TIMEOUT

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

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (124ms).
 | – Problem 2 was processed with processor PolynomialLinearRange4iUR (239ms).
 |    | – Problem 4 was processed with processor DependencyGraph (3ms).
 | – Problem 3 was processed with processor ForwardNarrowing (4ms).
 |    | – Problem 5 was processed with processor ForwardNarrowing (3ms).
 |    |    | – Problem 6 was processed with processor ForwardNarrowing (9ms).
 |    |    |    | – Problem 7 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    | – Problem 8 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    | – Problem 9 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (11ms).
 |    |    |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (38ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (11ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (14ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (16ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (18ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (48ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (13ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (13ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (56ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (13ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (17ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (36ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (117ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (380ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 remains open; application of the following processors failed [ForwardNarrowing (392ms), ForwardNarrowing (334ms), ForwardNarrowing (489ms), ForwardNarrowing (396ms), ForwardNarrowing (338ms), ForwardNarrowing (402ms), ForwardNarrowing (327ms), ForwardNarrowing (407ms), ForwardNarrowing (402ms), ForwardNarrowing (61ms), ForwardNarrowing (228ms), ForwardNarrowing (139ms), ForwardNarrowing (311ms), ForwardNarrowing (441ms), ForwardNarrowing (timeout)].

The following open problems remain:

Open Dependency Pair Problem 3

Dependency Pairs

eq#(n__s(X), n__s(Y)) → eq#(activate(X), activate(Y))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, eq, cons, nil

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

take#(s(X), cons(Y, L)) → activate#(X)inf#(X) → s#(X)
length#(cons(X, L)) → activate#(L)take#(s(X), cons(Y, L)) → activate#(Y)
eq#(n__s(X), n__s(Y)) → activate#(Y)length#(cons(X, L)) → s#(n__length(activate(L)))
take#(s(X), cons(Y, L)) → activate#(L)activate#(n__s(X)) → s#(X)
activate#(n__length(X)) → length#(X)activate#(n__inf(X)) → inf#(X)
eq#(n__s(X), n__s(Y)) → eq#(activate(X), activate(Y))eq#(n__s(X), n__s(Y)) → activate#(X)
activate#(n__0) → 0#activate#(n__take(X1, X2)) → take#(X1, X2)
length#(nil) → 0#

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, nil, cons, eq

Strategy

The following SCCs where found

eq#(n__s(X), n__s(Y)) → eq#(activate(X), activate(Y))
activate#(n__length(X)) → length#(X)take#(s(X), cons(Y, L)) → activate#(X)
length#(cons(X, L)) → activate#(L)take#(s(X), cons(Y, L)) → activate#(Y)
activate#(n__take(X1, X2)) → take#(X1, X2)take#(s(X), cons(Y, L)) → activate#(L)

Problem 2: PolynomialLinearRange4iUR

Dependency Pair Problem

Dependency Pairs

activate#(n__length(X)) → length#(X)take#(s(X), cons(Y, L)) → activate#(X)
length#(cons(X, L)) → activate#(L)take#(s(X), cons(Y, L)) → activate#(Y)
activate#(n__take(X1, X2)) → take#(X1, X2)take#(s(X), cons(Y, L)) → activate#(L)

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, nil, cons, eq

Strategy

Polynomial Interpretation

There are no usable rules

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

activate#(n__length(X)) → length#(X)length#(cons(X, L)) → activate#(L)
activate#(n__take(X1, X2)) → take#(X1, X2)

Problem 4: DependencyGraph

Dependency Pair Problem

Dependency Pairs

take#(s(X), cons(Y, L)) → activate#(X)take#(s(X), cons(Y, L)) → activate#(Y)
take#(s(X), cons(Y, L)) → activate#(L)

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, eq, cons, nil

Strategy

There are no SCCs!

Problem 3: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(X), n__s(Y)) → eq#(activate(X), activate(Y))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, nil, cons, eq

Strategy

The right-hand side of the rule eq#(n__s(X), n__s(Y)) → eq#(activate(X), activate(Y)) 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
eq#(activate(X), inf(_x31)) 
eq#(length(_x21), activate(Y)) 
eq#(activate(X), s(_x31)) 
eq#(inf(_x21), activate(Y)) 
eq#(take(_x21, _x22), activate(Y)) 
eq#(activate(X), _x31) 
eq#(activate(X), length(_x31)) 
eq#(_x21, activate(Y)) 
eq#(s(_x21), activate(Y)) 
eq#(0, activate(Y)) 
eq#(activate(X), 0) 
eq#(activate(X), take(_x31, _x32)) 
Thus, the rule eq#(n__s(X), n__s(Y)) → eq#(activate(X), activate(Y)) is replaced by the following rules:
eq#(n__s(X), n__s(n__length(_x31))) → eq#(activate(X), length(_x31))eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))
eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))
eq#(n__s(X), n__s(n__take(_x31, _x32))) → eq#(activate(X), take(_x31, _x32))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))
eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))

Problem 5: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(X), n__s(n__length(_x31))) → eq#(activate(X), length(_x31))eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))
eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))
eq#(n__s(X), n__s(n__take(_x31, _x32))) → eq#(activate(X), take(_x31, _x32))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))
eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, eq, cons, nil

Strategy

The right-hand side of the rule eq#(n__s(X), n__s(n__length(_x31))) → eq#(activate(X), length(_x31)) 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
eq#(0, length(_x31)) 
eq#(s(_x21), length(_x31)) 
eq#(_x21, length(_x31)) 
eq#(activate(X), n__length(_x41)) 
eq#(activate(X), s(n__length(activate(_x41)))) 
eq#(length(_x21), length(_x31)) 
eq#(take(_x21, _x22), length(_x31)) 
eq#(inf(_x21), length(_x31)) 
eq#(activate(X), 0) 
Thus, the rule eq#(n__s(X), n__s(n__length(_x31))) → eq#(activate(X), length(_x31)) is replaced by the following rules:
eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), s(n__length(activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))
eq#(n__s(n__inf(_x21)), n__s(n__length(_x31))) → eq#(inf(_x21), length(_x31))eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))
eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))
eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))

Problem 6: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), s(n__length(activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__length(_x31))) → eq#(inf(_x21), length(_x31))
eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))eq#(n__s(X), n__s(n__take(_x31, _x32))) → eq#(activate(X), take(_x31, _x32))
eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))
eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))
eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))
eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))
eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)
eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, nil, cons, eq

Strategy

The right-hand side of the rule eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), s(n__length(activate(_x41)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(activate(X), s(n__length(0))) 
eq#(activate(X), s(n__length(_x61))) 
eq#(inf(_x21), s(n__length(activate(_x41)))) 
eq#(s(_x21), s(n__length(activate(_x41)))) 
eq#(activate(X), s(n__length(take(_x61, _x62)))) 
eq#(length(_x21), s(n__length(activate(_x41)))) 
eq#(0, s(n__length(activate(_x41)))) 
eq#(_x21, s(n__length(activate(_x41)))) 
eq#(activate(X), s(n__length(length(_x61)))) 
eq#(take(_x21, _x22), s(n__length(activate(_x41)))) 
eq#(activate(X), s(n__length(s(_x61)))) 
eq#(activate(X), n__s(n__length(activate(_x41)))) 
eq#(activate(X), s(n__length(inf(_x61)))) 
Thus, the rule eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), s(n__length(activate(_x41)))) is replaced by the following rules:
eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), s(n__length(activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))
eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))

Problem 7: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__inf(_x21)), n__s(n__length(_x31))) → eq#(inf(_x21), length(_x31))eq#(n__s(X), n__s(n__take(_x31, _x32))) → eq#(activate(X), take(_x31, _x32))
eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), s(n__length(activate(_x41))))eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))
eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))
eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)
eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))
eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))
eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))
eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))
eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)
eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))
eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, eq, cons, nil

Strategy

The right-hand side of the rule eq#(n__s(n__inf(_x21)), n__s(n__length(_x31))) → eq#(inf(_x21), length(_x31)) 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
eq#(inf(_x21), n__length(_x41)) 
eq#(cons(_x31, n__inf(s(_x31))), length(_x31)) 
eq#(n__inf(_x31), length(_x31)) 
eq#(inf(_x21), 0) 
eq#(inf(_x21), s(n__length(activate(_x41)))) 
Thus, the rule eq#(n__s(n__inf(_x21)), n__s(n__length(_x31))) → eq#(inf(_x21), length(_x31)) is replaced by the following rules:
eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))

Problem 8: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))eq#(n__s(X), n__s(n__take(_x31, _x32))) → eq#(activate(X), take(_x31, _x32))
eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), s(n__length(activate(_x41))))eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))
eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)
eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))
eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))
eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))
eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))
eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))
eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)
eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))
eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))
eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, nil, cons, eq

Strategy

The right-hand side of the rule eq#(n__s(X), n__s(n__take(_x31, _x32))) → eq#(activate(X), take(_x31, _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
eq#(_x21, take(_x31, _x32)) 
eq#(activate(X), nil) 
eq#(length(_x21), take(_x31, _x32)) 
eq#(0, take(_x31, _x32)) 
eq#(s(_x21), take(_x31, _x32)) 
eq#(activate(X), n__take(_x41, _x42)) 
eq#(take(_x21, _x22), take(_x31, _x32)) 
eq#(inf(_x21), take(_x31, _x32)) 
eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), activate(_x41)))) 
Thus, the rule eq#(n__s(X), n__s(n__take(_x31, _x32))) → eq#(activate(X), take(_x31, _x32)) is replaced by the following rules:
eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))
eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))
eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))

Problem 9: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), s(n__length(activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))
eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))
eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))
eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))
eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))
eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))
eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))
eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))
eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)
eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))
eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))
eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, eq, cons, nil

Strategy

The right-hand side of the rule eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), activate(_x41)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41)))) 
eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41)))) 
eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41)))) 
eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0))) 
eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41)))) 
eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41)))) 
eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71)))) 
eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41)))) 
eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41)))) 
eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41)))) 
eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41)))) 
eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41)))) 
eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41)))) 
eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41)))) 
eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41)))) 
eq#(activate(X), cons(_x51, n__take(activate(_x43), activate(_x41)))) 
eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72)))) 
eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41)))) 
eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71)))) 
eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41)))) 
eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71))) 
eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41)))) 
eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71)))) 
Thus, the rule eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), activate(_x41)))) is replaced by the following rules:
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))

Problem 10: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), s(n__length(activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)
eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))
eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))
eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))
eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))
eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)
eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))
eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))
eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))
eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, nil, cons, eq

Strategy

The right-hand side of the rule eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), activate(_x41)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41)))) 
eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41)))) 
eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41)))) 
eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41)))) 
eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71)))) 
eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71)))) 
eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71))) 
eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41)))) 
eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41)))) 
eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41)))) 
eq#(_x21, cons(_x51, n__take(activate(_x43), activate(_x41)))) 
eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41)))) 
eq#(activate(X), cons(_x51, n__take(activate(_x43), 0))) 
eq#(activate(X), cons(_x51, n__take(0, activate(_x41)))) 
eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41)))) 
eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41)))) 
eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71)))) 
eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72)))) 
Thus, the rule eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), activate(_x41)))) is replaced by the following rules:
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))

Problem 11: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), s(n__length(activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))
eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))
eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))
eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))
eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))
eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))
eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))
eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))
eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))
eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))
eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, eq, cons, nil

Strategy

The right-hand side of the rule eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), activate(_x41)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(_x21, cons(_x51, n__take(length(_x61), activate(_x41)))) 
eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72)))) 
eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41)))) 
eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41)))) 
eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41)))) 
eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71)))) 
eq#(_x21, cons(_x51, n__take(_x61, activate(_x41)))) 
eq#(_x21, cons(_x51, n__take(activate(_x43), _x71))) 
eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71)))) 
eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71)))) 
eq#(_x21, cons(_x51, n__take(0, activate(_x41)))) 
eq#(_x21, cons(_x51, n__take(activate(_x43), 0))) 
Thus, the rule eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), activate(_x41)))) is replaced by the following rules:
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(length(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))

Problem 12: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(length(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), s(n__length(activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))
eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))
eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))
eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))
eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))
eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))
eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))
eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))
eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, nil, cons, eq

Strategy

The right-hand side of the rule eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(length(_x61), activate(_x41)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41)))) 
eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71)))) 
eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71)))) 
eq#(_x21, cons(_x51, n__take(length(_x61), _x71))) 
eq#(_x21, cons(_x51, n__take(length(_x61), 0))) 
eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41)))) 
eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72)))) 
eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71)))) 
eq#(_x21, cons(_x51, n__take(0, activate(_x41)))) 
Thus, the rule eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(length(_x61), activate(_x41)))) is replaced by the following rules:
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(length(_x61), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(length(_x61), 0)))

Problem 13: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(length(_x61), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), s(n__length(activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(length(_x61), 0)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))
eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))
eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))
eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))
eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))
eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, eq, cons, nil

Strategy

The right-hand side of the rule eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(length(_x61), _x71))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(_x21, cons(_x51, n__take(0, _x71))) 
eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), _x71))) 
eq#(_x21, cons(_x51, n__take(n__length(_x71), _x71))) 
Thus, the rule eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(length(_x61), _x71))) is replaced by the following rules:
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(0, _x71)))

Problem 14: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), s(n__length(activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)
eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(length(_x61), 0)))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(0, _x71)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)
eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), _x71)))eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))
eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))
eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))
eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))
eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), _x71)))eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, nil, cons, eq

Strategy

The right-hand side of the rule eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), s(n__length(activate(_x41)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(nil, s(n__length(activate(_x41)))) 
eq#(take(_x21, _x22), n__s(n__length(activate(_x41)))) 
eq#(take(_x21, _x22), s(n__length(inf(_x61)))) 
eq#(take(_x21, _x22), s(n__length(take(_x61, _x62)))) 
eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), s(n__length(activate(_x41)))) 
eq#(take(_x21, _x22), s(n__length(0))) 
eq#(take(_x21, _x22), s(n__length(s(_x61)))) 
eq#(take(_x21, _x22), s(n__length(_x61))) 
eq#(take(_x21, _x22), s(n__length(length(_x61)))) 
eq#(n__take(_x31, _x32), s(n__length(activate(_x41)))) 
Thus, the rule eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), s(n__length(activate(_x41)))) is replaced by the following rules:
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(take(_x21, _x22), s(n__length(length(_x61))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(take(_x21, _x22), s(n__length(take(_x61, _x62))))eq#(n__s(n__take(_x31, _x32)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__take(_x31, _x32), s(n__length(activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__0)))) → eq#(take(_x21, _x22), s(n__length(0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(take(_x21, _x22), s(n__length(inf(_x61))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), n__s(n__length(activate(_x41))))eq#(n__s(n__take(0, _x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(nil, s(n__length(activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x61)))) → eq#(take(_x21, _x22), s(n__length(_x61)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(take(_x21, _x22), s(n__length(s(_x61))))

