TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60001 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (637ms).
 | – Problem 2 was processed with processor SubtermCriterion (2ms).
 |    | – Problem 8 was processed with processor ReductionPairSAT (67ms).
 |    |    | – Problem 11 was processed with processor ReductionPairSAT (65ms).
 | – Problem 3 was processed with processor ReductionPairSAT (2218ms).
 |    | – Problem 10 was processed with processor ReductionPairSAT (2908ms).
 |    |    | – Problem 13 was processed with processor ReductionPairSAT (2268ms).
 |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (20ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (28ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (32ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (40ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (104ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (42ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (47ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 was processed with processor ForwardNarrowing (120ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 28 was processed with processor ForwardNarrowing (65ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 29 was processed with processor ForwardNarrowing (145ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 30 was processed with processor ForwardNarrowing (69ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 31 was processed with processor ForwardNarrowing (145ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 32 was processed with processor ForwardNarrowing (91ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 33 was processed with processor ForwardNarrowing (195ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 34 was processed with processor ForwardNarrowing (768ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 35 remains open; application of the following processors failed [ForwardNarrowing (663ms), ForwardNarrowing (780ms), ForwardNarrowing (519ms), ForwardNarrowing (559ms), ForwardNarrowing (432ms), ForwardNarrowing (656ms), ForwardNarrowing (595ms), ForwardNarrowing (708ms), ForwardNarrowing (713ms), ForwardNarrowing (674ms), ForwardNarrowing (1082ms), ForwardNarrowing (651ms), ForwardNarrowing (1339ms), ForwardNarrowing (783ms), ForwardNarrowing (timeout)].
 | – Problem 4 was processed with processor SubtermCriterion (1ms).
 | – Problem 5 was processed with processor SubtermCriterion (3ms).
 | – Problem 6 was processed with processor SubtermCriterion (1ms).
 |    | – Problem 9 was processed with processor ReductionPairSAT (83ms).
 |    |    | – Problem 12 was processed with processor ReductionPairSAT (65ms).
 | – Problem 7 was processed with processor SubtermCriterion (1ms).

The following open problems remain:



Open Dependency Pair Problem 14

Dependency Pairs

mark#(from(X))active#(from(mark(X)))mark#(from(X))mark#(X)
mark#(cons(X1, X2))mark#(X1)mark#(s(X))mark#(X)
active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)active#(from(X))mark#(cons(X, from(s(X))))
mark#(2nd(X))active#(2nd(mark(X)))mark#(cons1(X1, X2))mark#(X2)
active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))mark#(cons1(X1, X2))mark#(X1)
mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons


Problem 1: DependencyGraph



Dependency Pair Problem

Dependency Pairs

mark#(cons1(X1, X2))cons1#(mark(X1), mark(X2))mark#(cons(X1, X2))active#(cons(mark(X1), X2))
cons1#(X1, active(X2))cons1#(X1, X2)cons#(mark(X1), X2)cons#(X1, X2)
2nd#(mark(X))2nd#(X)active#(2nd(cons(X, X1)))2nd#(cons1(X, X1))
from#(mark(X))from#(X)mark#(s(X))s#(mark(X))
mark#(cons1(X1, X2))mark#(X1)active#(2nd(cons(X, X1)))cons1#(X, X1)
2nd#(active(X))2nd#(X)active#(from(X))cons#(X, from(s(X)))
cons1#(X1, mark(X2))cons1#(X1, X2)cons#(X1, mark(X2))cons#(X1, X2)
mark#(s(X))mark#(X)mark#(cons(X1, X2))cons#(mark(X1), X2)
mark#(cons1(X1, X2))active#(cons1(mark(X1), mark(X2)))mark#(2nd(X))2nd#(mark(X))
mark#(s(X))active#(s(mark(X)))mark#(from(X))mark#(X)
mark#(cons(X1, X2))mark#(X1)cons#(active(X1), X2)cons#(X1, X2)
active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)mark#(2nd(X))active#(2nd(mark(X)))
active#(from(X))mark#(cons(X, from(s(X))))mark#(cons1(X1, X2))mark#(X2)
active#(from(X))s#(X)s#(mark(X))s#(X)
cons#(X1, active(X2))cons#(X1, X2)mark#(from(X))from#(mark(X))
cons1#(mark(X1), X2)cons1#(X1, X2)mark#(from(X))active#(from(mark(X)))
from#(active(X))from#(X)s#(active(X))s#(X)
cons1#(active(X1), X2)cons1#(X1, X2)active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))
active#(from(X))from#(s(X))mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The following SCCs where found

from#(active(X)) → from#(X)from#(mark(X)) → from#(X)

mark#(cons(X1, X2)) → active#(cons(mark(X1), X2))mark#(s(X)) → active#(s(mark(X)))
mark#(from(X)) → mark#(X)mark#(cons(X1, X2)) → mark#(X1)
active#(2nd(cons1(X, cons(Y, Z)))) → mark#(Y)active#(from(X)) → mark#(cons(X, from(s(X))))
mark#(2nd(X)) → active#(2nd(mark(X)))mark#(cons1(X1, X2)) → mark#(X2)
mark#(cons1(X1, X2)) → mark#(X1)mark#(from(X)) → active#(from(mark(X)))
mark#(s(X)) → mark#(X)active#(2nd(cons(X, X1))) → mark#(2nd(cons1(X, X1)))
mark#(cons1(X1, X2)) → active#(cons1(mark(X1), mark(X2)))mark#(2nd(X)) → mark#(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)

2nd#(active(X)) → 2nd#(X)2nd#(mark(X)) → 2nd#(X)

cons1#(X1, active(X2)) → cons1#(X1, X2)cons1#(mark(X1), X2) → cons1#(X1, X2)
cons1#(X1, mark(X2)) → cons1#(X1, X2)cons1#(active(X1), X2) → cons1#(X1, X2)

Problem 2: SubtermCriterion



Dependency Pair Problem

Dependency Pairs

cons1#(X1, active(X2))cons1#(X1, X2)cons1#(mark(X1), X2)cons1#(X1, X2)
cons1#(X1, mark(X2))cons1#(X1, X2)cons1#(active(X1), X2)cons1#(X1, X2)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


Projection

The following projection was used:

Thus, the following dependency pairs are removed:

cons1#(mark(X1), X2)cons1#(X1, X2)cons1#(active(X1), X2)cons1#(X1, X2)

Problem 8: ReductionPairSAT



Dependency Pair Problem

Dependency Pairs

cons1#(X1, active(X2))cons1#(X1, X2)cons1#(X1, mark(X2))cons1#(X1, X2)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


Function Precedence

mark < active < 2nd = cons1# = cons1 = s = from = cons

Argument Filtering

2nd: all arguments are removed from 2nd
cons1#: collapses to 2
cons1: 2
s: 1
active: collapses to 1
mark: 1
from: all arguments are removed from from
cons: 1 2

Status

2nd: multiset
cons1: lexicographic with permutation 2 → 1
s: lexicographic with permutation 1 → 1
mark: multiset
from: multiset
cons: lexicographic with permutation 1 → 1 2 → 2

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.

cons1#(X1, mark(X2)) → cons1#(X1, X2)

Problem 11: ReductionPairSAT



Dependency Pair Problem

Dependency Pairs

cons1#(X1, active(X2))cons1#(X1, X2)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


Function Precedence

active < 2nd = cons1# = cons1 = s = mark = from = cons

Argument Filtering

2nd: all arguments are removed from 2nd
cons1#: collapses to 2
cons1: 1 2
s: all arguments are removed from s
active: 1
mark: all arguments are removed from mark
from: 1
cons: 1

Status

2nd: multiset
cons1: lexicographic with permutation 1 → 1 2 → 2
s: multiset
active: multiset
mark: multiset
from: lexicographic with permutation 1 → 1
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.

cons1#(X1, active(X2)) → cons1#(X1, X2)

Problem 3: ReductionPairSAT



Dependency Pair Problem

Dependency Pairs

mark#(cons(X1, X2))active#(cons(mark(X1), X2))mark#(s(X))active#(s(mark(X)))
mark#(from(X))mark#(X)mark#(cons(X1, X2))mark#(X1)
active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)mark#(2nd(X))active#(2nd(mark(X)))
active#(from(X))mark#(cons(X, from(s(X))))mark#(cons1(X1, X2))mark#(X2)
mark#(cons1(X1, X2))mark#(X1)mark#(from(X))active#(from(mark(X)))
mark#(s(X))mark#(X)mark#(cons1(X1, X2))active#(cons1(mark(X1), mark(X2)))
active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


Function Precedence

active < 2nd = cons1 = s = mark = from = active# = mark# < cons

Argument Filtering

2nd: all arguments are removed from 2nd
cons1: all arguments are removed from cons1
s: all arguments are removed from s
active: collapses to 1
mark: all arguments are removed from mark
from: all arguments are removed from from
active#: collapses to 1
mark#: all arguments are removed from mark#
cons: all arguments are removed from cons

Status

2nd: multiset
cons1: multiset
s: multiset
mark: multiset
from: multiset
mark#: multiset
cons: multiset

Usable Rules

cons(active(X1), X2) → cons(X1, X2)2nd(mark(X)) → 2nd(X)
from(mark(X)) → from(X)mark(2nd(X)) → active(2nd(mark(X)))
mark(s(X)) → active(s(mark(X)))cons1(active(X1), X2) → cons1(X1, X2)
active(2nd(cons1(X, cons(Y, Z)))) → mark(Y)cons1(X1, active(X2)) → cons1(X1, X2)
active(2nd(cons(X, X1))) → mark(2nd(cons1(X, X1)))cons(X1, mark(X2)) → cons(X1, X2)
cons1(mark(X1), X2) → cons1(X1, X2)cons(mark(X1), X2) → cons(X1, X2)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(from(X)) → active(from(mark(X)))
mark(cons1(X1, X2)) → active(cons1(mark(X1), mark(X2)))cons1(X1, mark(X2)) → cons1(X1, X2)
s(mark(X)) → s(X)active(from(X)) → mark(cons(X, from(s(X))))
2nd(active(X)) → 2nd(X)s(active(X)) → s(X)
from(active(X)) → from(X)cons(X1, active(X2)) → cons(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 10: ReductionPairSAT



Dependency Pair Problem

Dependency Pairs

mark#(s(X))active#(s(mark(X)))mark#(from(X))mark#(X)
mark#(cons(X1, X2))mark#(X1)active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)
mark#(2nd(X))active#(2nd(mark(X)))active#(from(X))mark#(cons(X, from(s(X))))
mark#(cons1(X1, X2))mark#(X2)mark#(cons1(X1, X2))mark#(X1)
mark#(from(X))active#(from(mark(X)))mark#(s(X))mark#(X)
mark#(cons1(X1, X2))active#(cons1(mark(X1), mark(X2)))active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))
mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


Function Precedence

active = mark < 2nd = s = from = active# = mark# < cons1 = cons

Argument Filtering

2nd: all arguments are removed from 2nd
cons1: all arguments are removed from cons1
s: all arguments are removed from s
active: all arguments are removed from active
mark: all arguments are removed from mark
from: all arguments are removed from from
active#: collapses to 1
mark#: all arguments are removed from mark#
cons: all arguments are removed from cons

Status

2nd: multiset
cons1: multiset
s: multiset
active: multiset
mark: multiset
from: multiset
mark#: multiset
cons: multiset

Usable Rules

cons(active(X1), X2) → cons(X1, X2)2nd(mark(X)) → 2nd(X)
from(mark(X)) → from(X)mark(2nd(X)) → active(2nd(mark(X)))
mark(s(X)) → active(s(mark(X)))cons1(active(X1), X2) → cons1(X1, X2)
active(2nd(cons1(X, cons(Y, Z)))) → mark(Y)cons1(X1, active(X2)) → cons1(X1, X2)
active(2nd(cons(X, X1))) → mark(2nd(cons1(X, X1)))cons(X1, mark(X2)) → cons(X1, X2)
cons1(mark(X1), X2) → cons1(X1, X2)cons(mark(X1), X2) → cons(X1, X2)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(from(X)) → active(from(mark(X)))
mark(cons1(X1, X2)) → active(cons1(mark(X1), mark(X2)))cons1(X1, mark(X2)) → cons1(X1, X2)
s(mark(X)) → s(X)active(from(X)) → mark(cons(X, from(s(X))))
2nd(active(X)) → 2nd(X)s(active(X)) → s(X)
from(active(X)) → from(X)cons(X1, active(X2)) → cons(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#(cons1(X1, X2)) → active#(cons1(mark(X1), mark(X2)))

Problem 13: ReductionPairSAT



Dependency Pair Problem

Dependency Pairs

mark#(s(X))active#(s(mark(X)))mark#(from(X))active#(from(mark(X)))
mark#(from(X))mark#(X)mark#(cons(X1, X2))mark#(X1)
mark#(s(X))mark#(X)active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)
active#(from(X))mark#(cons(X, from(s(X))))mark#(2nd(X))active#(2nd(mark(X)))
mark#(cons1(X1, X2))mark#(X2)active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))
mark#(cons1(X1, X2))mark#(X1)mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


Function Precedence

active < active# < 2nd = cons1 = mark = from = mark# = cons < s

Argument Filtering

2nd: all arguments are removed from 2nd
cons1: all arguments are removed from cons1
s: all arguments are removed from s
active: collapses to 1
mark: all arguments are removed from mark
from: all arguments are removed from from
active#: collapses to 1
mark#: all arguments are removed from mark#
cons: all arguments are removed from cons

Status

2nd: multiset
cons1: multiset
s: multiset
mark: multiset
from: multiset
mark#: multiset
cons: multiset

Usable Rules

cons(active(X1), X2) → cons(X1, X2)2nd(mark(X)) → 2nd(X)
from(mark(X)) → from(X)mark(2nd(X)) → active(2nd(mark(X)))
mark(s(X)) → active(s(mark(X)))cons1(active(X1), X2) → cons1(X1, X2)
active(2nd(cons1(X, cons(Y, Z)))) → mark(Y)cons1(X1, active(X2)) → cons1(X1, X2)
active(2nd(cons(X, X1))) → mark(2nd(cons1(X, X1)))cons(X1, mark(X2)) → cons(X1, X2)
cons1(mark(X1), X2) → cons1(X1, X2)cons(mark(X1), X2) → cons(X1, X2)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))mark(from(X)) → active(from(mark(X)))
mark(cons1(X1, X2)) → active(cons1(mark(X1), mark(X2)))cons1(X1, mark(X2)) → cons1(X1, X2)
s(mark(X)) → s(X)active(from(X)) → mark(cons(X, from(s(X))))
2nd(active(X)) → 2nd(X)s(active(X)) → s(X)
from(active(X)) → from(X)cons(X1, active(X2)) → cons(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 14: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(from(X))active#(from(mark(X)))mark#(from(X))mark#(X)
mark#(cons(X1, X2))mark#(X1)active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)
mark#(s(X))mark#(X)mark#(2nd(X))active#(2nd(mark(X)))
active#(from(X))mark#(cons(X, from(s(X))))mark#(cons1(X1, X2))mark#(X2)
mark#(cons1(X1, X2))mark#(X1)active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))
mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(X)) → active#(2nd(mark(X))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
active#(2nd(active(cons1(mark(_x31), mark(_x32))))) 
active#(2nd(active(cons(mark(_x31), _x32)))) 
active#(2nd(_x21)) 
active#(2nd(active(2nd(mark(_x31))))) 
active#(2nd(active(from(mark(_x31))))) 
active#(2nd(active(s(mark(_x31))))) 
Thus, the rule mark#(2nd(X)) → active#(2nd(mark(X))) is replaced by the following rules:
mark#(2nd(cons1(_x31, _x32))) → active#(2nd(active(cons1(mark(_x31), mark(_x32)))))mark#(2nd(_x21)) → active#(2nd(_x21))
mark#(2nd(2nd(_x31))) → active#(2nd(active(2nd(mark(_x31)))))mark#(2nd(s(_x31))) → active#(2nd(active(s(mark(_x31)))))
mark#(2nd(cons(_x31, _x32))) → active#(2nd(active(cons(mark(_x31), _x32))))mark#(2nd(from(_x31))) → active#(2nd(active(from(mark(_x31)))))

Problem 15: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(_x31, _x32)))active#(2nd(active(cons1(mark(_x31), mark(_x32)))))mark#(from(X))mark#(X)
mark#(cons(X1, X2))mark#(X1)mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))
mark#(2nd(s(_x31)))active#(2nd(active(s(mark(_x31)))))mark#(2nd(cons(_x31, _x32)))active#(2nd(active(cons(mark(_x31), _x32))))
active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)active#(from(X))mark#(cons(X, from(s(X))))
mark#(2nd(from(_x31)))active#(2nd(active(from(mark(_x31)))))mark#(cons1(X1, X2))mark#(X2)
mark#(cons1(X1, X2))mark#(X1)mark#(from(X))active#(from(mark(X)))
mark#(2nd(_x21))active#(2nd(_x21))mark#(s(X))mark#(X)
active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(_x31, _x32))) → active#(2nd(active(cons1(mark(_x31), mark(_x32))))) 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#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32))))) 
active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32))))) 
active#(2nd(active(cons1(mark(_x31), _x52)))) 
active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), mark(_x32))))) 
active#(2nd(cons1(mark(_x31), mark(_x32)))) 
active#(2nd(active(cons1(active(from(mark(_x61))), mark(_x32))))) 
active#(2nd(active(cons1(mark(_x31), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(s(mark(_x61))), mark(_x32))))) 
active#(2nd(active(cons1(mark(_x31), active(2nd(mark(_x71))))))) 
active#(2nd(active(cons1(mark(_x31), active(from(mark(_x71))))))) 
active#(2nd(active(cons1(_x51, mark(_x32))))) 
active#(2nd(active(cons1(mark(_x31), active(s(mark(_x71))))))) 
active#(2nd(active(cons1(mark(_x31), active(cons1(mark(_x71), mark(_x72))))))) 
Thus, the rule mark#(2nd(cons1(_x31, _x32))) → active#(2nd(active(cons1(mark(_x31), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(_x51, _x32))) → active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x32))) → active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), mark(_x32)))))
mark#(2nd(cons1(from(_x61), _x32))) → active#(2nd(active(cons1(active(from(mark(_x61))), mark(_x32)))))mark#(2nd(cons1(_x31, s(_x71)))) → active#(2nd(active(cons1(mark(_x31), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons1(_x61, _x62), _x32))) → active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))mark#(2nd(cons1(_x31, 2nd(_x71)))) → active#(2nd(active(cons1(mark(_x31), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(2nd(_x61), _x32))) → active#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32)))))mark#(2nd(cons1(_x31, cons1(_x71, _x72)))) → active#(2nd(active(cons1(mark(_x31), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(_x31, _x32))) → active#(2nd(cons1(mark(_x31), mark(_x32))))mark#(2nd(cons1(s(_x61), _x32))) → active#(2nd(active(cons1(active(s(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(_x31, cons(_x71, _x72)))) → active#(2nd(active(cons1(mark(_x31), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(_x31, from(_x71)))) → active#(2nd(active(cons1(mark(_x31), active(from(mark(_x71)))))))
mark#(2nd(cons1(_x31, _x52))) → active#(2nd(active(cons1(mark(_x31), _x52))))

