(g(mark(_x61))))), active(cons(mark(_x41), _x42))))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(f(s(_x71)), _x22)) → active#(sel(active(f(active(s(_x71)))), _x22))mark#(sel(f(cons(_x71, _x72)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(_x71, _x72)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(mark(_x81)))))))
mark#(sel(f(g(g(cons(_x101, _x102)))), X2)) → active#(sel(active(f(active(g(active(g(active(cons(mark(_x101), _x102)))))))), mark(X2)))mark#(sel(f(_x31), g(mark(_x31)))) → active#(sel(mark(cons(mark(_x31), f(g(mark(_x31))))), active(g(mark(_x41)))))
mark#(sel(f(cons(f(_x81), _x62)), sel(g(0), f(_x81)))) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(sel(active(g(active(0))), active(f(mark(_x81)))))))mark#(sel(cons(_x31, _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(cons(mark(_x71), _x72))))))
mark#(sel(f(cons(cons(_x81, _x82), _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(g(_x71), f(_x81)))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(active(g(mark(_x71))), active(f(mark(_x81)))))))
mark#(sel(f(sel(_x61, 0)), _x22)) → active#(sel(mark(cons(active(sel(mark(_x61), active(0))), f(g(active(sel(mark(_x61), active(0))))))), _x22))mark#(sel(f(sel(_x71, 0)), X2)) → active#(sel(active(f(active(sel(_x71, active(0))))), mark(X2)))
mark#(sel(f(sel(0, g(_x101))), _x22)) → active#(sel(active(f(active(sel(active(0), active(g(mark(_x101))))))), _x22))mark#(sel(f(sel(0, 0)), _x22)) → active#(sel(active(f(active(sel(active(0), 0)))), _x22))
mark#(sel(f(g(g(_x81))), sel(_x41, _x42))) → active#(sel(active(f(active(g(active(g(mark(_x81))))))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(_x31), s(_x41))) → active#(sel(active(f(mark(_x31))), active(s(mark(_x41)))))
mark#(sel(cons(_x31, _x32), cons(_x41, mark(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(0, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(0)), active(f(mark(_x81)))))))mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(_x41, f(sel(_x111, _x112))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(f(active(sel(mark(_x111), mark(_x112)))))))))mark#(sel(f(s(sel(_x81, _x82))), X2)) → active#(sel(active(f(active(s(active(sel(mark(_x81), mark(_x82))))))), mark(X2)))
mark#(sel(f(s(_x61)), cons(_x41, _x42))) → active#(sel(active(f(active(s(mark(_x61))))), cons(mark(_x41), _x42)))mark#(sel(f(cons(_x61, active(_x72))), sel(g(mark(_x61)), f(_x91)))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(mark(_x71))), active(f(_x91))))))
mark#(sel(f(sel(0, _x62)), _x22)) → active#(sel(active(f(active(sel(active(0), mark(_x62))))), _x22))mark#(sel(f(sel(g(mark(_x101)), f(_x101))), _x22)) → active#(sel(active(f(active(sel(active(g(mark(_x91))), mark(cons(mark(_x101), f(g(mark(_x101))))))))), _x22))
mark#(sel(f(sel(_x81, f(0))), _x22)) → active#(sel(active(f(active(sel(_x81, active(f(active(0))))))), _x22))mark#(sel(f(g(cons(_x81, _x82))), X2)) → active#(sel(active(f(active(g(active(cons(mark(_x81), _x82)))))), mark(X2)))
mark#(sel(f(cons(_x61, _x62)), sel(s(_x71), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(s(mark(_x71))), active(f(mark(_x81)))))))mark#(sel(f(cons(0, _x62)), sel(g(_x71), f(_x91)))) → active#(sel(active(f(active(cons(active(0), _x62)))), active(sel(active(g(mark(_x71))), active(f(_x91))))))
mark#(sel(f(sel(_x61, f(0))), _x22)) → active#(sel(mark(cons(active(sel(mark(_x61), active(f(active(0))))), f(g(active(sel(mark(_x61), active(f(active(0))))))))), _x22))mark#(sel(f(cons(_x61, active(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(0)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(active(0)))))))mark#(sel(f(sel(0, f(0))), _x22)) → active#(sel(mark(cons(active(sel(active(0), active(f(active(0))))), f(g(active(sel(active(0), active(f(active(0))))))))), _x22))
mark#(sel(f(cons(_x71, _x72)), X2)) → active#(sel(active(f(active(cons(_x71, _x72)))), mark(X2)))mark#(sel(f(cons(sel(_x81, _x82), _x72)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(sel(mark(_x81), mark(_x82)), _x72)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(cons(_x81, _x82), _x62)), X2)) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), mark(X2)))mark#(sel(cons(sel(f(cons(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(cons(mark(_x121), _x122)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(f(sel(cons(_x91, _x92), f(0))), _x22)) → active#(sel(active(f(active(sel(active(cons(mark(_x91), _x92)), active(f(active(0))))))), _x22))
mark#(sel(f(sel(g(_x91), 0)), _x22)) → active#(sel(active(f(active(sel(active(g(mark(_x91))), active(0))))), _x22))mark#(sel(f(sel(f(_x81), _x62)), X2)) → active#(sel(active(f(active(sel(active(f(mark(_x81))), mark(_x62))))), mark(X2)))
mark#(sel(f(g(_x61)), g(_x41))) → active#(sel(active(f(active(g(mark(_x61))))), active(g(mark(_x41)))))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(0, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(active(0), mark(_x102)))))))))
mark#(sel(f(sel(_x61, g(_x91))), X2)) → active#(sel(active(f(active(sel(mark(_x61), active(g(mark(_x91))))))), mark(X2)))mark#(sel(f(cons(mark(_x41), f(mark(_x81)))), sel(_x41, f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), f(mark(_x81))))))
mark#(sel(cons(s(_x61), mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(f(g(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(g(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(active(_x81))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(mark(_x71))), active(f(_x81))))))mark#(sel(f(s(g(_x81))), X2)) → active#(sel(active(f(active(s(active(g(mark(_x81))))))), mark(X2)))
mark#(sel(f(cons(g(_x91), mark(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(active(g(mark(_x91))), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(cons(_x51, _x52), X2)) → active#(sel(active(cons(_x51, _x52)), mark(X2)))
mark#(sel(f(g(g(0))), X2)) → active#(sel(active(f(active(g(active(g(active(0))))))), mark(X2)))mark#(sel(f(g(0)), X2)) → active#(sel(active(f(active(g(active(0))))), mark(X2)))
mark#(sel(X1, g(_x41))) → active#(sel(mark(X1), active(g(mark(_x41)))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, s(_x131)))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(s(mark(_x131)))))))))))
mark#(sel(f(s(_x61)), cons(cons(_x71, _x72), _x42))) → active#(sel(active(f(active(s(mark(_x61))))), cons(active(cons(mark(_x71), _x72)), _x42)))mark#(sel(cons(_x31, _x32), g(_x61))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(_x61))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), g(active(f(_x81)))))mark#(sel(f(sel(g(_x91), _x62)), _x22)) → active#(sel(active(f(active(sel(active(g(mark(_x91))), mark(_x62))))), _x22))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, g(_x131)))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(g(mark(_x131)))))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(mark(_x81)))))))
mark#(sel(f(sel(g(_x91), f(_x101))), mark(_x22))) → active#(sel(f(active(sel(active(g(mark(_x91))), active(f(mark(_x101)))))), _x22))mark#(sel(f(sel(_x61, g(sel(_x131, _x132)))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(g(active(sel(mark(_x131), mark(_x132))))))))), _x22))
mark#(sel(cons(sel(f(_x91), _x82), _x32), g(f(active(f(mark(_x91))))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(cons(mark(_x31), _x32), active(g(mark(_x41)))))
mark#(sel(f(sel(g(_x91), g(_x101))), _x22)) → active#(sel(active(f(active(sel(active(g(mark(_x91))), active(g(mark(_x101))))))), _x22))mark#(sel(cons(s(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(g(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), sel(_x41, _x42))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(sel(mark(_x101), mark(_x102))))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x92)), f(g(_x101))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(active(g(mark(_x101)))))))))mark#(sel(f(sel(g(_x91), f(s(_x91)))), _x32)) → active#(sel(f(active(sel(active(g(mark(_x91))), active(f(active(s(mark(_x91)))))))), _x32))
mark#(sel(f(sel(g(_x91), f(_x101))), _x22)) → active#(sel(active(f(active(sel(g(mark(_x91)), active(f(mark(_x101))))))), _x22))mark#(sel(f(sel(_x61, g(cons(_x131, _x132)))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(g(active(cons(mark(_x131), _x132)))))))), _x22))
mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, s(_x131)))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(s(mark(_x131)))))))))))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), sel(mark(_x41), mark(_x42))))
mark#(sel(f(s(_x61)), cons(cons(f(_x101), _x72), _x42))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(cons(active(f(mark(_x101))), _x72)), _x42))))mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(mark(_x71))), f(mark(_x81))))))
mark#(sel(f(s(_x71)), 0)) → active#(sel(mark(cons(active(s(_x71)), f(g(active(s(_x71)))))), active(0)))mark#(sel(f(_x31), g(g(_x71)))) → active#(sel(active(f(mark(_x31))), active(g(active(g(mark(_x71)))))))
mark#(sel(cons(sel(f(_x111), _x82), _x32), g(f(active(f(_x111)))))) → active#(sel(active(cons(active(sel(active(f(_x111)), _x82)), _x32)), active(g(active(f(_x81))))))mark#(sel(f(sel(_x81, f(_x101))), _x22)) → active#(sel(active(f(active(sel(_x81, active(f(mark(_x101))))))), _x22))
mark#(sel(f(sel(_x61, f(0))), active(_x32))) → active#(sel(active(f(active(sel(mark(_x61), active(f(active(0))))))), _x32))mark#(sel(cons(_x31, mark(_x52)), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(0)))))))
mark#(sel(cons(s(s(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(s(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, f(_x121))), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), active(f(mark(_x121))))))), active(f(mark(_x81)))))))
mark#(sel(f(cons(s(_x71), _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(active(s(mark(_x71))), _x62))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(sel(s(_x111), _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(active(s(mark(_x111))), mark(_x92))))), active(f(mark(_x81)))))))
mark#(sel(f(sel(_x61, cons(_x101, _x102))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))))), _x22))mark#(sel(f(sel(_x61, 0)), _x22)) → active#(sel(active(f(sel(mark(_x61), active(0)))), _x22))
mark#(sel(f(_x31), g(cons(_x71, _x72)))) → active#(sel(active(f(mark(_x31))), active(g(active(cons(mark(_x71), _x72))))))mark#(sel(f(cons(_x61, _x62)), sel(g(f(_x91)), f(_x91)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(f(mark(_x91))))), active(f(_x91))))))
mark#(sel(cons(sel(_x61, s(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, mark(_x52)), X2)) → active#(sel(active(cons(mark(_x31), _x52)), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(f(g(_x61)), sel(_x41, _x42))) → active#(sel(active(f(active(g(mark(_x61))))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(sel(_x71, _x72), _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(active(sel(mark(_x71), mark(_x72))), _x62))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(cons(_x31, active(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))
mark#(sel(f(cons(_x61, _x62)), sel(_x41, s(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(s(mark(_x81)))))))mark#(sel(f(cons(_x61, active(_x72))), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(f(mark(_x41)))))
mark#(sel(f(cons(f(_x81), _x62)), X2)) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), mark(X2)))mark#(sel(cons(sel(0, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(0))), _x52)), active(g(active(f(_x81))))))
mark#(sel(f(cons(f(_x81), _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(cons(s(_x91), mark(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(active(s(mark(_x91))), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(g(_x101))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(mark(_x71))), active(f(active(g(mark(_x101)))))))))mark#(sel(f(_x31), 0)) → active#(sel(active(f(mark(_x31))), active(0)))
mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(cons(_x121, _x122), _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(active(cons(mark(_x121), _x122)), mark(_x102)))))))))mark#(sel(cons(sel(0, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))
mark#(sel(f(g(s(_x81))), X2)) → active#(sel(active(f(active(g(active(s(mark(_x81))))))), mark(X2)))mark#(sel(f(s(_x61)), _x22)) → active#(sel(active(f(active(s(mark(_x61))))), _x22))
mark#(sel(f(sel(_x71, _x62)), 0)) → active#(sel(active(f(active(sel(_x71, mark(_x62))))), active(0)))mark#(sel(f(sel(_x71, _x62)), X2)) → active#(sel(f(active(sel(_x71, mark(_x62)))), mark(X2)))
mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(f(_x121), _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(active(f(mark(_x121))), mark(_x102)))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(mark(_x81)))))))