Problem 15: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(length(_x61), 0)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(0, _x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(nil, s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(0, _x71)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))
eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x61)))) → eq#(take(_x21, _x22), s(n__length(_x61)))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), s(n__length(activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(take(_x21, _x22), s(n__length(length(_x61))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(take(_x21, _x22), s(n__length(take(_x61, _x62))))
eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), _x71)))eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__0)))) → eq#(take(_x21, _x22), s(n__length(0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), n__s(n__length(activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))
eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(take(_x21, _x22), s(n__length(s(_x61))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))
eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), _x71)))
eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))
eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))
eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__take(_x31, _x32)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__take(_x31, _x32), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(take(_x21, _x22), s(n__length(inf(_x61))))eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, eq, cons, nil

Strategy

The right-hand side of the rule eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41)))) 
eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41)))) 
eq#(s(_x21), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), length(_x71)))) 
eq#(s(_x21), cons(activate(_x42), n__take(0, activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71)))) 
eq#(s(_x21), cons(activate(_x42), n__take(length(_x61), activate(_x41)))) 
eq#(n__s(_x31), cons(activate(_x42), n__take(activate(_x43), activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), _x71))) 
eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72)))) 
eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), s(_x71)))) 
eq#(s(_x21), cons(activate(_x42), n__take(s(_x61), activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), 0))) 
eq#(s(_x21), cons(activate(_x42), n__take(_x61, activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(inf(_x61), activate(_x41)))) 
eq#(s(_x21), cons(0, n__take(activate(_x43), activate(_x41)))) 
eq#(s(_x21), cons(inf(_x51), n__take(activate(_x43), activate(_x41)))) 
eq#(s(_x21), cons(length(_x51), n__take(activate(_x43), activate(_x41)))) 
Thus, the rule eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41)))) is replaced by the following rules:
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))

Problem 16: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(length(_x61), 0)))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(0, _x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(nil, s(n__length(activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(0, _x71)))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)
eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x61)))) → eq#(take(_x21, _x22), s(n__length(_x61)))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(take(_x21, _x22), s(n__length(length(_x61))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(take(_x21, _x22), s(n__length(take(_x61, _x62))))eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), _x71)))
eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__0)))) → eq#(take(_x21, _x22), s(n__length(0)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), n__s(n__length(activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), _x71)))eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))
eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(take(_x21, _x22), s(n__length(s(_x61))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))
eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))
eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), _x71)))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))
eq#(n__s(n__take(_x31, _x32)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__take(_x31, _x32), s(n__length(activate(_x41))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(take(_x21, _x22), s(n__length(inf(_x61))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, nil, cons, eq

Strategy

The right-hand side of the rule eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), _x71))) 
eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), length(_x71)))) 
eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(nil, activate(_x41)))) 
eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), activate(_x41)))) 
eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41)))) 
eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41)))) 
eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), s(_x71)))) 
eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71)))) 
eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), 0))) 
eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), take(_x71, _x72)))) 
Thus, the rule eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41)))) is replaced by the following rules:
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), activate(_x41))))

Problem 17: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(length(_x61), 0)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(0, _x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(nil, s(n__length(activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(0, _x71)))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), _x71)))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))
eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x61)))) → eq#(take(_x21, _x22), s(n__length(_x61)))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), s(n__length(activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(take(_x21, _x22), s(n__length(length(_x61))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(take(_x21, _x22), s(n__length(take(_x61, _x62))))
eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), _x71)))
eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__0)))) → eq#(take(_x21, _x22), s(n__length(0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), n__s(n__length(activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(_x61, activate(_x41))))eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(take(_x21, _x22), s(n__length(s(_x61))))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), _x71)))
eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__take(_x31, _x32), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(take(_x21, _x22), s(n__length(inf(_x61))))
eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), 0)))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, eq, cons, nil

Strategy

The right-hand side of the rule eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), activate(_x41)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), s(_x71)))) 
eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72)))) 
eq#(s(_x21), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41)))) 
eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), _x71))) 
eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), 0))) 
eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), length(_x71)))) 
eq#(s(_x21), cons(_x51, n__take(nil, activate(_x41)))) 
eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), activate(_x41)))) 
eq#(s(_x21), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41)))) 
eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), inf(_x71)))) 
Thus, the rule eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), activate(_x41)))) is replaced by the following rules:
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(nil, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))

Problem 18: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(length(_x61), 0)))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(0, _x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(nil, s(n__length(activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), 0)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), take(_x71, _x72))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(0, _x71)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))
eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x61)))) → eq#(take(_x21, _x22), s(n__length(_x61)))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(take(_x21, _x22), s(n__length(length(_x61))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(take(_x21, _x22), s(n__length(take(_x61, _x62))))eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), _x71)))eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__0)))) → eq#(take(_x21, _x22), s(n__length(0)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), n__s(n__length(activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), 0)))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))
eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(take(_x21, _x22), s(n__length(s(_x61))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))
eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))
eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(nil, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), length(_x71))))eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), _x71)))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))eq#(n__s(n__take(_x31, _x32)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__take(_x31, _x32), s(n__length(activate(_x41))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(take(_x21, _x22), s(n__length(inf(_x61))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), 0)))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, nil, cons, eq

Strategy

The right-hand side of the rule eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), 0))) 
eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41)))) 
eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), _x71))) 
eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), activate(_x41)))) 
eq#(s(_x21), cons(length(_x51), n__take(nil, activate(_x41)))) 
eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), take(_x71, _x72)))) 
eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), inf(_x71)))) 
eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41)))) 
eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41)))) 
eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), s(_x71)))) 
eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), activate(_x41)))) 
eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), length(_x71)))) 
eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), activate(_x41)))) 
Thus, the rule eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41)))) is replaced by the following rules:
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x41)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), take(_x71, _x72))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__inf(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x71)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), _x41)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__length(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__s(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), _x41)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), activate(_x41))))

Problem 19: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), 0)))eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(length(_x61), 0)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(0, _x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(nil, s(n__length(activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), 0)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), take(_x71, _x72))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(0, _x71)))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), _x71)))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__length(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))
eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), _x41)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__inf(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), take(_x71, _x72))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x61)))) → eq#(take(_x21, _x22), s(n__length(_x61)))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(take(_x21, _x22), s(n__length(length(_x61))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(take(_x21, _x22), s(n__length(take(_x61, _x62))))eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), _x71)))
eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__s(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__0)))) → eq#(take(_x21, _x22), s(n__length(0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x71)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), n__s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), 0)))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), _x71)))eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))
eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(take(_x21, _x22), s(n__length(s(_x61))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x41)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), _x41)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))
eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))
eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(nil, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), _x71)))eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))
eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__take(_x31, _x32)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__take(_x31, _x32), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(take(_x21, _x22), s(n__length(inf(_x61))))eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), 0)))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, eq, cons, nil

Strategy

The right-hand side of the rule eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), 0))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), 0))) 
eq#(s(_x21), cons(0, n__take(take(_x61, _x62), 0))) 
eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), n__0))) 
eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), 0))) 
eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), 0))) 
eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), 0))) 
eq#(s(_x21), cons(length(_x51), n__take(nil, 0))) 
eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), 0))) 
Thus, the rule eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), 0))) is replaced by the following rules:
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), n__0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), n__0)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), n__0)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), 0)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, 0)))

Problem 20: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), n__0)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), 0)))
eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(length(_x61), 0)))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(0, _x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(nil, s(n__length(activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), 0)))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, 0)))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(0, _x71)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__length(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))
eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), _x41)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))
eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__inf(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(s(_x61), activate(_x41))))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x61)))) → eq#(take(_x21, _x22), s(n__length(_x61)))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), s(n__length(activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(take(_x21, _x22), s(n__length(length(_x61))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(take(_x21, _x22), s(n__length(take(_x61, _x62))))
eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), 0)))eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), _x71)))
eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), n__0)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__s(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))
eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__0)))) → eq#(take(_x21, _x22), s(n__length(0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x71)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), n__s(n__length(activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), 0)))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))
eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), n__0)))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(take(_x21, _x22), s(n__length(s(_x61))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x41)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))
eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), _x41)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), 0)))eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))
eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(nil, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), length(_x71))))eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), _x71)))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))
eq#(n__s(n__take(_x31, _x32)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__take(_x31, _x32), s(n__length(activate(_x41))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(take(_x21, _x22), s(n__length(inf(_x61))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), 0)))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, nil, cons, eq

Strategy

The right-hand side of the rule eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y)) 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
eq#(s(_x21), _x31) 
eq#(s(_x21), inf(_x31)) 
eq#(s(_x21), length(_x31)) 
eq#(n__s(_x31), activate(Y)) 
eq#(s(_x21), take(_x31, _x32)) 
eq#(s(_x21), s(_x31)) 
eq#(s(_x21), 0) 
Thus, the rule eq#(n__s(n__s(_x21)), n__s(Y)) → eq#(s(_x21), activate(Y)) is replaced by the following rules:
eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))eq#(n__s(n__s(_x21)), n__s(_x31)) → eq#(s(_x21), _x31)
eq#(n__s(n__s(_x21)), n__s(n__0)) → eq#(s(_x21), 0)eq#(n__s(n__s(_x21)), n__s(n__inf(_x31))) → eq#(s(_x21), inf(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))eq#(n__s(n__s(_x21)), n__s(n__s(_x31))) → eq#(s(_x21), s(_x31))
eq#(n__s(n__s(_x31)), n__s(Y)) → eq#(n__s(_x31), activate(Y))

Problem 21: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), n__0)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), 0)))eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(length(_x61), 0)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(0, _x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(nil, s(n__length(activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), 0)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), take(_x71, _x72))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), 0)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, 0)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(0, _x71)))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__0)) → eq#(s(_x21), 0)eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__length(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)
eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), _x41)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))
eq#(n__s(n__s(_x21)), n__s(_x31)) → eq#(s(_x21), _x31)eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__inf(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), take(_x71, _x72))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x61)))) → eq#(take(_x21, _x22), s(n__length(_x61)))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(take(_x21, _x22), s(n__length(length(_x61))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(take(_x21, _x22), s(n__length(take(_x61, _x62))))eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__s(_x31))) → eq#(s(_x21), s(_x31))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), 0)))eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), _x71)))
eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), n__0)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__s(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__0)))) → eq#(take(_x21, _x22), s(n__length(0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x71)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), n__s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), 0)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(_x61, activate(_x41))))eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), n__0)))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(take(_x21, _x22), s(n__length(s(_x61))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x41)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), _x41)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), 0)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))eq#(n__s(n__s(_x31)), n__s(Y)) → eq#(n__s(_x31), activate(Y))
eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))
eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(nil, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__inf(_x31))) → eq#(s(_x21), inf(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), length(_x71))))eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), _x71)))
eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__take(_x31, _x32), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(take(_x21, _x22), s(n__length(inf(_x61))))
eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), 0)))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, eq, cons, nil

Strategy

The right-hand side of the rule eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), activate(_x41)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), 0))) 
eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), length(_x71)))) 
eq#(n__s(_x31), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41)))) 
eq#(n__s(_x31), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41)))) 
eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), _x71))) 
eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), s(_x71)))) 
eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72)))) 
eq#(n__s(_x31), cons(_x51, n__take(nil, activate(_x41)))) 
eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), inf(_x71)))) 
Thus, the rule eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), activate(_x41)))) is replaced by the following rules:
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), length(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(nil, activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), 0)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))

Problem 22: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0)eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), n__0)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), 0)))eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(length(_x61), 0)))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(0, _x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(nil, s(n__length(activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), 0)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, 0)))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(0, _x71)))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))eq#(n__s(n__s(_x21)), n__s(n__0)) → eq#(s(_x21), 0)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__length(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))
eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), _x41)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(n__s(_x21)), n__s(_x31)) → eq#(s(_x21), _x31)
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))
eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__inf(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(s(_x61), activate(_x41))))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x61)))) → eq#(take(_x21, _x22), s(n__length(_x61)))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(take(_x21, _x22), s(n__length(length(_x61))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(take(_x21, _x22), s(n__length(take(_x61, _x62))))eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__s(_x31))) → eq#(s(_x21), s(_x31))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), 0)))eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), _x71)))
eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), n__0)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__s(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__0)))) → eq#(take(_x21, _x22), s(n__length(0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x71)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), n__s(n__length(activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), 0)))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), _x71)))eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))
eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), n__0)))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(take(_x21, _x22), s(n__length(s(_x61))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x41)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), _x41)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), 0)))
eq#(n__s(n__s(_x31)), n__s(Y)) → eq#(n__s(_x31), activate(Y))eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))
eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(nil, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__inf(_x31))) → eq#(s(_x21), inf(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), _x71)))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))
eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))eq#(n__s(n__take(_x31, _x32)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__take(_x31, _x32), s(n__length(activate(_x41))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(take(_x21, _x22), s(n__length(inf(_x61))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(nil, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), 0)))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, nil, cons, eq

Strategy

The right-hand side of the rule eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(inf(_x21), n__0) 
eq#(cons(_x31, n__inf(s(_x31))), 0) 
eq#(n__inf(_x31), 0) 
Thus, the rule eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), 0) is replaced by the following rules:
eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), n__0)eq#(n__s(n__inf(_x31)), n__s(n__length(nil))) → eq#(cons(_x31, n__inf(s(_x31))), 0)
eq#(n__s(n__inf(_x31)), n__s(n__length(nil))) → eq#(n__inf(_x31), 0)

Problem 23: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), n__0)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), 0)))eq#(n__s(n__inf(_x31)), n__s(n__length(nil))) → eq#(cons(_x31, n__inf(s(_x31))), 0)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), 0)))eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), s(n__length(activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(length(_x61), 0)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(n__length(_x21)), n__s(n__length(_x31))) → eq#(length(_x21), length(_x31))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(0, _x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(nil, s(n__length(activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), 0)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, 0)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(0, _x71)))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__0)) → eq#(s(_x21), 0)eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__length(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)
eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), _x41)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(n__s(_x21)), n__s(_x31)) → eq#(s(_x21), _x31)
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))
eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__inf(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(s(_x61), activate(_x41))))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x61)))) → eq#(take(_x21, _x22), s(n__length(_x61)))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(take(_x21, _x22), s(n__length(length(_x61))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(take(_x21, _x22), s(n__length(take(_x61, _x62))))eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x31)), n__s(n__length(nil))) → eq#(n__inf(_x31), 0)
eq#(n__s(n__s(_x21)), n__s(n__s(_x31))) → eq#(s(_x21), s(_x31))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), 0)))
eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), _x71)))eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), n__0)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__s(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__0)))) → eq#(take(_x21, _x22), s(n__length(0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x71)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), n__s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), 0)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(_x61, activate(_x41))))eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), n__0)))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(take(_x21, _x22), s(n__length(s(_x61))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x41)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), _x41)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), 0)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))eq#(n__s(n__s(_x31)), n__s(Y)) → eq#(n__s(_x31), activate(Y))
eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))
eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), n__0)eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(nil, activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__inf(_x31))) → eq#(s(_x21), inf(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), _x71)))eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))
eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__take(_x31, _x32)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__take(_x31, _x32), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(take(_x21, _x22), s(n__length(inf(_x61))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(nil, activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), 0)))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, eq, cons, nil