Problem 16: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(_x51, _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(2nd(cons1(from(_x61), _x32)))active#(2nd(active(cons1(active(from(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), mark(_x32)))))mark#(2nd(cons1(cons1(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))
mark#(2nd(cons1(_x31, 2nd(_x71))))active#(2nd(active(cons1(mark(_x31), active(2nd(mark(_x71)))))))mark#(2nd(cons(_x31, _x32)))active#(2nd(active(cons(mark(_x31), _x32))))
mark#(cons1(X1, X2))mark#(X1)mark#(2nd(cons1(_x31, cons1(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(_x21))active#(2nd(_x21))mark#(s(X))mark#(X)
mark#(2nd(cons1(_x31, cons(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons(mark(_x71), _x72))))))mark#(from(X))mark#(X)
mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))mark#(cons(X1, X2))mark#(X1)
mark#(2nd(cons1(_x31, s(_x71))))active#(2nd(active(cons1(mark(_x31), active(s(mark(_x71)))))))mark#(2nd(s(_x31)))active#(2nd(active(s(mark(_x31)))))
active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)active#(from(X))mark#(cons(X, from(s(X))))
mark#(2nd(cons1(2nd(_x61), _x32)))active#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32)))))mark#(2nd(from(_x31)))active#(2nd(active(from(mark(_x31)))))
mark#(cons1(X1, X2))mark#(X2)mark#(from(X))active#(from(mark(X)))
mark#(2nd(cons1(_x31, _x32)))active#(2nd(cons1(mark(_x31), mark(_x32))))mark#(2nd(cons1(s(_x61), _x32)))active#(2nd(active(cons1(active(s(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(_x31, from(_x71))))active#(2nd(active(cons1(mark(_x31), active(from(mark(_x71)))))))active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))
mark#(2nd(cons1(_x31, _x52)))active#(2nd(active(cons1(mark(_x31), _x52))))mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(_x51, _x32))) → active#(2nd(active(cons1(_x51, mark(_x32))))) 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#(2nd(cons1(_x51, mark(_x32)))) 
active#(2nd(active(cons1(_x51, active(from(mark(_x81))))))) 
active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82))))))) 
active#(2nd(active(cons1(_x51, active(2nd(mark(_x81))))))) 
active#(2nd(active(cons1(_x61, mark(_x32))))) 
active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82)))))) 
active#(2nd(active(cons1(_x61, _x62)))) 
active#(2nd(active(cons1(_x51, active(s(mark(_x81))))))) 
Thus, the rule mark#(2nd(cons1(_x51, _x32))) → active#(2nd(active(cons1(_x51, mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(_x51, _x32))) → active#(2nd(cons1(_x51, mark(_x32))))mark#(2nd(cons1(_x51, s(_x81)))) → active#(2nd(active(cons1(_x51, active(s(mark(_x81)))))))
mark#(2nd(cons1(active(_x61), _x32))) → active#(2nd(active(cons1(_x61, mark(_x32)))))mark#(2nd(cons1(_x51, 2nd(_x81)))) → active#(2nd(active(cons1(_x51, active(2nd(mark(_x81)))))))
mark#(2nd(cons1(mark(_x61), _x32))) → active#(2nd(active(cons1(_x61, mark(_x32)))))mark#(2nd(cons1(_x51, cons(_x81, _x82)))) → active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))
mark#(2nd(cons1(_x51, from(_x81)))) → active#(2nd(active(cons1(_x51, active(from(mark(_x81)))))))mark#(2nd(cons1(_x61, _x62))) → active#(2nd(active(cons1(_x61, _x62))))
mark#(2nd(cons1(_x51, cons1(_x81, _x82)))) → active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82)))))))

Problem 17: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(active(_x61), _x32)))active#(2nd(active(cons1(_x61, mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), mark(_x32)))))
mark#(2nd(cons1(from(_x61), _x32)))active#(2nd(active(cons1(active(from(mark(_x61))), mark(_x32)))))mark#(2nd(cons1(cons1(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))
mark#(2nd(cons(_x31, _x32)))active#(2nd(active(cons(mark(_x31), _x32))))mark#(2nd(cons1(_x31, 2nd(_x71))))active#(2nd(active(cons1(mark(_x31), active(2nd(mark(_x71)))))))
mark#(cons1(X1, X2))mark#(X1)mark#(2nd(cons1(_x51, cons1(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82)))))))
mark#(2nd(cons1(_x31, cons1(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(_x21))active#(2nd(_x21))
mark#(2nd(cons1(_x31, cons(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons(mark(_x71), _x72))))))mark#(s(X))mark#(X)
mark#(2nd(cons1(mark(_x61), _x32)))active#(2nd(active(cons1(_x61, mark(_x32)))))mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))
mark#(2nd(cons1(_x51, _x32)))active#(2nd(cons1(_x51, mark(_x32))))mark#(2nd(cons1(_x51, 2nd(_x81))))active#(2nd(active(cons1(_x51, active(2nd(mark(_x81)))))))
mark#(from(X))mark#(X)mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))
mark#(cons(X1, X2))mark#(X1)mark#(2nd(cons1(_x31, s(_x71))))active#(2nd(active(cons1(mark(_x31), active(s(mark(_x71)))))))
mark#(2nd(s(_x31)))active#(2nd(active(s(mark(_x31)))))active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)
active#(from(X))mark#(cons(X, from(s(X))))mark#(2nd(cons1(2nd(_x61), _x32)))active#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32)))))
mark#(2nd(from(_x31)))active#(2nd(active(from(mark(_x31)))))mark#(cons1(X1, X2))mark#(X2)
mark#(2nd(cons1(_x51, from(_x81))))active#(2nd(active(cons1(_x51, active(from(mark(_x81)))))))mark#(2nd(cons1(_x51, s(_x81))))active#(2nd(active(cons1(_x51, active(s(mark(_x81)))))))
mark#(from(X))active#(from(mark(X)))mark#(2nd(cons1(_x31, _x32)))active#(2nd(cons1(mark(_x31), mark(_x32))))
mark#(2nd(cons1(s(_x61), _x32)))active#(2nd(active(cons1(active(s(mark(_x61))), mark(_x32)))))mark#(2nd(cons1(_x31, from(_x71))))active#(2nd(active(cons1(mark(_x31), active(from(mark(_x71)))))))
mark#(2nd(cons1(_x31, _x52)))active#(2nd(active(cons1(mark(_x31), _x52))))active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))
mark#(2nd(X))mark#(X)mark#(2nd(cons1(_x61, _x62)))active#(2nd(active(cons1(_x61, _x62))))

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(active(_x61), _x32))) → active#(2nd(active(cons1(_x61, mark(_x32))))) 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#(2nd(cons1(_x61, mark(_x32)))) 
active#(2nd(active(cons1(_x61, active(2nd(mark(_x71))))))) 
active#(2nd(active(cons1(_x61, active(from(mark(_x71))))))) 
active#(2nd(active(cons1(_x61, active(s(mark(_x71))))))) 
active#(2nd(active(cons1(_x61, active(cons1(mark(_x71), mark(_x72))))))) 
active#(2nd(active(cons1(_x51, _x52)))) 
active#(2nd(active(cons1(_x51, mark(_x32))))) 
active#(2nd(active(cons1(_x61, active(cons(mark(_x71), _x72)))))) 
Thus, the rule mark#(2nd(cons1(active(_x61), _x32))) → active#(2nd(active(cons1(_x61, mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(active(_x61), 2nd(_x71)))) → active#(2nd(active(cons1(_x61, active(2nd(mark(_x71)))))))mark#(2nd(cons1(active(_x61), cons(_x71, _x72)))) → active#(2nd(active(cons1(_x61, active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(active(_x51), _x52))) → active#(2nd(active(cons1(_x51, _x52))))mark#(2nd(cons1(active(mark(_x51)), _x32))) → active#(2nd(active(cons1(_x51, mark(_x32)))))
mark#(2nd(cons1(active(active(_x51)), _x32))) → active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(2nd(cons1(active(_x61), cons1(_x71, _x72)))) → active#(2nd(active(cons1(_x61, active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(active(_x61), from(_x71)))) → active#(2nd(active(cons1(_x61, active(from(mark(_x71)))))))mark#(2nd(cons1(active(_x61), _x32))) → active#(2nd(cons1(_x61, mark(_x32))))
mark#(2nd(cons1(active(_x61), s(_x71)))) → active#(2nd(active(cons1(_x61, active(s(mark(_x71)))))))

Problem 18: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(from(_x61), _x32)))active#(2nd(active(cons1(active(from(mark(_x61))), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons1(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))mark#(2nd(cons1(_x31, 2nd(_x71))))active#(2nd(active(cons1(mark(_x31), active(2nd(mark(_x71)))))))
mark#(2nd(cons(_x31, _x32)))active#(2nd(active(cons(mark(_x31), _x32))))mark#(2nd(cons1(active(_x61), cons1(_x71, _x72))))active#(2nd(active(cons1(_x61, active(cons1(mark(_x71), mark(_x72)))))))
mark#(cons1(X1, X2))mark#(X1)mark#(2nd(cons1(active(_x61), _x32)))active#(2nd(cons1(_x61, mark(_x32))))
mark#(2nd(cons1(active(_x61), s(_x71))))active#(2nd(active(cons1(_x61, active(s(mark(_x71)))))))mark#(2nd(cons1(_x51, cons1(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82)))))))
mark#(2nd(cons1(_x31, cons1(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(_x21))active#(2nd(_x21))
mark#(2nd(cons1(_x31, cons(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons(mark(_x71), _x72))))))mark#(s(X))mark#(X)
mark#(2nd(cons1(mark(_x61), _x32)))active#(2nd(active(cons1(_x61, mark(_x32)))))mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))
mark#(2nd(cons1(active(_x61), 2nd(_x71))))active#(2nd(active(cons1(_x61, active(2nd(mark(_x71)))))))mark#(2nd(cons1(_x51, _x32)))active#(2nd(cons1(_x51, mark(_x32))))
mark#(2nd(cons1(active(_x51), _x52)))active#(2nd(active(cons1(_x51, _x52))))mark#(2nd(cons1(active(mark(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))
mark#(2nd(cons1(_x51, 2nd(_x81))))active#(2nd(active(cons1(_x51, active(2nd(mark(_x81)))))))mark#(from(X))mark#(X)
mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))mark#(cons(X1, X2))mark#(X1)
mark#(2nd(cons1(_x31, s(_x71))))active#(2nd(active(cons1(mark(_x31), active(s(mark(_x71)))))))mark#(2nd(s(_x31)))active#(2nd(active(s(mark(_x31)))))
active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)mark#(2nd(cons1(2nd(_x61), _x32)))active#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32)))))
active#(from(X))mark#(cons(X, from(s(X))))mark#(2nd(from(_x31)))active#(2nd(active(from(mark(_x31)))))
mark#(cons1(X1, X2))mark#(X2)mark#(2nd(cons1(active(_x61), from(_x71))))active#(2nd(active(cons1(_x61, active(from(mark(_x71)))))))
mark#(2nd(cons1(_x51, from(_x81))))active#(2nd(active(cons1(_x51, active(from(mark(_x81)))))))mark#(2nd(cons1(_x51, s(_x81))))active#(2nd(active(cons1(_x51, active(s(mark(_x81)))))))
mark#(from(X))active#(from(mark(X)))mark#(2nd(cons1(active(_x61), cons(_x71, _x72))))active#(2nd(active(cons1(_x61, active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(_x31, _x32)))active#(2nd(cons1(mark(_x31), mark(_x32))))mark#(2nd(cons1(active(active(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))
mark#(2nd(cons1(s(_x61), _x32)))active#(2nd(active(cons1(active(s(mark(_x61))), mark(_x32)))))mark#(2nd(cons1(_x31, from(_x71))))active#(2nd(active(cons1(mark(_x31), active(from(mark(_x71)))))))
active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))mark#(2nd(cons1(_x31, _x52)))active#(2nd(active(cons1(mark(_x31), _x52))))
mark#(2nd(cons1(_x61, _x62)))active#(2nd(active(cons1(_x61, _x62))))mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(_x61, _x62), _x32))) → active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), mark(_x32))))) 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#(2nd(cons1(active(cons(mark(_x61), _x62)), mark(_x32)))) 
active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52)))) 
active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons(mark(_x91), _x92)), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(_x81, _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(from(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(s(mark(_x91))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons1(mark(_x71), mark(_x72))))))) 
active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(from(mark(_x91))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(2nd(mark(_x91))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(cons(mark(_x61), _x62), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), mark(_x32))))) 
Thus, the rule mark#(2nd(cons1(cons(_x61, _x62), _x32))) → active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(cons(2nd(_x91), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(2nd(mark(_x91))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x32))) → active#(2nd(cons1(active(cons(mark(_x61), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(_x81, _x82), _x32))) → active#(2nd(active(cons1(active(cons(_x81, _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons(_x91, _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons(mark(_x91), _x92)), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), s(_x71)))) → active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x71)))) → active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(_x61, _x62), from(_x71)))) → active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(_x61, mark(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(_x61, _x62), _x52))) → active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))mark#(2nd(cons1(cons(_x61, _x62), _x32))) → active#(2nd(active(cons1(cons(mark(_x61), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, active(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(s(_x91), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(s(mark(_x91))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), cons1(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(from(_x91), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(from(mark(_x91))), _x62)), mark(_x32)))))

Problem 19: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons(_x31, _x32)))active#(2nd(active(cons(mark(_x31), _x32))))mark#(2nd(cons1(active(_x61), _x32)))active#(2nd(cons1(_x61, mark(_x32))))
mark#(cons1(X1, X2))mark#(X1)mark#(2nd(cons1(_x31, cons1(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(_x61, active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))mark#(s(X))mark#(X)
mark#(2nd(cons1(_x31, cons(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))
mark#(2nd(cons1(active(_x61), 2nd(_x71))))active#(2nd(active(cons1(_x61, active(2nd(mark(_x71)))))))mark#(2nd(cons1(_x51, _x32)))active#(2nd(cons1(_x51, mark(_x32))))
mark#(2nd(cons1(active(_x51), _x52)))active#(2nd(active(cons1(_x51, _x52))))mark#(2nd(cons1(cons(_x81, _x82), _x32)))active#(2nd(active(cons1(active(cons(_x81, _x82)), mark(_x32)))))
mark#(2nd(cons1(active(mark(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(from(X))mark#(X)
mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))mark#(cons(X1, X2))mark#(X1)
mark#(2nd(cons1(_x31, s(_x71))))active#(2nd(active(cons1(mark(_x31), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(_x61, _x62), from(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(from(mark(_x71)))))))
mark#(2nd(s(_x31)))active#(2nd(active(s(mark(_x31)))))mark#(2nd(cons1(2nd(_x61), _x32)))active#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32)))))
active#(from(X))mark#(cons(X, from(s(X))))mark#(2nd(cons1(_x51, from(_x81))))active#(2nd(active(cons1(_x51, active(from(mark(_x81)))))))
mark#(from(X))active#(from(mark(X)))mark#(2nd(cons1(_x31, from(_x71))))active#(2nd(active(cons1(mark(_x31), active(from(mark(_x71)))))))
mark#(2nd(cons1(_x31, _x52)))active#(2nd(active(cons1(mark(_x31), _x52))))mark#(2nd(cons1(_x61, _x62)))active#(2nd(active(cons1(_x61, _x62))))
mark#(2nd(cons1(cons(2nd(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(2nd(mark(_x91))), _x62)), mark(_x32)))))mark#(2nd(cons1(from(_x61), _x32)))active#(2nd(active(cons1(active(from(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(cons1(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(active(_x61), cons1(_x71, _x72))))active#(2nd(active(cons1(_x61, active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(_x31, 2nd(_x71))))active#(2nd(active(cons1(mark(_x31), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(active(_x61), s(_x71))))active#(2nd(active(cons1(_x61, active(s(mark(_x71)))))))mark#(2nd(cons1(_x51, cons1(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82)))))))
mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(active(cons1(cons(mark(_x61), _x62), mark(_x32)))))mark#(2nd(_x21))active#(2nd(_x21))
mark#(2nd(cons1(cons(s(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(s(mark(_x91))), _x62)), mark(_x32)))))mark#(2nd(cons1(mark(_x61), _x32)))active#(2nd(active(cons1(_x61, mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(from(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(from(mark(_x91))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x51, 2nd(_x81))))active#(2nd(active(cons1(_x51, active(2nd(mark(_x81)))))))mark#(2nd(cons1(cons(cons(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons(mark(_x91), _x92)), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), s(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(_x61, mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)
mark#(2nd(from(_x31)))active#(2nd(active(from(mark(_x31)))))mark#(cons1(X1, X2))mark#(X2)
mark#(2nd(cons1(active(_x61), from(_x71))))active#(2nd(active(cons1(_x61, active(from(mark(_x71)))))))mark#(2nd(cons1(cons(_x61, _x62), _x52)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))
mark#(2nd(cons1(_x51, s(_x81))))active#(2nd(active(cons1(_x51, active(s(mark(_x81)))))))mark#(2nd(cons1(active(_x61), cons(_x71, _x72))))active#(2nd(active(cons1(_x61, active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(_x31, _x32)))active#(2nd(cons1(mark(_x31), mark(_x32))))mark#(2nd(cons1(active(active(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))
mark#(2nd(cons1(s(_x61), _x32)))active#(2nd(active(cons1(active(s(mark(_x61))), mark(_x32)))))active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))
mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(_x61, _x62), _x32))) → active#(2nd(cons1(active(cons(mark(_x61), _x62)), mark(_x32)))) 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#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61)))))) 
active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x61), _x62))))) 
active#(2nd(cons1(active(cons(active(2nd(mark(_x81))), _x62)), mark(_x32)))) 
active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61)))))) 
active#(2nd(cons1(active(cons(_x71, _x72)), mark(_x32)))) 
active#(2nd(cons1(active(cons(mark(_x61), _x62)), _x42))) 
active#(2nd(cons1(active(cons(active(cons(mark(_x81), _x82)), _x62)), mark(_x32)))) 
active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32)))) 
active#(2nd(cons1(cons(mark(_x61), _x62), mark(_x32)))) 
active#(2nd(cons1(active(cons(active(from(mark(_x81))), _x62)), mark(_x32)))) 
active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(from(mark(_x61)))))) 
active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons1(mark(_x61), mark(_x62)))))) 
active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32)))) 
active#(2nd(cons1(active(cons(active(cons1(mark(_x81), mark(_x82))), _x62)), mark(_x32)))) 
Thus, the rule mark#(2nd(cons1(cons(_x61, _x62), _x32))) → active#(2nd(cons1(active(cons(mark(_x61), _x62)), mark(_x32)))) is replaced by the following rules:
mark#(2nd(cons1(cons(_x61, _x62), s(_x61)))) → active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))mark#(2nd(cons1(cons(_x61, mark(_x72)), _x32))) → active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))
mark#(2nd(cons1(cons(cons(_x81, _x82), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons(mark(_x81), _x82)), _x62)), mark(_x32))))mark#(2nd(cons1(cons(2nd(_x81), _x62), _x32))) → active#(2nd(cons1(active(cons(active(2nd(mark(_x81))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x61)))) → active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61))))))mark#(2nd(cons1(cons(_x61, _x62), from(_x61)))) → active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(from(mark(_x61))))))
mark#(2nd(cons1(cons(_x71, _x72), _x32))) → active#(2nd(cons1(active(cons(_x71, _x72)), mark(_x32))))mark#(2nd(cons1(cons(s(_x81), _x62), _x32))) → active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(_x61, _x62), cons(_x61, _x62)))) → active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x61), _x62)))))mark#(2nd(cons1(cons(cons1(_x81, _x82), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons1(mark(_x81), mark(_x82))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(from(_x81), _x62), _x32))) → active#(2nd(cons1(active(cons(active(from(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(_x61, active(_x72)), _x32))) → active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))
mark#(2nd(cons1(cons(_x61, _x62), cons1(_x61, _x62)))) → active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons1(mark(_x61), mark(_x62))))))mark#(2nd(cons1(cons(_x61, _x62), _x42))) → active#(2nd(cons1(active(cons(mark(_x61), _x62)), _x42)))
mark#(2nd(cons1(cons(_x61, _x62), _x32))) → active#(2nd(cons1(cons(mark(_x61), _x62), mark(_x32))))