mark#(sel(f(s(_x61)), cons(cons(s(_x101), _x72), _x42))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(cons(active(s(mark(_x101))), _x72)), _x42))))mark#(sel(f(cons(mark(_x41), _x62)), sel(_x41, _x62))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), _x62))))
mark#(sel(f(sel(_x61, f(_x101))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), mark(cons(mark(_x101), f(g(mark(_x101))))))))), _x22))mark#(sel(f(cons(_x61, _x62)), sel(_x41, f(g(_x111))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(f(active(g(mark(_x111)))))))))
mark#(sel(f(cons(0, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(active(0), _x62))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(sel(g(_x91), f(_x101))), _x22)) → active#(sel(active(f(sel(active(g(mark(_x91))), active(f(mark(_x101)))))), _x22))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(sel(_x111, _x112), _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(sel(mark(_x111), mark(_x112))), _x92)))), active(f(mark(_x81)))))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(0, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(0), _x92)))), active(f(mark(_x81)))))))
mark#(sel(f(cons(_x61, _x62)), cons(_x41, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(cons(mark(_x41), _x42))))mark#(sel(f(s(mark(_x61))), 0)) → active#(sel(active(f(active(s(_x61)))), active(0)))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(_x81)))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(mark(_x81)))))))mark#(sel(cons(sel(f(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(f(_x61), mark(_x52)), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x52)), active(g(mark(_x41)))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, sel(_x131, _x132)))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(sel(mark(_x131), mark(_x132)))))))))))
mark#(sel(f(sel(_x61, 0)), _x22)) → active#(sel(active(f(active(sel(mark(_x61), 0)))), _x22))mark#(sel(cons(_x31, _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(f(sel(_x61, g(_x101))), mark(_x32))) → active#(sel(active(f(active(sel(mark(_x61), active(g(mark(_x101))))))), _x32))mark#(sel(f(sel(s(_x91), _x62)), _x22)) → active#(sel(active(f(active(sel(active(s(mark(_x91))), mark(_x62))))), _x22))
mark#(sel(f(sel(g(f(_x81)), f(_x101))), _x32)) → active#(sel(f(active(sel(active(g(active(f(mark(_x81))))), active(f(mark(_x101)))))), _x32))mark#(sel(f(g(_x61)), 0)) → active#(sel(active(f(active(g(mark(_x61))))), active(0)))
mark#(sel(f(cons(_x61, _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), sel(mark(_x41), mark(_x42))))mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), mark(cons(mark(_x41), f(g(mark(_x41)))))))
mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(f(active(cons(mark(_x61), _x62))), mark(X2)))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(0)))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), mark(cons(mark(_x81), f(g(mark(_x81)))))))))mark#(sel(f(_x31), g(s(_x71)))) → active#(sel(active(f(mark(_x31))), active(g(active(s(mark(_x71)))))))
mark#(sel(f(s(f(_x81))), cons(cons(_x71, _x72), _x42))) → active#(sel(active(f(active(s(active(f(mark(_x81))))))), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(f(sel(_x61, _x62)), _x32)) → active#(sel(f(active(sel(mark(_x61), mark(_x62)))), _x32))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(0)), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(g(_x71), f(_x91)))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(active(g(mark(_x71))), active(f(_x91))))))
mark#(sel(cons(sel(sel(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(_x91, f(g(_x91)))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, s(_x121))), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), active(s(mark(_x121))))))), active(f(mark(_x81)))))))mark#(sel(f(cons(_x51, _x52)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(_x51, _x52))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(mark(_x81)))))))mark#(sel(cons(_x51, _x52), g(f(_x71)))) → active#(sel(active(cons(_x51, _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(cons(_x71, _x72), _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(active(cons(mark(_x71), _x72)), mark(_x42)))))mark#(sel(f(cons(sel(g(_x111), _x82), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(active(g(mark(_x111))), mark(_x82))), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, sel(_x131, _x132)))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(sel(mark(_x131), mark(_x132)))))))))))mark#(sel(f(cons(_x61, active(_x72))), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(mark(_x81)))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(cons(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(active(cons(mark(_x101), _x102))))))))mark#(sel(f(sel(s(_x91), f(_x101))), _x22)) → active#(sel(active(f(active(sel(active(s(mark(_x91))), active(f(mark(_x101))))))), _x22))
mark#(sel(cons(g(_x61), _x32), g(0))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(f(cons(sel(s(_x111), _x82), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(active(s(mark(_x111))), mark(_x82))), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, sel(_x121, _x122))), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), active(sel(mark(_x121), mark(_x122))))))), active(f(mark(_x81)))))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(0, mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(s(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(f(f(_x61)), g(_x41))) → active#(sel(active(f(active(f(mark(_x61))))), active(g(mark(_x41)))))
mark#(sel(f(g(g(_x81))), X2)) → active#(sel(active(f(active(g(g(mark(_x81)))))), mark(X2)))mark#(sel(f(s(f(_x81))), cons(_x41, _x42))) → active#(sel(active(f(active(s(active(f(mark(_x81))))))), active(cons(mark(_x41), _x42))))
mark#(sel(cons(sel(mark(_x71), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(f(sel(cons(_x91, _x92), g(_x101))), _x22)) → active#(sel(active(f(active(sel(active(cons(mark(_x91), _x92)), active(g(mark(_x101))))))), _x22))
mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, cons(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(_x81))))))
mark#(sel(f(s(cons(_x81, _x82))), cons(cons(_x71, _x72), _x42))) → active#(sel(active(f(active(s(active(cons(mark(_x81), _x82)))))), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(f(cons(_x71, _x72)), f(_x41))) → active#(sel(active(f(active(cons(_x71, _x72)))), active(f(mark(_x41)))))
mark#(sel(f(cons(cons(_x91, _x92), mark(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(active(cons(mark(_x91), _x92)), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(cons(sel(0, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(f(_x61), _x32), g(g(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(g(mark(_x71)))))))mark#(sel(f(cons(_x61, _x62)), sel(_x41, cons(_x81, _x82)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(cons(mark(_x81), _x82))))))
mark#(sel(cons(cons(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(f(sel(_x61, 0)), _x32)) → active#(sel(f(active(sel(mark(_x61), active(0)))), _x32))
mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(_x41, sel(_x81, _x82)))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(mark(_x41), active(sel(mark(_x81), mark(_x82)))))))mark#(sel(cons(sel(_x61, sel(_x91, _x92)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(s(_x61)), cons(s(_x71), _x42))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(s(mark(_x71))), _x42))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(cons(mark(_x91), _x92))))))))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), g(active(f(_x81)))))mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(mark(_x71))), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(f(sel(active(_x81), _x62)), X2)) → active#(sel(active(f(active(sel(_x81, mark(_x62))))), mark(X2)))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(cons(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(cons(mark(_x101), _x102))))))))
mark#(sel(f(cons(_x61, _x62)), sel(cons(mark(_x61), _x62), f(_x81)))) → active#(sel(active(f(cons(mark(_x61), _x62))), active(sel(mark(_x41), active(f(mark(_x81)))))))mark#(sel(f(sel(0, f(0))), _x22)) → active#(sel(active(f(active(sel(0, active(f(active(0))))))), _x22))
mark#(sel(f(g(_x61)), _x22)) → active#(sel(active(f(active(g(mark(_x61))))), _x22))mark#(sel(f(s(_x71)), cons(_x41, _x42))) → active#(sel(active(f(active(s(_x71)))), active(cons(mark(_x41), _x42))))
mark#(sel(f(cons(sel(_x81, g(_x121)), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), active(g(mark(_x121))))), _x62)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(_x111)), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(f(cons(_x61, mark(_x72))), sel(_x41, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(sel(_x81, _x82)), X2)) → active#(sel(active(f(active(sel(_x81, _x82)))), mark(X2)))
mark#(sel(cons(sel(sel(_x81, _x82), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(f(_x111))))) → active#(sel(active(cons(active(sel(f(_x111), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(s(_x61)), X2)) → active#(sel(f(active(s(mark(_x61)))), mark(X2)))mark#(sel(cons(sel(f(sel(_x121, _x122)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(sel(mark(_x121), mark(_x122))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(cons(sel(_x81, _x82), mark(_x72))), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x72)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(sel(f(_x111), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), f(mark(_x81))))))mark#(sel(cons(sel(f(f(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(f(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(_x41, _x42))) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(g(active(sel(mark(_x91), mark(_x92)))), active(f(mark(_x81)))))))
mark#(sel(f(s(_x61)), cons(g(_x71), _x42))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(g(mark(_x71))), _x42))))mark#(sel(cons(g(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(f(_x31), f(_x41))) → active#(sel(active(f(mark(_x31))), active(f(mark(_x41)))))mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, g(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(g(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(f(_x31), g(0))) → active#(sel(active(f(mark(_x31))), active(g(active(0)))))
mark#(sel(f(cons(sel(_x81, sel(_x121, _x122)), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), active(sel(mark(_x121), mark(_x122))))), _x62)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(_x91)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(g(mark(_x71)), active(f(_x91))))))
mark#(sel(f(sel(_x61, f(0))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(f(0)))))), _x22))mark#(sel(cons(_x31, _x32), cons(g(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(g(mark(_x71))), _x42))))
mark#(sel(cons(s(_x61), _x32), cons(s(_x71), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(s(mark(_x71))), _x42))))mark#(sel(cons(f(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(cons(0, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(0), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(mark(_x81)))))))mark#(sel(f(sel(_x61, 0)), mark(_x32))) → active#(sel(active(f(active(sel(mark(_x61), active(0))))), _x32))
mark#(sel(f(cons(_x61, active(f(mark(_x81))))), sel(_x61, f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(_x61, active(f(mark(_x81)))))))mark#(sel(f(sel(_x61, 0)), active(_x32))) → active#(sel(active(f(active(sel(mark(_x61), active(0))))), _x32))
mark#(sel(f(cons(s(_x81), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), sel(mark(_x41), mark(_x42))))mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(s(_x121)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(s(mark(_x121))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(f(sel(_x61, g(_x101))), _x32)) → active#(sel(f(active(sel(mark(_x61), active(g(mark(_x101)))))), _x32))
mark#(sel(cons(_x31, _x32), cons(_x41, active(_x62)))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(mark(_x41), _x62))))mark#(sel(f(sel(g(sel(_x111, _x112)), f(_x101))), _x22)) → active#(sel(active(f(active(sel(active(g(active(sel(mark(_x111), mark(_x112))))), active(f(mark(_x101))))))), _x22))
mark#(sel(f(sel(g(_x91), f(_x101))), _x22)) → active#(sel(active(f(active(sel(active(g(mark(_x91))), f(mark(_x101)))))), _x22))mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x92)), f(_x91)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(_x91))))))
mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(_x41, s(_x81)))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(mark(_x41), active(s(mark(_x81)))))))mark#(sel(f(s(_x61)), cons(cons(_x71, mark(_x92)), _x42))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(cons(mark(_x71), _x92)), _x42))))
mark#(sel(f(cons(sel(_x81, f(_x121)), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), active(f(mark(_x121))))), _x62)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(s(_x81), _x62)), sel(0, _x42))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(active(0), mark(_x42)))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x61)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(_x61, f(g(_x61))))))))mark#(sel(f(_x51), g(_x41))) → active#(sel(active(f(_x51)), active(g(mark(_x41)))))
mark#(sel(f(cons(_x61, mark(mark(_x82)))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x82)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(g(_x31), X2)) → active#(sel(active(g(mark(_x31))), mark(X2)))
mark#(sel(f(sel(_x61, f(_x121))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(f(_x121)))))), _x22))mark#(sel(f(sel(sel(_x91, _x92), f(_x101))), _x22)) → active#(sel(active(f(active(sel(active(sel(mark(_x91), mark(_x92))), active(f(mark(_x101))))))), _x22))
mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(f(cons(_x61, active(_x72))), sel(_x41, f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(mark(_x41), active(f(mark(_x81)))))))
mark#(sel(f(s(_x61)), sel(_x41, _x42))) → active#(sel(active(f(active(s(mark(_x61))))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(g(_x81), _x62)), sel(g(0), f(_x81)))) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(sel(active(g(active(0))), active(f(mark(_x81)))))))
mark#(sel(f(cons(_x71, _x72)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(_x71, _x72)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), f(mark(_x41))))
mark#(sel(f(g(_x61)), X2)) → active#(sel(active(f(g(mark(_x61)))), mark(X2)))mark#(sel(f(0), g(_x41))) → active#(sel(active(f(active(0))), active(g(mark(_x41)))))
mark#(sel(f(s(mark(_x41))), cons(_x41, mark(_x62)))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(mark(_x41), _x62))))mark#(sel(cons(_x31, _x32), f(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(f(mark(_x41)))))
mark#(sel(cons(0, _x32), g(_x41))) → active#(sel(active(cons(active(0), _x32)), active(g(mark(_x41)))))mark#(sel(cons(s(_x71), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(s(mark(_x71))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(cons(_x71, _x72)), sel(g(_x71), f(_x91)))) → active#(sel(active(f(active(cons(_x71, _x72)))), active(sel(active(g(mark(_x71))), active(f(_x91))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), sel(active(g(active(0))), active(f(mark(_x81))))))mark#(sel(f(sel(_x61, g(_x101))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), g(mark(_x101)))))), _x22))
mark#(sel(f(s(s(_x81))), cons(cons(_x71, _x72), _x42))) → active#(sel(active(f(active(s(active(s(mark(_x81))))))), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(f(sel(_x71, f(_x101))), X2)) → active#(sel(active(f(active(sel(_x71, active(f(mark(_x101))))))), mark(X2)))
mark#(sel(f(sel(0, f(0))), _x22)) → active#(sel(active(f(sel(active(0), active(f(active(0)))))), _x22))mark#(sel(cons(sel(_x61, _x62), _x52), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(sel(_x61, f(_x101))), active(_x32))) → active#(sel(active(f(active(sel(mark(_x61), active(f(mark(_x101))))))), _x32))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(mark(cons(active(cons(mark(_x61), _x72)), f(g(active(cons(mark(_x61), _x72)))))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(f(_x31), g(f(_x71)))) → active#(sel(active(f(mark(_x31))), active(g(active(f(mark(_x71)))))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(_x81)))) → active#(sel(active(f(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(mark(_x81)))))))
mark#(sel(X1, 0)) → active#(sel(mark(X1), active(0)))mark#(sel(f(s(mark(_x61))), X2)) → active#(sel(active(f(active(s(_x61)))), mark(X2)))
mark#(sel(f(sel(g(0), f(_x101))), _x32)) → active#(sel(f(active(sel(active(g(active(0))), active(f(mark(_x101)))))), _x32))mark#(sel(cons(sel(_x61, _x62), mark(_x42)), g(f(_x71)))) → active#(sel(active(cons(sel(mark(_x61), mark(_x62)), _x42)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(f(_x111), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(s(_x121), _x102))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(active(sel(active(s(mark(_x121))), mark(_x102)))))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(cons(sel(_x81, _x82), mark(_x42))), sel(_x61, _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(_x61, mark(_x42)))))
mark#(sel(f(cons(cons(_x81, _x82), _x62)), sel(g(_x71), f(_x91)))) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(sel(active(g(mark(_x71))), active(f(_x91))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(_x81))))))
mark#(sel(f(cons(s(_x81), _x72)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(s(mark(_x81)), _x72)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(f(g(_x71)), X2)) → active#(sel(active(f(active(g(_x71)))), mark(X2)))mark#(sel(f(s(_x71)), X2)) → active#(sel(active(f(s(_x71))), mark(X2)))
mark#(sel(cons(s(_x61), _x32), X2)) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), mark(X2)))mark#(sel(_x21, X2)) → active#(sel(_x21, mark(X2)))
mark#(sel(f(s(_x61)), cons(cons(sel(_x101, _x102), _x72), _x42))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(cons(active(sel(mark(_x101), mark(_x102))), _x72)), _x42))))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(_x41, g(_x81)))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(mark(_x41), active(g(mark(_x81)))))))
mark#(sel(cons(f(g(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(g(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(f(sel(g(cons(_x111, _x112)), f(_x101))), _x22)) → active#(sel(active(f(active(sel(active(g(active(cons(mark(_x111), _x112)))), active(f(mark(_x101))))))), _x22))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(sel(cons(_x31, active(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(f(cons(_x61, _x62)), f(cons(_x71, _x72)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(cons(mark(_x71), _x72))))))mark#(sel(f(cons(cons(_x81, _x82), _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(f(mark(_x41)))))
mark#(sel(cons(sel(f(_x111), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(f(s(_x71)), f(_x41))) → active#(sel(active(f(active(s(_x71)))), active(f(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x111, _x102))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(active(sel(_x111, mark(_x102)))))))))mark#(sel(f(cons(g(_x81), _x62)), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(mark(_x81)))))))
mark#(sel(f(sel(_x71, sel(_x101, _x102))), X2)) → active#(sel(active(f(active(sel(_x71, active(sel(mark(_x101), mark(_x102))))))), mark(X2)))mark#(sel(cons(_x31, _x32), sel(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(sel(g(_x101), f(_x101))), _x22)) → active#(sel(active(f(active(sel(active(g(_x101)), active(f(mark(_x101))))))), _x22))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(_x41, _x62))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(mark(_x41), _x62))))
mark#(sel(f(cons(_x61, mark(_x72))), X2)) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), mark(X2)))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(0))))
mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(cons(mark(_x61), _x72))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(cons(s(g(_x111)), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(s(active(g(mark(_x111))))), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(sel(_x81, _x82), _x62)), X2)) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), mark(X2)))mark#(sel(cons(sel(f(_x91), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))mark#(g(X)) → mark#(X)
mark#(sel(f(g(g(_x81))), cons(_x41, _x42))) → active#(sel(active(f(active(g(active(g(mark(_x81))))))), active(cons(mark(_x41), _x42))))mark#(sel(f(cons(_x61, active(_x72))), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(mark(_x81)))))))
mark#(sel(f(s(_x61)), cons(sel(_x71, _x72), _x42))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))mark#(sel(f(cons(sel(sel(_x111, _x112), _x82), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(active(sel(mark(_x111), mark(_x112))), mark(_x82))), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(g(_x61), _x32), g(f(_x71)))) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(mark(_x62))), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x62)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(sel(_x61, cons(_x91, _x92))), X2)) → active#(sel(active(f(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))))), mark(X2)))mark#(sel(cons(_x31, mark(_x52)), cons(_x41, _x42))) → active#(sel(active(cons(mark(_x31), _x52)), active(cons(mark(_x41), _x42))))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, 0)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), active(0))))), active(f(mark(_x81)))))))mark#(sel(f(cons(s(_x81), _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(cons(sel(0, _x62), active(active(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(g(active(0)), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(f(_x31), sel(_x41, _x42))) → active#(sel(active(f(mark(_x31))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(_x61, _x62)), sel(_x41, f(_x81)))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(mark(_x41), active(f(mark(_x81)))))))
mark#(sel(f(sel(sel(_x81, _x82), _x62)), X2)) → active#(sel(active(f(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))))), mark(X2)))mark#(sel(f(sel(g(_x91), f(_x101))), active(_x32))) → active#(sel(active(f(active(sel(active(g(mark(_x91))), active(f(mark(_x101))))))), _x32))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(s(_x121), _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(active(s(mark(_x121))), mark(_x102)))))))))mark#(sel(f(cons(_x61, _x62)), sel(cons(_x71, _x72), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(cons(mark(_x71), _x72)), active(f(mark(_x81)))))))
mark#(sel(f(sel(_x61, _x62)), X2)) → active#(sel(mark(cons(active(sel(mark(_x61), mark(_x62))), f(g(active(sel(mark(_x61), mark(_x62))))))), mark(X2)))mark#(sel(cons(_x31, _x32), _x22)) → active#(sel(active(cons(mark(_x31), _x32)), _x22))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(f(_x101))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(active(f(mark(_x101)))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(sel(f(_x111), _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(active(f(mark(_x111))), mark(_x92))))), active(f(mark(_x81)))))))
mark#(sel(cons(sel(_x61, f(_x91)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x91))))), _x52)), active(g(active(f(_x81))))))mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(_x91)))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(mark(_x71))), active(f(_x91))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102))))))))mark#(sel(cons(sel(f(_x91), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(mark(_x91))), mark(_x62)), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), cons(mark(_x41), _x42)))mark#(sel(f(_x31), cons(_x41, _x42))) → active#(sel(active(f(mark(_x31))), active(cons(mark(_x41), _x42))))
mark#(sel(cons(s(_x61), _x32), cons(sel(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(sel(mark(_x71), mark(_x72))), _x42))))mark#(sel(cons(sel(_x81, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(_x81, mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(_x31, _x32), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(_x81))))))mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x101, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(_x101, mark(_x92))))), active(f(mark(_x81)))))))
mark#(sel(f(sel(_x61, f(0))), _x32)) → active#(sel(f(active(sel(mark(_x61), active(f(active(0)))))), _x32))mark#(sel(cons(sel(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(mark(_x41)))))
mark#(sel(cons(sel(g(_x81), _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(_x81))))))mark#(sel(f(sel(0, f(0))), _x22)) → active#(sel(active(f(active(sel(active(0), f(active(0)))))), _x22))
mark#(sel(cons(sel(_x61, _x62), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(g(mark(_x71)), active(f(mark(_x81)))))))
mark#(sel(f(s(_x61)), cons(cons(_x71, active(_x92)), _x42))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(cons(mark(_x71), _x92)), _x42))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(sel(_x121, _x122), _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(active(sel(mark(_x121), mark(_x122))), mark(_x102)))))))))