Strategy

The right-hand side of the rule eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, activate(_x41)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(s(_x21), cons(length(_x51), n__take(0, activate(_x41)))) 
eq#(s(_x21), cons(take(_x51, _x52), n__take(0, activate(_x41)))) 
eq#(s(_x21), cons(inf(_x51), n__take(0, activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(0, s(_x71)))) 
eq#(s(_x21), cons(0, n__take(0, activate(_x41)))) 
eq#(s(_x21), cons(_x51, n__take(0, activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(n__0, activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(0, length(_x71)))) 
eq#(s(_x21), cons(activate(_x42), n__take(0, 0))) 
eq#(s(_x21), cons(activate(_x42), n__take(0, _x71))) 
eq#(n__s(_x31), cons(activate(_x42), n__take(0, activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(0, inf(_x71)))) 
eq#(s(_x21), cons(s(_x51), n__take(0, activate(_x41)))) 
eq#(s(_x21), cons(activate(_x42), n__take(0, take(_x71, _x72)))) 
Thus, the rule eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, activate(_x41)))) is replaced by the following rules:
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(0, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(0, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(0, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__0, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(0, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(0, activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(0, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, _x71)))

Problem 24: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__length(_x31))) → eq#(s(n__length(activate(_x31))), length(_x31))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(s(n__length(activate(_x71))), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(_x61, inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__length(_x31)), n__s(n__length(_x31))) → eq#(n__length(_x31), length(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), n__length(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x41), _x71)))) → eq#(inf(_x21), cons(n__s(_x41), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))
eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(0, length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), n__s(_x71))))) → eq#(s(_x21), cons(s(_x51), n__take(0, s(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(0, _x71)))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__0)) → eq#(s(_x21), 0)eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))
eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), take(_x71, _x72))))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(inf(_x21), s(n__length(take(_x61, _x62))))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x61)))) → eq#(take(_x21, _x22), s(n__length(_x61)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(_x61, inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x81))))) → eq#(inf(_x21), cons(inf(_x51), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, n__s(_x81))))) → eq#(s(_x21), cons(0, n__take(n__0, n__s(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(nil, _x71)))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), _x71)))) → eq#(length(_x21), cons(s(_x51), n__take(cons(_x71, n__inf(s(_x71))), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(nil))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x61)))) → eq#(inf(_x21), s(n__length(_x61)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(0, activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__0), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))eq#(n__s(X), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(nil, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), n__s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(0, _x71)))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(_x42, n__s(_x71))))) → eq#(n__s(_x31), cons(activate(_x42), n__take(0, s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, n__0)))) → eq#(inf(_x21), s(n__length(0)))
eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(s(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), 0)))eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(length(_x61), length(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(_x21, cons(n__s(_x41), n__take(activate(_x43), _x71)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x81))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), n__s(_x81))))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(0, activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(length(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), n__length(_x71))))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(n__0), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(length(_x61), _x71)))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(take(_x21, _x22), s(n__length(inf(_x61))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(_x61, activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), n__inf(_x71))))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), length(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(length(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x41), _x41)))) → eq#(activate(X), cons(n__s(_x41), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x41), n__length(_x71))))) → eq#(activate(X), cons(n__s(_x41), n__take(activate(_x43), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(_x21, cons(s(_x51), n__take(length(_x61), _x71)))eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(n__s(_x31), cons(n__s(_x41), n__take(activate(_x43), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(0, activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(length(_x61), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), n__0)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(s(_x61), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(length(_x61), 0)))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__length(_x21)), n__s(n__length(_x41))) → eq#(length(_x21), n__length(_x41))
eq#(n__s(n__take(0, _x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(nil, s(n__length(activate(_x41))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), length(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(_x61, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), 0)))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__0)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), 0)))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x71))))) → eq#(_x21, cons(inf(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(0, s(_x71))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(0, cons(n__s(_x41), n__take(activate(_x43), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(n__inf(_x71), _x71)))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(n__0, s(_x71))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), n__s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(n__take(_x71, _x72), 0)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__inf(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(n__take(0, _x31)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(nil, cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(s(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(n__0, n__take(0, s(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), 0)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(inf(_x61), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(take(_x21, _x22), s(n__length(length(_x61))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(n__inf(_x31), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(n__inf(_x31), cons(s(_x51), n__take(nil, _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(length(_x61), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(activate(_x43), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__length(_x51), n__s(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(0, s(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(0, _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(cons(_x31, n__inf(s(_x31))), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(length(_x61), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), n__0)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), 0)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x41), n__inf(_x71))))) → eq#(inf(_x21), cons(n__inf(_x41), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x71))))) → eq#(n__inf(_x31), cons(inf(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(n__0, n__s(_x81))))) → eq#(n__s(_x31), cons(n__0, n__take(0, n__s(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(nil, 0)))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(length(_x21), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(0, n__take(n__0, s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(_x61, activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(length(_x21), cons(s(_x51), n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, inf(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(take(_x21, _x22), s(n__length(s(_x61))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(length(_x21), cons(n__s(_x41), n__take(activate(_x43), _x71)))eq#(n__s(n__length(nil)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(inf(_x61), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(nil, _x71)))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(nil, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(s(_x61), inf(_x71))))
eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__s(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(0, s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__inf(_x51), n__s(_x71))))) → eq#(s(_x21), cons(inf(_x51), n__take(0, s(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(length(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(inf(_x21), s(n__length(s(_x61))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(_x31, n__inf(s(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), _x71)))) → eq#(length(_x21), cons(n__s(_x41), n__take(inf(_x61), _x71)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(nil, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(inf(_x61), _x71)))eq#(n__s(n__inf(_x31)), n__s(n__length(nil))) → eq#(cons(_x31, n__inf(s(_x31))), 0)
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x71))))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x41), n__inf(_x71))))) → eq#(inf(_x21), cons(cons(_x41, n__inf(s(_x41))), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(0, cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), n__0)))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, n__s(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(n__take(_x71, _x72), s(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(_x21, cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(nil))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), 0)))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(s(_x61), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(0, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, 0)))
eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(0, inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(inf(_x21), cons(n__s(_x41), n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))
eq#(n__s(n__length(_x31)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(n__length(_x31), cons(s(_x51), n__take(inf(_x61), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__s(_x61)), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(s(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(_x61, inf(_x71))))
eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(activate(_x43), _x71)))eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(s(n__length(activate(_x31))), cons(s(_x51), n__take(inf(_x61), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(0, inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(length(_x21), cons(s(_x51), n__take(activate(_x43), length(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(_x21, cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(s(_x61), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), _x71)))
eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(0, cons(s(_x51), n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(cons(_x71, n__inf(s(_x71))), _x71)))eq#(n__s(n__inf(_x31)), n__s(n__length(nil))) → eq#(n__inf(_x31), 0)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(n__inf(_x31), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(n__length(nil)), n__s(n__length(_x31))) → eq#(0, length(_x31))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x41), _x71)))) → eq#(inf(_x21), cons(n__s(_x41), n__take(nil, _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__0, activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(0, inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(_x81))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__0), n__s(n__take(s(_x61), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(_x61, _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), _x71)))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(0, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__take(_x71, _x72))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(n__0, n__s(_x81))))) → eq#(n__s(_x31), cons(0, n__take(n__0, n__s(_x81))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), length(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__0, n__inf(_x71))))) → eq#(_x21, cons(0, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__0)))) → eq#(take(_x21, _x22), s(n__length(0)))eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))
eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), n__0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__length(_x71))))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(inf(_x21), cons(s(_x51), n__take(activate(_x43), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(cons(_x31, n__inf(s(_x31))), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__s(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x41)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), _x41)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(n__take(_x31, _x32), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(0, activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(nil, _x71)))
eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, n__s(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), s(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), s(n__length(activate(_x81))))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(inf(_x21), cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(inf(_x61), activate(_x41))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(n__inf(_x31), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__take(_x31, _x32)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__take(_x31, _x32), s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(length(_x61), _x71)))
eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(_x71))))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(n__length(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), _x71)))) → eq#(length(_x21), cons(s(_x51), n__take(n__inf(_x71), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(inf(_x61), inf(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(_x31, n__inf(s(_x31))), s(n__length(activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(n__inf(_x31), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(inf(_x21), s(n__length(length(_x61))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), n__0)))) → eq#(n__s(_x31), cons(n__length(_x41), n__take(take(_x61, _x62), 0)))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__0), n__s(n__take(s(n__0), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(0, _x71)))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(length(_x61), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__length(_x51), n__inf(_x71))))) → eq#(_x21, cons(length(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__0), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(s(_x61), _x71)))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, n__inf(_x71))))) → eq#(activate(X), cons(0, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(_x21, cons(s(_x51), n__take(inf(_x61), _x71)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x81))))) → eq#(inf(_x21), cons(inf(_x51), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, 0)))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__length(nil))) → eq#(length(_x21), 0)
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(inf(_x61), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__length(_x71)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(n__length(_x71), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(_x61, inf(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(inf(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), inf(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, n__s(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(nil, s(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(s(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), _x71)))eq#(n__s(n__length(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(length(_x21), cons(s(_x51), n__take(length(_x61), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__length(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__length(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), _x41)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(_x31)) → eq#(s(_x21), _x31)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(s(_x61), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(inf(_x61), inf(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__length(_x51), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(length(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(length(_x61), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(length(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(take(_x21, _x22), s(n__length(take(_x61, _x62))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), length(_x71))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(n__0, cons(s(_x51), n__take(activate(_x43), _x71)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), 0)))eq#(n__s(n__s(_x21)), n__s(n__s(_x31))) → eq#(s(_x21), s(_x31))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(n__s(_x31), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(inf(_x61), _x71)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(inf(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(_x61, _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__0, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(0, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(s(_x61), length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__s(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x41), _x71)))) → eq#(inf(_x21), cons(n__s(_x41), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(s(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x71)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), 0)))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(0, _x71)))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(0, activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(length(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(cons(_x82, _x81)))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), s(n__length(activate(_x81))))))
eq#(n__s(n__take(0, _x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(nil, cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, n__length(_x71))))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__0, n__inf(_x71))))) → eq#(inf(_x21), cons(0, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(inf(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), 0)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__0), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(0, inf(_x71))))eq#(n__s(n__s(_x31)), n__s(Y)) → eq#(n__s(_x31), activate(Y))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__s(_x81))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, n__s(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), n__0)eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(inf(_x21), s(n__length(inf(_x61))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(inf(_x61), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__inf(_x31))) → eq#(s(_x21), inf(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), length(_x71))))eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), _x71)))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__inf(_x31), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(_x61, _x71)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(n__0, n__s(_x71))))) → eq#(n__s(_x31), cons(0, n__take(0, s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, n__s(_x81))))) → eq#(s(_x21), cons(n__0, n__take(n__0, n__s(_x81))))eq#(n__s(n__0), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(inf(_x61), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x71))))) → eq#(cons(_x31, n__inf(s(_x31))), cons(inf(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(0, inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))
eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(_x61, length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), 0)))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, nil, cons, eq

Strategy

The right-hand side of the rule eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), inf(_x71)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(_x21, cons(s(_x51), n__take(s(_x61), inf(_x71)))) 
eq#(_x21, cons(s(_x51), n__take(inf(_x61), inf(_x71)))) 
eq#(_x21, cons(s(_x51), n__take(length(_x61), inf(_x71)))) 
eq#(_x21, cons(s(_x51), n__take(take(_x61, _x62), inf(_x71)))) 
eq#(_x21, cons(n__s(_x41), n__take(activate(_x43), inf(_x71)))) 
eq#(_x21, cons(s(_x51), n__take(_x61, inf(_x71)))) 
eq#(_x21, cons(s(_x51), n__take(0, inf(_x71)))) 
eq#(_x21, cons(s(_x51), n__take(activate(_x43), n__inf(_x81)))) 
eq#(_x21, cons(s(_x51), n__take(activate(_x43), cons(_x81, n__inf(s(_x81)))))) 
Thus, the rule eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), inf(_x71)))) is replaced by the following rules:
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x41), n__inf(_x71))))) → eq#(_x21, cons(n__s(_x41), n__take(activate(_x43), inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x81))))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(inf(_x61), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(length(_x61), inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x81))))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(_x21), n__s(n__take(s(n__0), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(0, inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(_x61, inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(s(_x61), inf(_x71))))