Problem 20: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(_x61, _x62), s(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons(_x31, _x32)))active#(2nd(active(cons(mark(_x31), _x32))))mark#(2nd(cons1(active(_x61), _x32)))active#(2nd(cons1(_x61, mark(_x32))))
mark#(cons1(X1, X2))mark#(X1)mark#(2nd(cons1(_x31, cons1(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(_x71, _x72), _x32)))active#(2nd(cons1(active(cons(_x71, _x72)), mark(_x32))))mark#(2nd(cons1(cons(_x61, active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))
mark#(s(X))mark#(X)mark#(2nd(cons1(_x31, cons(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))mark#(2nd(cons1(active(_x61), 2nd(_x71))))active#(2nd(active(cons1(_x61, active(2nd(mark(_x71)))))))
mark#(2nd(cons1(_x51, _x32)))active#(2nd(cons1(_x51, mark(_x32))))mark#(2nd(cons1(cons(_x61, mark(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))
mark#(2nd(cons1(active(_x51), _x52)))active#(2nd(active(cons1(_x51, _x52))))mark#(2nd(cons1(cons(_x81, _x82), _x32)))active#(2nd(active(cons1(active(cons(_x81, _x82)), mark(_x32)))))
mark#(from(X))mark#(X)mark#(2nd(cons1(active(mark(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61))))))mark#(2nd(cons1(cons(_x61, _x62), from(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(_x31, s(_x71))))active#(2nd(active(cons1(mark(_x31), active(s(mark(_x71)))))))mark#(cons(X1, X2))mark#(X1)
mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))mark#(2nd(s(_x31)))active#(2nd(active(s(mark(_x31)))))
mark#(2nd(cons1(2nd(_x61), _x32)))active#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32)))))active#(from(X))mark#(cons(X, from(s(X))))
mark#(2nd(cons1(_x51, from(_x81))))active#(2nd(active(cons1(_x51, active(from(mark(_x81)))))))mark#(from(X))active#(from(mark(X)))
mark#(2nd(cons1(cons(from(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(from(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(_x31, from(_x71))))active#(2nd(active(cons1(mark(_x31), active(from(mark(_x71)))))))
mark#(2nd(cons1(_x31, _x52)))active#(2nd(active(cons1(mark(_x31), _x52))))mark#(2nd(cons1(_x61, _x62)))active#(2nd(active(cons1(_x61, _x62))))
mark#(2nd(cons1(cons(2nd(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(2nd(mark(_x91))), _x62)), mark(_x32)))))mark#(2nd(cons1(from(_x61), _x32)))active#(2nd(active(cons1(active(from(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(cons1(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(active(_x61), cons1(_x71, _x72))))active#(2nd(active(cons1(_x61, active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(_x31, 2nd(_x71))))active#(2nd(active(cons1(mark(_x31), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(active(_x61), s(_x71))))active#(2nd(active(cons1(_x61, active(s(mark(_x71)))))))mark#(2nd(cons1(_x51, cons1(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82)))))))
mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(active(cons1(cons(mark(_x61), _x62), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), cons(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x61), _x62)))))
mark#(2nd(cons1(cons(cons1(_x81, _x82), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x81), mark(_x82))), _x62)), mark(_x32))))mark#(2nd(_x21))active#(2nd(_x21))
mark#(2nd(cons1(cons(_x61, active(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))mark#(2nd(cons1(cons(s(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(s(mark(_x91))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), _x42)))active#(2nd(cons1(active(cons(mark(_x61), _x62)), _x42)))mark#(2nd(cons1(mark(_x61), _x32)))active#(2nd(active(cons1(_x61, mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(from(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(from(mark(_x91))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons(_x81, _x82), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons(mark(_x81), _x82)), _x62)), mark(_x32))))mark#(2nd(cons1(cons(2nd(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(2nd(mark(_x81))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons(mark(_x91), _x92)), _x62)), mark(_x32)))))mark#(2nd(cons1(_x51, 2nd(_x81))))active#(2nd(active(cons1(_x51, active(2nd(mark(_x81)))))))
mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(_x61, _x62), s(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(_x61, mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)
mark#(2nd(from(_x31)))active#(2nd(active(from(mark(_x31)))))mark#(2nd(cons1(active(_x61), from(_x71))))active#(2nd(active(cons1(_x61, active(from(mark(_x71)))))))
mark#(cons1(X1, X2))mark#(X2)mark#(2nd(cons1(cons(_x61, _x62), _x52)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))
mark#(2nd(cons1(cons(_x61, _x62), from(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(from(mark(_x61))))))mark#(2nd(cons1(_x51, s(_x81))))active#(2nd(active(cons1(_x51, active(s(mark(_x81)))))))
mark#(2nd(cons1(cons(s(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(active(_x61), cons(_x71, _x72))))active#(2nd(active(cons1(_x61, active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(_x31, _x32)))active#(2nd(cons1(mark(_x31), mark(_x32))))mark#(2nd(cons1(cons(_x61, _x62), cons1(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons1(mark(_x61), mark(_x62))))))
mark#(2nd(cons1(active(active(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(2nd(cons1(s(_x61), _x32)))active#(2nd(active(cons1(active(s(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(cons1(cons(mark(_x61), _x62), mark(_x32))))active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))
mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), mark(_x32))))) 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#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(2nd(mark(_x131))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), _x112)), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(s(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(2nd(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(_x111, mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(s(mark(_x131))))), _x62)), mark(_x32))))) 
active#(2nd(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), mark(_x32)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(cons1(mark(_x91), mark(_x92)), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(from(mark(_x131))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(from(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), _x52)))) 
Thus, the rule mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), cons1(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), s(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x111, _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(_x111, mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(2nd(_x121), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), active(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), 2nd(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, from(_x131)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(from(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32))) → active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x52))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), _x52))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), from(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), mark(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(s(_x121), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, 2nd(_x131)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(2nd(mark(_x131))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x82), _x32))) → active#(2nd(active(cons1(active(cons(cons1(mark(_x91), mark(_x92)), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, s(_x131)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(s(mark(_x131))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, _x112), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), _x112)), _x62)), mark(_x32)))))

Problem 21: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(_x61, _x62), s(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons(_x31, _x32)))active#(2nd(active(cons(mark(_x31), _x32))))mark#(2nd(cons1(cons(cons1(_x91, from(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(from(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), mark(_x32))))mark#(2nd(cons1(active(_x61), _x32)))active#(2nd(cons1(_x61, mark(_x32))))
mark#(cons1(X1, X2))mark#(X1)mark#(2nd(cons1(_x31, cons1(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(_x71, _x72), _x32)))active#(2nd(cons1(active(cons(_x71, _x72)), mark(_x32))))mark#(2nd(cons1(cons(_x61, active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, _x92), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), mark(_x92)), _x82)), mark(_x32)))))mark#(2nd(cons1(_x31, cons(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons(mark(_x71), _x72))))))
mark#(s(X))mark#(X)mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))
mark#(2nd(cons1(active(_x61), 2nd(_x71))))active#(2nd(active(cons1(_x61, active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(_x61, mark(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))
mark#(2nd(cons1(_x51, _x32)))active#(2nd(cons1(_x51, mark(_x32))))mark#(2nd(cons1(active(_x51), _x52)))active#(2nd(active(cons1(_x51, _x52))))
mark#(2nd(cons1(cons(_x81, _x82), _x32)))active#(2nd(active(cons1(active(cons(_x81, _x82)), mark(_x32)))))mark#(2nd(cons1(active(mark(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))
mark#(from(X))mark#(X)mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61))))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), from(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(_x31, s(_x71))))active#(2nd(active(cons1(mark(_x31), active(s(mark(_x71)))))))mark#(cons(X1, X2))mark#(X1)
mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))mark#(2nd(cons1(cons(cons1(from(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(s(_x31)))active#(2nd(active(s(mark(_x31)))))mark#(2nd(cons1(2nd(_x61), _x32)))active#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32)))))
active#(from(X))mark#(cons(X, from(s(X))))mark#(2nd(cons1(_x51, from(_x81))))active#(2nd(active(cons1(_x51, active(from(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(s(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))mark#(from(X))active#(from(mark(X)))
mark#(2nd(cons1(cons(cons1(_x91, s(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(s(mark(_x131))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(from(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(from(mark(_x81))), _x62)), mark(_x32))))
mark#(2nd(cons1(_x31, from(_x71))))active#(2nd(active(cons1(mark(_x31), active(from(mark(_x71)))))))mark#(2nd(cons1(_x31, _x52)))active#(2nd(active(cons1(mark(_x31), _x52))))
mark#(2nd(cons1(_x61, _x62)))active#(2nd(active(cons1(_x61, _x62))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(2nd(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(2nd(mark(_x91))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x111, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(2nd(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(from(_x61), _x32)))active#(2nd(active(cons1(active(from(mark(_x61))), mark(_x32)))))mark#(2nd(cons1(cons1(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(_x31, 2nd(_x71))))active#(2nd(active(cons1(mark(_x31), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(active(_x61), cons1(_x71, _x72))))active#(2nd(active(cons1(_x61, active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(active(_x61), s(_x71))))active#(2nd(active(cons1(_x61, active(s(mark(_x71)))))))
mark#(2nd(cons1(_x51, cons1(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82)))))))mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(active(cons1(cons(mark(_x61), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), _x52))))mark#(2nd(cons1(cons(_x61, _x62), cons(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x61), _x62)))))
mark#(2nd(_x21))active#(2nd(_x21))mark#(2nd(cons1(cons(cons1(_x81, _x82), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x81), mark(_x82))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, 2nd(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(2nd(mark(_x131))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, active(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))
mark#(2nd(cons1(cons(s(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(s(mark(_x91))), _x62)), mark(_x32)))))mark#(2nd(cons1(mark(_x61), _x32)))active#(2nd(active(cons1(_x61, mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), _x42)))active#(2nd(cons1(active(cons(mark(_x61), _x62)), _x42)))mark#(2nd(cons1(cons(_x61, _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(from(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(from(mark(_x91))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(2nd(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(2nd(mark(_x81))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons(_x81, _x82), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons(mark(_x81), _x82)), _x62)), mark(_x32))))mark#(2nd(cons1(_x51, 2nd(_x81))))active#(2nd(active(cons1(_x51, active(2nd(mark(_x81)))))))
mark#(2nd(cons1(cons(cons(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons(mark(_x91), _x92)), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), s(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(_x61, mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))
active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)mark#(2nd(from(_x31)))active#(2nd(active(from(mark(_x31)))))
mark#(cons1(X1, X2))mark#(X2)mark#(2nd(cons1(active(_x61), from(_x71))))active#(2nd(active(cons1(_x61, active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x52)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))
mark#(2nd(cons1(cons(_x61, _x62), from(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(from(mark(_x61))))))mark#(2nd(cons1(cons(s(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32))))
mark#(2nd(cons1(_x51, s(_x81))))active#(2nd(active(cons1(_x51, active(s(mark(_x81)))))))mark#(2nd(cons1(active(_x61), cons(_x71, _x72))))active#(2nd(active(cons1(_x61, active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(_x31, _x32)))active#(2nd(cons1(mark(_x31), mark(_x32))))mark#(2nd(cons1(cons(_x61, _x62), cons1(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons1(mark(_x61), mark(_x62))))))
mark#(2nd(cons1(active(active(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(2nd(cons1(s(_x61), _x32)))active#(2nd(active(cons1(active(s(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(cons1(cons(mark(_x61), _x62), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), _x112)), _x62)), mark(_x32)))))active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))
mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 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#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(from(mark(_x161))), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), _x52)))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), _x152)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(s(mark(_x171))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(2nd(mark(_x161))), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(2nd(mark(_x171))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(from(mark(_x171))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons1(mark(_x171), mark(_x172))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons(mark(_x161), _x162)), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons1(mark(_x71), mark(_x72))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(s(mark(_x161))), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons1(mark(_x161), mark(_x162))), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(_x151, mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons1(mark(_x131), mark(_x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(2nd(mark(_x71))))))) 
active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(mark(_x171), _x172)))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(from(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62), mark(_x32))))) 
Thus, the rule mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(cons(cons1(_x91, cons1(s(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(s(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(2nd(_x121), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), mark(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), 2nd(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x111, cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(2nd(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(2nd(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, s(_x171))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(s(mark(_x171))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), cons1(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(from(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(from(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(s(_x121), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(_x171, _x172))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(mark(_x171), _x172)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons1(_x171, _x172))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons1(mark(_x171), mark(_x172))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x151, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(_x151, mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons1(mark(_x131), mark(_x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(cons1(_x161, _x162), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons1(mark(_x161), mark(_x162))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x82), _x32))) → active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, from(_x171))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(from(mark(_x171))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x52))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), _x52))))mark#(2nd(cons1(cons(cons1(_x91, cons1(cons(_x161, _x162), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons(mark(_x161), _x162)), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, 2nd(_x171))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(2nd(mark(_x171))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), active(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), from(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), s(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x152)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), _x152)))), _x62)), mark(_x32)))))

Problem 22: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(_x61, _x62), s(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x31, cons1(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(_x91, _x92), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(_x171, _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(mark(_x171), _x172)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons1(_x171, _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons1(mark(_x171), mark(_x172))))))), _x62)), mark(_x32)))))
mark#(s(X))mark#(X)mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))
mark#(2nd(cons1(cons(_x61, mark(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))mark#(2nd(cons1(_x51, _x32)))active#(2nd(cons1(_x51, mark(_x32))))
mark#(2nd(cons1(active(_x51), _x52)))active#(2nd(active(cons1(_x51, _x52))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61))))))
mark#(2nd(cons1(active(mark(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))mark#(cons(X1, X2))mark#(X1)
mark#(2nd(cons1(_x31, s(_x71))))active#(2nd(active(cons1(mark(_x31), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(_x61, _x62), from(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(s(_x31)))active#(2nd(active(s(mark(_x31)))))
mark#(2nd(cons1(cons(cons1(from(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), _x52))))
active#(from(X))mark#(cons(X, from(s(X))))mark#(2nd(cons1(_x51, from(_x81))))active#(2nd(active(cons1(_x51, active(from(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(s(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(from(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(from(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(_x31, _x52)))active#(2nd(active(cons1(mark(_x31), _x52))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(2nd(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(2nd(mark(_x91))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(2nd(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons1(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(_x31, 2nd(_x71))))active#(2nd(active(cons1(mark(_x31), active(2nd(mark(_x71)))))))mark#(2nd(cons1(active(_x61), cons1(_x71, _x72))))active#(2nd(active(cons1(_x61, active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(_x111, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(active(cons1(cons(mark(_x61), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), cons(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x61), _x62)))))mark#(2nd(cons1(cons(cons1(_x81, _x82), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x81), mark(_x82))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(_x61, active(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))mark#(2nd(cons1(cons(s(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(s(mark(_x91))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(cons1(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons1(mark(_x161), mark(_x162))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(2nd(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(2nd(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(_x51, 2nd(_x81))))active#(2nd(active(cons1(_x51, active(2nd(mark(_x81)))))))
mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(_x61, _x62), s(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(_x61, mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(from(_x31)))active#(2nd(active(from(mark(_x31)))))mark#(2nd(cons1(active(_x61), from(_x71))))active#(2nd(active(cons1(_x61, active(from(mark(_x71)))))))
mark#(cons1(X1, X2))mark#(X2)mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62), mark(_x32)))))
mark#(2nd(cons1(_x51, s(_x81))))active#(2nd(active(cons1(_x51, active(s(mark(_x81)))))))mark#(2nd(cons1(_x31, _x32)))active#(2nd(cons1(mark(_x31), mark(_x32))))
mark#(2nd(cons1(cons(_x61, _x62), cons1(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons1(mark(_x61), mark(_x62))))))mark#(2nd(cons1(s(_x61), _x32)))active#(2nd(active(cons1(active(s(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(cons1(cons(mark(_x61), _x62), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x152)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), _x152)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(s(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(s(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons(_x31, _x32)))active#(2nd(active(cons(mark(_x31), _x32))))mark#(2nd(cons1(cons(cons1(_x91, from(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(from(mark(_x131))))), _x62)), mark(_x32)))))
mark#(cons1(X1, X2))mark#(X1)mark#(2nd(cons1(active(_x61), _x32)))active#(2nd(cons1(_x61, mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(2nd(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(_x61, active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(_x71, _x72), _x32)))active#(2nd(cons1(active(cons(_x71, _x72)), mark(_x32))))mark#(2nd(cons1(cons(cons1(s(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), mark(_x92)), _x82)), mark(_x32)))))
mark#(2nd(cons1(_x31, cons(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(active(_x61), 2nd(_x71))))active#(2nd(active(cons1(_x61, active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(_x81, _x82), _x32)))active#(2nd(active(cons1(active(cons(_x81, _x82)), mark(_x32)))))mark#(from(X))mark#(X)
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, from(_x171))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(from(mark(_x171))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(2nd(_x61), _x32)))active#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(cons(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons(mark(_x161), _x162)), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(from(mark(_x71)))))))
mark#(from(X))active#(from(mark(X)))mark#(2nd(cons1(cons(cons1(_x91, s(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(s(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x31, from(_x71))))active#(2nd(active(cons1(mark(_x31), active(from(mark(_x71)))))))mark#(2nd(cons1(_x61, _x62)))active#(2nd(active(cons1(_x61, _x62))))
mark#(2nd(cons1(cons(cons1(2nd(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x111, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(from(_x61), _x32)))active#(2nd(active(cons1(active(from(mark(_x61))), mark(_x32)))))mark#(2nd(cons1(active(_x61), s(_x71))))active#(2nd(active(cons1(_x61, active(s(mark(_x71)))))))
mark#(2nd(cons1(_x51, cons1(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82)))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, s(_x171))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(s(mark(_x171))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), _x52))))mark#(2nd(cons1(cons(cons1(_x91, cons1(from(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(from(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(_x21))active#(2nd(_x21))mark#(2nd(cons1(cons(cons1(_x91, 2nd(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(2nd(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x151, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(_x151, mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons1(mark(_x131), mark(_x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(mark(_x61), _x32)))active#(2nd(active(cons1(_x61, mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x42)))active#(2nd(cons1(active(cons(mark(_x61), _x62)), _x42)))
mark#(2nd(cons1(cons(_x61, _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(from(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(from(mark(_x91))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons(_x81, _x82), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons(mark(_x81), _x82)), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons(mark(_x91), _x92)), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x82)), mark(_x32)))))
active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), _x52)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, 2nd(_x171))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(2nd(mark(_x171))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), from(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(from(mark(_x61))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(s(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(active(_x61), cons(_x71, _x72))))active#(2nd(active(cons1(_x61, active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(active(active(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), _x112)), _x62)), mark(_x32)))))
active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 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#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(2nd(mark(_x131))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(from(mark(_x131))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(from(mark(_x161))))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons1(mark(_x161), mark(_x162))))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x112)), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(s(mark(_x161))))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(cons1(mark(_x121), mark(_x122)), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(s(mark(_x131))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x141, mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), _x52)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons1(mark(_x151), mark(_x152))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(from(mark(_x71))))))) 
active#(2nd(active(cons1(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x151), _x152)), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(2nd(mark(_x161))))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), _x142)), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92)), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(from(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons(mark(_x161), _x162)))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(2nd(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(2nd(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72))))))) 
Thus, the rule mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(cons(cons1(cons1(2nd(_x151), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(2nd(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons1(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), active(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), from(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(cons(_x151, _x152), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x151), _x152)), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(cons1(_x151, _x152), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons1(mark(_x151), mark(_x152))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), s(_x131)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(s(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(from(_x151), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(from(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, cons(_x161, _x162)), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons(mark(_x161), _x162)))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), mark(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x52))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), _x52))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), s(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, cons1(_x161, _x162)), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons1(mark(_x161), mark(_x162))))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, from(_x161)), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(from(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), cons(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(cons1(mark(_x121), mark(_x122)), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x142), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), _x142)), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), 2nd(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, 2nd(_x161)), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(2nd(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), from(_x131)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(from(mark(_x131))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x141, _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x141, mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x112), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x112)), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x82), _x32))) → active#(2nd(active(cons1(active(cons(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92)), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), 2nd(_x131)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(2nd(mark(_x131))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, s(_x161)), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(s(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))