mark#(sel(cons(s(_x81), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(_x81)), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), 0)) → active#(sel(active(cons(mark(_x31), _x32)), active(0)))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x92)), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(cons(s(_x81), _x62)), sel(_x41, 0))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(mark(_x41), active(0)))))
mark#(sel(f(s(_x61)), cons(cons(_x71, _x72), _x42))) → active#(sel(active(f(s(mark(_x61)))), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(mark(_x81)))))))
mark#(sel(f(g(g(_x81))), 0)) → active#(sel(active(f(active(g(active(g(mark(_x81))))))), active(0)))mark#(sel(f(sel(_x61, f(0))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), mark(cons(active(0), f(g(active(0))))))))), _x22))
mark#(sel(f(cons(f(_x81), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(_x31, _x32), cons(f(_x71), _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(f(mark(_x71))), _x42))))
mark#(sel(cons(0, _x32), X2)) → active#(sel(active(cons(active(0), _x32)), mark(X2)))mark#(sel(f(cons(s(_x81), _x62)), sel(f(_x71), _x42))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(active(f(mark(_x71))), mark(_x42)))))
mark#(sel(f(sel(g(_x91), f(_x101))), active(_x22))) → active#(sel(f(active(sel(active(g(mark(_x91))), active(f(mark(_x101)))))), _x22))mark#(sel(f(cons(_x61, _x62)), sel(sel(_x71, _x72), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(sel(mark(_x71), mark(_x72))), active(f(mark(_x81)))))))
mark#(sel(f(cons(f(_x81), _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(f(mark(_x41)))))mark#(sel(f(cons(s(cons(_x111, _x112)), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(s(active(cons(mark(_x111), _x112)))), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(s(_x71)), X2)) → active#(sel(f(active(s(_x71))), mark(X2)))mark#(sel(f(sel(g(_x91), f(s(_x121)))), _x22)) → active#(sel(active(f(active(sel(active(g(mark(_x91))), active(f(active(s(mark(_x121))))))))), _x22))
mark#(sel(f(cons(s(_x81), _x62)), sel(_x41, _x42))) → active#(sel(f(active(cons(active(s(mark(_x81))), _x62))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(_x51, _x52), g(0))) → active#(sel(active(cons(_x51, _x52)), active(g(active(0)))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), f(active(sel(mark(_x101), mark(_x102))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, g(_x131)))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(g(mark(_x131)))))))))))
mark#(sel(f(cons(_x61, _x62)), sel(s(_x71), _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(s(mark(_x71))), mark(_x42)))))mark#(sel(f(cons(f(_x71), _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(active(f(mark(_x71))), _x62))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(g(mark(_x91)))))))))mark#(sel(f(sel(g(g(_x81)), f(_x101))), _x32)) → active#(sel(f(active(sel(active(g(active(g(mark(_x81))))), active(f(mark(_x101)))))), _x32))
mark#(sel(f(sel(_x81, g(_x101))), _x22)) → active#(sel(active(f(active(sel(_x81, active(g(mark(_x101))))))), _x22))mark#(sel(f(sel(g(_x91), f(_x81))), _x32)) → active#(sel(f(active(sel(active(g(mark(_x91))), active(f(_x81))))), _x32))
mark#(sel(f(sel(_x61, _x62)), _x22)) → active#(sel(active(f(sel(mark(_x61), mark(_x62)))), _x22))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(0)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(0)))))))
mark#(sel(f(cons(s(_x81), _x62)), sel(g(_x71), f(_x91)))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(active(g(mark(_x71))), active(f(_x91))))))mark#(sel(cons(0, _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(0), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(f(cons(cons(_x71, _x72), _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(active(cons(mark(_x71), _x72)), _x62))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(s(_x61)), cons(cons(g(_x101), _x72), _x42))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(cons(active(g(mark(_x101))), _x72)), _x42))))
mark#(sel(f(sel(cons(_x91, _x92), 0)), _x22)) → active#(sel(active(f(active(sel(active(cons(mark(_x91), _x92)), active(0))))), _x22))mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), sel(active(g(mark(_x71))), active(f(mark(_x81))))))
mark#(sel(cons(s(_x61), _x32), cons(_x41, _x42))) → active#(sel(cons(active(s(mark(_x61))), _x32), active(cons(mark(_x41), _x42))))mark#(sel(f(sel(sel(_x91, _x92), _x62)), _x22)) → active#(sel(active(f(active(sel(active(sel(mark(_x91), mark(_x92))), mark(_x62))))), _x22))
mark#(sel(f(sel(g(_x91), f(_x101))), mark(_x32))) → active#(sel(active(f(active(sel(active(g(mark(_x91))), active(f(mark(_x101))))))), _x32))mark#(sel(cons(f(_x61), _x32), g(_x61))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(_x61))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x101, _x102)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(_x101, _x102)))), active(f(mark(_x81)))))))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(cons(active(sel(mark(_x81), mark(_x82))), _x62), _x42))) → active#(sel(active(f(cons(active(sel(mark(_x81), mark(_x82))), _x62))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(sel(f(_x91), cons(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), g(s(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(s(mark(_x71)))))))
mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(f(s(_x71)), s(_x41))) → active#(sel(active(f(active(s(_x71)))), active(s(mark(_x41)))))
mark#(sel(cons(f(0), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(0))), _x32)), active(g(mark(_x41)))))mark#(sel(f(cons(_x61, _x62)), sel(g(g(_x91)), f(_x91)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(g(mark(_x91))))), active(f(_x91))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x92)), f(f(_x101))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(active(f(mark(_x101)))))))))
mark#(sel(cons(cons(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x71), _x72)), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(f(cons(s(_x81), _x62)), sel(g(_x71), f(_x81)))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(active(g(mark(_x71))), active(f(mark(_x81)))))))
mark#(sel(f(s(_x61)), cons(cons(_x91, _x92), _x42))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(cons(_x91, _x92)), _x42))))mark#(sel(cons(sel(_x61, _x72), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(sel(mark(_x101), mark(_x102))))))))mark#(sel(cons(sel(_x71, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(_x71, mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(cons(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(mark(_x71))), active(f(active(cons(mark(_x101), _x102))))))))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(sel(_x71, _x72), _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(active(sel(mark(_x71), mark(_x72))), mark(_x42)))))
mark#(sel(cons(s(_x61), _x32), cons(_x61, _x62))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(_x61, _x62))))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(0, _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(active(0), mark(_x42)))))
mark#(sel(f(cons(s(_x81), _x62)), sel(_x41, f(_x81)))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(mark(_x41), active(f(mark(_x81)))))))mark#(sel(f(sel(sel(_x91, _x92), g(_x101))), _x22)) → active#(sel(active(f(active(sel(active(sel(mark(_x91), mark(_x92))), active(g(mark(_x101))))))), _x22))
active#(g(s(X))) → mark#(s(s(g(X))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(cons(mark(_x61), _x62))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(mark(_x81)))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(_x81)))) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(sel(active(g(active(0))), active(f(mark(_x81)))))))mark#(sel(f(sel(g(_x91), f(g(_x121)))), _x22)) → active#(sel(active(f(active(sel(active(g(mark(_x91))), active(f(active(g(mark(_x121))))))))), _x22))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(cons(active(f(mark(_x61))), _x32), active(g(mark(_x41)))))mark#(sel(cons(f(_x61), _x32), g(cons(_x71, _x72)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(cons(mark(_x71), _x72))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(mark(_x71))), mark(_x42)))))mark#(sel(cons(_x31, _x32), s(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), active(s(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(f(cons(_x61, _x62)), s(_x41))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(s(mark(_x41)))))
mark#(sel(f(sel(g(_x91), f(cons(_x91, _x92)))), _x32)) → active#(sel(f(active(sel(active(g(mark(_x91))), active(f(active(cons(mark(_x91), _x92))))))), _x32))mark#(sel(cons(_x31, _x32), g(_x41))) → active#(sel(active(cons(mark(_x31), _x32)), g(mark(_x41))))
mark#(sel(cons(sel(_x61, 0), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(cons(_x31, mark(_x52)), g(0))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(0)))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(_x81)))))
mark#(sel(cons(sel(_x61, s(_x91)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(s(mark(_x91))))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(f(sel(_x61, f(_x101))), mark(_x32))) → active#(sel(active(f(active(sel(mark(_x61), active(f(mark(_x101))))))), _x32))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x102)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), _x102)))), active(f(mark(_x81)))))))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102))))))))
mark#(sel(f(cons(s(_x81), _x62)), sel(sel(_x71, _x72), _x42))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(active(sel(mark(_x71), mark(_x72))), mark(_x42)))))mark#(sel(f(cons(s(_x101), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(s(_x101)), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(cons(mark(_x31), _x32), active(g(active(0)))))mark#(sel(X1, _x22)) → active#(sel(mark(X1), _x22))
mark#(sel(f(sel(g(s(_x81)), f(_x101))), _x32)) → active#(sel(f(active(sel(active(g(active(s(mark(_x81))))), active(f(mark(_x101)))))), _x32))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(g(active(0)), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(f(sel(f(_x91), _x62)), _x22)) → active#(sel(active(f(active(sel(active(f(mark(_x91))), mark(_x62))))), _x22))mark#(sel(f(sel(g(_x91), f(_x101))), _x32)) → active#(sel(f(active(sel(active(g(mark(_x91))), f(mark(_x101))))), _x32))
mark#(sel(f(cons(s(_x81), _x62)), sel(g(0), f(_x81)))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(active(g(active(0))), active(f(mark(_x81)))))))mark#(sel(f(s(_x61)), cons(cons(_x71, _x72), _x42))) → active#(sel(f(active(s(mark(_x61)))), active(cons(active(cons(mark(_x71), _x72)), _x42))))
mark#(sel(f(g(g(g(_x101)))), X2)) → active#(sel(active(f(active(g(active(g(active(g(mark(_x101))))))))), mark(X2)))mark#(sel(f(cons(sel(_x81, _x82), active(_x72))), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x72)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(s(_x101))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(s(mark(_x101)))))))))mark#(sel(cons(sel(_x61, 0), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(sel(0, _x62)), X2)) → active#(sel(active(f(active(sel(active(0), mark(_x62))))), mark(X2)))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, 0))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(0)))))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(_x81)))) → active#(sel(active(f(cons(mark(_x61), _x62))), active(sel(active(g(mark(_x71))), active(f(mark(_x81)))))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x91)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(_x91))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(cons(sel(f(_x91), f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(cons(cons(_x81, _x82), _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(mark(_x81)))))))mark#(sel(f(sel(g(_x91), f(0))), _x22)) → active#(sel(active(f(active(sel(active(g(mark(_x91))), active(f(active(0))))))), _x22))
mark#(sel(f(s(cons(_x81, _x82))), cons(_x41, _x42))) → active#(sel(active(f(active(s(active(cons(mark(_x81), _x82)))))), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), g(f(g(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(f(sel(_x61, _x62)), active(_x32))) → active#(sel(active(f(active(sel(mark(_x61), mark(_x62))))), _x32))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(f(_x61)), X2)) → active#(sel(active(f(active(f(mark(_x61))))), mark(X2)))mark#(sel(X1, f(_x41))) → active#(sel(mark(X1), active(f(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), sel(_x41, sel(_x81, _x82)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(sel(mark(_x81), mark(_x82)))))))mark#(sel(f(cons(_x61, _x62)), f(sel(_x71, _x72)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(f(sel(g(_x91), f(_x101))), _x32)) → active#(sel(f(active(sel(active(g(mark(_x91))), mark(cons(mark(_x101), f(g(mark(_x101)))))))), _x32))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(0, _x102))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(active(sel(active(0), mark(_x102)))))))))