Problem 25: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__length(_x31))) → eq#(s(n__length(activate(_x31))), length(_x31))eq#(n__s(n__length(_x31)), n__s(n__length(_x31))) → eq#(n__length(_x31), length(_x31))
eq#(n__s(X), n__s(n__take(s(n__inf(_x71)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(n__inf(_x71), inf(_x71))))eq#(n__s(n__take(s(_x33), cons(n__take(_x31, _x32), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(n__take(_x31, _x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), take(_x71, _x72))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(_x51, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(_x51, n__take(inf(_x61), n__inf(_x81))))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__length(_x61)), cons(n__length(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(length(_x51), n__take(length(_x61), n__inf(_x81))))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(_x61, inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(inf(_x61), inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, n__s(_x81))))) → eq#(s(_x21), cons(0, n__take(n__0, n__s(_x81))))
eq#(n__s(n__0), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(0, cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(nil, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__take(s(n__0), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(0, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(nil))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), 0)))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(0, cons(take(_x51, _x52), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x41), n__length(_x81))))) → eq#(activate(X), cons(n__s(_x41), n__take(activate(_x43), n__length(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(length(_x61), n__s(_x81))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__0), cons(n__length(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(length(_x51), n__take(0, n__inf(_x81))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(n__inf(_x31), cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__0)) → eq#(s(_x21), n__0)eq#(n__s(X), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(0, inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(_x21, cons(s(_x51), n__take(length(_x61), n__length(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(inf(_x21), cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(0, inf(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(_x42, n__s(_x71))))) → eq#(n__s(_x31), cons(activate(_x42), n__take(0, s(_x71))))eq#(n__s(n__take(s(_x33), cons(n__length(_x41), n__0))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), 0)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(n__s(_x51), n__length(_x81))))) → eq#(length(_x21), cons(s(_x51), n__take(s(n__length(activate(_x71))), n__length(_x81))))eq#(n__s(n__take(s(n__s(_x51)), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(s(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, n__0)))) → eq#(inf(_x21), s(n__length(0)))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(n__length(_x71), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__0)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), 0)))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), s(_x71))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))eq#(n__s(n__take(s(_x33), cons(_x41, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(_x41, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(s(_x61), inf(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(n__s(_x31), cons(0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(0, cons(take(_x51, _x52), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(0, inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__0), cons(_x51, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(_x51, n__take(0, n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(s(_x21), cons(n__take(_x41, _x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(length(_x61), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(_x21, cons(n__s(_x41), n__take(activate(_x43), _x71)))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(0, activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(length(_x61), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), n__length(_x71))))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(n__take(s(_x33), cons(_x32, n__length(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), length(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__length(nil)), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(n__s(_x51), n__length(_x81))))) → eq#(0, cons(s(_x51), n__take(s(n__length(activate(_x71))), n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), n__inf(_x81))))eq#(n__s(n__0), n__s(n__take(s(n__length(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(0, cons(take(_x51, _x52), n__take(length(_x61), inf(_x71))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(take(_x21, _x22), s(n__length(inf(_x61))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x81))))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(_x61, activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(0, n__length(_x81))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), n__inf(_x71))))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x71))))) → eq#(s(_x21), cons(s(_x51), n__take(0, length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x41), _x41)))) → eq#(activate(X), cons(n__s(_x41), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x42, n__take(_x71, _x72))))) → eq#(_x21, cons(activate(_x42), n__take(0, take(_x71, _x72))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x41), n__length(_x71))))) → eq#(activate(X), cons(n__s(_x41), n__take(activate(_x43), length(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__s(_x41), _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(s(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(_x21, cons(s(_x51), n__take(length(_x61), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(0, activate(_x41))))eq#(n__s(n__take(s(_x33), cons(n__inf(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(inf(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(length(_x61), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), n__0)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(s(_x61), _x71)))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(inf(_x51), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(_x21, cons(inf(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(0, cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(n__length(_x21)), n__s(n__length(_x41))) → eq#(length(_x21), n__length(_x41))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(activate(_x42), n__take(take(_x61, _x62), n__inf(_x81))))
eq#(n__s(n__take(0, _x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(nil, s(n__length(activate(_x41))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(take(_x51, _x52), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x81))))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), n__length(_x81))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(_x43), cons(_x51, n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(_x51, n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(cons(_x31, n__inf(s(_x31))), cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(_x51, n__inf(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(_x61, inf(_x71))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(0, cons(n__s(_x41), n__take(activate(_x43), _x71)))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(n__0, s(_x71))))eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(take(_x61, _x62), n__length(_x81))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(_x61, inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__take(_x51, _x52), _x71)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(n__take(_x71, _x72), 0)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__inf(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(n__inf(_x31), cons(activate(_x42), n__take(_x61, cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(n__0, n__take(0, s(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), 0)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(inf(_x61), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(take(_x21, _x22), s(n__length(length(_x61))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(n__inf(_x31), cons(s(_x51), n__take(nil, _x71)))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(n__inf(_x31), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(s(n__length(_x51)), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(length(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(0, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, _x71)))) → eq#(s(_x21), cons(0, n__take(activate(_x43), _x71)))eq#(n__s(n__take(s(n__inf(_x51)), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(inf(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(length(_x61), _x71)))eq#(n__s(n__take(s(n__0), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(0, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__length(_x71)), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(n__length(_x71), n__length(_x81))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(cons(_x31, n__inf(s(_x31))), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(length(_x61), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x51, n__s(_x81))))) → eq#(cons(_x31, n__inf(s(_x31))), cons(_x51, n__take(activate(_x43), n__s(_x81))))eq#(n__s(n__take(s(_x33), cons(_x32, n__inf(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), inf(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(take(_x61, _x62), n__s(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(s(_x21), cons(n__0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x71))))) → eq#(n__inf(_x31), cons(inf(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(nil, 0)))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(0, inf(_x71))))eq#(n__s(n__length(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(length(_x21), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(_x41, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(_x41, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(n__inf(_x31), cons(take(_x51, _x52), n__take(_x61, inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(nil, _x71)))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(take(_x21, _x22), s(n__length(s(_x61))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(n__take(s(_x33), cons(_x32, n__inf(_x61)))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), inf(_x61))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__length(nil)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), n__length(_x81))))) → eq#(0, cons(n__s(_x41), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(nil, _x71)))eq#(n__s(n__take(s(_x33), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(s(_x21), cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x61), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(_x61, inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__length(nil), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(0, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(s(_x51), n__take(_x61, inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__0, _x41)))) → eq#(_x21, cons(0, n__take(length(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(s(_x61), inf(_x71))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(n__0, cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))
eq#(n__s(n__take(0, _x31)), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(nil, cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__s(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(0, s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__inf(_x51), n__s(_x71))))) → eq#(s(_x21), cons(inf(_x51), n__take(0, s(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))
eq#(n__s(n__take(s(n__take(_x51, _x52)), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(take(_x51, _x52), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(inf(_x61), cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(_x51, n__s(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(_x61, n__s(_x81))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), _x71)))) → eq#(length(_x21), cons(n__s(_x41), n__take(inf(_x61), _x71)))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(_x31, n__inf(s(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(inf(_x61), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(0, n__take(cons(_x71, n__inf(s(_x71))), s(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__take(s(_x33), cons(n__length(_x41), n__s(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), s(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(n__length(_x51), n__inf(_x71))))) → eq#(n__inf(_x31), cons(length(_x51), n__take(_x61, inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__take(_x71, _x72))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x81))))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(0, cons(n__take(_x41, _x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__length(_x71)), cons(n__s(_x51), n__length(_x81))))) → eq#(length(_x21), cons(s(_x51), n__take(n__length(_x71), n__length(_x81))))eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__take(s(n__length(_x71)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(activate(_x31))), cons(s(_x51), n__take(n__length(_x71), n__length(_x81))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), inf(_x71))))eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), n__length(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), length(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__length(nil)), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), n__length(_x81))))) → eq#(0, cons(s(_x51), n__take(0, n__length(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(length(_x61), inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x41), n__inf(_x71))))) → eq#(inf(_x21), cons(cons(_x41, n__inf(s(_x41))), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(inf(_x21), cons(take(_x51, _x52), n__take(_x61, inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(n__0, n__inf(_x71))))) → eq#(n__inf(_x31), cons(0, n__take(_x61, inf(_x71))))
eq#(n__s(n__take(s(_x51), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(_x51, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__0, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(0, n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), n__0)))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(n__length(_x51), _x41)))) → eq#(_x21, cons(length(_x51), n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(s(_x61), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(length(_x61), n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(0, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__inf(_x71))))) → eq#(s(_x21), cons(0, n__take(n__inf(_x71), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(0, inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(inf(_x21), cons(n__s(_x41), n__take(activate(_x43), _x71)))
eq#(n__s(n__take(0, _x31)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(nil, cons(activate(_x42), n__take(_x61, n__inf(_x81))))eq#(n__s(n__take(s(_x33), cons(n__length(cons(_x32, _x31)), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(s(n__length(activate(_x31))), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(0, s(_x71))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__length(_x31)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(n__length(_x31), cons(s(_x51), n__take(inf(_x61), _x71)))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(_x61, inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(activate(_x31))), cons(s(_x51), n__take(0, n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(length(_x61), n__inf(_x81))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(length(_x21), cons(s(_x51), n__take(activate(_x43), length(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(n__length(_x41), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(n__length(_x41), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(_x21, cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, n__length(_x71))))) → eq#(s(_x21), cons(0, n__take(activate(_x43), length(_x71))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(n__length(cons(_x42, _x41)), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(s(n__length(activate(_x41))), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(0, cons(s(_x51), n__take(activate(_x43), length(_x71))))
eq#(n__s(n__inf(_x31)), n__s(n__length(nil))) → eq#(n__inf(_x31), 0)eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(activate(_x31))), cons(s(_x51), n__take(s(n__length(activate(_x71))), n__length(_x81))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(n__inf(_x31), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x41, _x42), _x71)))) → eq#(s(_x21), cons(n__take(_x41, _x42), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(s(n__0), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(0, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(length(_x61), inf(_x71))))
eq#(n__s(n__length(nil)), n__s(n__length(_x31))) → eq#(0, length(_x31))eq#(n__s(n__length(cons(_x32, n__0))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(0)), cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__0), n__s(n__take(s(_x61), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(_x61, _x71)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), _x41)))) → eq#(n__s(_x31), cons(take(_x51, _x52), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(0, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x61), cons(n__s(_x41), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(_x61, n__inf(_x81))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(n__0, n__s(_x81))))) → eq#(n__s(_x31), cons(0, n__take(n__0, n__s(_x81))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__take(_x71, _x72))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__take(s(_x51), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(_x51, activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__inf(_x71))))) → eq#(s(_x21), cons(0, n__take(inf(_x61), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(_x21), cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x61)), cons(n__length(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(length(_x51), n__take(inf(_x61), n__inf(_x81))))eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), n__0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__length(_x71))))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))
eq#(n__s(n__0), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(0, cons(s(_x51), n__take(length(_x61), n__length(_x81))))eq#(n__s(X), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(s(n__length(activate(_x71))), n__length(_x81))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__s(_x71))))) → eq#(n__s(_x31), cons(n__0, n__take(inf(_x61), s(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__s(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(n__take(_x31, _x32), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x71))))) → eq#(cons(_x31, n__inf(s(_x31))), cons(activate(_x42), n__take(_x61, inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(nil, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__s(_x81))))) → eq#(s(_x21), cons(n__0, n__take(cons(_x71, n__inf(s(_x71))), n__s(_x81))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, n__s(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), s(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), s(n__length(activate(_x81))))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(n__take(0, _x31)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(nil, cons(activate(_x42), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x61), cons(n__length(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(length(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__length(_x71))))) → eq#(s(_x21), cons(0, n__take(n__inf(_x71), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__take(_x71, _x72))))) → eq#(s(_x21), cons(0, n__take(n__inf(_x71), take(_x71, _x72))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(_x61, s(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(inf(_x21), cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(n__inf(_x31), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))
eq#(n__s(n__take(s(_x33), cons(n__0, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(0, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(length(_x61), _x71)))eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(0, n__length(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__inf(_x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(_x31, n__inf(s(_x31))), s(n__length(activate(_x41))))eq#(n__s(n__take(s(_x33), cons(_x32, n__0))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), 0)), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(n__inf(_x51), n__inf(_x71))))) → eq#(n__inf(_x31), cons(inf(_x51), n__take(_x61, inf(_x71))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(nil, _x71)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(0, _x41), n__inf(_x71))))) → eq#(activate(X), cons(nil, n__take(activate(_x43), inf(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(n__inf(_x31), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__0, _x71)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__s(_x71))))) → eq#(n__s(_x31), cons(0, n__take(inf(_x61), s(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(inf(_x21), s(n__length(length(_x61))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), n__0)))) → eq#(n__s(_x31), cons(n__length(_x41), n__take(take(_x61, _x62), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__0, _x71)))) → eq#(s(_x21), cons(0, n__take(inf(_x61), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(s(_x61), inf(_x71))))
eq#(n__s(n__0), n__s(n__take(s(n__0), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(0, _x71)))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(length(_x61), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, inf(_x71))))eq#(n__s(n__take(s(n__inf(_x51)), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(inf(_x51), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(n__length(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(length(_x51), n__take(_x61, inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__length(_x51), n__inf(_x71))))) → eq#(_x21, cons(length(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__0), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(s(_x61), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__0), cons(_x51, n__s(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(0, s(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(n__s(_x31), cons(take(_x51, _x52), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(_x21, cons(s(_x51), n__take(inf(_x61), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(_x21, cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, 0)))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(n__s(_x51), n__length(_x81))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(s(n__length(activate(_x71))), n__length(_x81))))eq#(n__s(n__length(_x21)), n__s(n__length(nil))) → eq#(length(_x21), 0)
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(inf(_x61), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(n__take(_x41, _x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(length(_x61), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__length(_x71)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(n__length(_x71), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(inf(_x61), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(s(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(n__0, n__take(cons(_x71, n__inf(s(_x71))), s(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__inf(_x41), _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(inf(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), _x71)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), _x41)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x51, n__s(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(inf(_x61), n__s(_x81))))eq#(n__s(n__s(_x21)), n__s(_x31)) → eq#(s(_x21), _x31)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(0, activate(_x41))))eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(s(_x61), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(s(_x43), cons(_x42, _x41)), _x71)))) → eq#(s(_x21), cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__length(_x51), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(length(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(length(_x61), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(s(_x61), n__inf(_x81))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__0, _x41)))) → eq#(s(_x21), cons(n__0, n__take(inf(_x61), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(_x51, n__take(length(_x61), n__inf(_x81))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), 0)))eq#(n__s(n__s(_x21)), n__s(n__s(_x31))) → eq#(s(_x21), s(_x31))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(n__s(_x31), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x42, n__length(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(length(_x61), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(s(_x43), cons(_x42, _x41)), n__inf(_x81))))) → eq#(s(_x21), cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(s(_x21), cons(n__take(_x41, _x42), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x51, n__s(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(s(_x61), n__s(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__s(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__inf(_x71)), cons(n__0, _x41)))) → eq#(n__s(_x31), cons(0, n__take(n__inf(_x71), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x41), _x71)))) → eq#(inf(_x21), cons(n__s(_x41), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(s(_x61), inf(_x71))))
eq#(n__s(n__length(cons(_x32, _x51))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(_x51)), cons(s(_x51), n__take(length(_x61), n__length(_x81))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x41), n__inf(_x71))))) → eq#(_x21, cons(n__s(_x41), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x61), cons(n__length(_x51), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(length(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x71)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), 0)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x71)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(s(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(length(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(0, _x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(nil, cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(activate(_x42), n__take(inf(_x61), n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(s(_x61), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, n__length(_x71))))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__take(s(_x33), cons(_x32, n__length(_x61)))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), length(_x61))), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), s(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__s(_x81))))) → eq#(s(_x21), cons(0, n__take(inf(_x61), n__s(_x81))))
eq#(n__s(n__length(cons(_x32, n__s(_x51)))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(s(_x51))), cons(s(_x51), n__take(length(_x61), n__length(_x81))))eq#(n__s(n__take(0, _x31)), n__s(n__take(s(_x43), cons(_x51, n__inf(_x81))))) → eq#(nil, cons(_x51, n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x81))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), n__s(_x81))))eq#(n__s(n__take(s(_x33), cons(n__s(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(s(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__s(_x81))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, n__s(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), n__0)eq#(n__s(n__length(nil)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(n__0, cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(inf(_x21), s(n__length(inf(_x61))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(inf(_x61), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x41), n__length(_x71))))) → eq#(activate(X), cons(n__s(_x41), n__take(0, length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__inf(_x31))) → eq#(s(_x21), inf(_x31))eq#(n__s(n__length(cons(_x32, n__take(_x51, _x52)))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(take(_x51, _x52))), cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), length(_x71))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(inf(_x61), n__inf(_x81))))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), _x71)))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(0, n__take(activate(_x43), s(_x71))))eq#(n__s(n__take(s(n__length(_x51)), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(length(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__0), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(inf(_x61), _x71)))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__s(_x61)), cons(n__length(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(length(_x51), n__take(s(_x61), n__inf(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(n__0, n__inf(_x71))))) → eq#(inf(_x21), cons(0, n__take(_x61, inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(0, n__take(n__inf(_x71), s(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__length(_x31), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(n__length(_x31), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(s(n__inf(_x51)), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(inf(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, n__s(_x81))))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), n__s(_x81))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(n__0, length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), n__s(_x71))))) → eq#(s(_x21), cons(s(_x51), n__take(n__0, s(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(_x61, length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, _x71)))