Problem 23: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(_x61, _x62), s(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(cons(_x151, _x152), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x151), _x152)), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(cons1(_x151, _x152), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons1(mark(_x151), mark(_x152))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), s(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(s(mark(_x131))))), _x62)), mark(_x32)))))mark#(2nd(cons1(_x31, cons1(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(_x171, _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(mark(_x171), _x172)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons1(_x171, _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons1(mark(_x171), mark(_x172))))))), _x62)), mark(_x32)))))mark#(s(X))mark#(X)
mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))mark#(2nd(cons1(cons(_x61, mark(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))
mark#(2nd(cons1(_x51, _x32)))active#(2nd(cons1(_x51, mark(_x32))))mark#(2nd(cons1(active(_x51), _x52)))active#(2nd(active(cons1(_x51, _x52))))
mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61))))))mark#(2nd(cons1(active(mark(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))mark#(cons(X1, X2))mark#(X1)
mark#(2nd(cons1(_x31, s(_x71))))active#(2nd(active(cons1(mark(_x31), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(_x61, _x62), from(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(from(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(s(_x31)))active#(2nd(active(s(mark(_x31)))))
active#(from(X))mark#(cons(X, from(s(X))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), _x52))))
mark#(2nd(cons1(_x51, from(_x81))))active#(2nd(active(cons1(_x51, active(from(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(s(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(from(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(from(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(_x31, _x52)))active#(2nd(active(cons1(mark(_x31), _x52))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, s(_x161)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(s(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(2nd(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(2nd(mark(_x91))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(2nd(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons1(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(active(_x61), cons1(_x71, _x72))))active#(2nd(active(cons1(_x61, active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(_x31, 2nd(_x71))))active#(2nd(active(cons1(mark(_x31), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x111, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(from(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(from(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(active(cons1(cons(mark(_x61), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, cons(_x161, _x162)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons(mark(_x161), _x162)))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), cons(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x61), _x62)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x81, _x82), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x81), mark(_x82))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(_x61, active(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))mark#(2nd(cons1(cons(s(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(s(mark(_x91))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(cons1(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons1(mark(_x161), mark(_x162))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(2nd(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(2nd(mark(_x81))), _x62)), mark(_x32))))
mark#(2nd(cons1(_x51, 2nd(_x81))))active#(2nd(active(cons1(_x51, active(2nd(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(cons1(mark(_x121), mark(_x122)), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(_x61, _x62), s(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(_x61, mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x142), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), _x142)), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(from(_x31)))active#(2nd(active(from(mark(_x31)))))mark#(2nd(cons1(active(_x61), from(_x71))))active#(2nd(active(cons1(_x61, active(from(mark(_x71)))))))
mark#(cons1(X1, X2))mark#(X2)mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62), mark(_x32)))))
mark#(2nd(cons1(_x51, s(_x81))))active#(2nd(active(cons1(_x51, active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, 2nd(_x161)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(2nd(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), from(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(from(mark(_x131))))), _x62)), mark(_x32)))))mark#(2nd(cons1(_x31, _x32)))active#(2nd(cons1(mark(_x31), mark(_x32))))
mark#(2nd(cons1(cons(_x61, _x62), cons1(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons1(mark(_x61), mark(_x62))))))mark#(2nd(cons1(s(_x61), _x32)))active#(2nd(active(cons1(active(s(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(cons1(cons(mark(_x61), _x62), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x152)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), _x152)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(s(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(s(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons(_x31, _x32)))active#(2nd(active(cons(mark(_x31), _x32))))
mark#(2nd(cons1(cons(cons1(_x91, from(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(from(mark(_x131))))), _x62)), mark(_x32)))))mark#(cons1(X1, X2))mark#(X1)
mark#(2nd(cons1(active(_x61), _x32)))active#(2nd(cons1(_x61, mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons1(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(2nd(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(_x61, active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(_x71, _x72), _x32)))active#(2nd(cons1(active(cons(_x71, _x72)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(s(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), mark(_x92)), _x82)), mark(_x32)))))
mark#(2nd(cons1(_x31, cons(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(active(_x61), 2nd(_x71))))active#(2nd(active(cons1(_x61, active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), _x52))))mark#(2nd(cons1(cons(_x81, _x82), _x32)))active#(2nd(active(cons1(active(cons(_x81, _x82)), mark(_x32)))))
mark#(from(X))mark#(X)mark#(2nd(cons1(cons(cons1(cons1(_x121, from(_x161)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(from(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, from(_x171))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(from(mark(_x171))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(2nd(_x61), _x32)))active#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(cons(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons(mark(_x161), _x162)), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(from(mark(_x71)))))))
mark#(from(X))active#(from(mark(X)))mark#(2nd(cons1(cons(cons1(_x91, s(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(s(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x141, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x141, mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(_x31, from(_x71))))active#(2nd(active(cons1(mark(_x31), active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92)), _x82)), mark(_x32)))))mark#(2nd(cons1(_x61, _x62)))active#(2nd(active(cons1(_x61, _x62))))
mark#(2nd(cons1(cons(cons1(2nd(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(2nd(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(2nd(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x111, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(from(_x61), _x32)))active#(2nd(active(cons1(active(from(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(active(_x61), s(_x71))))active#(2nd(active(cons1(_x61, active(s(mark(_x71)))))))mark#(2nd(cons1(_x51, cons1(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, s(_x171))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(s(mark(_x171))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(from(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(from(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, 2nd(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(2nd(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(_x21))active#(2nd(_x21))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x151, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(_x151, mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons1(mark(_x131), mark(_x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x42)))active#(2nd(cons1(active(cons(mark(_x61), _x62)), _x42)))
mark#(2nd(cons1(mark(_x61), _x32)))active#(2nd(active(cons1(_x61, mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(from(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(from(mark(_x91))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons(_x81, _x82), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons(mark(_x81), _x82)), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons(mark(_x91), _x92)), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, cons1(_x161, _x162)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons1(mark(_x161), mark(_x162))))), mark(_x92))), _x62)), mark(_x32)))))
active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, 2nd(_x171))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(2nd(mark(_x171))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x52)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))
mark#(2nd(cons1(cons(_x61, _x62), from(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(from(mark(_x61))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(s(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(active(_x61), cons(_x71, _x72))))active#(2nd(active(cons1(_x61, active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(active(active(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x112)), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), 2nd(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(2nd(mark(_x131))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), _x112)), _x62)), mark(_x32)))))
active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(2nd(mark(_x151))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(cons1(mark(_x121), mark(_x122)), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x82)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x102)), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(from(mark(_x151))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), cons(mark(_x71), _x72))))) 
active#(2nd(active(cons1(active(cons(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92)), _x72)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(cons1(mark(_x91), mark(_x92))), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x141), _x142)), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(_x81, _x82)))))) 
active#(2nd(active(cons1(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), _x132)), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x131, mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(from(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(s(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons1(mark(_x141), mark(_x142))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(s(mark(_x91))), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(2nd(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons1(mark(_x121), mark(_x122))))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons1(mark(_x151), mark(_x152))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(cons(mark(_x91), _x92)), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(from(mark(_x91))), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(s(mark(_x151))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(2nd(mark(_x91))), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(from(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(2nd(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons(mark(_x121), _x122)))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons(mark(_x151), _x152)))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
Thus, the rule mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) is replaced by the following rules:
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), from(_x121)), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(from(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), cons1(_x121, _x122)), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons1(mark(_x121), mark(_x122))))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), s(_x121)), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(s(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x131, _x122), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x131, mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), cons(_x121, _x122)), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons(mark(_x121), _x122)))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), mark(_x72)), cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(2nd(_x141), _x122), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(2nd(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, mark(_x82))))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x82))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, active(_x82))))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x82))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), active(_x72)), cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, from(_x151)), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(from(mark(_x151))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, s(_x151)), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(s(mark(_x151))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(s(_x141), _x122), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(cons1(_x141, _x142), _x122), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons1(mark(_x141), mark(_x142))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, cons(_x151, _x152)), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons(mark(_x151), _x152)))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x72), cons(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92)), _x72)))) → active#(2nd(active(cons1(active(cons(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92)), _x72)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(cons1(_x91, _x92), _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(cons1(mark(_x91), mark(_x92))), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(from(_x141), _x122), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(from(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x132), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), _x132)), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), 2nd(_x121)), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(2nd(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(cons(_x141, _x142), _x122), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x141), _x142)), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x102), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x102)), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x81, _x82)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(_x81, _x82))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(cons1(mark(_x121), mark(_x122)), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, cons1(_x151, _x152)), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons1(mark(_x151), mark(_x152))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(2nd(_x91), _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(2nd(mark(_x91))), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), cons(mark(_x71), _x72)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(s(_x91), _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(s(mark(_x91))), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(from(_x91), _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(from(mark(_x91))), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, 2nd(_x151)), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(2nd(mark(_x151))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(cons(_x91, _x92), _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(cons(mark(_x91), _x92)), _x72))))))

Problem 24: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), cons1(_x121, _x122)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons1(mark(_x121), mark(_x122))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), s(_x121)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(s(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(_x61, _x62), s(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), cons(_x121, _x122)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons(mark(_x121), _x122)))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(cons(_x151, _x152), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x151), _x152)), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), s(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(s(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(cons1(_x151, _x152), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons1(mark(_x151), mark(_x152))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, from(_x151)), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(from(mark(_x151))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(_x31, cons1(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(_x91, _x92), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(_x171, _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(mark(_x171), _x172)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons1(_x171, _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons1(mark(_x171), mark(_x172))))))), _x62)), mark(_x32)))))
mark#(s(X))mark#(X)mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))
mark#(2nd(cons1(cons(cons1(cons1(cons1(_x141, _x142), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons1(mark(_x141), mark(_x142))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(cons1(_x91, _x92), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(cons1(mark(_x91), mark(_x92))), _x72))))))
mark#(2nd(cons1(cons(_x61, mark(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))mark#(2nd(cons1(_x51, _x32)))active#(2nd(cons1(_x51, mark(_x32))))
mark#(2nd(cons1(active(_x51), _x52)))active#(2nd(active(cons1(_x51, _x52))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61))))))
mark#(2nd(cons1(active(mark(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), from(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(_x31, s(_x71))))active#(2nd(active(cons1(mark(_x31), active(s(mark(_x71)))))))mark#(cons(X1, X2))mark#(X1)
mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(s(_x31)))active#(2nd(active(s(mark(_x31)))))
mark#(2nd(cons1(cons(cons1(from(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x102), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x102)), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x81, _x82))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(_x81, _x82))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), _x52))))
active#(from(X))mark#(cons(X, from(s(X))))mark#(2nd(cons1(_x51, from(_x81))))active#(2nd(active(cons1(_x51, active(from(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(s(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(from(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(from(mark(_x81))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(s(_x91), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(s(mark(_x91))), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, s(_x161)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(s(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x31, _x52)))active#(2nd(active(cons1(mark(_x31), _x52))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(from(_x91), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(from(mark(_x91))), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), from(_x121)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(from(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), mark(_x72)), cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))
mark#(2nd(cons1(cons(2nd(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(2nd(mark(_x91))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(2nd(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons1(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, mark(_x82)))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x82))))))mark#(2nd(cons1(cons(_x61, _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(active(_x61), cons1(_x71, _x72))))active#(2nd(active(cons1(_x61, active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(_x31, 2nd(_x71))))active#(2nd(active(cons1(mark(_x31), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x111, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(from(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(from(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(active(cons1(cons(mark(_x61), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, cons(_x161, _x162)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons(mark(_x161), _x162)))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), cons(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x61), _x62)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x81, _x82), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x81), mark(_x82))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(_x61, active(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))
mark#(2nd(cons1(cons(s(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(s(mark(_x91))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x72), cons(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92)), _x72))))active#(2nd(active(cons1(active(cons(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92)), _x72)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(from(_x141), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(from(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(cons1(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons1(mark(_x161), mark(_x162))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(2nd(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(2nd(mark(_x81))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x132), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), _x132)), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(_x51, 2nd(_x81))))active#(2nd(active(cons1(_x51, active(2nd(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), 2nd(_x121)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(2nd(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(cons1(mark(_x121), mark(_x122)), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(_x61, _x62), s(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(_x61, mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x142), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), _x142)), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(from(_x31)))active#(2nd(active(from(mark(_x31)))))mark#(2nd(cons1(active(_x61), from(_x71))))active#(2nd(active(cons1(_x61, active(from(mark(_x71)))))))
mark#(cons1(X1, X2))mark#(X2)mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62), mark(_x32)))))
mark#(2nd(cons1(_x51, s(_x81))))active#(2nd(active(cons1(_x51, active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, 2nd(_x161)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(2nd(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), from(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(from(mark(_x131))))), _x62)), mark(_x32)))))mark#(2nd(cons1(_x31, _x32)))active#(2nd(cons1(mark(_x31), mark(_x32))))
mark#(2nd(cons1(cons(_x61, _x62), cons1(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons1(mark(_x61), mark(_x62))))))mark#(2nd(cons1(s(_x61), _x32)))active#(2nd(active(cons1(active(s(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(cons1(cons(mark(_x61), _x62), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x152)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), _x152)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, 2nd(_x151)), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(2nd(mark(_x151))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(s(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(s(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons(_x31, _x32)))active#(2nd(active(cons(mark(_x31), _x32))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, active(_x82)))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x82))))))
mark#(2nd(cons1(cons(cons1(_x91, from(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(from(mark(_x131))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), mark(_x32))))
mark#(2nd(cons1(active(_x61), _x32)))active#(2nd(cons1(_x61, mark(_x32))))mark#(cons1(X1, X2))mark#(X1)
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(2nd(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(_x71, _x72), _x32)))active#(2nd(cons1(active(cons(_x71, _x72)), mark(_x32))))
mark#(2nd(cons1(cons(_x61, active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(s(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), mark(_x92)), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x141), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(_x31, cons(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, cons(_x151, _x152)), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons(mark(_x151), _x152)))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(active(_x61), 2nd(_x71))))active#(2nd(active(cons1(_x61, active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), _x52))))mark#(2nd(cons1(cons(_x81, _x82), _x32)))active#(2nd(active(cons1(active(cons(_x81, _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, from(_x161)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(from(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))mark#(from(X))mark#(X)
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, from(_x171))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(from(mark(_x171))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(2nd(_x61), _x32)))active#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(cons1(mark(_x121), mark(_x122)), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(cons(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons(mark(_x161), _x162)), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(from(mark(_x71)))))))mark#(from(X))active#(from(mark(X)))
mark#(2nd(cons1(cons(cons1(_x91, s(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(s(mark(_x131))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x141, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x141, mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(2nd(_x91), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(2nd(mark(_x91))), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92)), _x82)), mark(_x32)))))
mark#(2nd(cons1(_x31, from(_x71))))active#(2nd(active(cons1(mark(_x31), active(from(mark(_x71)))))))mark#(2nd(cons1(_x61, _x62)))active#(2nd(active(cons1(_x61, _x62))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(cons(_x91, _x92), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(cons(mark(_x91), _x92)), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x131, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x131, mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(2nd(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(2nd(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(2nd(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x111, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(from(_x61), _x32)))active#(2nd(active(cons1(active(from(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(2nd(_x141), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(2nd(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), active(_x72)), cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(active(_x61), s(_x71))))active#(2nd(active(cons1(_x61, active(s(mark(_x71)))))))mark#(2nd(cons1(_x51, cons1(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, s(_x171))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(s(mark(_x171))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, s(_x151)), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(s(mark(_x151))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), _x52))))mark#(2nd(cons1(cons(cons1(_x91, cons1(from(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(from(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(_x21))active#(2nd(_x21))mark#(2nd(cons1(cons(cons1(_x91, 2nd(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(2nd(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x151, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(_x151, mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons1(mark(_x131), mark(_x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(mark(_x61), _x32)))active#(2nd(active(cons1(_x61, mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x42)))active#(2nd(cons1(active(cons(mark(_x61), _x62)), _x42)))
mark#(2nd(cons1(cons(_x61, _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(from(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(from(mark(_x91))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons(_x81, _x82), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons(mark(_x81), _x82)), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, cons1(_x161, _x162)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons1(mark(_x161), mark(_x162))))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons(mark(_x91), _x92)), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(cons(_x141, _x142), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x141), _x142)), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), _x52)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, 2nd(_x171))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(2nd(mark(_x171))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), from(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(from(mark(_x61))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, cons1(_x151, _x152)), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons1(mark(_x151), mark(_x152))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(s(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32))))
mark#(2nd(cons1(active(_x61), cons(_x71, _x72))))active#(2nd(active(cons1(_x61, active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(active(active(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x112)), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), cons(mark(_x71), _x72)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), 2nd(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(2nd(mark(_x131))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), _x112)), _x62)), mark(_x32)))))
active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))) 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#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), _x52)))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons(mark(_x131), _x132))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x152)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(cons1(mark(_x161), mark(_x162))), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(s(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(cons1(mark(_x71), mark(_x72))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(s(mark(_x161))), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(mark(_x131), _x132))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(_x151, _x152)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(cons(mark(_x161), _x162)), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(from(mark(_x161))), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(from(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(2nd(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))) 
Thus, the rule mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), cons1(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons(mark(_x131), _x132))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x52))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(cons(_x161, _x162), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(cons(mark(_x161), _x162)), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons(cons1(_x161, _x162), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(cons1(mark(_x161), mark(_x162))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x151, _x152)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(_x151, _x152)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), mark(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), cons(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x111, cons(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), from(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, active(_x152))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x152)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(s(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(s(mark(_x161))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), cons(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x82), _x32))) → active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(mark(_x131), _x132))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(s(_x121), cons(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), 2nd(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(2nd(_x121), cons(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(from(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(from(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), active(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, mark(_x152))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x152)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), s(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(s(mark(_x71)))))))