mark#(sel(f(cons(g(_x81), _x62)), sel(_x41, f(_x81)))) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(sel(mark(_x41), active(f(mark(_x81)))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(f(mark(_x91)))))) → active#(sel(active(cons(active(sel(f(mark(_x91)), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), mark(cons(active(sel(mark(_x101), mark(_x102))), f(g(active(sel(mark(_x101), mark(_x102)))))))))))mark#(sel(f(cons(_x61, mark(_x42))), sel(_x61, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(_x61, mark(_x42)))))
mark#(sel(f(cons(_x61, _x62)), _x22)) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), _x22))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(f(sel(0, 0)), active(_x32))) → active#(sel(active(f(active(sel(active(0), active(0))))), _x32))mark#(sel(f(cons(_x61, mark(_x72))), sel(_x41, f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(mark(_x41), active(f(mark(_x81)))))))
mark#(sel(f(s(mark(_x41))), cons(_x41, active(_x62)))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(mark(_x41), _x62))))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), g(active(f(mark(_x71))))))
mark#(sel(cons(sel(_x61, sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))mark#(sel(f(sel(_x61, g(_x101))), _x22)) → active#(sel(active(f(sel(mark(_x61), active(g(mark(_x101)))))), _x22))
mark#(sel(cons(s(sel(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(sel(mark(_x91), mark(_x92))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(0, X2)) → active#(sel(active(0), mark(X2)))
mark#(sel(cons(sel(f(_x91), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(0))), _x32)), active(g(active(f(_x81))))))mark#(sel(f(cons(s(_x81), _x62)), sel(cons(active(s(mark(_x81))), _x62), _x42))) → active#(sel(active(f(cons(active(s(mark(_x81))), _x62))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x92)), f(s(_x101))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(active(s(mark(_x101)))))))))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(_x41, 0))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(mark(_x41), active(0)))))
mark#(sel(f(sel(_x61, _x62)), cons(_x41, _x42))) → active#(sel(active(f(active(sel(mark(_x61), mark(_x62))))), active(cons(mark(_x41), _x42))))mark#(sel(cons(sel(f(_x111), 0), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), active(0))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(0), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(active(0))), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(g(_x121), _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(active(g(mark(_x121))), mark(_x102)))))))))
mark#(sel(f(cons(_x61, mark(active(_x82)))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x82)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(sel(f(_x91), g(_x101))), _x22)) → active#(sel(active(f(active(sel(active(f(mark(_x91))), active(g(mark(_x101))))))), _x22))
mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(_x81)))) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(sel(active(g(mark(_x71))), active(f(mark(_x81)))))))
mark#(sel(f(cons(s(_x81), mark(_x42))), sel(_x61, _x42))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(_x61, mark(_x42)))))mark#(sel(f(sel(_x81, _x62)), _x22)) → active#(sel(active(f(active(sel(_x81, mark(_x62))))), _x22))
mark#(sel(cons(sel(sel(_x81, _x82), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(sel(mark(_x81), mark(_x82))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(f(cons(s(_x81), _x62)), sel(cons(_x71, _x72), _x42))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(active(cons(mark(_x71), _x72)), mark(_x42)))))
mark#(sel(f(s(_x61)), X2)) → active#(sel(active(f(s(mark(_x61)))), mark(X2)))mark#(sel(f(cons(0, _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(0), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(f(mark(_x41)))))mark#(sel(f(cons(_x61, _x62)), sel(_x41, f(f(_x111))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(f(active(f(mark(_x111)))))))))
mark#(sel(f(sel(s(_x91), g(_x101))), _x22)) → active#(sel(active(f(active(sel(active(s(mark(_x91))), active(g(mark(_x101))))))), _x22))mark#(sel(f(s(_x61)), cons(cons(0, _x72), _x42))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(cons(active(0), _x72)), _x42))))
mark#(sel(f(sel(_x61, f(_x101))), _x22)) → active#(sel(mark(cons(active(sel(mark(_x61), active(f(mark(_x101))))), f(g(active(sel(mark(_x61), active(f(mark(_x101))))))))), _x22))mark#(sel(f(sel(_x61, f(_x101))), _x22)) → active#(sel(active(f(sel(mark(_x61), active(f(mark(_x101)))))), _x22))
mark#(sel(f(cons(s(_x81), _x62)), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(mark(_x81)))))))mark#(sel(cons(_x31, mark(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))
mark#(sel(f(sel(_x61, g(s(_x131)))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(g(active(s(mark(_x131))))))))), _x22))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(g(active(0)), active(f(mark(_x81)))))))
mark#(sel(f(cons(0, mark(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(active(0), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(g(_x121), _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(active(g(mark(_x121))), mark(_x102)))))))))
mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(f(_x81)))))mark#(sel(cons(sel(f(_x111), _x62), mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x52)), active(g(active(f(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(g(_x91)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(g(mark(_x91))))), active(f(mark(_x81)))))))mark#(sel(f(sel(g(_x91), f(cons(_x121, _x122)))), _x22)) → active#(sel(active(f(active(sel(active(g(mark(_x91))), active(f(active(cons(mark(_x121), _x122)))))))), _x22))
mark#(sel(f(sel(sel(_x91, _x92), f(0))), _x22)) → active#(sel(active(f(active(sel(active(sel(mark(_x91), mark(_x92))), active(f(active(0))))))), _x22))mark#(sel(cons(_x31, _x32), g(0))) → active#(sel(active(cons(mark(_x31), _x32)), g(active(0))))
mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(active(f(cons(mark(_x61), _x62))), mark(X2)))mark#(sel(f(s(f(_x81))), X2)) → active#(sel(active(f(active(s(active(f(mark(_x81))))))), mark(X2)))
mark#(sel(cons(cons(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), mark(X2)))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(f(_x81)))))
mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(0)), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(sel(mark(_x101), mark(_x102))))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(_x31, _x32), g(g(_x71)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(g(mark(_x71)))))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(0)))))mark#(sel(cons(_x31, _x32), g(f(f(_x91))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(f(mark(_x91)))))))))
mark#(sel(f(cons(g(_x81), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(sel(_x61, cons(_x101, _x102)), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x101), _x102)))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(s(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(s(mark(_x91)))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(_x71)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(mark(_x71))), mark(cons(_x71, f(g(_x71))))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(_x91)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(mark(_x71))), f(_x91)))))mark#(sel(f(sel(_x81, 0)), _x22)) → active#(sel(active(f(active(sel(_x81, active(0))))), _x22))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(0)), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(mark(_x61), _x62))), sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102))))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(g(_x101))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(active(g(mark(_x101)))))))))mark#(sel(f(g(g(_x81))), s(_x41))) → active#(sel(active(f(active(g(active(g(mark(_x81))))))), active(s(mark(_x41)))))
mark#(sel(f(s(active(_x61))), X2)) → active#(sel(active(f(active(s(_x61)))), mark(X2)))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x111, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(_x111, mark(_x102)))))))))
mark#(sel(f(cons(s(_x81), _x62)), sel(g(_x71), _x42))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(active(g(mark(_x71))), mark(_x42)))))mark#(sel(f(sel(_x61, g(_x121))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(g(_x121)))))), _x22))
mark#(sel(f(cons(sel(_x81, s(_x121)), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), active(s(mark(_x121))))), _x62)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(sel(_x81, _x82), _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(f(mark(_x41)))))
mark#(sel(cons(s(_x61), _x32), cons(0, _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(0), _x42))))mark#(sel(f(s(_x61)), g(_x41))) → active#(sel(active(f(active(s(mark(_x61))))), active(g(mark(_x41)))))
mark#(sel(f(cons(_x61, _x62)), sel(g(_x81), f(_x91)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(_x81)), active(f(_x91))))))mark#(sel(f(cons(_x71, _x72)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(_x71, _x72)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, f(_x131)))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(f(mark(_x131)))))))))))mark#(sel(f(sel(0, 0)), _x32)) → active#(sel(f(active(sel(active(0), active(0)))), _x32))
mark#(sel(cons(cons(_x61, _x62), _x32), g(_x41))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(mark(_x41)))))mark#(sel(f(sel(g(sel(_x81, _x82)), f(_x101))), _x32)) → active#(sel(f(active(sel(active(g(active(sel(mark(_x81), mark(_x82))))), active(f(mark(_x101)))))), _x32))
mark#(sel(s(_x31), X2)) → active#(sel(active(s(mark(_x31))), mark(X2)))mark#(sel(f(cons(_x61, _x62)), f(_x61))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(_x61))))
mark#(sel(f(s(_x71)), sel(_x41, _x42))) → active#(sel(active(f(active(s(_x71)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(sel(0, f(0))), _x32)) → active#(sel(f(active(sel(active(0), active(f(active(0)))))), _x32))
mark#(sel(f(sel(s(_x81), _x62)), X2)) → active#(sel(active(f(active(sel(active(s(mark(_x81))), mark(_x62))))), mark(X2)))mark#(sel(f(sel(0, f(0))), active(_x32))) → active#(sel(active(f(active(sel(active(0), active(f(active(0))))))), _x32))
mark#(sel(f(sel(g(_x91), f(f(_x121)))), _x22)) → active#(sel(active(f(active(sel(active(g(mark(_x91))), active(f(active(f(mark(_x121))))))))), _x22))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(cons(_x121, _x122), _x102))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(active(sel(active(cons(mark(_x121), _x122)), mark(_x102)))))))))
mark#(sel(f(sel(0, 0)), _x22)) → active#(sel(active(f(active(sel(0, active(0))))), _x22))mark#(sel(cons(_x31, mark(_x52)), g(f(s(_x91))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(s(mark(_x91)))))))))
mark#(sel(f(s(s(_x81))), X2)) → active#(sel(active(f(active(s(active(s(mark(_x81))))))), mark(X2)))mark#(sel(f(cons(0, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(active(0), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(f(cons(_x61, _x62)), sel(0, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(0), mark(_x42)))))mark#(sel(f(sel(f(_x91), f(0))), _x22)) → active#(sel(active(f(active(sel(active(f(mark(_x91))), active(f(active(0))))))), _x22))
mark#(sel(cons(sel(_x61, _x82), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), _x82)), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(_x61, f(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(f(mark(_x101))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(cons(_x111, _x112), _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(cons(mark(_x111), _x112)), _x92)))), active(f(mark(_x81)))))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(f(_x121), _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(active(f(mark(_x121))), mark(_x102)))))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(f(_x111), _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(f(mark(_x111))), _x92)))), active(f(mark(_x81)))))))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(mark(_x61), _x72))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))