eq#(n__s(n__take(s(n__s(_x51)), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(s(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x51, n__s(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(inf(_x61), s(_x71))))
eq#(n__s(X), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(s(n__length(activate(_x71))), _x71)))eq#(n__s(n__take(s(_x33), cons(_x32, n__take(_x61, _x62)))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), take(_x61, _x62))), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x41), _x71)))) → eq#(inf(_x21), cons(n__s(_x41), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))
eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(inf(_x21), s(n__length(take(_x61, _x62))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__length(_x71))))) → eq#(s(_x21), cons(0, n__take(inf(_x61), length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x61)))) → eq#(take(_x21, _x22), s(n__length(_x61)))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(_x51, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(_x51, n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__length(_x21)), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), n__length(_x81))))) → eq#(length(_x21), cons(s(_x51), n__take(0, n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, _x41)))) → eq#(s(_x21), cons(n__0, n__take(n__inf(_x71), activate(_x41))))eq#(n__s(n__take(s(_x33), cons(_x32, _x61))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), _x61)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(s(n__length(activate(_x71))), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(length(_x61), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(s(_x61), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x81))))) → eq#(inf(_x21), cons(inf(_x51), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(_x21), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x71))))) → eq#(_x21, cons(s(_x51), n__take(0, length(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(s(n__length(_x51)), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(length(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(nil))))) → eq#(activate(X), cons(s(_x51), n__take(0, 0)))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), _x71)))) → eq#(length(_x21), cons(s(_x51), n__take(cons(_x71, n__inf(s(_x71))), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x81))))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), n__length(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x61)))) → eq#(inf(_x21), s(n__length(_x61)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__length(_x51), _x41)))) → eq#(_x21, cons(length(_x51), n__take(length(_x61), activate(_x41))))eq#(n__s(n__0), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(_x21, cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(nil, _x71)))eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))
eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))eq#(n__s(n__0), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(0, cons(take(_x51, _x52), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(_x71)), cons(n__s(_x51), n__length(_x81))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(n__length(_x71), n__length(_x81))))eq#(n__s(_x21), n__s(n__take(s(n__0), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(0, inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), n__s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))eq#(n__s(X), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(0, _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(s(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), _x71)))) → eq#(n__s(_x31), cons(take(_x51, _x52), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(inf(_x61), s(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(n__length(nil), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(0, n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__take(s(_x33), cons(_x32, n__take(_x61, _x62)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), take(_x61, _x62))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__take(0, _x31), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(nil, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(_x32, n__0))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), 0)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__take(0, _x41), n__inf(_x71))))) → eq#(0, cons(nil, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__s(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x81))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), n__s(_x81))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x81))))) → eq#(length(_x21), cons(s(_x51), n__take(activate(_x43), n__length(_x81))))eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x42, n__0)))) → eq#(_x21, cons(activate(_x42), n__take(0, 0)))eq#(n__s(n__0), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(length(_x61), _x71)))
eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(n__take(0, _x41), n__inf(_x81))))) → eq#(s(_x21), cons(nil, n__take(_x61, n__inf(_x81))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(length(_x61), inf(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(n__s(_x51), n__s(_x71))))) → eq#(n__s(_x31), cons(s(_x51), n__take(0, s(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(n__s(_x31), cons(n__s(_x41), n__take(activate(_x43), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))
eq#(n__s(n__0), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(0, cons(take(_x51, _x52), n__take(0, inf(_x71))))eq#(n__s(n__take(0, _x31)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(nil, cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(length(_x21), cons(n__take(_x41, _x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(0, _x41), n__inf(_x71))))) → eq#(s(_x21), cons(nil, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(n__s(_x31), cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(length(_x61), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), _x71)))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(n__inf(_x31), cons(activate(_x42), n__take(_x61, n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), 0)))
eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__inf(_x61)), cons(n__0, _x41)))) → eq#(n__s(_x31), cons(0, n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(_x61, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), 0)))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__0)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), 0)))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x71))))) → eq#(length(_x21), cons(s(_x51), n__take(0, length(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(_x51, n__inf(_x71))))) → eq#(n__inf(_x31), cons(_x51, n__take(_x61, inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x71))))) → eq#(_x21, cons(inf(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(0, s(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x61), cons(n__inf(_x51), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(inf(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(0, n__inf(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(inf(_x21), cons(n__take(_x41, _x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, n__take(_x71, _x72))))) → eq#(s(_x21), cons(0, n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(n__0, _x41)))) → eq#(_x21, cons(0, n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(n__inf(_x71), _x71)))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), s(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), n__s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(n__length(cons(_x32, n__length(_x51)))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(length(_x51))), cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__take(0, _x31)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(nil, cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(activate(_x43), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))eq#(n__s(X), n__s(n__take(s(_x61), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(_x61, n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(n__take(s(_x43), cons(_x42, _x41)), n__inf(_x81))))) → eq#(s(_x21), cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(_x61, n__inf(_x81))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__0), cons(_x51, n__s(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(0, n__s(_x81))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x42, _x71)))) → eq#(_x21, cons(activate(_x42), n__take(0, _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(length(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__length(_x51), n__s(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(0, s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(0, _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x51, n__s(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(s(_x61), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), n__length(_x81))))) → eq#(activate(X), cons(n__s(_x41), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), n__0))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), 0)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), n__0)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), 0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__s(_x61)), cons(_x51, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(_x51, n__take(s(_x61), n__inf(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x41), n__inf(_x71))))) → eq#(inf(_x21), cons(n__inf(_x41), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__0), n__s(n__take(s(n__s(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(0, cons(take(_x51, _x52), n__take(s(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(s(_x43), cons(_x42, _x41)), n__inf(_x71))))) → eq#(s(_x21), cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(activate(_x43), inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x42, n__s(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(0, s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x41), n__s(_x71))))) → eq#(s(_x21), cons(n__s(_x41), n__take(0, s(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(n__0, n__s(_x81))))) → eq#(n__s(_x31), cons(n__0, n__take(0, n__s(_x81))))
eq#(n__s(n__take(s(n__take(_x51, _x52)), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(take(_x51, _x52), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(_x21, cons(n__take(_x41, _x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__0, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(0, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(0, n__take(n__0, s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(_x61, activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(length(_x21), cons(s(_x51), n__take(activate(_x43), _x71)))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(length(_x21), cons(n__s(_x41), n__take(activate(_x43), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(inf(_x51), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__length(nil)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(inf(_x61), _x71)))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(n__take(s(_x33), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(0, _x41), _x71)))) → eq#(s(_x21), cons(nil, n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(nil, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__take(s(_x43), cons(_x42, _x41)), n__inf(_x71))))) → eq#(0, cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x81))))) → eq#(inf(_x21), cons(s(_x51), n__take(activate(_x43), n__length(_x81))))
eq#(n__s(n__take(s(n__0), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(0, activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__s(_x81))))) → eq#(n__s(_x31), cons(n__0, n__take(inf(_x61), n__s(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x61), cons(n__0, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(0, n__take(_x61, n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__take(_x71, _x72))))) → eq#(s(_x21), cons(0, n__take(inf(_x61), take(_x71, _x72))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(length(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), n__length(_x81))))) → eq#(length(_x21), cons(n__s(_x41), n__take(length(_x61), n__length(_x81))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(activate(_x42), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, n__inf(_x71))))) → eq#(s(_x21), cons(0, n__take(activate(_x43), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(inf(_x21), s(n__length(s(_x61))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(activate(_x42), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(length(_x51), n__take(take(_x61, _x62), n__inf(_x81))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(nil, activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x81))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), n__length(_x81))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(_x61), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(n__s(_x31), cons(take(_x51, _x52), n__take(_x61, n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(_x61, inf(_x71))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__length(nil)), n__s(n__take(s(n__length(_x71)), cons(n__s(_x51), n__length(_x81))))) → eq#(0, cons(s(_x51), n__take(n__length(_x71), n__length(_x81))))
eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), n__length(_x81))))) → eq#(s(n__length(activate(_x31))), cons(n__s(_x41), n__take(length(_x61), n__length(_x81))))eq#(n__s(n__inf(_x31)), n__s(n__length(nil))) → eq#(cons(_x31, n__inf(s(_x31))), 0)
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x71))))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(0, _x41), n__inf(_x81))))) → eq#(s(_x21), cons(nil, n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(s(_x21), cons(n__take(_x41, _x42), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__0), n__s(n__take(s(_x61), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(0, cons(take(_x51, _x52), n__take(_x61, inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__inf(_x51), _x41)))) → eq#(_x21, cons(inf(_x51), n__take(length(_x61), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__0), cons(_x42, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(0, n__inf(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(inf(_x21), cons(s(_x51), n__take(length(_x61), n__length(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x41, _x42), _x41)))) → eq#(s(_x21), cons(n__take(_x41, _x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__0), cons(_x42, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(activate(_x42), n__take(0, n__inf(_x81))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(0, cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, n__s(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(n__take(_x71, _x72), s(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(n__0, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(0, n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x42, n__s(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(length(_x61), s(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(n__take(s(n__length(_x51)), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(length(_x51), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(_x21, cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(s(_x43), cons(_x42, _x41)), n__inf(_x71))))) → eq#(activate(X), cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(nil))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), 0)))
eq#(n__s(n__0), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(0, cons(take(_x51, _x52), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(_x21, cons(0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(length(_x61), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(length(_x61), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))eq#(n__s(n__take(s(n__take(_x51, _x52)), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(take(_x51, _x52), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(take(_x51, _x52), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(n__take(_x51, _x52), _x41)))) → eq#(_x21, cons(take(_x51, _x52), n__take(0, activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__s(_x61)), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(s(_x61), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(s(_x61), s(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(activate(_x43), _x71)))
eq#(n__s(n__take(s(n__s(_x51)), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(s(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(s(n__length(activate(_x31))), cons(s(_x51), n__take(inf(_x61), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(0, inf(_x71))))eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), n__inf(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), inf(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(s(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(_x21, cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), _x71)))eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))
eq#(n__s(X), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(cons(_x71, n__inf(s(_x71))), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(inf(_x21), cons(activate(_x42), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(inf(_x21), cons(activate(_x42), n__take(_x61, cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__take(s(n__inf(_x51)), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(inf(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x51, n__s(_x81))))) → eq#(n__inf(_x31), cons(_x51, n__take(activate(_x43), n__s(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(n__0, n__take(n__inf(_x71), s(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x41), _x71)))) → eq#(inf(_x21), cons(n__s(_x41), n__take(nil, _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__0, activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(0, inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x71))))) → eq#(inf(_x21), cons(s(_x51), n__take(0, length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(_x81))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), n__length(_x81))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), _x71)))
eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(n__s(n__length(activate(_x31))), cons(s(_x51), n__take(length(_x61), n__length(_x81))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(inf(_x61), n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__0)))) → eq#(s(_x21), cons(0, n__take(n__inf(_x71), 0)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__0, n__inf(_x71))))) → eq#(_x21, cons(0, n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), n__take(_x61, _x62)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), take(_x61, _x62))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__0)))) → eq#(take(_x21, _x22), s(n__length(0)))eq#(n__s(n__s(_x31)), n__s(n__0)) → eq#(n__s(_x31), 0)
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__s(_x81))))) → eq#(s(_x21), cons(n__0, n__take(n__inf(_x71), n__s(_x81))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), n__length(_x81))))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(cons(_x71, n__inf(s(_x71))), activate(_x41))))eq#(n__s(n__length(cons(_x32, n__inf(_x51)))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(inf(_x51))), cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x42, n__length(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(0, length(_x71))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(inf(_x21), cons(s(_x51), n__take(activate(_x43), length(_x71))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(cons(_x31, n__inf(s(_x31))), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(activate(X), cons(s(_x51), n__take(0, s(n__length(activate(_x81))))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x41)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(n__0, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(s(_x61), n__length(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), _x41)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(0, activate(_x41))))eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))
eq#(n__s(n__take(s(_x51), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(_x51, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(s(_x43), cons(_x42, _x41)), _x41)))) → eq#(s(_x21), cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__0)))) → eq#(s(_x21), cons(0, n__take(inf(_x61), 0)))eq#(n__s(n__take(s(_x51), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(_x51, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x41)))) → eq#(_x21, cons(s(_x51), n__take(length(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__take(_x51, _x52), _x71)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(nil, _x71)))eq#(n__s(n__take(_x31, _x32)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__take(_x31, _x32), s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(_x71))))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))eq#(n__s(n__length(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), _x71)))) → eq#(length(_x21), cons(s(_x51), n__take(n__inf(_x71), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__length(_x51), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(length(_x51), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__take(s(_x33), cons(_x32, _x61))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), _x61)), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x42, _x71)))) → eq#(_x21, cons(activate(_x42), n__take(length(_x61), _x71)))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(_x61, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), _x41)))) → eq#(_x21, cons(s(_x51), n__take(0, activate(_x41))))eq#(n__s(n__take(s(_x33), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x81))))) → eq#(0, cons(s(_x51), n__take(activate(_x43), n__length(_x81))))eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, n__inf(_x71))))) → eq#(activate(X), cons(0, n__take(activate(_x43), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(_x61, s(_x71))))eq#(n__s(n__take(s(_x33), cons(n__length(_x41), _x61))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), _x61)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), length(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__take(_x51, _x52), _x71)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(n__take(s(_x33), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(nil, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x81))))) → eq#(inf(_x21), cons(inf(_x51), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(length(_x21), cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71))))eq#(n__s(n__take(s(_x33), cons(n__length(_x41), n__length(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), length(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(s(_x33), cons(_x32, n__s(_x61)))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), s(_x61))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(activate(_x42), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(inf(_x61), n__inf(_x81))))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(s(n__take(_x51, _x52)), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(take(_x51, _x52), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(inf(_x61), n__length(_x81))))eq#(n__s(n__take(s(_x33), cons(n__take(s(_x33), cons(_x32, _x31)), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(take(_x61, _x62), n__inf(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(_x61, inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), n__length(_x81))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(0, n__length(_x81))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, n__s(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(nil, s(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x71))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(0, length(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(s(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__length(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(length(_x21), cons(s(_x51), n__take(length(_x61), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__length(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(s(_x61), n__inf(_x81))))
eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__length(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), _x61))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), _x61)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x42, n__take(_x71, _x72))))) → eq#(_x21, cons(activate(_x42), n__take(length(_x61), take(_x71, _x72))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(length(_x61), inf(_x71))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(activate(_x42), n__take(length(_x61), n__inf(_x81))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), s(n__length(activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), n__s(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), s(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(take(_x21, _x22), s(n__length(take(_x61, _x62))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x61), cons(_x51, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(_x51, n__take(_x61, n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), length(_x71))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(n__0, cons(s(_x51), n__take(activate(_x43), _x71)))eq#(n__s(n__take(s(n__s(_x51)), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(s(_x51), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(inf(_x61), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(nil, activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(inf(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(activate(_x42), n__take(s(_x61), n__inf(_x81))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(_x61, _x71)))eq#(n__s(n__take(s(_x33), cons(_x32, n__s(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), s(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__0, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(0, n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(s(_x61), length(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__take(s(_x33), cons(n__length(_x41), n__take(_x61, _x62)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), take(_x61, _x62))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(n__s(_x41), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(_x61, n__inf(_x81))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, _x71)))) → eq#(s(_x21), cons(0, n__take(n__inf(_x71), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__take(_x51, _x52), _x41)))) → eq#(_x21, cons(take(_x51, _x52), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(_x51, n__take(take(_x61, _x62), n__inf(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(0, _x71)))
eq#(n__s(n__0), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x71))))) → eq#(0, cons(s(_x51), n__take(0, length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(0, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(length(_x61), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(cons(_x82, _x81)))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), s(n__length(activate(_x81))))))
eq#(n__s(n__take(s(_x33), cons(n__length(_x41), _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(length(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), n__s(_x81))))) → eq#(s(_x21), cons(s(_x51), n__take(0, n__s(_x81))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(n__inf(_x51), _x41)))) → eq#(_x21, cons(inf(_x51), n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(inf(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__0, n__inf(_x71))))) → eq#(inf(_x21), cons(0, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__length(_x41), n__inf(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), inf(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), 0)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__0), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(0, inf(_x71))))eq#(n__s(n__s(_x31)), n__s(Y)) → eq#(n__s(_x31), activate(Y))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x42, n__0)))) → eq#(_x21, cons(activate(_x42), n__take(length(_x61), 0)))eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x71))))) → eq#(n__inf(_x31), cons(s(_x51), n__take(_x61, inf(_x71))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(length(_x21), cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(0, _x41), _x41)))) → eq#(s(_x21), cons(nil, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))eq#(n__s(X), n__s(n__take(s(n__inf(_x71)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(cons(_x71, n__inf(s(_x71))), inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(_x51, n__s(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(_x61, s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__inf(_x31), s(n__length(activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x61), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(_x61, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, n__0)))) → eq#(s(_x21), cons(0, n__take(activate(_x43), 0)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(n__0, n__s(_x71))))) → eq#(n__s(_x31), cons(0, n__take(0, s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, n__s(_x81))))) → eq#(s(_x21), cons(n__0, n__take(n__0, n__s(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x71))))) → eq#(cons(_x31, n__inf(s(_x31))), cons(inf(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(0, inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x61), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(take(_x51, _x52), n__take(_x61, n__inf(_x81))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(s(_x61), inf(_x71))))eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))
eq#(n__s(n__length(_x31)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(n__length(_x31), cons(s(_x51), n__take(length(_x61), n__length(_x81))))eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)
eq#(n__s(X), n__s(n__take(s(_x61), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(_x61, inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, _x71)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), 0)))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, nil, cons, eq