Problem 25: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(_x61, _x62), s(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(cons(_x151, _x152), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x151), _x152)), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(cons1(_x151, _x152), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons1(mark(_x151), mark(_x152))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(_x171, _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(mark(_x171), _x172)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))
mark#(s(X))mark#(X)mark#(2nd(cons1(cons(cons1(_x91, cons(_x151, _x152)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(_x151, _x152)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))mark#(2nd(cons1(_x51, _x32)))active#(2nd(cons1(_x51, mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons(s(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(s(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(active(_x51), _x52)))active#(2nd(active(cons1(_x51, _x52))))
mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61))))))mark#(2nd(cons1(active(mark(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))
mark#(2nd(cons1(_x31, s(_x71))))active#(2nd(active(cons1(mark(_x31), active(s(mark(_x71)))))))mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x102), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x102)), _x62)), active(cons(mark(_x71), _x72))))))active#(from(X))mark#(cons(X, from(s(X))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(mark(_x131), _x132))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(_x31, _x52)))active#(2nd(active(cons1(mark(_x31), _x52))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), from(_x121)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(from(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(2nd(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(2nd(mark(_x91))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), mark(_x72)), cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons1(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, mark(_x82)))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x82))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x111, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(from(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(from(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), cons(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x61), _x62)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, cons(_x161, _x162)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons(mark(_x161), _x162)))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, active(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(cons1(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons1(mark(_x161), mark(_x162))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(from(_x141), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(from(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(2nd(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(2nd(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(_x51, 2nd(_x81))))active#(2nd(active(cons1(_x51, active(2nd(mark(_x81)))))))
mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), 2nd(_x121)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(2nd(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x142), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), _x142)), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(from(_x31)))active#(2nd(active(from(mark(_x31)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(from(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(from(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(s(_x61), _x32)))active#(2nd(active(cons1(active(s(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(cons1(cons(mark(_x61), _x62), mark(_x32))))mark#(2nd(cons1(cons(cons1(cons1(_x121, 2nd(_x151)), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(2nd(mark(_x151))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
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mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, active(_x82)))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x82))))))mark#(2nd(cons1(active(_x61), _x32)))active#(2nd(cons1(_x61, mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(2nd(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x71, _x72), _x32)))active#(2nd(cons1(active(cons(_x71, _x72)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(s(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), mark(_x92)), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x141), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(cons1(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(cons1(mark(_x161), mark(_x162))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x111, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(active(_x61), 2nd(_x71))))active#(2nd(active(cons1(_x61, active(2nd(mark(_x71)))))))mark#(from(X))mark#(X)
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, from(_x171))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(from(mark(_x171))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(2nd(_x61), _x32)))active#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(from(mark(_x71)))))))mark#(from(X))active#(from(mark(X)))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(2nd(_x91), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(2nd(mark(_x91))), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x141, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x141, mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x31, from(_x71))))active#(2nd(active(cons1(mark(_x31), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92)), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(cons(_x91, _x92), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(cons(mark(_x91), _x92)), _x72))))))mark#(2nd(cons1(_x61, _x62)))active#(2nd(active(cons1(_x61, _x62))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(cons1(_x131, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x131, mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons(mark(_x131), _x132))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(2nd(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x111, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(2nd(_x141), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(2nd(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), active(_x72)), cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(_x51, cons1(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, s(_x151)), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(s(mark(_x151))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(from(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(from(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(_x21))active#(2nd(_x21))mark#(2nd(cons1(cons(cons(_x81, _x82), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons(mark(_x81), _x82)), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, cons1(_x161, _x162)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons1(mark(_x161), mark(_x162))))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons(mark(_x91), _x92)), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(cons(_x141, _x142), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x141), _x142)), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x52)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(s(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(active(active(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x112)), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), cons(mark(_x71), _x72)))))
active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32))))) 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#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(from(mark(_x191))))), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(s(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(from(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x152)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(cons1(mark(_x71), mark(_x72))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(2nd(mark(_x191))))), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(2nd(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(2nd(mark(_x161)), _x152)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(s(mark(_x191))))), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(_x181)), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons(active(2nd(mark(_x161))), _x132))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(cons1(mark(_x191), mark(_x192))))), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), _x52)))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(cons(mark(_x191), _x192)))), _x132)))), _x62)), mark(_x32))))) 
Thus, the rule mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons(active(2nd(mark(_x161))), _x132))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), mark(_x152))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x152)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), active(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), 2nd(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), cons(2nd(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(cons(_x191, _x192)), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(cons(mark(_x191), _x192)))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), active(_x152))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x152)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(s(_x121), cons(2nd(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(cons1(_x191, _x192)), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(cons1(mark(_x191), mark(_x192))))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), from(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x111, cons(2nd(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(s(_x191)), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(s(mark(_x191))))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), mark(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), s(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), cons(2nd(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x152)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(2nd(mark(_x161)), _x152)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(2nd(_x191)), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(2nd(mark(_x191))))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons(2nd(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), cons1(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x181), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(_x181)), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x82), _x32))) → active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(2nd(_x121), cons(2nd(_x161), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(from(_x191)), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(from(mark(_x191))))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x52))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), _x52))))

Problem 26: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(_x61, _x62), s(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(cons(_x151, _x152), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x151), _x152)), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(cons1(_x151, _x152), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons1(mark(_x151), mark(_x152))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(_x171, _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(mark(_x171), _x172)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(s(_x191)), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(s(mark(_x191))))), _x132)))), _x62)), mark(_x32)))))
mark#(s(X))mark#(X)mark#(2nd(cons1(cons(cons1(_x91, cons(_x151, _x152)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(_x151, _x152)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))mark#(2nd(cons1(_x51, _x32)))active#(2nd(cons1(_x51, mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons(s(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(s(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(active(_x51), _x52)))active#(2nd(active(cons1(_x51, _x52))))
mark#(2nd(cons1(active(mark(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))mark#(2nd(cons1(_x31, s(_x71))))active#(2nd(active(cons1(mark(_x31), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(from(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x102), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x102)), _x62)), active(cons(mark(_x71), _x72))))))
active#(from(X))mark#(cons(X, from(s(X))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(mark(_x131), _x132))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(_x31, _x52)))active#(2nd(active(cons1(mark(_x31), _x52))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons(active(2nd(mark(_x161))), _x132))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), from(_x121)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(from(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(2nd(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(2nd(mark(_x91))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), mark(_x72)), cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons1(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, mark(_x82)))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x82))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x111, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(from(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(from(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), cons(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x61), _x62)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, cons(_x161, _x162)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons(mark(_x161), _x162)))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, active(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons1(from(_x141), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(from(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(cons1(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons1(mark(_x161), mark(_x162))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(2nd(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(2nd(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(_x51, 2nd(_x81))))active#(2nd(active(cons1(_x51, active(2nd(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), 2nd(_x121)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(2nd(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(from(_x31)))active#(2nd(active(from(mark(_x31)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x142), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), _x142)), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(2nd(_x191)), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(2nd(mark(_x191))))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(from(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(from(mark(_x161))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(s(_x61), _x32)))active#(2nd(active(cons1(active(s(mark(_x61))), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(cons1(cons(mark(_x61), _x62), mark(_x32))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, 2nd(_x151)), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(2nd(mark(_x151))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), mark(_x152))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x152)))), _x62)), mark(_x32)))))
mark#(2nd(cons(_x31, _x32)))active#(2nd(active(cons(mark(_x31), _x32))))mark#(2nd(cons1(cons(cons1(_x91, from(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(from(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), _x52))))mark#(cons1(X1, X2))mark#(X1)
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(_x61, active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(cons(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(cons(mark(_x161), _x162)), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))
mark#(2nd(cons1(_x31, cons(_x71, _x72))))active#(2nd(active(cons1(mark(_x31), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, cons(_x151, _x152)), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons(mark(_x151), _x152)))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), _x52))))mark#(2nd(cons1(cons(_x81, _x82), _x32)))active#(2nd(active(cons1(active(cons(_x81, _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, from(_x161)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(from(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(cons1(mark(_x121), mark(_x122)), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(cons(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons(mark(_x161), _x162)), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, s(_x131)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(s(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(2nd(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(2nd(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(from(_x61), _x32)))active#(2nd(active(cons1(active(from(mark(_x61))), mark(_x32)))))
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mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons1(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(2nd(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x71, _x72), _x32)))active#(2nd(cons1(active(cons(_x71, _x72)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(s(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), mark(_x92)), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x141), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(cons1(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(cons1(mark(_x161), mark(_x162))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x111, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(active(_x61), 2nd(_x71))))active#(2nd(active(cons1(_x61, active(2nd(mark(_x71)))))))
mark#(from(X))mark#(X)mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, from(_x171))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(from(mark(_x171))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(2nd(_x61), _x32)))active#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(from(mark(_x71)))))))
mark#(from(X))active#(from(mark(X)))mark#(2nd(cons1(cons(cons1(cons1(_x141, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x141, mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(2nd(_x91), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(2nd(mark(_x91))), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92)), _x82)), mark(_x32)))))
mark#(2nd(cons1(_x31, from(_x71))))active#(2nd(active(cons1(mark(_x31), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(2nd(_x121), cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x61, _x62)))active#(2nd(active(cons1(_x61, _x62))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(cons(_x91, _x92), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(cons(mark(_x91), _x92)), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons(mark(_x131), _x132))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x131, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x131, mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(2nd(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x111, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(2nd(_x141), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(2nd(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), active(_x72)), cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(cons1(_x191, _x192)), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(cons1(mark(_x191), mark(_x192))))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x51, cons1(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, s(_x151)), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(s(mark(_x151))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(from(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(from(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(_x21))active#(2nd(_x21))
mark#(2nd(cons1(cons(cons(_x81, _x82), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons(mark(_x81), _x82)), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons(mark(_x91), _x92)), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, cons1(_x161, _x162)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons1(mark(_x161), mark(_x162))))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(cons(_x141, _x142), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x141), _x142)), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62), mark(_x32)))))active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x52)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(s(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32))))
mark#(2nd(cons1(active(active(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x112)), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), cons(mark(_x71), _x72)))))
active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 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#(2nd(active(cons1(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), _x52)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(s(mark(_x151))), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(s(mark(_x141))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(_x141, mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), cons1(mark(_x131), mark(_x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(from(mark(_x141))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(2nd(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(from(mark(_x161))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons1(mark(_x151), mark(_x152))), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(s(mark(_x161))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(from(mark(_x151))), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(2nd(mark(_x161))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(_x131)), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons(mark(_x151), _x152)), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x141))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(from(mark(_x121)), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(mark(_x121), from(s(mark(_x121))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(from(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons1(mark(_x71), mark(_x72))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), _x142)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons(mark(_x161), _x162)))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(2nd(mark(_x151))), mark(_x132))))), _x62)), mark(_x32))))) 
Thus, the rule mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(2nd(_x151), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(2nd(mark(_x151))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, 2nd(_x161))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(2nd(mark(_x161))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), cons1(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(from(from(_x141)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(from(mark(_x141))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, s(_x161))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(s(mark(_x161))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(mark(_x121), from(s(mark(_x121))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(from(mark(_x121)), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), s(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x141, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(_x141, mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), mark(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(cons1(_x151, _x152), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons1(mark(_x151), mark(_x152))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(s(_x141)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(s(mark(_x141))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), from(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons(mark(_x161), _x162)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(from(_x151), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(from(mark(_x151))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(s(_x151), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(s(mark(_x151))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), 2nd(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x52))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, from(_x161))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(from(mark(_x161))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(cons(_x151, _x152), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons(mark(_x151), _x152)), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x82), _x32))) → active#(2nd(active(cons1(active(cons(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x141)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x141))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x131), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(_x131)), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), cons1(mark(_x131), mark(_x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x142)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), _x142)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), active(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))

Problem 27: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(_x61, _x62), s(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(cons(_x151, _x152), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x151), _x152)), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(cons1(_x151, _x152), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons1(mark(_x151), mark(_x152))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(_x171, _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(mark(_x171), _x172)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(s(_x191)), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(s(mark(_x191))))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x151, _x152)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(_x151, _x152)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(from(mark(_x71)))))))mark#(s(X))mark#(X)
mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))mark#(2nd(cons1(_x51, _x32)))active#(2nd(cons1(_x51, mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons(s(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(s(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(active(_x51), _x52)))active#(2nd(active(cons1(_x51, _x52))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61))))))
mark#(2nd(cons1(active(mark(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(2nd(cons1(_x31, s(_x71))))active#(2nd(active(cons1(mark(_x31), active(s(mark(_x71)))))))
mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x102), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x102)), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, from(_x161))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(from(mark(_x161))))))), _x62)), mark(_x32)))))active#(from(X))mark#(cons(X, from(s(X))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(mark(_x131), _x132))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x142)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), _x142)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x31, _x52)))active#(2nd(active(cons1(mark(_x31), _x52))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons(active(2nd(mark(_x161))), _x132))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), from(_x121)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(from(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(2nd(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(2nd(mark(_x91))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), mark(_x72)), cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons1(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, mark(_x82)))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x82))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x111, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(from(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(from(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), cons(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x61), _x62)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, cons(_x161, _x162)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons(mark(_x161), _x162)))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, active(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons(mark(_x161), _x162)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(cons1(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons1(mark(_x161), mark(_x162))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(from(_x141), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(from(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(2nd(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(2nd(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(_x51, 2nd(_x81))))active#(2nd(active(cons1(_x51, active(2nd(mark(_x81)))))))
mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), 2nd(_x121)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(2nd(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x142), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), _x142)), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(from(_x31)))active#(2nd(active(from(mark(_x31)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62), mark(_x32)))))
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mark#(2nd(cons1(cons(cons(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons(mark(_x91), _x92)), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(cons(_x141, _x142), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x141), _x142)), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(s(mark(_x71)))))))active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), _x52)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))mark#(2nd(cons1(cons(cons1(from(_x121), cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(s(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132))), _x82)), mark(_x32)))))
mark#(2nd(cons1(active(active(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x112)), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), cons(mark(_x71), _x72)))))active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))
mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 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#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(s(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons(mark(_x201), _x202)))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(from(mark(_x141))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons1(mark(_x151), mark(_x152))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(s(mark(_x141))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162)))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), _x182)))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x191), _x192)), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(2nd(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(mark(_x121), from(s(mark(_x121))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(cons1(mark(_x191), mark(_x192))), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(from(mark(_x201))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(from(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x141))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(2nd(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(s(mark(_x201))))))))), _x62)), mark(_x32))))) 
active#(2nd(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(s(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), cons1(mark(_x161), mark(_x162)))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), _x52)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(_x181, mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(_x141, active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(from(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(s(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons1(mark(_x71), mark(_x72))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(2nd(mark(_x201))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(from(mark(_x121)), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(_x131)), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(from(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162)))))), _x82)), mark(_x32))))) 
Thus, the rule mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), cons1(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(cons1(_x151, _x152), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons1(mark(_x151), mark(_x152))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, from(_x201)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(from(mark(_x201))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(s(_x191), _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(s(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x131), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(_x131)), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons(mark(_x201), _x202)))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), cons1(mark(_x161), mark(_x162)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(from(_x141)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(from(mark(_x141))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(cons(_x151, _x152), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(from(mark(_x121)), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(from(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(from(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x141)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x141))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x52))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, s(_x201)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(s(mark(_x201))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), active(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x182))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), _x182)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(cons1(_x191, _x192), _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(cons1(mark(_x191), mark(_x192))), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x141, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(_x141, active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(s(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(s(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(2nd(_x191), _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(2nd(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), mark(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(mark(_x121), from(s(mark(_x121))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), s(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x181, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(_x181, mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), from(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), 2nd(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(from(_x191), _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(from(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x82), _x32))) → active#(2nd(active(cons1(active(cons(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162)))))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, 2nd(_x201)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(2nd(mark(_x201))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(s(_x141)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(s(mark(_x141))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(cons(_x191, _x192), _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x191), _x192)), mark(_x162))))))), _x62)), mark(_x32)))))