mark#(sel(f(cons(_x61, _x62)), sel(sel(_x71, _x72), _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(sel(mark(_x71), mark(_x72))), mark(_x42)))))mark#(sel(f(_x31), _x22)) → active#(sel(active(f(mark(_x31))), _x22))
mark#(sel(f(cons(_x61, _x62)), sel(_x41, f(_x101)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(f(_x101))))))mark#(sel(f(g(f(_x81))), X2)) → active#(sel(active(f(active(g(active(f(mark(_x81))))))), mark(X2)))
mark#(sel(f(cons(_x61, mark(_x72))), sel(g(mark(_x61)), f(_x91)))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(mark(_x71))), active(f(_x91))))))mark#(sel(f(cons(_x61, _x62)), sel(_x41, g(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(g(mark(_x81)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(f(_x81)))))mark#(sel(f(cons(_x61, _x62)), sel(g(s(_x91)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(s(mark(_x91))))), active(f(mark(_x81)))))))
mark#(sel(cons(f(s(_x91)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(s(mark(_x91))))), _x32)), active(g(mark(_x41)))))mark#(sel(f(s(s(_x81))), cons(_x41, _x42))) → active#(sel(active(f(active(s(active(s(mark(_x81))))))), active(cons(mark(_x41), _x42))))
mark#(sel(cons(0, _x32), g(0))) → active#(sel(active(cons(active(0), _x32)), active(g(active(0)))))mark#(sel(f(_x31), X2)) → active#(sel(mark(cons(mark(_x31), f(g(mark(_x31))))), mark(X2)))
mark#(sel(f(s(active(cons(mark(_x71), _x72)))), cons(cons(_x71, _x72), active(_x62)))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(cons(mark(_x71), _x72)), _x62))))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(sel(_x121, _x122), _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(active(sel(mark(_x121), mark(_x122))), mark(_x102)))))))))
mark#(sel(cons(sel(_x61, cons(_x91, _x92)), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(cons(mark(_x91), _x92)))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(f(s(_x71)), g(_x41))) → active#(sel(active(f(active(s(_x71)))), active(g(mark(_x41)))))
mark#(sel(f(cons(g(_x81), _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(f(mark(_x41)))))active#(g(0)) → mark#(s(0))
mark#(sel(cons(sel(f(active(_x101)), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(_x101)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(_x31, _x32), cons(_x41, _x42))) → active#(sel(cons(mark(_x31), _x32), active(cons(mark(_x41), _x42))))
mark#(sel(f(cons(f(_x81), _x62)), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(mark(_x81)))))))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(_x41, f(_x81)))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(mark(_x41), active(f(mark(_x81)))))))
mark#(sel(cons(f(sel(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(sel(mark(_x91), mark(_x92))))), _x32)), active(g(mark(_x41)))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), g(active(f(mark(_x71))))))
mark#(sel(f(sel(g(_x91), f(sel(_x91, _x92)))), _x32)) → active#(sel(f(active(sel(active(g(mark(_x91))), active(f(active(sel(mark(_x91), mark(_x92)))))))), _x32))mark#(sel(cons(sel(_x61, _x62), _x32), g(f(g(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(g(mark(_x91)))))))))
mark#(sel(f(s(active(_x61))), 0)) → active#(sel(active(f(active(s(_x61)))), active(0)))mark#(sel(f(cons(sel(_x81, cons(_x121, _x122)), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), active(cons(mark(_x121), _x122)))), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(g(active(cons(mark(_x91), _x92))), active(f(mark(_x81)))))))mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(_x91)))) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(sel(active(g(mark(_x71))), active(f(_x91))))))
mark#(sel(f(s(_x61)), cons(f(_x71), _x42))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(f(mark(_x71))), _x42))))mark#(sel(cons(g(_x61), _x32), X2)) → active#(sel(active(cons(active(g(mark(_x61))), _x32)), mark(X2)))
mark#(sel(f(cons(0, _x62)), f(_x41))) → active#(sel(active(f(active(cons(active(0), _x62)))), active(f(mark(_x41)))))mark#(sel(f(cons(_x61, active(_x72))), X2)) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), mark(X2)))
mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(g(_x71), _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(active(g(mark(_x71))), mark(_x42)))))mark#(sel(f(_x51), X2)) → active#(sel(active(f(_x51)), mark(X2)))
mark#(sel(f(cons(_x61, _x62)), 0)) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(0)))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x111, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(_x111, mark(_x102)))))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x81)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(_x81))))))mark#(sel(f(cons(cons(_x81, _x82), _x62)), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(mark(_x81)))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(active(f(cons(mark(_x61), _x62))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(mark(_x81)))))))mark#(sel(f(sel(_x71, s(_x101))), X2)) → active#(sel(active(f(active(sel(_x71, active(s(mark(_x101))))))), mark(X2)))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(mark(_x71))))))mark#(sel(cons(sel(f(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(f(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(sel(sel(_x91, _x92), 0)), _x22)) → active#(sel(active(f(active(sel(active(sel(mark(_x91), mark(_x92))), active(0))))), _x22))active#(sel(s(X), cons(Y, Z))) → mark#(sel(X, Z))
mark#(sel(cons(_x31, active(_x52)), g(_x41))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(_x41)))))mark#(sel(X1, X2)) → mark#(X2)
mark#(sel(cons(sel(g(_x81), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x81))), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))mark#(sel(f(cons(s(_x81), _x62)), sel(_x41, g(_x81)))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(mark(_x41), active(g(mark(_x81)))))))
mark#(sel(f(0), X2)) → active#(sel(active(f(active(0))), mark(X2)))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(mark(_x81)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(active(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(f(sel(_x61, f(0))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), f(active(0)))))), _x22))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(f(_x121), _x102))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(active(sel(active(f(mark(_x121))), mark(_x102)))))))))mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(cons(active(sel(mark(_x61), mark(_x62))), _x52), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(0))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(0)))))mark#(sel(cons(sel(0, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(mark(_x81))))))mark#(sel(cons(f(cons(_x91, _x92)), _x32), g(_x41))) → active#(sel(active(cons(active(f(active(cons(mark(_x91), _x92)))), _x32)), active(g(mark(_x41)))))
mark#(sel(f(sel(g(_x91), f(_x101))), _x22)) → active#(sel(mark(cons(active(sel(active(g(mark(_x91))), active(f(mark(_x101))))), f(g(active(sel(active(g(mark(_x91))), active(f(mark(_x101))))))))), _x22))mark#(sel(f(cons(_x61, _x62)), sel(_x41, f(0)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(f(active(0)))))))
mark#(sel(cons(_x51, _x52), cons(_x41, _x42))) → active#(sel(active(cons(_x51, _x52)), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), cons(0, _x42))) → active#(sel(active(cons(mark(_x31), _x32)), active(cons(active(0), _x42))))
mark#(sel(f(cons(s(_x81), _x62)), sel(_x41, s(_x81)))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(mark(_x41), active(s(mark(_x81)))))))mark#(sel(X1, cons(_x41, _x42))) → active#(sel(mark(X1), active(cons(mark(_x41), _x42))))
mark#(sel(f(cons(cons(_x81, _x82), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(_x31, _x32), g(sel(_x71, _x72)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(sel(mark(_x71), mark(_x72)))))))
mark#(sel(f(cons(f(_x81), _x62)), sel(g(_x71), f(_x81)))) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(sel(active(g(mark(_x71))), active(f(mark(_x81)))))))mark#(sel(f(cons(_x61, _x62)), f(g(_x71)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(g(mark(_x71)))))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(cons(mark(_x31), _x52), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32), active(g(active(f(_x81))))))
mark#(sel(f(sel(cons(_x91, _x92), f(_x101))), _x22)) → active#(sel(active(f(active(sel(active(cons(mark(_x91), _x92)), active(f(mark(_x101))))))), _x22))mark#(sel(f(s(g(_x81))), cons(_x41, _x42))) → active#(sel(active(f(active(s(active(g(mark(_x81))))))), active(cons(mark(_x41), _x42))))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), mark(cons(mark(_x81), f(g(mark(_x81)))))))))mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(_x61)))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(mark(cons(_x61, f(g(_x61))))))))
mark#(sel(f(sel(_x61, 0)), X2)) → active#(sel(active(f(active(sel(mark(_x61), active(0))))), mark(X2)))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(_x41, cons(_x81, _x82)))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(mark(_x41), active(cons(mark(_x81), _x82))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(_x71))))))
mark#(sel(f(cons(_x61, _x62)), f(cons(mark(_x61), _x62)))) → active#(sel(active(f(cons(mark(_x61), _x62))), active(f(mark(_x41)))))mark#(sel(f(sel(_x61, g(_x101))), _x22)) → active#(sel(mark(cons(active(sel(mark(_x61), active(g(mark(_x101))))), f(g(active(sel(mark(_x61), active(g(mark(_x101))))))))), _x22))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(s(_x101))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(active(s(mark(_x101)))))))))mark#(sel(sel(_x31, _x32), X2)) → active#(sel(active(sel(mark(_x31), mark(_x32))), mark(X2)))
mark#(sel(f(g(g(_x81))), X2)) → active#(sel(mark(cons(active(g(active(g(mark(_x81))))), f(g(active(g(active(g(mark(_x81))))))))), mark(X2)))mark#(sel(cons(sel(0, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, sel(_x91, _x92)), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))), _x52)), active(g(active(f(_x81))))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(cons(mark(_x91), f(g(mark(_x91))))), mark(_x62))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(_x61, _x62), _x32), g(f(f(_x91))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), active(g(active(f(active(f(mark(_x91)))))))))mark#(sel(f(sel(g(s(_x111)), f(_x101))), _x22)) → active#(sel(active(f(active(sel(active(g(active(s(mark(_x111))))), active(f(mark(_x101))))))), _x22))
mark#(sel(f(cons(_x61, active(_x72))), sel(_x41, _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(f(cons(s(0), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(s(active(0))), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))mark#(sel(cons(_x51, _x52), g(_x41))) → active#(sel(active(cons(_x51, _x52)), active(g(mark(_x41)))))
mark#(sel(f(g(g(_x81))), g(_x41))) → active#(sel(active(f(active(g(active(g(mark(_x81))))))), active(g(mark(_x41)))))mark#(sel(cons(sel(f(_x91), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(_x71))))))
mark#(sel(f(cons(_x61, mark(_x72))), sel(g(mark(_x61)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(mark(_x71))), active(f(mark(_x81)))))))mark#(sel(f(sel(g(_x81), _x62)), X2)) → active#(sel(active(f(active(sel(active(g(mark(_x81))), mark(_x62))))), mark(X2)))
mark#(sel(f(sel(0, 0)), _x22)) → active#(sel(active(f(sel(active(0), active(0)))), _x22))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), mark(cons(active(sel(mark(_x101), mark(_x102))), f(g(active(sel(mark(_x101), mark(_x102)))))))))))
mark#(sel(f(cons(_x61, mark(_x52))), sel(g(0), f(sel(_x101, _x102))))) → active#(sel(f(active(cons(mark(_x61), _x52))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), mark(_x102)))))))))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, _x112))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), _x112))))))))
mark#(sel(f(sel(0, 0)), mark(_x32))) → active#(sel(active(f(active(sel(active(0), active(0))))), _x32))mark#(sel(f(s(_x61)), 0)) → active#(sel(active(f(active(s(mark(_x61))))), active(0)))
mark#(sel(f(s(g(_x81))), cons(cons(_x71, _x72), _x42))) → active#(sel(active(f(active(s(active(g(mark(_x81))))))), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(f(cons(_x61, _x62)), X2)) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), mark(X2)))
mark#(sel(cons(_x61, mark(_x62)), g(f(_x71)))) → active#(sel(active(cons(_x61, _x62)), active(g(active(f(mark(_x71)))))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, 0))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(0)))))))))
mark#(sel(cons(sel(0, _x62), active(mark(_x42))), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x42)), active(g(active(f(_x81))))))mark#(sel(f(sel(_x71, _x62)), cons(_x41, _x42))) → active#(sel(active(f(active(sel(_x71, mark(_x62))))), active(cons(mark(_x41), _x42))))