Strategy

The right-hand side of the rule eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, take(_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
eq#(s(_x21), cons(activate(_x42), n__take(n__0, take(_x71, _x72)))) 
eq#(s(_x21), cons(take(_x51, _x52), n__take(0, take(_x71, _x72)))) 
eq#(s(_x21), cons(inf(_x51), n__take(0, take(_x71, _x72)))) 
eq#(s(_x21), cons(length(_x51), n__take(0, take(_x71, _x72)))) 
eq#(s(_x21), cons(activate(_x42), n__take(0, nil))) 
eq#(s(_x21), cons(0, n__take(0, take(_x71, _x72)))) 
eq#(s(_x21), cons(_x51, n__take(0, take(_x71, _x72)))) 
eq#(s(_x21), cons(s(_x51), n__take(0, take(_x71, _x72)))) 
eq#(s(_x21), cons(activate(_x42), n__take(0, cons(activate(_x82), n__take(activate(_x83), activate(_x81)))))) 
eq#(n__s(_x31), cons(activate(_x42), n__take(0, take(_x71, _x72)))) 
eq#(s(_x21), cons(activate(_x42), n__take(0, n__take(_x81, _x82)))) 
Thus, the rule eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, take(_x71, _x72)))) is replaced by the following rules:
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__take(0, _x81))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, nil)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(n__0, take(_x71, _x72))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__take(s(_x83), cons(_x82, _x81)))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, cons(activate(_x82), n__take(activate(_x83), activate(_x81))))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(s(_x51), n__take(0, take(_x71, _x72))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__inf(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(inf(_x51), n__take(0, take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__length(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(length(_x51), n__take(0, take(_x71, _x72))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__take(_x71, _x72))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(0, take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__take(_x81, _x82))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, n__take(_x81, _x82))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x51, n__take(_x71, _x72))))) → eq#(s(_x21), cons(_x51, n__take(0, take(_x71, _x72))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(_x42, n__take(_x71, _x72))))) → eq#(n__s(_x31), cons(activate(_x42), n__take(0, take(_x71, _x72))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, n__take(_x71, _x72))))) → eq#(s(_x21), cons(0, n__take(0, take(_x71, _x72))))