Problem 28: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), s(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(s(_x191), _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(s(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(cons(_x151, _x152), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x151), _x152)), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(cons1(_x151, _x152), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons1(mark(_x151), mark(_x152))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(_x171, _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(mark(_x171), _x172)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(s(_x191)), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(s(mark(_x191))))), _x132)))), _x62)), mark(_x32)))))mark#(s(X))mark#(X)
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x151, _x152)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(_x151, _x152)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), _x52))))mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))
mark#(2nd(cons1(_x51, _x32)))active#(2nd(cons1(_x51, mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons(s(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(s(mark(_x161))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x82)), mark(_x32)))))mark#(2nd(cons1(active(_x51), _x52)))active#(2nd(active(cons1(_x51, _x52))))
mark#(2nd(cons1(active(mark(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62), mark(_x32)))))mark#(2nd(cons1(_x31, s(_x71))))active#(2nd(active(cons1(mark(_x31), active(s(mark(_x71)))))))
mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x102), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x102)), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, from(_x161))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(from(mark(_x161))))))), _x62)), mark(_x32)))))active#(from(X))mark#(cons(X, from(s(X))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(mark(_x131), _x132))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x142)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), _x142)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(cons(_x191, _x192), _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x191), _x192)), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x31, _x52)))active#(2nd(active(cons1(mark(_x31), _x52))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons(active(2nd(mark(_x161))), _x132))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), from(_x121)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(from(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(2nd(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(2nd(mark(_x91))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), mark(_x72)), cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, from(_x201)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(from(mark(_x201))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))mark#(2nd(cons1(cons1(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, mark(_x82)))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x82))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x111, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(from(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(from(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), cons1(mark(_x161), mark(_x162)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, cons(_x161, _x162)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons(mark(_x161), _x162)))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), cons(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x61), _x62)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(_x61, active(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons(mark(_x161), _x162)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons1(from(_x141), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(from(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(cons1(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons1(mark(_x161), mark(_x162))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(2nd(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(2nd(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(_x51, 2nd(_x81))))active#(2nd(active(cons1(_x51, active(2nd(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), 2nd(_x121)), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), active(2nd(mark(_x121))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(from(_x31)))active#(2nd(active(from(mark(_x31)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x142), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), _x142)), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62), mark(_x32)))))
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mark#(from(X))active#(from(mark(X)))mark#(2nd(cons1(cons(cons1(from(_x131), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(_x131)), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x141, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x141, mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(2nd(_x91), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(2nd(mark(_x91))), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92)), _x82)), mark(_x32)))))mark#(2nd(cons1(_x31, from(_x71))))active#(2nd(active(cons1(mark(_x31), active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(2nd(_x121), cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, 2nd(_x201)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(2nd(mark(_x201))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(_x61, _x62)))active#(2nd(active(cons1(_x61, _x62))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(cons(_x91, _x92), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(cons(mark(_x91), _x92)), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons(mark(_x131), _x132))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x131, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x131, mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(cons1(_x151, _x152), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons1(mark(_x151), mark(_x152))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(2nd(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x111, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, 2nd(_x161))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(2nd(mark(_x161))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(from(_x141)), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(from(mark(_x141))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(2nd(_x141), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(2nd(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(mark(_x121), from(s(mark(_x121))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), active(_x72)), cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(cons1(_x191, _x192)), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(cons1(mark(_x191), mark(_x192))))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x131), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(_x131)), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x51, cons1(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, s(_x151)), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(s(mark(_x151))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(from(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(from(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(from(_x141)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(from(mark(_x141))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(_x21))active#(2nd(_x21))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x182))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), _x182)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(cons1(_x191, _x192), _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(cons1(mark(_x191), mark(_x192))), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons(_x81, _x82), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons(mark(_x81), _x82)), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons(mark(_x91), _x92)), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, cons1(_x161, _x162)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons1(mark(_x161), mark(_x162))))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(cons(_x141, _x142), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x141), _x142)), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62), mark(_x32)))))
active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(mark(_x121), from(s(mark(_x121))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), _x52)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))mark#(2nd(cons1(cons(cons1(from(_x121), cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(s(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(active(active(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x112)), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), cons(mark(_x71), _x72)))))active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))
mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 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#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), _x52)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(_x151, _x152)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(cons1(mark(_x161), mark(_x162))), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(_x141, active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(2nd(mark(_x201))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(s(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(2nd(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(active(2nd(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons(mark(_x201), _x202)))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162)))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x152)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(cons(mark(_x161), _x162)), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(s(mark(_x161))), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(cons(mark(_x141), _x142))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(from(mark(_x201))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(active(cons(mark(_x141), _x142)), from(s(active(cons(mark(_x141), _x142)))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(active(from(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(from(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons1(mark(_x71), mark(_x72))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(from(mark(_x161))), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(2nd(mark(_x161))), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(s(mark(_x201))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162)))))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), cons1(mark(_x161), mark(_x162)))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x191), _x192)), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(cons1(mark(_x151), mark(_x152))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(_x181, mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), _x182)))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(from(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(active(cons1(mark(_x191), mark(_x192))), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(s(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(active(s(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(from(active(cons(mark(_x141), _x142))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62), mark(_x32))))) 
Thus, the rule mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), cons1(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), active(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(2nd(_x161), _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(2nd(mark(_x161))), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, active(cons1(mark(_x161), mark(_x162))))), cons1(_x141, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(_x141, active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(s(_x191), _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(active(s(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(cons(_x191, _x192), _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x191), _x192)), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(cons1(_x151, _x152), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(cons1(mark(_x151), mark(_x152))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, from(_x201)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(from(mark(_x201))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), s(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(active(cons(mark(_x141), _x142)), from(s(active(cons(mark(_x141), _x142)))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(cons(mark(_x141), _x142))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(cons(_x161, _x162), _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(cons(mark(_x161), _x162)), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x151, _x152)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(_x151, _x152)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(from(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(from(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(from(active(cons(mark(_x141), _x142))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(cons1(_x161, _x162), _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(cons1(mark(_x161), mark(_x162))), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, 2nd(_x201)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(2nd(mark(_x201))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(from(_x161), _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(from(mark(_x161))), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(2nd(_x191), _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(active(2nd(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), from(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(cons(_x151, _x152), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x82), _x32))) → active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162)))))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), 2nd(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x182))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), _x182)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(from(_x191), _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(active(from(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(s(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(s(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), mark(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(cons1(_x191, _x192), _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(active(cons1(mark(_x191), mark(_x192))), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, active(_x152))), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x152)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(from(cons(mark(_x131), cons1(mark(_x161), mark(_x162)))), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), cons1(mark(_x161), mark(_x162)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, s(_x201)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(s(mark(_x201))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, cons(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons(mark(_x201), _x202)))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x181, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(_x181, mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, mark(_x152))), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x152)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x52))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), _x52))))mark#(2nd(cons1(cons(cons1(from(cons(s(_x161), _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(s(mark(_x161))), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))

Problem 29: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(_x61, _x62), s(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(s(_x191), _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(s(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(cons(_x151, _x152), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x151), _x152)), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(cons1(_x151, _x152), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons1(mark(_x151), mark(_x152))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(cons(_x161, _x162), _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(cons(mark(_x161), _x162)), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(_x171, _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(mark(_x171), _x172)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(s(_x191)), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(s(mark(_x191))))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x151, _x152)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(_x151, _x152)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(from(mark(_x71)))))))
mark#(s(X))mark#(X)mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), _x52))))
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mark#(2nd(cons1(cons(cons1(_x91, _x92), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), mark(_x92)), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x141), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(cons1(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(cons1(mark(_x161), mark(_x162))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x111, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x141, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(_x141, active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(active(_x61), 2nd(_x71))))active#(2nd(active(cons1(_x61, active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(2nd(_x191), _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(active(2nd(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(from(X))mark#(X)mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, from(_x171))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(from(mark(_x171))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), _x52))))mark#(2nd(cons1(2nd(_x61), _x32)))active#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(s(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(s(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(from(mark(_x71)))))))
mark#(from(X))active#(from(mark(X)))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, cons(_x201, _x202)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons(mark(_x201), _x202)))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(2nd(_x91), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(2nd(mark(_x91))), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x141, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x141, mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x131), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(_x131)), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(2nd(_x121), cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x31, from(_x71))))active#(2nd(active(cons1(mark(_x31), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92)), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, 2nd(_x201)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(2nd(mark(_x201))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(s(_x161), _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(s(mark(_x161))), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(cons(_x91, _x92), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(cons(mark(_x91), _x92)), _x72))))))
mark#(2nd(cons1(_x61, _x62)))active#(2nd(active(cons1(_x61, _x62))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(cons1(_x151, _x152), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons1(mark(_x151), mark(_x152))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x131, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x131, mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons(mark(_x131), _x132))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(2nd(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x111, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(_x111, mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, 2nd(_x161))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(2nd(mark(_x161))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(2nd(_x141), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(2nd(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(from(from(_x141)), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(from(mark(_x141))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), active(_x72)), cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(mark(_x121), from(s(mark(_x121))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(cons1(_x191, _x192)), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(cons1(mark(_x191), mark(_x192))))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x131), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(_x131)), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(_x51, cons1(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82)))))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, from(_x201)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(from(mark(_x201))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, s(_x151)), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(s(mark(_x151))))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), _x52))))mark#(2nd(cons1(cons(cons1(from(_x121), cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(from(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(from(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(from(_x141)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(from(mark(_x141))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(_x21))active#(2nd(_x21))mark#(2nd(cons1(cons(cons1(from(cons(_x151, _x152)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(_x151, _x152)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x182))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), _x182)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(cons1(_x191, _x192), _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(cons1(mark(_x191), mark(_x192))), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons(_x81, _x82), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons(mark(_x81), _x82)), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, cons1(_x161, _x162)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons1(mark(_x161), mark(_x162))))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons(mark(_x91), _x92)), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(cons(_x141, _x142), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x141), _x142)), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(s(mark(_x71)))))))active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(mark(_x121), from(s(mark(_x121))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), _x52)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))mark#(2nd(cons1(cons(cons1(from(_x121), cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(s(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, active(_x152))), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x152)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132))), _x82)), mark(_x32)))))
mark#(2nd(cons1(active(active(_x51)), _x32)))active#(2nd(active(cons1(_x51, mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x112)), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), cons(mark(_x71), _x72)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), _x52))))
active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))mark#(2nd(X))mark#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 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#(2nd(active(cons1(active(cons(active(cons1(mark(cons(active(cons(mark(_x141), _x142)), from(s(active(cons(mark(_x141), _x142)))))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(2nd(mark(_x161))), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162)))))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), active(2nd(mark(_x191))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(cons(mark(_x141), _x142))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(cons(mark(_x161), _x162)), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), _x172)))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(active(2nd(mark(_x171))))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), active(from(mark(_x191))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(active(cons1(mark(_x181), mark(_x182))), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(cons1(mark(_x161), mark(_x162))), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), active(cons(mark(_x191), _x192)))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons1(mark(_x71), mark(_x72))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), active(s(mark(_x191))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), _x52)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(from(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(_x151, _x152)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(2nd(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(s(mark(_x161))), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(active(2nd(mark(_x181))), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(active(from(mark(_x181))), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(active(cons1(mark(_x171), mark(_x172))))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(_x161)), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(from(mark(_x161))), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(_x171, mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(s(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(2nd(mark(_x151)), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(active(s(mark(_x181))), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(active(from(mark(_x171))))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), active(cons1(mark(_x191), mark(_x192))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(active(cons(mark(_x181), _x182)), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x152)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(active(s(mark(_x171))))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(active(cons(mark(_x171), _x172)))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), cons1(mark(_x161), mark(_x162)))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(from(active(cons(mark(_x141), _x142))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162)))))), _x62)), mark(_x32))))) 
Thus, the rule mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(cons1(_x171, _x172)), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(active(cons1(mark(_x171), mark(_x172))))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, from(_x191)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), active(from(mark(_x191))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), s(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, s(_x191)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), active(s(mark(_x191))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x171, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(_x171, mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(cons(_x161, _x162), _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(cons(mark(_x161), _x162)), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), from(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), 2nd(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(from(_x181), _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(active(from(mark(_x181))), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(cons1(_x161, _x162), _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(cons1(mark(_x161), mark(_x162))), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, mark(_x152))), cons1(2nd(mark(_x141)), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x152)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x151, _x152)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(_x151, _x152)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(from(_x171)), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(active(from(mark(_x171))))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(cons1(_x181, _x182), _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(active(cons1(mark(_x181), mark(_x182))), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(active(cons(mark(_x141), _x142)), from(s(active(cons(mark(_x141), _x142)))))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(from(active(cons(mark(_x141), _x142))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, 2nd(_x191)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), active(2nd(mark(_x191))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(s(_x171)), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(active(s(mark(_x171))))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(s(_x181), _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(active(s(mark(_x181))), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x161), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(_x161)), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, active(_x152))), cons1(2nd(mark(_x141)), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x152)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(2nd(mark(_x151)), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(2nd(_x161), _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(2nd(mark(_x161))), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), cons1(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, cons1(_x191, _x192)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), active(cons1(mark(_x191), mark(_x192))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x172))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), _x172)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), cons1(mark(_x161), mark(_x162)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(cons(mark(_x141), _x142))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(2nd(_x181), _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(active(2nd(mark(_x181))), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), active(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(s(_x161), _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(s(mark(_x161))), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), mark(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, cons(_x191, _x192)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), active(cons(mark(_x191), _x192)))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(cons(_x171, _x172)), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(active(cons(mark(_x171), _x172)))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(from(_x161), _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(from(mark(_x161))), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x52))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(2nd(_x171)), cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(active(2nd(mark(_x171))))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(cons(_x181, _x182), _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(active(cons(mark(_x181), _x182)), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x82), _x32))) → active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162)))))), _x82)), mark(_x32)))))

Problem 30: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(_x61, _x62), s(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(cons(_x161, _x162), _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(cons(mark(_x161), _x162)), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(_x171, _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(mark(_x171), _x172)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x151, _x152)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(_x151, _x152)))), _x62)), mark(_x32)))))mark#(s(X))mark#(X)
mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61))))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x102), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x102)), _x62)), active(cons(mark(_x71), _x72))))))active#(from(X))mark#(cons(X, from(s(X))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(2nd(_x171)), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(active(2nd(mark(_x171))))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons(active(2nd(mark(_x161))), _x132))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(cons1(_x171, _x172)), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(active(cons1(mark(_x171), mark(_x172))))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), mark(_x72)), cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(2nd(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(2nd(mark(_x91))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, from(_x201)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(from(mark(_x201))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons1(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, mark(_x152))), cons1(2nd(mark(_x141)), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x152)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), cons(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x61), _x62)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(active(cons(mark(_x141), _x142)), from(s(active(cons(mark(_x141), _x142)))))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, active(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(cons1(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons1(mark(_x161), mark(_x162))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(2nd(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(2nd(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(from(_x31)))active#(2nd(active(from(mark(_x31)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(cons(mark(_x141), _x142))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(from(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(from(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, mark(_x152))), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x152)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), _x32)))active#(2nd(cons1(cons(mark(_x61), _x62), mark(_x32))))mark#(2nd(cons1(cons(cons1(from(s(_x141)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(s(mark(_x141))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162)))))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), mark(_x152))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x152)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(2nd(_x151), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(2nd(mark(_x151))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(s(_x191), _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(active(s(mark(_x191))), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(mark(_x61), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(from(mark(_x121)), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, cons(_x151, _x152)), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), active(cons(mark(_x151), _x152)))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(from(_x151), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(from(mark(_x151))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(from(_x161), _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(from(mark(_x161))), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x52)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(_x81, _x82), _x32)))active#(2nd(active(cons1(active(cons(_x81, _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(cons1(mark(_x121), mark(_x122)), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(cons(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons(mark(_x161), _x162)), mark(_x132))))), _x62)), mark(_x32)))))
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mark#(2nd(_x21))active#(2nd(_x21))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x182))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), _x182)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, 2nd(_x191)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), active(2nd(mark(_x191))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(cons(_x141, _x142), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x141), _x142)), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62), mark(_x32)))))active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), _x52)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))mark#(2nd(cons1(cons(cons1(from(cons(s(_x161), _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(s(mark(_x161))), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(s(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x112)), _x62)), mark(_x32)))))

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 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#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(active(2nd(mark(_x181))))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), active(from(mark(_x131))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), active(cons(mark(_x161), _x162)))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), _x142)), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), active(from(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(active(s(mark(_x181))))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), _x112)), _x62)), mark(_x32))))) 
active#(2nd(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))) 
active#(2nd(active(cons1(active(cons(active(cons1(cons1(active(s(mark(_x151))), mark(_x122)), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), active(2nd(mark(_x131))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), active(2nd(mark(_x161))))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), active(s(mark(_x131))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92)), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(active(cons(mark(_x181), _x182)))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(_x171)), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), _x52)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), active(s(mark(_x161))))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), active(2nd(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(active(from(mark(_x181))))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), active(from(mark(_x161))))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(active(cons1(mark(_x181), mark(_x182))))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72))))))) 
Thus, the rule mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), cons(_x161, _x162)), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), active(cons(mark(_x161), _x162)))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), 2nd(_x161)), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), active(2nd(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), active(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(cons1(active(s(mark(_x151))), mark(_x122)), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), cons(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x112), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), _x112)), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(s(_x181)), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(active(s(mark(_x181))))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), s(_x161)), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), active(s(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(cons1(_x181, _x182)), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(active(cons1(mark(_x181), mark(_x182))))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x142), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), _x142)), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x52))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), cons1(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), cons1(_x161, _x162)), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(cons1(s(cons(_x181, _x182)), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(active(cons(mark(_x181), _x182)))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(from(_x181)), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(active(from(mark(_x181))))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), from(_x161)), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), active(from(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), mark(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), from(_x131)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), active(from(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), from(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(s(2nd(_x181)), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(active(2nd(mark(_x181))))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), s(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), 2nd(_x131)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), active(2nd(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), s(_x131)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), active(s(mark(_x131))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x171), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(_x171)), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), 2nd(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x82), _x32))) → active#(2nd(active(cons1(active(cons(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92)), _x82)), mark(_x32)))))

Problem 31: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(_x61, _x62), s(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(cons(_x161, _x162), _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(cons(mark(_x161), _x162)), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(_x171, _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(mark(_x171), _x172)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x82)), mark(_x32)))))
mark#(s(X))mark#(X)mark#(2nd(cons1(cons(cons1(_x91, cons(_x151, _x152)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(_x151, _x152)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61))))))
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mark#(2nd(cons1(cons(cons1(from(from(_x141)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(from(mark(_x141))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(_x21))active#(2nd(_x21))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x182))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), _x182)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, 2nd(_x191)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), active(2nd(mark(_x191))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(cons(_x141, _x142), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x141), _x142)), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(s(mark(_x71)))))))
active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(s(_x161), _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(s(mark(_x161))), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x52)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(s(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x112)), _x62)), mark(_x32)))))

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 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#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(active(from(mark(_x171)))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), active(2nd(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(active(2nd(mark(_x171)))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), active(from(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), _x52)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(active(cons1(mark(_x171), mark(_x172)))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), _x142)), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(cons1(s(mark(_x151)), mark(_x122)), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(s(mark(_x161))))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92)), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), active(from(mark(_x131))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(2nd(mark(_x161))))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), _x112)), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), active(s(mark(_x131))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), active(2nd(mark(_x131))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(cons1(mark(_x161), mark(_x162))))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(from(mark(_x161))))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(cons(mark(_x161), _x162)))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62), mark(_x32))))) 
active#(2nd(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(active(s(mark(_x171)))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(active(cons(mark(_x171), _x172))), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(_x161), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) 
Thus, the rule mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x142), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), _x142)), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), from(_x131)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), active(from(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(cons(_x171, _x172)), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(active(cons(mark(_x171), _x172))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(from(_x171)), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(active(from(mark(_x171)))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x112), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), _x112)), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x161), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(_x161), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), mark(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), s(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), active(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x82), _x32))) → active#(2nd(active(cons1(active(cons(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92)), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), 2nd(_x131)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), active(2nd(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), cons(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), s(_x131)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), active(s(mark(_x131))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(cons1(_x171, _x172)), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(active(cons1(mark(_x171), mark(_x172)))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), cons1(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), 2nd(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), 2nd(_x161)), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(2nd(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), cons(_x161, _x162)), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(cons(mark(_x161), _x162)))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), from(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x52))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), cons1(_x161, _x162)), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(cons1(mark(_x161), mark(_x162))))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(2nd(_x171)), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(active(2nd(mark(_x171)))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), s(_x161)), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(s(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(cons1(s(mark(_x151)), mark(_x122)), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), from(_x161)), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(from(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(s(_x171)), _x122), _x92), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(active(s(mark(_x171)))), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))

Problem 32: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(_x61, _x62), s(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(cons(_x161, _x162), _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(cons(mark(_x161), _x162)), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(_x171, _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(mark(_x171), _x172)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x151, _x152)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(_x151, _x152)))), _x62)), mark(_x32)))))
mark#(s(X))mark#(X)mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61))))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))
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active#(2nd(cons(X, X1)))mark#(2nd(cons1(X, X1)))mark#(2nd(X))mark#(X)
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mark#(2nd(cons1(2nd(_x61), _x32)))active#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(s(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(s(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x82)), mark(_x32)))))mark#(from(X))active#(from(mark(X)))
mark#(2nd(cons1(cons(cons1(cons1(s(_x171), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(_x171)), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, cons(_x201, _x202)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons(mark(_x201), _x202)))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x141, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x141, mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(2nd(_x121), cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(s(_x161), _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(s(mark(_x161))), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(cons(_x91, _x92), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(cons(mark(_x91), _x92)), _x72))))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(cons1(_x131, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x131, mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(cons1(_x151, _x152), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons1(mark(_x151), mark(_x152))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(2nd(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x131), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(_x131)), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x51, cons1(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(from(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(from(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(from(_x141)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(from(mark(_x141))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(_x21))active#(2nd(_x21))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x182))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), _x182)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, 2nd(_x191)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), active(2nd(mark(_x191))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(cons(_x141, _x142), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x141), _x142)), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62), mark(_x32)))))
active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x52)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(from(cons(s(_x161), _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(s(mark(_x161))), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(s(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), s(_x161)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(s(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x112)), _x62)), mark(_x32)))))