mark#(sel(f(sel(_x71, _x62)), _x22)) → active#(sel(active(f(active(sel(_x71, mark(_x62))))), _x22))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(_x101, f(_x131)))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(f(mark(_x131)))))))))))
mark#(sel(f(sel(_x61, sel(_x91, _x92))), X2)) → active#(sel(active(f(active(sel(mark(_x61), active(sel(mark(_x91), mark(_x92))))))), mark(X2)))mark#(sel(f(sel(_x61, f(s(_x131)))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(f(active(s(mark(_x131))))))))), _x22))
mark#(sel(cons(sel(f(_x111), _x62), _x32), g(f(mark(_x71))))) → active#(sel(active(cons(active(sel(active(f(_x111)), mark(_x62))), _x32)), active(g(active(f(_x71))))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(g(_x111), _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(g(mark(_x111))), _x92)))), active(f(mark(_x81)))))))
mark#(sel(f(cons(sel(_x81, 0), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), active(0))), _x62)))), active(sel(mark(_x41), mark(_x42)))))mark#(sel(cons(sel(mark(_x71), _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(mark(cons(mark(_x71), f(g(mark(_x71)))))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(s(_x111), _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(s(mark(_x111))), _x92)))), active(f(mark(_x81)))))))mark#(sel(cons(sel(_x61, _x62), active(_x52)), g(f(_x81)))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), g(active(f(_x81)))))
mark#(sel(f(s(_x61)), cons(0, _x42))) → active#(sel(active(f(active(s(mark(_x61))))), active(cons(active(0), _x42))))mark#(sel(f(sel(0, 0)), _x22)) → active#(sel(mark(cons(active(sel(active(0), active(0))), f(g(active(sel(active(0), active(0))))))), _x22))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(sel(mark(_x91), mark(_x92)))), active(f(mark(_x81)))))))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(0), f(sel(s(_x121), _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(0))), active(f(active(sel(active(s(mark(_x121))), mark(_x102)))))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, active(_x102))), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x102)))), active(f(mark(_x81)))))))mark#(sel(f(sel(_x61, _x72)), X2)) → active#(sel(active(f(active(sel(mark(_x61), _x72)))), mark(X2)))
mark#(sel(f(s(_x61)), cons(s(mark(_x61)), _x42))) → active#(sel(active(f(s(mark(_x61)))), active(cons(mark(_x41), _x42))))mark#(sel(cons(_x31, _x32), g(f(0)))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(0)))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(mark(_x81)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(mark(_x71))), mark(cons(mark(_x81), f(g(mark(_x81)))))))))mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(g(0), f(_x81)))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(active(g(active(0))), active(f(mark(_x81)))))))
mark#(sel(cons(sel(f(_x91), g(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(g(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(f(s(0)), X2)) → active#(sel(active(f(active(s(active(0))))), mark(X2)))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(0, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(active(0), mark(_x102)))))))))mark#(sel(f(cons(g(_x81), _x62)), sel(g(_x71), f(_x81)))) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(sel(active(g(mark(_x71))), active(f(mark(_x81)))))))
mark#(sel(f(s(_x71)), 0)) → active#(sel(active(f(active(s(_x71)))), 0))mark#(sel(cons(_x31, _x32), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x32)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))
mark#(sel(cons(cons(_x61, _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(cons(mark(_x61), _x62)), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(sel(0, _x62), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(0), mark(_x62))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(cons(s(_x61), _x32), cons(cons(_x71, _x72), _x42))) → active#(sel(active(cons(active(s(mark(_x61))), _x32)), active(cons(active(cons(mark(_x71), _x72)), _x42))))mark#(sel(f(sel(_x61, f(0))), mark(_x32))) → active#(sel(active(f(active(sel(mark(_x61), active(f(active(0))))))), _x32))
mark#(sel(f(sel(_x61, f(0))), _x22)) → active#(sel(active(f(sel(mark(_x61), active(f(active(0)))))), _x22))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(cons(_x121, _x122), _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(active(cons(mark(_x121), _x122)), mark(_x102)))))))))
mark#(sel(cons(sel(f(_x111), _x62), _x52), g(f(_x81)))) → active#(sel(active(cons(sel(active(f(_x111)), mark(_x62)), _x52)), active(g(active(f(_x81))))))mark#(sel(f(sel(cons(_x91, _x92), _x62)), _x22)) → active#(sel(active(f(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))))), _x22))
mark#(sel(f(sel(g(_x91), f(_x111))), _x22)) → active#(sel(active(f(active(sel(active(g(mark(_x91))), active(f(_x111)))))), _x22))mark#(sel(f(_x31), X2)) → active#(sel(f(mark(_x31)), mark(X2)))
mark#(sel(cons(f(_x61), _x32), g(0))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(0)))))mark#(sel(f(g(g(sel(_x101, _x102)))), X2)) → active#(sel(active(f(active(g(active(g(active(sel(mark(_x101), mark(_x102))))))))), mark(X2)))
mark#(sel(f(cons(_x61, _x62)), sel(f(_x71), _x42))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(f(mark(_x71))), mark(_x42)))))mark#(sel(f(cons(_x61, _x62)), sel(g(_x71), f(_x91)))) → active#(sel(active(f(cons(mark(_x61), _x62))), active(sel(active(g(mark(_x71))), active(f(_x91))))))
mark#(sel(cons(sel(_x61, _x62), mark(_x52)), g(f(cons(_x91, _x92))))) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x52)), active(g(active(f(active(cons(mark(_x91), _x92))))))))mark#(sel(cons(sel(f(_x91), sel(_x101, _x102)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(sel(mark(_x101), mark(_x102))))), _x32)), active(g(active(f(_x81))))))
mark#(sel(cons(sel(f(_x91), s(_x101)), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(f(mark(_x91))), active(s(mark(_x101))))), _x32)), active(g(active(f(_x81))))))mark#(sel(cons(sel(_x61, _x72), mark(_x52)), g(f(mark(_x61))))) → active#(sel(active(cons(active(sel(mark(_x61), _x72)), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(cons(_x61, _x62)), sel(_x41, f(s(_x111))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(mark(_x41), active(f(active(s(mark(_x111)))))))))mark#(sel(cons(sel(_x71, _x72), mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x71), mark(_x72))), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, sel(_x131, _x132)))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(sel(mark(_x131), mark(_x132)))))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, _x92)), f(cons(_x101, _x102))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(active(cons(mark(_x101), _x102))))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, cons(_x131, _x132)))))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(cons(mark(_x131), _x132))))))))))mark#(sel(f(sel(_x61, _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(sel(mark(_x61), mark(_x62))))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(s(f(_x91)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(f(mark(_x91))))), _x32)), active(cons(mark(_x41), _x42))))mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, _x112))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), _x112))))))))
mark#(sel(f(cons(_x61, _x62)), sel(_x41, f(_x81)))) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(sel(mark(_x41), active(f(mark(_x81)))))))mark#(sel(f(cons(_x61, _x62)), f(_x41))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(f(mark(_x41)))))
mark#(sel(cons(sel(_x61, _x62), _x32), X2)) → active#(sel(active(cons(active(sel(mark(_x61), mark(_x62))), _x32)), mark(X2)))mark#(sel(f(sel(_x61, g(f(_x131)))), _x22)) → active#(sel(active(f(active(sel(mark(_x61), active(g(active(f(mark(_x131))))))))), _x22))
mark#(sel(cons(f(_x61), _x32), g(_x41))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), g(mark(_x41))))mark#(sel(f(sel(g(_x91), f(_x101))), _x32)) → active#(sel(f(active(sel(g(mark(_x91)), active(f(mark(_x101)))))), _x32))
mark#(sel(f(sel(_x71, _x62)), X2)) → active#(sel(mark(cons(active(sel(_x71, mark(_x62))), f(g(active(sel(_x71, mark(_x62))))))), mark(X2)))mark#(sel(f(cons(sel(cons(_x111, _x112), _x82), _x62)), sel(_x41, _x42))) → active#(sel(active(f(active(cons(active(sel(active(cons(mark(_x111), _x112)), mark(_x82))), _x62)))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(cons(_x31, mark(_x52)), g(f(sel(_x91, _x92))))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(active(sel(mark(_x91), mark(_x92)))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(sel(0, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(active(0), mark(_x92))))), active(f(mark(_x81)))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, g(_x121))), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), active(g(mark(_x121))))))), active(f(mark(_x81)))))))mark#(sel(cons(sel(s(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(s(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(g(sel(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(active(g(active(sel(mark(_x91), mark(_x92))))), active(f(mark(_x81)))))))mark#(sel(cons(s(cons(_x91, _x92)), _x32), cons(_x41, _x42))) → active#(sel(active(cons(active(s(active(cons(mark(_x91), _x92)))), _x32)), active(cons(mark(_x41), _x42))))
mark#(sel(cons(f(_x61), _x32), g(s(_x71)))) → active#(sel(active(cons(active(f(mark(_x61))), _x32)), active(g(active(s(mark(_x71)))))))mark#(sel(f(sel(s(_x91), 0)), _x22)) → active#(sel(active(f(active(sel(active(s(mark(_x91))), active(0))))), _x22))
mark#(sel(f(cons(_x61, _x62)), sel(g(0), f(sel(_x101, s(_x131)))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(0))), active(f(active(sel(mark(_x101), active(s(mark(_x131)))))))))))mark#(sel(f(cons(_x61, _x62)), sel(cons(mark(_x61), _x62), _x42))) → active#(sel(active(f(cons(mark(_x61), _x62))), active(sel(mark(_x41), mark(_x42)))))
mark#(sel(f(cons(_x61, _x62)), f(s(_x71)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(s(mark(_x71)))))))mark#(sel(f(sel(_x61, g(_x101))), active(_x32))) → active#(sel(active(f(active(sel(mark(_x61), active(g(mark(_x101))))))), _x32))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(_x91, cons(_x121, _x122))), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(mark(_x91), active(cons(mark(_x121), _x122)))))), active(f(mark(_x81)))))))mark#(sel(f(s(_x61)), X2)) → active#(sel(mark(cons(active(s(mark(_x61))), f(g(active(s(mark(_x61))))))), mark(X2)))
mark#(sel(f(cons(_x61, _x62)), sel(g(sel(g(_x111), _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(sel(active(g(mark(_x111))), mark(_x92))))), active(f(mark(_x81)))))))mark#(f(X)) → active#(f(mark(X)))
mark#(sel(cons(sel(cons(_x91, _x92), _x62), _x32), g(f(_x81)))) → active#(sel(active(cons(active(sel(active(cons(mark(_x91), _x92)), mark(_x62))), _x32)), active(g(active(f(_x81))))))mark#(sel(f(sel(g(_x91), f(sel(_x121, _x122)))), _x22)) → active#(sel(active(f(active(sel(active(g(mark(_x91))), active(f(active(sel(mark(_x121), mark(_x122))))))))), _x22))
mark#(sel(f(cons(cons(_x81, _x82), _x62)), sel(g(_x71), f(_x81)))) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(sel(active(g(mark(_x71))), active(f(mark(_x81)))))))mark#(sel(f(cons(_x61, _x62)), f(f(_x71)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(f(active(f(mark(_x71)))))))
mark#(sel(f(g(_x61)), X2)) → active#(sel(mark(cons(active(g(mark(_x61))), f(g(active(g(mark(_x61))))))), mark(X2)))mark#(sel(cons(_x31, active(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(active(f(mark(_x71)))))))
mark#(sel(f(cons(s(_x81), _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(mark(_x81)))))))mark#(sel(f(cons(f(_x81), _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), active(f(mark(_x81)))))))
mark#(sel(cons(sel(_x61, 0), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(mark(_x61), active(0))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(cons(_x31, mark(_x52)), g(f(_x71)))) → active#(sel(active(cons(mark(_x31), _x52)), active(g(f(mark(_x71))))))
mark#(sel(f(sel(_x61, _x62)), s(_x41))) → active#(sel(active(f(active(sel(mark(_x61), mark(_x62))))), active(s(mark(_x41)))))mark#(sel(f(sel(_x71, cons(_x101, _x102))), X2)) → active#(sel(active(f(active(sel(_x71, active(cons(mark(_x101), _x102)))))), mark(X2)))
mark#(sel(cons(sel(g(_x91), _x62), _x32), g(f(_x71)))) → active#(sel(active(cons(active(sel(active(g(mark(_x91))), mark(_x62))), _x32)), active(g(active(f(mark(_x71)))))))mark#(sel(f(sel(_x61, _x62)), X2)) → active#(sel(f(active(sel(mark(_x61), mark(_x62)))), mark(X2)))