Problem 26: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

eq#(n__s(n__take(s(n__0), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(take(_x41, _x42), n__take(0, activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__length(_x31))) → eq#(s(n__length(activate(_x31))), length(_x31))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(cons(_x82, n__take(_x101, _x102))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(cons(_x71, n__inf(s(_x71))), s(n__length(take(_x101, _x102))))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__0, n__take(_x71, _x72))))) → eq#(n__s(_x31), cons(0, n__take(n__take(_x71, _x72), take(_x71, _x72))))
eq#(n__s(n__length(_x31)), n__s(n__length(_x31))) → eq#(n__length(_x31), length(_x31))eq#(n__s(X), n__s(n__take(s(n__inf(_x71)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(n__inf(_x71), inf(_x71))))
eq#(n__s(n__take(s(n__0), cons(_x32, _x61))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(0, _x61)), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(_x21, cons(take(_x51, _x52), n__take(_x61, cons(_x81, n__inf(s(_x81))))))
eq#(n__s(n__take(s(_x33), cons(n__take(_x31, _x32), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(n__take(_x31, _x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(cons(_x31, n__inf(s(_x31))), length(_x31))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x71)), cons(_x51, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(_x51, n__take(cons(_x71, n__inf(s(_x71))), n__inf(_x81))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(0, cons(take(_x51, _x52), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(inf(_x21), cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, n__inf(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), n__inf(_x81))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(length(_x61), take(_x71, _x72))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__length(nil))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), s(n__length(0)))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__length(_x41))) → eq#(activate(X), n__length(_x41))
eq#(n__s(n__take(s(n__0), cons(_x41, n__0))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(_x41, n__take(0, 0)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(0, inf(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(_x42, n__s(_x71))))) → eq#(n__s(_x31), cons(activate(_x42), n__take(0, s(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(cons(_x82, _x81)))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(n__length(activate(_x81))))))
eq#(n__s(n__take(s(_x33), cons(n__length(_x41), n__0))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), 0)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, n__inf(_x71))))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(n__s(_x51), n__length(_x81))))) → eq#(length(_x21), cons(s(_x51), n__take(s(n__length(activate(_x71))), n__length(_x81))))eq#(n__s(n__take(s(n__s(_x51)), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(s(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(inf(_x61), n__inf(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, n__0)))) → eq#(inf(_x21), s(n__length(0)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(n__length(_x71), activate(_x41))))eq#(n__s(n__take(s(n__0), cons(n__inf(_x41), _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(inf(_x41), n__take(0, activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__0)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), 0)))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), s(_x71))))
eq#(n__s(X), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(activate(X), s(n__length(s(_x61))))eq#(n__s(n__take(s(_x33), cons(_x41, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(_x41, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(n__s(_x31), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(s(_x61), inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(0, _x41), n__take(_x71, _x72))))) → eq#(s(_x21), cons(nil, n__take(0, take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__take(s(n__inf(_x51)), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(inf(_x51), activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(0, cons(take(_x51, _x52), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(0, inf(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__0), cons(_x51, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(_x51, n__take(0, n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(s(_x21), cons(n__take(_x41, _x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(length(_x61), length(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(_x21, cons(n__s(_x41), n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__take(s(_x43), cons(_x42, _x41)), n__inf(_x71))))) → eq#(activate(X), cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(length(_x61), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), n__length(_x71))))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__0, n__take(_x61, _x62)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(0, n__take(activate(_x33), take(_x61, _x62))), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__take(s(_x33), cons(_x32, n__length(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), length(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__length(nil)), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(n__s(_x51), n__length(_x81))))) → eq#(0, cons(s(_x51), n__take(s(n__length(activate(_x71))), n__length(_x81))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x41)))) → eq#(activate(X), cons(n__s(_x41), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), n__inf(_x81))))eq#(n__s(n__0), n__s(n__take(s(n__length(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(0, cons(take(_x51, _x52), n__take(length(_x61), inf(_x71))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(0, cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(take(_x21, _x22), s(n__length(inf(_x61))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x81))))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(_x61, activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(0, n__length(_x81))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__take(0, _x41), n__inf(_x71))))) → eq#(activate(X), cons(nil, n__take(inf(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__length(_x51), n__inf(_x71))))) → eq#(activate(X), cons(length(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(s(_x33), cons(_x32, n__0))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), 0)), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(take(_x51, _x52), n__take(inf(_x61), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(n__inf(_x51), n__inf(_x71))))) → eq#(_x21, cons(inf(_x51), n__take(_x61, inf(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(_x32, n__length(_x61)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), length(_x61))), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__take(s(n__0), cons(n__inf(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(inf(_x41), n__take(0, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x71))))) → eq#(s(_x21), cons(s(_x51), n__take(0, length(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x41), _x41)))) → eq#(activate(X), cons(n__s(_x41), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x42, n__take(_x71, _x72))))) → eq#(_x21, cons(activate(_x42), n__take(0, take(_x71, _x72))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(n__length(activate(_x81)))), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(n__inf(_x71), n__s(n__length(activate(_x81))))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x41), n__length(_x71))))) → eq#(activate(X), cons(n__s(_x41), n__take(activate(_x43), length(_x71))))eq#(n__s(n__take(s(_x33), cons(n__s(_x41), _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(s(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(_x21, cons(s(_x51), n__take(length(_x61), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(0, activate(_x41))))
eq#(n__s(n__take(s(n__0), cons(n__s(_x41), n__0))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(s(_x41), n__take(0, 0)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(n__take(0, _x41), n__inf(_x71))))) → eq#(_x21, cons(nil, n__take(_x61, inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__inf(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(inf(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(length(_x61), _x71)))
eq#(n__s(X), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(cons(_x82, n__inf(_x101))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(n__inf(_x71), s(n__length(inf(_x101))))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), n__0)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), 0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x71)), cons(_x51, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(_x51, n__take(n__inf(_x71), n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(s(_x61), _x71)))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(inf(_x51), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__take(s(_x33), cons(_x32, n__s(_x61)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), s(_x61))), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(_x21, cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(activate(_x42), n__take(take(_x61, _x62), n__inf(_x81))))eq#(n__s(n__length(_x21)), n__s(n__length(_x41))) → eq#(length(_x21), n__length(_x41))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(0, cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(nil)), cons(_x51, n__s(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(0, n__s(_x81))))
eq#(n__s(n__take(s(n__0), cons(_x32, n__length(_x61)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(0, length(_x61))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(_x51, n__s(_x71))))) → eq#(n__inf(_x31), cons(_x51, n__take(_x61, s(_x71))))
eq#(n__s(n__take(0, _x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(nil, s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(take(_x51, _x52), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), length(_x71))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x61))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), _x61)), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x81))))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), n__length(_x81))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(_x43), cons(_x51, n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(_x51, n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(cons(_x31, n__inf(s(_x31))), cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(n__take(s(n__s(_x51)), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(s(_x51), activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(n__inf(_x71), length(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__0, n__0)))) → eq#(n__s(_x31), cons(0, n__take(n__take(_x71, _x72), 0)))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__take(_x101, _x102))))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(inf(_x61), s(n__length(take(_x101, _x102))))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(_x51, n__inf(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(_x61, inf(_x71))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(cons(_x31, n__inf(s(_x31))), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(0, cons(n__s(_x41), n__take(activate(_x43), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__take(_x81, _x82))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(0, n__take(_x81, _x82))))eq#(n__s(n__take(s(n__0), cons(_x32, n__0))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(0, 0)), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(cons(_x82, n__take(_x101, _x102))))))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(inf(_x61), s(n__length(take(_x101, _x102))))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(s(_x21), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(n__0, s(_x71))))eq#(n__s(X), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(activate(X), s(n__length(inf(_x61))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(take(_x61, _x62), n__length(_x81))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(0, activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(_x61, inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(cons(_x82, n__s(_x101))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(n__inf(_x71), s(n__length(s(_x101))))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__take(s(n__0), cons(_x32, n__0))), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(0, 0)), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__take(_x51, _x52), _x71)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__0), cons(n__length(cons(_x42, _x41)), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(s(n__length(activate(_x41))), n__take(0, n__inf(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(nil))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(n__take(_x71, _x72), 0)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), 0)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__inf(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(n__inf(_x31), cons(activate(_x42), n__take(_x61, cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(_x61, length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(n__0, n__take(0, s(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), 0)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(inf(_x61), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(take(_x21, _x22), s(n__length(length(_x61))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(n__inf(_x31), cons(s(_x51), n__take(nil, _x71)))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(n__inf(_x31), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(s(n__length(_x51)), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(length(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, _x71)))) → eq#(s(_x21), cons(0, n__take(activate(_x43), _x71)))
eq#(n__s(n__take(s(n__inf(_x51)), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(inf(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(length(_x61), _x71)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__take(_x71, _x72))))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__take(s(n__0), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(0, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__length(_x71)), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(n__length(_x71), n__length(_x81))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(cons(_x31, n__inf(s(_x31))), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(inf(_x61), length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(length(_x61), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__take(s(n__0), cons(_x32, n__s(_x61)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(0, s(_x61))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x51, n__s(_x81))))) → eq#(cons(_x31, n__inf(s(_x31))), cons(_x51, n__take(activate(_x43), n__s(_x81))))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__take(0, _x41), n__inf(_x71))))) → eq#(activate(X), cons(nil, n__take(0, inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(_x21, cons(activate(_x42), n__take(_x61, n__inf(_x81))))eq#(n__s(n__take(s(_x33), cons(_x32, n__inf(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), inf(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(take(_x61, _x62), n__s(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(s(_x21), cons(n__0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x71))))) → eq#(n__inf(_x31), cons(inf(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(nil, 0)))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(0, inf(_x71))))eq#(n__s(n__take(s(n__0), cons(n__s(_x41), _x61))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(s(_x41), n__take(0, _x61)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(length(_x21), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(n__0, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(nil))))) → eq#(cons(0, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(inf(_x61), 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__take(0, _x81))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(0, nil)))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(_x41, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(_x41, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(n__inf(_x31), cons(take(_x51, _x52), n__take(_x61, inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(nil, _x71)))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(take(_x21, _x22), s(n__length(s(_x61))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(n__take(s(_x33), cons(_x32, n__inf(_x61)))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), inf(_x61))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__length(nil)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), n__length(_x81))))) → eq#(0, cons(n__s(_x41), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__take(s(n__0), cons(n__s(_x41), _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(s(_x41), n__take(0, activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(nil, _x71)))
eq#(n__s(n__take(s(_x33), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(s(_x21), cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), n__length(_x81))))eq#(n__s(X), n__s(n__take(s(_x61), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(_x61, inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, n__take(_x71, _x72))))) → eq#(s(_x21), cons(0, n__take(0, take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(nil))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))
eq#(n__s(n__take(s(_x33), cons(n__length(nil), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(0, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(s(_x51), n__take(_x61, inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__0, _x41)))) → eq#(_x21, cons(0, n__take(length(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(s(_x61), inf(_x71))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(n__0, cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(0, _x31)), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(nil, cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__0), n__s(n__length(_x31))) → eq#(0, length(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__s(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(0, s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__inf(_x51), n__s(_x71))))) → eq#(s(_x21), cons(inf(_x51), n__take(0, s(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(Y)) → eq#(take(_x21, _x22), activate(Y))
eq#(n__s(n__take(s(n__take(_x51, _x52)), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(take(_x51, _x52), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(inf(_x61), cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__take(s(n__0), cons(_x41, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(_x41, n__take(0, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(_x51, n__s(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(_x61, n__s(_x81))))eq#(n__s(n__take(s(_x33), cons(n__0, _x31))), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(0, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(n__inf(_x71), length(_x71))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__0), cons(n__length(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(length(_x51), n__take(n__0, n__inf(_x81))))eq#(n__s(n__length(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), _x71)))) → eq#(length(_x21), cons(n__s(_x41), n__take(inf(_x61), _x71)))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(_x31, n__inf(s(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(inf(_x61), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(0, n__take(cons(_x71, n__inf(s(_x71))), s(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, n__s(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(s(n__length(activate(_x71))), n__s(_x81))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(cons(_x71, n__inf(s(_x71))), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__take(s(_x83), cons(_x82, _x81)))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(0, cons(activate(_x82), n__take(activate(_x83), activate(_x81))))))
eq#(n__s(n__take(s(_x33), cons(n__length(_x41), n__s(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), s(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(s(n__0), cons(n__s(_x31), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(n__s(_x31), n__take(0, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(0, _x31)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(nil, cons(s(_x51), n__take(n__inf(_x71), s(n__length(activate(_x81))))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(n__length(_x51), n__inf(_x71))))) → eq#(n__inf(_x31), cons(length(_x51), n__take(_x61, inf(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__0)) → eq#(n__s(_x31), n__0)eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, n__length(nil))))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), 0)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(inf(_x21), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__take(_x71, _x72))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), take(_x71, _x72))))
eq#(n__s(n__take(s(n__inf(_x51)), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(inf(_x51), activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x81))))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__take(s(n__length(_x51)), cons(n__0, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(0, n__take(length(_x51), activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(0, cons(n__take(_x41, _x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__length(_x21)), n__s(n__take(s(n__length(_x71)), cons(n__s(_x51), n__length(_x81))))) → eq#(length(_x21), cons(s(_x51), n__take(n__length(_x71), n__length(_x81))))
eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__take(s(n__length(_x71)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(activate(_x31))), cons(s(_x51), n__take(n__length(_x71), n__length(_x81))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), inf(_x71))))
eq#(n__s(n__take(s(n__0), cons(n__s(_x41), _x31))), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(cons(s(_x41), n__take(0, activate(_x31))), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__0, _x41)))) → eq#(n__s(_x31), cons(n__0, n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__take(0, _x81))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, nil)))eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), n__length(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), length(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__length(nil))))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), 0)))eq#(n__s(n__length(nil)), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), n__length(_x81))))) → eq#(0, cons(s(_x51), n__take(0, n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(length(_x61), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x41), n__inf(_x71))))) → eq#(inf(_x21), cons(cons(_x41, n__inf(s(_x41))), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(inf(_x21), cons(take(_x51, _x52), n__take(_x61, inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(n__0, n__inf(_x71))))) → eq#(n__inf(_x31), cons(0, n__take(_x61, inf(_x71))))eq#(n__s(n__take(s(_x51), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(_x51, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__0, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(0, n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(_x31))) → eq#(take(_x21, _x22), length(_x31))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), n__0)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), n__0)))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(_x61, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(n__0, inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(n__length(_x51), _x41)))) → eq#(_x21, cons(length(_x51), n__take(0, activate(_x41))))eq#(n__s(n__take(s(n__s(_x51)), cons(n__0, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(0, n__take(s(_x51), activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(s(_x61), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(length(_x61), n__inf(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__inf(_x101))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), s(n__length(inf(_x101))))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__inf(_x61)), cons(_x51, n__s(_x71))))) → eq#(n__inf(_x31), cons(_x51, n__take(inf(_x61), s(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__0, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(cons(0, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(inf(_x61), s(n__length(activate(_x81))))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(0, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), take(_x71, _x72))))
eq#(n__s(n__take(s(n__0), cons(n__length(_x41), n__0))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(0, 0)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__inf(_x71))))) → eq#(s(_x21), cons(0, n__take(n__inf(_x71), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__length(nil))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), 0)))eq#(n__s(n__length(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(length(_x21), cons(take(_x51, _x52), n__take(inf(_x61), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(0, inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(inf(_x21), cons(n__s(_x41), n__take(activate(_x43), _x71)))
eq#(n__s(n__take(0, _x31)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(nil, cons(activate(_x42), n__take(_x61, n__inf(_x81))))eq#(n__s(n__take(s(_x33), cons(n__length(cons(_x32, _x31)), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(s(n__length(activate(_x31))), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(n__inf(_x31), cons(_x51, n__take(take(_x61, _x62), s(_x71))))eq#(n__s(X), n__s(n__take(s(n__0), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(0, s(_x71))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(inf(_x61), activate(_x41))))eq#(n__s(n__length(_x31)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(n__length(_x31), cons(s(_x51), n__take(inf(_x61), _x71)))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(inf(_x61), s(n__length(activate(_x81))))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(cons(_x82, n__length(_x101))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(n__inf(_x71), s(n__length(length(_x101))))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), 0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(_x61, inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__length(_x21)), n__s(n__take(_x31, _x32))) → eq#(length(_x21), take(_x31, _x32))
eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(activate(_x31))), cons(s(_x51), n__take(0, n__length(_x81))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(_x51, n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(_x51, n__take(inf(_x61), n__inf(_x81))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__0, n__length(_x71))))) → eq#(n__s(_x31), cons(0, n__take(n__take(_x71, _x72), length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(n__0, _x61))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(0, n__take(activate(_x33), _x61)), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(length(_x61), n__inf(_x81))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, n__0)))) → eq#(n__s(_x31), cons(0, n__take(take(_x61, _x62), 0)))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(length(_x21), cons(s(_x51), n__take(activate(_x43), length(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(n__length(_x41), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(n__length(_x41), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(_x21, cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, n__length(_x71))))) → eq#(s(_x21), cons(0, n__take(activate(_x43), length(_x71))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(n__length(cons(_x42, _x41)), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(s(n__length(activate(_x41))), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(0, cons(s(_x51), n__take(activate(_x43), length(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x41), n__length(_x81))))) → eq#(inf(_x21), cons(n__s(_x41), n__take(activate(_x43), n__length(_x81))))eq#(n__s(n__inf(_x31)), n__s(n__length(nil))) → eq#(n__inf(_x31), 0)
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), n__length(_x81))))) → eq#(_x21, cons(n__s(_x41), n__take(length(_x61), n__length(_x81))))eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(activate(_x31))), cons(s(_x51), n__take(s(n__length(activate(_x71))), n__length(_x81))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(n__inf(_x31), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(s(_x33), cons(n__length(_x41), _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(length(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x41, _x42), _x71)))) → eq#(s(_x21), cons(n__take(_x41, _x42), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(s(n__0), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(0, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__0)))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(inf(_x61), s(n__length(0)))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(length(_x61), inf(_x71))))
eq#(n__s(n__length(nil)), n__s(n__length(_x31))) → eq#(0, length(_x31))eq#(n__s(n__length(cons(_x32, n__0))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(0)), cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), n__take(_x71, _x72))))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(n__length(_x51), n__inf(_x71))))) → eq#(_x21, cons(length(_x51), n__take(_x61, inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(cons(_x71, n__inf(s(_x71))), s(n__length(activate(_x81))))))eq#(n__s(n__0), n__s(n__take(s(_x61), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(_x61, _x71)))