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 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#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), _x52)))) 
active#(2nd(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), _x142)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), active(from(mark(_x171))))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), _x152)))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(active(cons1(mark(_x141), mark(_x142))), from(s(active(cons1(mark(_x141), mark(_x142))))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(active(2nd(mark(_x161))), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons(mark(_x71), _x72)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(_x151, mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(active(s(mark(_x151))), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), active(cons(mark(_x171), _x172)))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(active(s(mark(_x161))), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons1(mark(_x71), mark(_x72))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(active(from(mark(_x161))), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), active(from(mark(_x161))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(cons1(mark(_x141), mark(_x142)))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), active(2nd(mark(_x171))))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), active(s(mark(_x161))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(from(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(active(cons(mark(_x161), _x162)), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), active(s(mark(_x171))))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(from(active(cons1(mark(_x141), mark(_x142)))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(2nd(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), cons1(mark(_x131), mark(_x132)))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), active(cons1(mark(_x171), mark(_x172))))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(active(from(mark(_x151))), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), active(cons(mark(_x161), _x162)))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(active(2nd(mark(_x151))), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(_x141, mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(active(cons1(mark(_x161), mark(_x162))), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(active(cons1(mark(_x151), mark(_x152))), mark(_x132))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), active(2nd(mark(_x161))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(active(cons(mark(_x151), _x152)), mark(_x132))))), _x62)), mark(_x32))))) 
Thus, the rule mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(2nd(_x151), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(active(2nd(mark(_x151))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), from(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, cons(_x171, _x172))), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), active(cons(mark(_x171), _x172)))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(from(_x161), _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(active(from(mark(_x161))), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, s(_x171))), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), active(s(mark(_x171))))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), mark(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(cons(_x161, _x162), _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(active(cons(mark(_x161), _x162)), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x82), _x32))) → active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(cons1(mark(_x141), mark(_x142)))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), 2nd(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), cons(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(s(_x151), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(active(s(mark(_x151))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, cons1(_x171, _x172))), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), active(cons1(mark(_x171), mark(_x172))))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(s(_x161), _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(active(s(mark(_x161))), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(cons1(_x151, _x152), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(active(cons1(mark(_x151), mark(_x152))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, mark(_x132))), cons1(_x141, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(_x141, mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(cons(_x151, _x152), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(active(cons(mark(_x151), _x152)), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(from(active(cons1(mark(_x141), mark(_x142)))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(from(_x151), _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(active(from(mark(_x151))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), cons1(_x71, _x72)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, s(_x161))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), active(s(mark(_x161))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(2nd(_x161), _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(active(2nd(mark(_x161))), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), active(_x82)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), cons1(mark(_x131), mark(_x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, from(_x161))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), active(from(mark(_x161))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x52))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), _x52))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(active(cons1(mark(_x141), mark(_x142))), from(s(active(cons1(mark(_x141), mark(_x142))))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, cons(_x161, _x162))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), active(cons(mark(_x161), _x162)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, from(_x171))), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), active(from(mark(_x171))))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(cons1(_x161, _x162), _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(active(cons1(mark(_x161), mark(_x162))), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), s(_x71)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, 2nd(_x161))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), active(2nd(mark(_x161))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x152)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), _x152)))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, 2nd(_x171))), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), active(2nd(mark(_x171))))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x151, _x142)), cons1(_x131, _x132)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(_x151, mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(mark(_x131), _x142)), cons1(_x131, _x142)), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), _x142)))), _x62)), mark(_x32)))))

Problem 33: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(_x61, _x62), s(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(cons(_x161, _x162), _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(cons(mark(_x161), _x162)), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(_x171, _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(mark(_x171), _x172)))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71)))))))mark#(s(X))mark#(X)
mark#(2nd(cons1(cons(cons1(_x91, cons(_x151, _x152)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(_x151, _x152)))), _x62)), mark(_x32)))))mark#(2nd(cons1(_x51, cons(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons(mark(_x81), _x82))))))
mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61))))))mark#(2nd(2nd(_x31)))active#(2nd(active(2nd(mark(_x31)))))
mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x102), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x102)), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))active#(from(X))mark#(cons(X, from(s(X))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), cons1(_x161, _x162)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(cons1(mark(_x161), mark(_x162))))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, 2nd(_x161))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), active(2nd(mark(_x161))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), from(_x161)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(from(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(2nd(_x171)), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(active(2nd(mark(_x171))))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons(active(2nd(mark(_x161))), _x132))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(cons1(_x171, _x172)), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(active(cons1(mark(_x171), mark(_x172))))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), mark(_x72)), cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x72)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(2nd(_x91), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(2nd(mark(_x91))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, from(_x201)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(from(mark(_x201))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons1(_x61, _x62), _x32)))active#(2nd(active(cons1(active(cons1(mark(_x61), mark(_x62))), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), _x112)), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, mark(_x152))), cons1(2nd(mark(_x141)), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x152)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(_x61, _x62), cons(_x61, _x62))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(cons(mark(_x61), _x62)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))
mark#(2nd(cons1(cons(_x61, active(_x72)), _x32)))active#(2nd(cons1(active(cons(mark(_x61), _x72)), mark(_x32))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(active(cons(mark(_x141), _x142)), from(s(active(cons(mark(_x141), _x142)))))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(cons1(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(cons1(mark(_x161), mark(_x162))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(2nd(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(2nd(mark(_x81))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), mark(_x92))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
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mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x162))), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(s(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(s(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(cons(_x191, _x192)), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(active(cons(mark(_x191), _x192)))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(2nd(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons(_x121, _x122), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons(mark(_x121), _x122)), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(s(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(s(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(cons1(_x181, _x182), _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(active(cons1(mark(_x181), mark(_x182))), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x141), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x141))), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))mark#(2nd(cons1(cons(cons1(_x91, cons(cons1(_x161, _x162), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(cons1(mark(_x161), mark(_x162))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x141, mark(_x132))), cons1(_x141, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(_x141, mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x141, _x142)), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x141), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92)), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62), mark(_x32)))))mark#(from(X))mark#(X)
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), active(from(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, from(_x171))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(from(mark(_x171))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(s(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(s(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(2nd(_x61), _x32)))active#(2nd(active(cons1(active(2nd(mark(_x61))), mark(_x32)))))
mark#(from(X))active#(from(mark(X)))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), mark(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x171), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(_x171)), mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, cons(_x201, _x202)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons(mark(_x201), _x202)))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(_x141, _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x141, mark(_x122))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(2nd(_x121), cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(s(_x161), _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(s(mark(_x161))), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x92), _x62), cons(cons(_x91, _x92), _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), mark(_x92))), _x62)), active(cons(active(cons(mark(_x91), _x92)), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(_x131, cons1(_x161, _x162))), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(cons1(_x151, _x152), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons1(mark(_x151), mark(_x152))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x131, _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(_x131, mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(2nd(_x121), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(2nd(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x131), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(_x131)), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(_x51, cons1(_x81, _x82))))active#(2nd(active(cons1(_x51, active(cons1(mark(_x81), mark(_x82)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons(mark(_x131), _x132)))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(from(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(active(from(mark(_x161))), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(from(_x141)), cons1(_x131, cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(from(mark(_x141))))), active(cons1(mark(_x131), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(_x21))active#(2nd(_x21))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(s(mark(_x151))), mark(_x122))), mark(_x92))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, _x182))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), _x182)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, 2nd(_x191)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), active(2nd(mark(_x191))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(cons(_x141, _x142), _x122), _x92), _x62), cons(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(active(cons(mark(_x141), _x142)), mark(_x122))), mark(_x92))), _x62)), active(cons(mark(_x71), _x72))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132)))), _x62)), active(s(mark(_x71)))))))active#(2nd(cons1(X, cons(Y, Z))))mark#(Y)
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), from(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), mark(_x122))), mark(_x92))), _x62)), active(from(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(from(cons(s(_x161), _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(s(mark(_x161))), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), _x52)))active#(2nd(active(cons1(active(cons(mark(_x61), _x62)), _x52))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(2nd(mark(_x71)))))))mark#(2nd(cons1(cons(s(_x81), _x62), _x32)))active#(2nd(cons1(active(cons(active(s(mark(_x81))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(from(cons1(cons1(_x161, _x162), _x142)), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(active(cons1(mark(_x161), mark(_x162))), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), s(_x161)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(s(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(cons1(_x121, _x122), _x112), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(mark(_x121), mark(_x122))), _x112)), _x62)), mark(_x32)))))

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 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#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(active(2nd(mark(_x231))), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(active(cons(mark(_x231), _x232)), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(from(mark(_x191))), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(from(mark(_x121)), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), active(cons1(mark(_x241), mark(_x242))))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x191), _x192)), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(s(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), active(cons1(mark(_x91), mark(_x92))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), active(2nd(mark(_x241))))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), cons1(mark(_x201), mark(_x202)))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(2nd(mark(_x191))), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x92)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202)))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons1(mark(_x161), mark(_x162))), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(from(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(active(cons1(mark(_x231), mark(_x232))), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x151), mark(_x152))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), active(s(mark(_x91))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(active(s(mark(_x231))), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), _x222)))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), active(from(mark(_x91))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x151), _x152)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x221, mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(from(mark(_x161))), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), active(from(mark(_x241))))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(s(mark(_x161))), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(2nd(mark(_x161))), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons(mark(_x161), _x162)), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), active(cons(mark(_x91), _x92)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(_x151, active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), active(2nd(mark(_x91))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(_x181, active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(mark(_x121), from(s(mark(_x121))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), _x72)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(_x141)), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202)))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202)))))))), _x92)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), active(s(mark(_x241))))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(s(mark(_x191))), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(active(from(mark(_x231))), mark(_x202))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(cons1(mark(_x191), mark(_x192))), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) 
Thus, the rule mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x222)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), _x222)))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x141), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(_x141)), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(s(_x161), cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(s(mark(_x161))), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x72))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), _x72))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(s(_x231), _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(active(s(mark(_x231))), mark(_x202))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(s(_x151)), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(s(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202)))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, cons1(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), active(cons1(mark(_x241), mark(_x242))))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(2nd(_x191), cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(2nd(mark(_x191))), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, s(_x241))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), active(s(mark(_x241))))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(from(mark(_x121)), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons(_x151, _x152)), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x151), _x152)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), from(_x91)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), active(from(mark(_x91)))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), cons1(_x91, _x92)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), active(cons1(mark(_x91), mark(_x92)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), cons1(mark(_x201), mark(_x202)))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), mark(_x92)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x92)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(from(_x151)), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(from(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(cons(_x231, _x232), _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(active(cons(mark(_x231), _x232)), mark(_x202))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(cons1(_x191, _x192), cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(cons1(mark(_x191), mark(_x192))), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(cons(_x161, _x162), cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons(mark(_x161), _x162)), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(mark(_x121), cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(mark(_x121), from(s(mark(_x121))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), 2nd(_x91)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), active(2nd(mark(_x91)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x181, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(_x181, active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202)))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x221, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x221, mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(s(_x191), cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(s(mark(_x191))), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(from(_x161), cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(from(mark(_x161))), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), s(_x91)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), active(s(mark(_x91)))))))mark#(2nd(cons1(cons(cons1(from(cons1(_x151, _x152)), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(mark(_x151), mark(_x152))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x151, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(_x151, active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, 2nd(_x241))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), active(2nd(mark(_x241))))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(cons1(_x161, _x162), cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(cons1(mark(_x161), mark(_x162))), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(2nd(_x161), cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(2nd(mark(_x161))), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x92), _x32))) → active#(2nd(active(cons1(active(cons(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202)))))))), _x92)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(from(_x231), _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(active(from(mark(_x231))), mark(_x202))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), active(_x92)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x92)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(2nd(_x231), _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(active(2nd(mark(_x231))), mark(_x202))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, from(_x241))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), active(from(mark(_x241))))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(cons1(_x231, _x232), _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(active(cons1(mark(_x231), mark(_x232))), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), cons(_x91, _x92)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), active(cons(mark(_x91), _x92))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(from(_x191), cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(from(mark(_x191))), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(cons(_x191, _x192), cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x191), _x192)), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), mark(_x32))))