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

The right-hand side of the rule mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81)))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(sel(mark(_x111), mark(_x112))), _x92)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(active(g(mark(_x91)))))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81))))) 
active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(active(sel(mark(_x91), mark(_x92)))))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(g(active(cons(mark(_x91), _x92))), f(mark(_x81)))))) 
active#(sel(active(f(cons(mark(_x61), _x62))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(cons(mark(_x91), _x92))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(active(0)))))) 
active#(sel(active(f(active(cons(active(0), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(active(cons(mark(_x91), _x92))))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(cons(mark(_x111), _x112)), _x92)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(active(s(mark(_x91)))))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(0), _x92)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(f(mark(_x111))), _x92)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(_x101, _x102)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(_x71))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(s(mark(_x111))), _x92)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(active(f(mark(_x91)))))))) 
active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(g(mark(_x111))), _x92)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81)))))) 
active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x102)))), f(mark(_x81)))))) 
active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81)))))) 
active#(sel(active(f(active(cons(_x71, _x72)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81)))))) 
Thus, the rule mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81)))))) is replaced by the following rules:
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(cons(_x91, _x92))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(active(cons(mark(_x91), _x92)))))))mark#(sel(f(cons(_x61, mark(_x72))), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81))))))
mark#(sel(f(cons(sel(_x81, _x82), _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(sel(mark(_x81), mark(_x82))), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81))))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(s(_x91))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(active(s(mark(_x91))))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(cons(mark(_x61), _x62))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81))))))mark#(sel(f(cons(_x61, active(_x72))), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x72)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, active(_x102))), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x102)))), f(mark(_x81))))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(sel(_x111, _x112), _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(sel(mark(_x111), mark(_x112))), _x92)))), f(mark(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(cons(mark(_x91), _x92))), f(mark(_x81))))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(mark(cons(active(cons(mark(_x61), _x62)), f(g(active(cons(mark(_x61), _x62)))))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(0)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(active(0))))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(f(_x111), _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(f(mark(_x111))), _x92)))), f(mark(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, mark(_x102))), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x102)))), f(mark(_x81))))))mark#(sel(f(cons(s(_x81), _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(s(mark(_x81))), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81))))))
mark#(sel(f(cons(f(_x81), _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(f(mark(_x81))), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81))))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81)))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(cons(_x111, _x112), _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(cons(mark(_x111), _x112)), _x92)))), f(mark(_x81))))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(g(_x91))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(active(g(mark(_x91))))))))
mark#(sel(f(cons(_x71, _x72)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(_x71, _x72)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81))))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(sel(_x91, _x92))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(active(sel(mark(_x91), mark(_x92))))))))
mark#(sel(f(cons(g(_x81), _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(g(mark(_x81))), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81))))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x71)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(_x71)))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(g(active(cons(mark(_x91), _x92))), f(mark(_x81))))))mark#(sel(f(cons(0, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(0), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(0, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(0), _x92)))), f(mark(_x81))))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(f(active(cons(mark(_x61), _x62))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x91, _x92)), f(f(_x91))))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(active(f(mark(_x91))))))))mark#(sel(f(cons(_x61, _x62)), sel(g(cons(s(_x111), _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(s(mark(_x111))), _x92)))), f(mark(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(_x101, _x102)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(_x101, _x102)))), f(mark(_x81))))))mark#(sel(f(cons(cons(_x81, _x82), _x62)), sel(g(cons(_x91, _x92)), f(_x81)))) → active#(sel(active(f(active(cons(active(cons(mark(_x81), _x82)), _x62)))), active(sel(active(g(active(cons(mark(_x91), _x92)))), f(mark(_x81))))))
mark#(sel(f(cons(_x61, _x62)), sel(g(cons(g(_x111), _x92)), f(_x81)))) → active#(sel(active(f(active(cons(mark(_x61), _x62)))), active(sel(active(g(active(cons(active(g(mark(_x111))), _x92)))), f(mark(_x81))))))

Problem 5: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

g#(active(X)) → g#(X)g#(mark(X)) → g#(X)

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

g#(active(X)) → g#(X)g#(mark(X)) → g#(X)

Problem 6: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

sel#(active(X1), X2) → sel#(X1, X2)sel#(mark(X1), X2) → sel#(X1, X2)
sel#(X1, active(X2)) → sel#(X1, X2)sel#(X1, mark(X2)) → sel#(X1, X2)

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

sel#(mark(X1), X2) → sel#(X1, X2)sel#(active(X1), X2) → sel#(X1, X2)

Problem 9: ReductionPairSAT

Dependency Pair Problem

Dependency Pairs

sel#(X1, active(X2)) → sel#(X1, X2)sel#(X1, mark(X2)) → sel#(X1, X2)

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

Function Precedence

sel# < active = mark < f = g = 0 = s = sel = cons

Argument Filtering

f: all arguments are removed from f
g: all arguments are removed from g
0: all arguments are removed from 0
s: collapses to 1
active: collapses to 1
mark: 1
sel#: collapses to 2
sel: all arguments are removed from sel
cons: 1

Status

f: multiset
g: multiset
0: multiset
mark: multiset
sel: multiset
cons: lexicographic with permutation 1 → 1

Usable Rules

There are no usable rules.

The dependency pairs and usable rules are stronlgy conservative!

Eliminated dependency pairs

The following dependency pairs (at least) can be eliminated according to the given precedence.

sel#(X1, mark(X2)) → sel#(X1, X2)

Problem 12: ReductionPairSAT

Dependency Pair Problem

Dependency Pairs

sel#(X1, active(X2)) → sel#(X1, X2)

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

Function Precedence

active < f = g = 0 = s = mark = sel# = sel = cons

Argument Filtering

f: all arguments are removed from f
g: all arguments are removed from g
0: all arguments are removed from 0
s: all arguments are removed from s
active: 1
mark: all arguments are removed from mark
sel#: collapses to 2
sel: all arguments are removed from sel
cons: 1

Status

f: multiset
g: multiset
0: multiset
s: multiset
active: multiset
mark: multiset
sel: multiset
cons: lexicographic with permutation 1 → 1

Usable Rules

There are no usable rules.

The dependency pairs and usable rules are stronlgy conservative!

Eliminated dependency pairs

The following dependency pairs (at least) can be eliminated according to the given precedence.

sel#(X1, active(X2)) → sel#(X1, X2)

Problem 7: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

f#(active(X)) → f#(X)f#(mark(X)) → f#(X)

Rewrite Rules

active(f(X)) → mark(cons(X, f(g(X))))active(g(0)) → mark(s(0))
active(g(s(X))) → mark(s(s(g(X))))active(sel(0, cons(X, Y))) → mark(X)
active(sel(s(X), cons(Y, Z))) → mark(sel(X, Z))mark(f(X)) → active(f(mark(X)))
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(g(X)) → active(g(mark(X)))
mark(0) → active(0)mark(s(X)) → active(s(mark(X)))
mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))f(mark(X)) → f(X)
f(active(X)) → f(X)cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)g(mark(X)) → g(X)
g(active(X)) → g(X)s(mark(X)) → s(X)
s(active(X)) → s(X)sel(mark(X1), X2) → sel(X1, X2)
sel(X1, mark(X2)) → sel(X1, X2)sel(active(X1), X2) → sel(X1, X2)
sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: f, g, 0, s, active, mark, sel, cons

Strategy

Projection

The following projection was used:

Thus, the following dependency pairs are removed:

f#(active(X)) → f#(X)f#(mark(X)) → f#(X)