Problem 34: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

mark#(2nd(cons1(cons(_x61, _x62), s(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(s(mark(_x61))))))mark#(2nd(cons1(cons(cons1(from(from(_x131)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x92), _x32)))active#(2nd(active(cons1(active(cons(cons1(active(from(active(from(mark(_x131))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242))))))))), _x92)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(_x61, _x62), 2nd(_x61))))active#(2nd(cons1(active(cons(mark(_x61), _x62)), active(2nd(mark(_x61))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(mark(_x231), 2nd(_x241))))), _x92), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(cons(mark(_x121), from(s(mark(_x121))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(2nd(mark(_x241)))))))))), _x92)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(s(mark(_x121)), _x112)), cons1(cons(_x121, mark(_x142)), cons1(cons(s(_x181), _x152), cons1(mark(mark(_x171)), 2nd(cons(_x241, _x242)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(cons1(active(s(mark(_x141))), mark(_x112)))), active(cons1(active(cons(mark(_x121), _x142)), active(cons1(active(cons(active(s(mark(_x181))), _x152)), active(cons1(_x171, active(2nd(active(cons(_x241, _x242))))))))))), _x92)), active(s(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), s(s(_x81)))))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(s(active(s(mark(_x81))))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), active(_x82)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), from(_x161)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(from(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x111, s(from(_x181)))), cons1(_x131, cons1(_x161, cons1(mark(_x231), 2nd(_x241))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), active(s(active(from(mark(_x181))))))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(2nd(mark(_x241)))))))))), _x92)), active(s(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x112)), cons1(cons1(_x121, _x122), cons1(cons(_x151, _x152), cons1(mark(_x231), 2nd(_x241))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(active(cons1(mark(_x121), mark(_x122))), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x231, active(2nd(mark(_x241)))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(from(cons1(s(mark(_x121)), _x112)), cons1(cons(_x121, mark(_x142)), cons1(cons(_x151, _x152), cons1(mark(mark(_x171)), 2nd(cons(_x221, _x222)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(s(mark(_x141)), mark(_x112))))), active(cons1(active(cons(mark(_x121), _x142)), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x171, active(2nd(active(cons(mark(_x221), _x222))))))))))), _x92)), active(s(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), cons(active(2nd(mark(_x161))), _x132))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(mark(_x131)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x92), _x32)))active#(2nd(active(cons1(active(cons(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))), _x92)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x111, cons(_x151, _x152))), cons1(cons(_x121, _x122), cons1(cons(_x151, _x152), cons1(mark(mark(_x171)), 2nd(cons(_x221, _x222)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), active(cons(mark(_x151), _x152)))))), active(cons1(active(cons(mark(_x121), _x122)), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x171, active(2nd(active(cons(mark(_x221), _x222))))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x112)), cons1(_x131, cons1(cons(_x151, _x152), cons1(mark(_x231), 2nd(2nd(_x211)))))), _x92), s(_x81))))active#(2nd(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x231, active(2nd(active(2nd(mark(_x211)))))))))))), _x92)), active(s(mark(_x81))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(_x201, _x202)))), _x62), cons1(2nd(_x101), _x92))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), active(cons1(active(2nd(mark(_x101))), mark(_x92)))))))mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x112)), cons1(s(_x121), cons1(cons(_x151, active(_x172)), cons1(mark(_x231), 2nd(_x241))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(active(s(mark(_x121))), active(cons1(active(cons(mark(_x151), _x172)), active(cons1(_x231, active(2nd(mark(_x241)))))))))), _x92)), active(s(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, _x132)), _x62), s(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), mark(_x132))))), _x62)), active(s(mark(_x71)))))))mark#(2nd(cons1(cons(cons1(from(cons1(s(_x141), _x112)), cons1(cons(_x121, _x122), cons1(cons(_x151, active(_x172)), cons1(mark(mark(mark(_x151))), 2nd(cons(_x221, _x222)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(active(s(mark(_x141))), mark(_x112))))), active(cons1(active(cons(mark(_x121), _x122)), active(cons1(active(cons(mark(_x151), _x172)), active(cons1(_x171, active(2nd(active(cons(mark(_x221), _x222))))))))))), _x92)), active(s(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(from(_x201), _x172))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(active(from(mark(_x201))), _x172)))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(s(mark(_x121)), _x112)), cons1(cons(_x121, mark(_x142)), cons1(cons(_x151, _x152), cons1(mark(mark(_x171)), 2nd(cons(_x221, _x222)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(cons1(active(s(mark(_x141))), mark(_x112)))), active(cons1(active(cons(mark(_x121), _x142)), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x171, active(2nd(cons(mark(_x221), _x222)))))))))), _x92)), active(s(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x112)), cons1(cons(_x121, _x122), cons1(cons(s(_x181), _x152), cons1(mark(_x231), 2nd(_x241))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(active(cons(mark(_x121), _x122)), active(cons1(active(cons(active(s(mark(_x181))), _x152)), active(cons1(_x231, active(2nd(mark(_x241)))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(mark(_x171), 2nd(_x241))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x171, 2nd(mark(_x241))))))))), _x92)), active(s(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x112)), cons1(_x131, cons1(s(_x151), cons1(mark(_x231), 2nd(_x241))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(mark(_x131), active(cons1(active(s(mark(_x151))), active(cons1(_x231, active(2nd(mark(_x241)))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x211, _x212))))), _x92), _x32)))active#(2nd(active(cons1(active(cons(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(_x211, _x212))))))))), _x92)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(s(_x151), cons1(_x161, cons1(_x201, _x202)))), _x62), cons1(_x91, _x92))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(s(mark(_x151))), active(cons1(mark(_x161), active(cons1(mark(_x201), mark(_x202))))))))), _x62)), active(cons1(mark(_x91), mark(_x92)))))))mark#(2nd(cons1(cons(cons1(cons1(s(_x151), 2nd(_x161)), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(cons1(s(mark(_x151)), active(2nd(mark(_x161))))), mark(_x92))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x112)), cons1(cons(_x121, _x122), cons1(cons(_x151, _x152), cons1(mark(mark(_x171)), 2nd(cons1(_x221, _x222)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(active(cons(mark(_x121), _x122)), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x171, active(2nd(active(cons1(mark(_x221), mark(_x222)))))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x112)), cons1(_x131, cons1(from(_x151), cons1(mark(_x231), 2nd(_x241))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(mark(_x131), active(cons1(active(from(mark(_x151))), active(cons1(_x231, active(2nd(mark(_x241)))))))))), _x92)), active(s(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), mark(_x92)), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x92)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x112)), cons1(cons(s(_x151), _x122), cons1(cons(_x151, _x152), cons1(mark(_x231), 2nd(_x241))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(active(cons(active(s(mark(_x151))), _x122)), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x231, active(2nd(mark(_x241)))))))))), _x92)), active(s(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(cons1(s(_x151), _x122), _x92), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(cons1(s(mark(_x151)), mark(_x122)), mark(_x92))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(cons(_x171, _x172), cons1(mark(_x231), cons(_x241, _x242))))), _x92), _x32)))active#(2nd(active(cons1(active(cons(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x171), _x172)), active(cons1(_x231, active(cons(mark(_x241), _x242))))))))), _x92)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(_x91, cons(from(_x161), _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(active(from(mark(_x161))), _x132)))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(cons1(_x111, active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x231, active(2nd(mark(_x241))))))))), cons1(_x111, cons1(cons(_x151, _x152), cons1(mark(_x231), 2nd(_x241))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(_x111, active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x231, active(2nd(mark(_x241)))))))))), _x92)), active(s(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(from(cons1(s(mark(_x121)), _x112)), cons1(cons(_x121, mark(_x142)), cons1(cons(_x151, _x152), cons1(mark(mark(_x171)), 2nd(cons(_x241, _x242)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(cons1(active(s(mark(_x141))), mark(_x112)))), active(cons1(active(cons(mark(_x121), _x142)), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x171, active(2nd(active(cons(_x241, _x242))))))))))), _x92)), s(mark(_x81))))))mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162)))))), _x82)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x132)), cons1(mark(_x111), cons1(cons(_x171, _x172), cons1(mark(_x231), 2nd(2nd(_x211)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), _x132)))), active(cons1(mark(_x131), active(cons1(active(cons(_x171, _x172)), active(cons1(_x231, active(2nd(active(2nd(mark(_x211)))))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), active(_x52)), s(_x61))))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x52)), active(s(mark(_x61))))))
mark#(2nd(cons1(cons(cons1(from(cons1(s(mark(_x121)), _x112)), cons1(cons(_x121, mark(_x142)), cons1(cons(_x151, _x152), cons1(mark(mark(mark(_x181))), 2nd(cons(_x221, _x222)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(active(s(mark(_x141))), mark(_x112))))), active(cons1(active(cons(mark(_x121), _x142)), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x181, active(2nd(active(cons(mark(_x221), _x222))))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(s(_x161), cons1(_x161, cons1(_x221, _x202)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(active(s(mark(_x161))), active(cons1(mark(_x161), active(cons1(_x221, mark(_x202))))))))), _x62)), mark(_x32)))))
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mark#(2nd(cons1(cons(cons1(from(cons1(s(active(cons(mark(_x151), _x152))), _x112)), cons1(cons(_x121, _x122), cons1(cons(_x151, _x152), cons1(mark(mark(_x171)), 2nd(cons(_x221, _x222)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(active(s(mark(_x141))), mark(_x112))))), active(cons1(active(cons(mark(_x121), _x122)), active(cons1(active(cons(mark(_x151), _x152)), cons1(_x171, active(2nd(active(cons(mark(_x221), _x222)))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(mark(_x231), 2nd(_x241))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(2nd(mark(_x241)))))))))), _x92)), s(mark(_x81))))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x111, s(_x151))), cons1(_x131, cons1(_x141, cons1(mark(_x231), 2nd(_x241))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), active(s(mark(_x151))))))), active(cons1(mark(_x131), active(cons1(_x141, active(cons1(_x231, active(2nd(mark(_x241)))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x112)), cons1(_x131, cons1(cons(_x151, _x152), cons1(mark(_x231), 2nd(2nd(_x211)))))), _x92), s(s(_x101)))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x231, active(2nd(active(2nd(mark(_x211)))))))))))), _x92)), active(s(active(s(mark(_x101)))))))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x112)), cons1(_x131, cons1(cons(_x151, active(_x172)), cons1(mark(_x231), 2nd(s(_x211)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x151), _x172)), active(cons1(_x231, active(2nd(active(s(mark(_x211)))))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32)))active#(2nd(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(_x171, _x172))), _x62), 2nd(cons1(_x91, _x92)))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(mark(_x171), _x172)))))), _x62)), active(2nd(active(cons1(mark(_x91), mark(_x92)))))))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), cons1(_x71, _x72))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(cons1(mark(_x71), mark(_x72)))))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x112)), cons1(cons(_x121, _x122), cons1(cons(_x151, _x152), cons1(mark(mark(_x181)), 2nd(_x241))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(active(cons(mark(_x121), _x122)), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x181, 2nd(mark(_x241))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x112)), cons1(s(_x121), cons1(cons(_x171, _x172), cons1(mark(_x231), 2nd(2nd(_x211)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(active(s(mark(_x121))), active(cons1(active(cons(_x171, _x172)), active(cons1(_x231, active(2nd(active(2nd(mark(_x211)))))))))))), _x92)), active(s(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x82), s(_x91))))active#(2nd(active(cons1(active(cons(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242))))))))), _x82)), active(s(mark(_x91)))))))mark#(2nd(cons1(cons(cons1(from(cons1(_x131, _x112)), cons1(_x131, cons1(cons(_x151, _x152), cons1(mark(_x231), 2nd(2nd(_x211)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(_x131, mark(_x112))))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x231, active(2nd(active(2nd(mark(_x211)))))))))))), _x92)), active(s(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x112)), cons1(_x131, cons1(cons(_x151, _x152), cons1(mark(_x231), 2nd(_x241))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x151), _x152)), cons1(_x231, active(2nd(mark(_x241))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(from(cons1(s(mark(_x121)), _x112)), cons1(cons(_x121, mark(_x142)), cons1(cons(cons(_x181, _x182), _x152), cons1(mark(mark(_x171)), 2nd(cons(_x241, _x242)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(cons1(active(s(mark(_x141))), mark(_x112)))), active(cons1(active(cons(mark(_x121), _x142)), active(cons1(active(cons(active(cons(mark(_x181), _x182)), _x152)), active(cons1(_x171, active(2nd(active(cons(_x241, _x242))))))))))), _x92)), active(s(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(from(cons1(s(mark(_x121)), _x112)), cons1(cons(_x121, mark(_x142)), cons1(cons(_x151, _x152), cons1(mark(mark(_x171)), 2nd(cons(_x221, _x222)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(active(s(active(cons1(mark(_x171), mark(_x172))))), mark(_x112))))), active(cons1(active(cons(mark(_x121), _x142)), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x171, active(2nd(active(cons(mark(_x221), _x222))))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x112)), cons1(cons(cons(_x151, _x152), _x122), cons1(cons(_x151, _x152), cons1(mark(mark(_x171)), 2nd(_x241))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(active(cons(active(cons(mark(_x151), _x152)), _x122)), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x171, active(2nd(mark(_x241)))))))))), _x92)), active(s(mark(_x81)))))))
mark#(2nd(cons1(cons(cons1(from(cons(_x141, _x142)), cons1(2nd(_x151), cons1(_x161, 2nd(_x191)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(mark(_x141), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), active(2nd(mark(_x191))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x121), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(cons1(_x261, _x262), _x242))))), _x62), s(_x91))))active#(2nd(active(cons1(active(cons(active(cons1(active(from(mark(_x121))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(active(cons1(mark(_x261), mark(_x262))), _x242)))))))))), _x62)), active(s(mark(_x91)))))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x131)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x92), _x32)))active#(2nd(active(cons1(active(cons(cons1(active(from(active(2nd(mark(_x131))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242))))))))), _x92)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(2nd(_x191), _x172))), _x62), 2nd(_x71))))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(active(2nd(mark(_x191))), _x172)))))), _x62)), active(2nd(mark(_x71)))))))
mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons1(mark(_x131), mark(_x132)))), _x82)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, _x92), _x62), _x32)))active#(2nd(active(cons1(cons(active(cons1(mark(_x91), mark(_x92))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(_x111, cons1(_x151, _x152))), cons1(_x131, cons1(cons(_x151, _x152), cons1(mark(_x231), 2nd(_x241))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), active(cons1(mark(_x151), mark(_x152))))))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x231, active(2nd(mark(_x241)))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(_x91, cons1(_x131, cons(2nd(_x201), mark(_x192)))), _x62), _x72)))active#(2nd(active(cons1(active(cons(active(cons1(mark(_x91), active(cons1(mark(_x131), active(cons(active(2nd(mark(_x201))), _x192)))))), _x62)), _x72))))
mark#(2nd(cons1(cons(cons1(from(cons(s(_x161), _x142)), cons1(2nd(_x151), cons1(_x161, _x162))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons(active(s(mark(_x161))), _x142)))), active(cons1(active(2nd(mark(_x151))), active(cons1(mark(_x161), mark(_x162))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(_x91, cons(_x131, _x132)), _x62), s(2nd(_x81)))))active#(2nd(cons1(active(cons(active(cons1(mark(_x91), active(cons(mark(_x131), _x132)))), _x62)), active(s(active(2nd(mark(_x81))))))))
mark#(2nd(cons1(cons(cons1(from(cons1(cons1(_x161, _x162), _x142)), cons1(_x131, _x132)), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(cons1(active(cons1(mark(_x161), mark(_x162))), mark(_x142))))), active(cons1(mark(_x131), mark(_x132))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(_x141), cons1(_x131, cons1(_x161, cons1(_x221, _x202)))), _x62), _x32)))active#(2nd(active(cons1(active(cons(active(cons1(active(from(_x141)), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x221, mark(_x202))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(cons1(s(_x141), _x112)), cons1(cons(_x121, _x122), cons1(cons(_x151, _x152), cons1(mark(mark(_x171)), 2nd(cons(cons1(_x251, _x252), _x222)))))), _x92), s(_x81))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(active(s(mark(_x141))), mark(_x112))))), active(cons1(active(cons(mark(_x121), _x122)), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x171, active(2nd(active(cons(active(cons1(mark(_x251), mark(_x252))), _x222))))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(from(cons1(_x111, _x112)), cons1(_x131, cons1(_x161, cons1(mark(_x231), 2nd(_x241))))), _x92), s(from(_x101)))))active#(2nd(active(cons1(active(cons(cons1(active(from(active(cons1(mark(_x111), mark(_x112))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(2nd(mark(_x241)))))))))), _x92)), active(s(active(from(mark(_x101)))))))))
mark#(2nd(cons1(cons(cons1(from(cons1(s(mark(_x121)), _x112)), cons1(cons(_x121, mark(_x142)), cons1(cons(_x151, _x152), cons1(mark(mark(_x171)), 2nd(cons(_x221, _x222)))))), _x92), s(active(from(cons1(active(s(mark(_x141))), mark(_x112))))))))active#(2nd(active(cons1(active(cons(cons1(active(from(cons1(active(s(mark(_x141))), mark(_x112)))), cons1(active(cons(mark(_x121), _x142)), active(cons1(active(cons(mark(_x151), _x152)), active(cons1(_x171, active(2nd(active(cons(mark(_x221), _x222)))))))))), _x92)), active(s(mark(_x81)))))))mark#(2nd(cons1(cons(cons1(_x91, cons(2nd(_x161), _x132)), _x82), _x32)))active#(2nd(active(cons1(active(cons(cons1(mark(_x91), active(cons(active(2nd(mark(_x161))), _x132))), _x82)), mark(_x32)))))

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


The right-hand side of the rule mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 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#(2nd(active(cons1(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(active(s(mark(_x161))), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(active(from(mark(_x161))), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(active(2nd(mark(_x161))), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(active(2nd(mark(_x171))))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(active(cons1(mark(_x261), mark(_x262))), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(active(from(mark(_x261))), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(active(2nd(mark(_x191))), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x252)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(_x181, active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(_x151, active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(active(s(mark(_x171))))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x191), _x192)), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(active(cons1(mark(_x191), mark(_x192))), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(active(cons1(mark(_x161), mark(_x162))), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x211, cons(mark(_x241), _x242))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x92)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), active(s(mark(_x91))))))) 
active#(2nd(active(cons1(active(cons(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242))))))))), _x92)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(active(s(mark(_x261))), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(from(active(2nd(mark(_x151)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(_x161)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(active(2nd(mark(_x151))), from(s(active(2nd(mark(_x151))))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(active(cons1(mark(_x171), mark(_x172))))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), active(cons1(mark(_x91), mark(_x92))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), cons1(_x231, active(cons(mark(_x241), _x242))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(active(from(mark(_x171))))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(_x251, _x252)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(active(cons(mark(_x171), _x172)))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(active(from(mark(_x191))), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), active(from(mark(_x91))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), active(cons(mark(_x91), _x92)))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x211, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(active(cons(mark(_x161), _x162)), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(active(cons(mark(_x261), _x262)), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(active(s(mark(_x191))), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(2nd(mark(_x151)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(active(2nd(mark(_x261))), _x242)))))))))), _x62)), mark(_x32))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), active(2nd(mark(_x91))))))) 
active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), _x72)))) 
Thus, the rule mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))) is replaced by the following rules:
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(from(_x161), cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(active(from(mark(_x161))), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(from(_x261), _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(active(from(mark(_x261))), _x242)))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x92), _x32))) → active#(2nd(active(cons1(active(cons(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242))))))))), _x92)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(cons1(_x191, _x192), cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(active(cons1(mark(_x191), mark(_x192))), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), mark(_x92)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x92)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(cons(_x261, _x262), _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(active(cons(mark(_x261), _x262)), _x242)))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(mark(_x211)), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x211, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(cons1(_x261, _x262), _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(active(cons1(mark(_x261), mark(_x262))), _x242)))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), 2nd(_x91)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), active(2nd(mark(_x91)))))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(mark(cons(active(2nd(mark(_x151))), from(s(active(2nd(mark(_x151))))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x161)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(_x161)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(s(_x171))), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(active(s(mark(_x171))))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x72))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), _x72))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(s(_x261), _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(active(s(mark(_x261))), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), cons1(_x231, active(cons(mark(_x241), _x242))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(s(_x161), cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(active(s(mark(_x161))), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x181, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(_x181, active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(from(active(2nd(mark(_x151)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(active(_x211)), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x211, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(2nd(_x161), cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(active(2nd(mark(_x161))), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x151, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(_x151, active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(cons(_x171, _x172))), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(active(cons(mark(_x171), _x172)))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(from(_x191), cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(active(from(mark(_x191))), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), from(_x91)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), active(from(mark(_x91)))))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x251, _x252))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(_x251, _x252)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(s(_x191), cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(active(s(mark(_x191))), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(cons(_x191, _x192), cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(active(cons(mark(_x191), _x192)), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), s(_x91)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), active(s(mark(_x91)))))))
mark#(2nd(cons1(cons(cons1(from(2nd(from(_x171))), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(active(from(mark(_x171))))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(2nd(_x171))), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(active(2nd(mark(_x171))))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), cons(_x91, _x92)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), active(cons(mark(_x91), _x92))))))
mark#(2nd(cons1(cons(cons1(from(2nd(mark(_x131))), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(2nd(mark(_x151)), cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(2nd(mark(_x151)))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(2nd(_x191), cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(active(2nd(mark(_x191))), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x211), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x211, cons(mark(_x241), _x242))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, mark(_x252)))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x252)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), active(_x92)), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x92)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(cons(_x161, _x162), cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(active(cons(mark(_x161), _x162)), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(cons1(_x161, _x162), cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(active(cons1(mark(_x161), mark(_x162))), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(2nd(_x261), _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(active(2nd(mark(_x261))), _x242)))))))))), _x62)), mark(_x32)))))mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, active(_x252)))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x252)))))))))), _x62)), mark(_x32)))))
mark#(2nd(cons1(cons(cons1(from(2nd(_x151)), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), cons1(_x91, _x92)))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(mark(_x151))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), active(cons1(mark(_x91), mark(_x92)))))))mark#(2nd(cons1(cons(cons1(from(2nd(cons1(_x171, _x172))), cons1(_x131, cons1(_x161, cons1(mark(_x231), cons(_x241, _x242))))), _x62), _x32))) → active#(2nd(active(cons1(active(cons(active(cons1(active(from(active(2nd(active(cons1(mark(_x171), mark(_x172))))))), active(cons1(mark(_x131), active(cons1(mark(_x161), active(cons1(_x231, active(cons(mark(_x241), _x242)))))))))), _x62)), mark(_x32)))))

Problem 4: SubtermCriterion



Dependency Pair Problem

Dependency Pairs

2nd#(active(X))2nd#(X)2nd#(mark(X))2nd#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


Projection

The following projection was used:

Thus, the following dependency pairs are removed:

2nd#(active(X))2nd#(X)2nd#(mark(X))2nd#(X)

Problem 5: SubtermCriterion



Dependency Pair Problem

Dependency Pairs

from#(active(X))from#(X)from#(mark(X))from#(X)

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


Projection

The following projection was used:

Thus, the following dependency pairs are removed:

from#(active(X))from#(X)from#(mark(X))from#(X)

Problem 6: 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(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, 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 9: ReductionPairSAT



Dependency Pair Problem

Dependency Pairs

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

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


Function Precedence

cons# < active = mark < 2nd = cons1 = s = from = cons

Argument Filtering

2nd: 1
cons#: 2
cons1: 1 2
s: 1
active: collapses to 1
mark: 1
from: all arguments are removed from from
cons: all arguments are removed from cons

Status

2nd: lexicographic with permutation 1 → 1
cons#: lexicographic with permutation 2 → 1
cons1: lexicographic with permutation 1 → 2 2 → 1
s: lexicographic with permutation 1 → 1
mark: multiset
from: multiset
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 12: ReductionPairSAT



Dependency Pair Problem

Dependency Pairs

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

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, cons

Strategy


Function Precedence

2nd = cons# = cons1 = s = active = mark = from = cons

Argument Filtering

2nd: all arguments are removed from 2nd
cons#: 2
cons1: 1 2
s: all arguments are removed from s
active: 1
mark: collapses to 1
from: all arguments are removed from from
cons: 1 2

Status

2nd: multiset
cons#: multiset
cons1: lexicographic with permutation 1 → 2 2 → 1
s: multiset
active: multiset
from: multiset
cons: lexicographic with permutation 1 → 2 2 → 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.

cons#(X1, active(X2)) → cons#(X1, X2)

Problem 7: SubtermCriterion



Dependency Pair Problem

Dependency Pairs

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

Rewrite Rules

active(2nd(cons1(X, cons(Y, Z))))mark(Y)active(2nd(cons(X, X1)))mark(2nd(cons1(X, X1)))
active(from(X))mark(cons(X, from(s(X))))mark(2nd(X))active(2nd(mark(X)))
mark(cons1(X1, X2))active(cons1(mark(X1), mark(X2)))mark(cons(X1, X2))active(cons(mark(X1), X2))
mark(from(X))active(from(mark(X)))mark(s(X))active(s(mark(X)))
2nd(mark(X))2nd(X)2nd(active(X))2nd(X)
cons1(mark(X1), X2)cons1(X1, X2)cons1(X1, mark(X2))cons1(X1, X2)
cons1(active(X1), X2)cons1(X1, X2)cons1(X1, active(X2))cons1(X1, X2)
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)
from(mark(X))from(X)from(active(X))from(X)
s(mark(X))s(X)s(active(X))s(X)

Original Signature

Termination of terms over the following signature is verified: 2nd, cons1, s, active, mark, from, 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)