eq#(n__s(n__take(s(_x33), cons(_x32, n__s(_x61)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), s(_x61))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), _x41)))) → eq#(n__s(_x31), cons(take(_x51, _x52), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(0, _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x61), cons(n__s(_x41), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(_x61, n__inf(_x81))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(0, length(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(n__0, n__s(_x81))))) → eq#(n__s(_x31), cons(0, n__take(n__0, n__s(_x81))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__take(_x71, _x72))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(n__take(s(_x51), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(_x51, activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(_x21, cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__inf(_x71))))) → eq#(s(_x21), cons(0, n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(_x21), cons(s(_x51), n__take(length(_x61), n__length(_x81))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x61)), cons(n__length(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(length(_x51), n__take(inf(_x61), n__inf(_x81))))
eq#(n__s(n__take(s(_x33), cons(n__length(_x41), _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(length(_x41), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__take(_x81, _x82))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), n__take(_x81, _x82))))
eq#(n__s(X), n__s(n__s(_x31))) → eq#(activate(X), s(_x31))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__0), cons(n__length(nil), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(0, n__take(0, n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), n__0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__length(_x71))))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(_x21, cons(take(_x51, _x52), n__take(inf(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__length(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), length(_x71))))eq#(n__s(n__0), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(0, cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(X), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(s(n__length(activate(_x71))), n__length(_x81))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__s(_x71))))) → eq#(n__s(_x31), cons(n__0, n__take(inf(_x61), s(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__s(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__take(s(_x83), cons(_x82, _x81)))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, cons(activate(_x82), n__take(activate(_x83), activate(_x81))))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(_x31, _x32))) → eq#(take(_x21, _x22), take(_x31, _x32))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(n__take(_x31, _x32), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x71))))) → eq#(cons(_x31, n__inf(s(_x31))), cons(activate(_x42), n__take(_x61, inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(nil, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__s(_x81))))) → eq#(s(_x21), cons(n__0, n__take(cons(_x71, n__inf(s(_x71))), n__s(_x81))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), length(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__0, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(0, n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), 0)))
eq#(n__s(n__0), n__s(n__take(_x31, _x32))) → eq#(0, take(_x31, _x32))eq#(n__s(n__take(s(n__0), cons(_x32, _x31))), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(0, activate(_x31))), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__0, n__0)))) → eq#(s(_x21), cons(0, n__take(nil, 0)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, n__s(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), s(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), s(n__length(activate(_x81))))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(s(_x61), activate(_x41))))eq#(n__s(n__take(0, _x31)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(nil, cons(activate(_x42), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x61), cons(n__length(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(length(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__length(_x71))))) → eq#(s(_x21), cons(0, n__take(n__inf(_x71), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__take(0, _x81))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), nil)))eq#(n__s(n__take(s(n__0), cons(_x32, n__0))), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(0, 0)), cons(s(_x51), n__take(nil, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__take(_x71, _x72))))) → eq#(s(_x21), cons(0, n__take(n__inf(_x71), take(_x71, _x72))))eq#(n__s(n__take(s(_x51), cons(n__0, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(0, n__take(_x51, activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(_x61, s(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(inf(_x21), cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__0, n__s(_x71))))) → eq#(n__s(_x31), cons(0, n__take(n__take(_x71, _x72), s(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(s(_x33), cons(n__s(_x41), _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(s(_x41), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__take(s(n__0), cons(_x32, n__inf(_x61)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(0, inf(_x61))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__take(_x91, _x92))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), s(n__length(n__take(_x91, _x92))))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(n__inf(_x71), length(_x71))))eq#(n__s(X), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(activate(X), s(n__length(length(_x61))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(n__inf(_x31), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(n__0, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(0, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(length(_x61), _x71)))
eq#(n__s(_x21), n__s(n__length(cons(_x42, _x41)))) → eq#(_x21, s(n__length(activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(cons(_x82, n__take(_x101, _x102))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(n__inf(_x71), s(n__length(take(_x101, _x102))))))
eq#(n__s(n__inf(_x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(_x31, n__inf(s(_x31))), s(n__length(activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(inf(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(0, n__length(_x81))))eq#(n__s(n__take(s(_x33), cons(n__0, n__0))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(0, n__take(activate(_x33), 0)), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__take(s(_x33), cons(_x32, n__0))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), 0)), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__take(s(_x33), cons(n__0, n__length(_x61)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(0, n__take(activate(_x33), length(_x61))), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(n__inf(_x51), n__inf(_x71))))) → eq#(n__inf(_x31), cons(inf(_x51), n__take(_x61, inf(_x71))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(nil, _x71)))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(n__inf(_x31), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(0, _x41), n__inf(_x71))))) → eq#(activate(X), cons(nil, n__take(activate(_x43), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__0, _x71)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__s(_x71))))) → eq#(n__s(_x31), cons(0, n__take(inf(_x61), s(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, n__length(_x61))))) → eq#(inf(_x21), s(n__length(length(_x61))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), n__0)))) → eq#(n__s(_x31), cons(n__length(_x41), n__take(take(_x61, _x62), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__0, _x71)))) → eq#(s(_x21), cons(0, n__take(inf(_x61), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(s(_x61), inf(_x71))))
eq#(n__s(n__0), n__s(n__take(s(n__0), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(0, _x71)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(0, _x71)), cons(n__0, _x41)))) → eq#(n__s(_x31), cons(0, n__take(nil, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(length(_x61), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, inf(_x71))))
eq#(n__s(n__take(s(n__inf(_x51)), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(inf(_x51), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(n__length(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(length(_x51), n__take(_x61, inf(_x71))))
eq#(n__s(n__0), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(s(_x61), _x71)))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__length(_x51), n__inf(_x71))))) → eq#(_x21, cons(length(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__0), cons(_x51, n__s(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(0, s(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(n__s(_x31), cons(take(_x51, _x52), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__s(_x41), n__length(_x81))))) → eq#(length(_x21), cons(n__s(_x41), n__take(activate(_x43), n__length(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(_x21, cons(s(_x51), n__take(inf(_x61), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(cons(_x82, n__length(_x101))))))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(inf(_x61), s(n__length(length(_x101))))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(_x21, cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71))))eq#(n__s(n__length(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(length(_x21), cons(take(_x51, _x52), n__take(0, inf(_x71))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(cons(_x82, _x81)))))) → eq#(n__take(_x31, _x32), cons(n__s(_x41), n__take(inf(_x61), s(n__length(activate(_x81))))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, 0)))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(length(_x21), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, _x101)))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(inf(_x61), s(n__length(_x101)))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(n__s(_x51), n__length(_x81))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(s(n__length(activate(_x71))), n__length(_x81))))
eq#(n__s(n__length(_x21)), n__s(n__length(nil))) → eq#(length(_x21), 0)eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, n__0)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), n__0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, n__0)))) → eq#(s(_x21), cons(n__0, n__take(take(_x61, _x62), 0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), n__s(n__length(activate(_x81))))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(activate(X), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(inf(_x61), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(length(_x61), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(n__take(_x41, _x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__inf(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(nil), _x41)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__length(_x71)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(n__length(_x71), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(s(_x61), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), n__take(_x71, _x72))))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(n__0, n__take(cons(_x71, n__inf(s(_x71))), s(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__inf(_x41), _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(inf(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x51, n__take(_x71, _x72))))) → eq#(s(_x21), cons(_x51, n__take(0, take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), _x41)))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(_x71))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(n__inf(_x71), length(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x51, n__s(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(inf(_x61), n__s(_x81))))
eq#(n__s(n__s(_x21)), n__s(_x31)) → eq#(s(_x21), _x31)eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(nil))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(inf(_x61), 0)))eq#(n__s(_x21), n__s(n__length(_x31))) → eq#(_x21, length(_x31))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(s(_x61), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__length(_x51), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(length(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(s(_x43), cons(_x42, _x41)), _x71)))) → eq#(s(_x21), cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(s(_x61), n__inf(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(length(_x61), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(inf(_x21), cons(0, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__0, _x41)))) → eq#(s(_x21), cons(n__0, n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(cons(_x82, _x101)))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(n__inf(_x71), s(n__length(_x101)))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x71)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(cons(_x71, n__inf(s(_x71))), inf(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__0), cons(_x51, n__s(_x71))))) → eq#(n__inf(_x31), cons(_x51, n__take(0, s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__0, n__length(_x71))))) → eq#(s(_x21), cons(0, n__take(n__take(_x71, _x72), length(_x71))))eq#(n__s(n__take(s(n__0), cons(_x32, _x61))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(0, _x61)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(_x51, n__take(length(_x61), n__inf(_x81))))
eq#(n__s(n__take(s(n__0), cons(_x32, n__0))), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(0, 0)), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(n__s(_x21)), n__s(n__s(_x31))) → eq#(s(_x21), s(_x31))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__0)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), 0)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(n__s(_x31), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(_x42, n__take(_x71, _x72))))) → eq#(n__s(_x31), cons(activate(_x42), n__take(0, take(_x71, _x72))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__0), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(0, cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__take(0, _x31)), n__s(n__take(s(n__inf(_x61)), cons(_x51, n__inf(_x81))))) → eq#(nil, cons(_x51, n__take(inf(_x61), n__inf(_x81))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(s(_x43), cons(_x42, _x41)), n__inf(_x81))))) → eq#(s(_x21), cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x42, n__length(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(length(_x61), length(_x71))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__take(_x71, _x72))))) → eq#(activate(X), cons(s(_x51), n__take(take(_x61, _x62), take(_x71, _x72))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(s(_x21), cons(n__take(_x41, _x42), n__take(_x61, n__inf(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x51, n__s(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(s(_x61), n__s(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__0, _x71)))) → eq#(n__s(_x31), cons(0, n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__inf(_x71)), cons(n__0, _x41)))) → eq#(n__s(_x31), cons(0, n__take(n__inf(_x71), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__s(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(s(_x61), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x41), _x71)))) → eq#(inf(_x21), cons(n__s(_x41), n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(n__length(cons(_x32, _x51))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(_x51)), cons(s(_x51), n__take(length(_x61), n__length(_x81))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__length(cons(_x92, _x91)))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), s(n__length(s(n__length(activate(_x91))))))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x41), n__inf(_x71))))) → eq#(_x21, cons(n__s(_x41), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__length(_x101))))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(inf(_x61), s(n__length(length(_x101))))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x61), cons(n__length(_x51), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(length(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x71)))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(s(n__0), cons(n__s(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(s(_x41), n__take(n__0, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__0)))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), 0)))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(s(_x61), inf(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x71)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), _x71)))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(length(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(n__s(_x51), n__length(_x81))))) → eq#(_x21, cons(s(_x51), n__take(s(n__length(activate(_x71))), n__length(_x81))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(length(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__inf(_x101))))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(inf(_x61), s(n__length(inf(_x101))))))
eq#(n__s(n__take(0, _x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(nil, cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(activate(_x42), n__take(inf(_x61), n__inf(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(_x61, activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(s(_x61), s(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__0, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(n__0, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x81))))) → eq#(n__inf(_x31), cons(_x51, n__take(length(_x61), n__s(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, n__length(_x71))))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(_x32, n__length(_x61)))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), length(_x61))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(_x61), activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__s(_x81))))) → eq#(s(_x21), cons(0, n__take(inf(_x61), n__s(_x81))))eq#(n__s(n__length(cons(_x32, n__s(_x51)))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(s(_x51))), cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__take(0, _x31)), n__s(n__take(s(_x43), cons(_x51, n__inf(_x81))))) → eq#(nil, cons(_x51, n__take(activate(_x43), n__inf(_x81))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__s(_x81))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), n__s(_x81))))
eq#(n__s(n__take(s(_x33), cons(n__s(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(s(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__s(_x81))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, n__s(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__length(nil))) → eq#(inf(_x21), n__0)
eq#(n__s(n__length(nil)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(n__0, cons(s(_x51), n__take(length(_x61), n__length(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, n__inf(_x61))))) → eq#(inf(_x21), s(n__length(inf(_x61))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(inf(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x41), n__length(_x71))))) → eq#(activate(X), cons(n__s(_x41), n__take(0, length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__inf(_x31))) → eq#(s(_x21), inf(_x31))
eq#(n__s(n__length(cons(_x32, n__take(_x51, _x52)))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(take(_x51, _x52))), cons(s(_x51), n__take(length(_x61), n__length(_x81))))eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), length(_x71))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(inf(_x61), n__inf(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__take(_x101, _x102))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), n__s(n__length(take(_x101, _x102))))))eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), _x71)))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(nil))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), 0)))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(length(_x21), cons(_x51, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(n__inf(_x31), cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(0, n__take(activate(_x43), s(_x71))))
eq#(n__s(n__take(s(n__length(_x51)), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(length(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), _x41)))) → eq#(inf(_x21), cons(length(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__0), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(inf(_x61), _x71)))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__s(_x61)), cons(n__length(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(length(_x51), n__take(s(_x61), n__inf(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(n__0, n__inf(_x71))))) → eq#(inf(_x21), cons(0, n__take(_x61, inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(0, n__take(n__inf(_x71), s(_x71))))eq#(n__s(n__take(s(n__0), cons(n__s(_x41), n__inf(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(s(_x41), n__take(0, inf(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(s(_x33), cons(n__length(_x31), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(n__length(_x31), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(s(n__inf(_x51)), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(inf(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__0), n__s(n__length(cons(_x42, _x41)))) → eq#(0, s(n__length(activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x51, n__s(_x81))))) → eq#(s(_x21), cons(_x51, n__take(activate(_x43), n__s(_x81))))
eq#(n__s(n__take(s(n__0), cons(n__take(_x41, _x42), n__0))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(0, 0)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(n__0, length(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), n__s(_x71))))) → eq#(s(_x21), cons(s(_x51), n__take(n__0, s(_x71))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__length(_x61)), cons(n__length(_x41), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(n__length(_x41), n__take(length(_x61), n__inf(_x81))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(_x61, length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(0, _x71)))
eq#(n__s(n__take(s(n__s(_x51)), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(s(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x51, n__s(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(inf(_x61), s(_x71))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(n__inf(_x71), s(n__length(activate(_x81))))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(nil))))) → eq#(activate(X), cons(s(_x51), n__take(inf(_x61), 0)))eq#(n__s(n__take(s(_x33), cons(n__inf(_x41), _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(inf(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(X), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(s(n__length(activate(_x71))), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(_x61, inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, n__length(nil))))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), 0)))eq#(n__s(n__take(s(n__0), cons(_x32, n__0))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(0, n__0)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(s(n__0), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x81))))) → eq#(cons(activate(_x32), n__take(0, activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), n__length(_x81))))
eq#(n__s(n__take(s(_x33), cons(_x32, n__take(_x61, _x62)))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), take(_x61, _x62))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__take(s(_x33), cons(_x32, _x61))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), _x61)), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__take(_x101, _x102))))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(inf(_x61), s(n__length(take(_x101, _x102))))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__0, n__0)))) → eq#(s(_x21), cons(0, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), 0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(cons(_x82, _x81)))))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(inf(_x61), s(n__length(activate(_x81))))))
eq#(n__s(n__take(s(n__0), cons(_x32, n__0))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(n__0, 0)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x41), _x71)))) → eq#(inf(_x21), cons(n__s(_x41), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__0, n__0)))) → eq#(s(_x21), cons(0, n__take(n__take(_x71, _x72), 0)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x51, n__inf(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(inf(_x61), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(n__take(s(_x43), cons(_x42, _x41)), n__inf(_x71))))) → eq#(_x21, cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(_x61, inf(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__0), cons(n__length(_x41), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(n__length(_x41), n__take(n__0, n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(n__0, take(_x71, _x72))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__take(s(n__0), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(n__0, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(_x31, _x32))) → eq#(s(_x21), take(_x31, _x32))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__length(_x101))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), n__s(n__length(length(_x101))))))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(inf(_x21), s(n__length(take(_x61, _x62))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__length(_x71))))) → eq#(s(_x21), cons(0, n__take(inf(_x61), length(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x61)))) → eq#(take(_x21, _x22), s(n__length(_x61)))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(_x51, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(_x51, n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__length(_x21)), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), n__length(_x81))))) → eq#(length(_x21), cons(s(_x51), n__take(0, n__length(_x81))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__s(_x101))))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(inf(_x61), s(n__length(s(_x101))))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, _x41)))) → eq#(s(_x21), cons(n__0, n__take(n__inf(_x71), activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x61))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), _x61)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__take(_x71, _x72))))) → eq#(n__s(_x31), cons(take(_x51, _x52), n__take(0, take(_x71, _x72))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(inf(_x21), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(s(n__length(activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(cons(_x31, n__inf(s(_x31))), cons(s(_x51), n__take(nil, _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x81))))) → eq#(inf(_x21), cons(inf(_x51), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(_x21), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x71))))) → eq#(_x21, cons(s(_x51), n__take(0, length(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(s(n__length(_x51)), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(length(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x41), n__length(cons(_x82, _x81)))))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(n__inf(_x71), s(n__length(activate(_x81))))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(nil))))) → eq#(activate(X), cons(s(_x51), n__take(0, 0)))eq#(n__s(n__length(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), _x71)))) → eq#(length(_x21), cons(s(_x51), n__take(cons(_x71, n__inf(s(_x71))), _x71)))
eq#(n__s(n__0), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(0, cons(n__take(_x41, _x42), n__take(inf(_x61), cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x81))))) → eq#(_x21, cons(s(_x51), n__take(activate(_x43), n__length(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x61)))) → eq#(inf(_x21), s(n__length(_x61)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__take(_x71, _x72))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__length(_x51), _x41)))) → eq#(_x21, cons(length(_x51), n__take(length(_x61), activate(_x41))))eq#(n__s(n__take(s(n__0), cons(n__length(_x41), _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(length(_x41), n__take(0, activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(_x21, cons(activate(_x42), n__take(_x61, cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__0), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(_x21, cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(X), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(nil, _x71)))eq#(n__s(n__s(_x21)), n__s(n__length(_x31))) → eq#(s(_x21), length(_x31))
eq#(n__s(_x21), n__s(n__take(_x31, _x32))) → eq#(_x21, take(_x31, _x32))eq#(n__s(n__0), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(0, cons(take(_x51, _x52), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__length(_x61)), cons(n__length(nil), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(0, n__take(length(_x61), n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__take(_x71, _x72))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(n__0, take(_x71, _x72))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(_x71)), cons(n__s(_x51), n__length(_x81))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(n__length(_x71), n__length(_x81))))eq#(n__s(_x21), n__s(n__take(s(n__0), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(0, inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__s(_x41), n__length(_x81))))) → eq#(_x21, cons(n__s(_x41), n__take(activate(_x43), n__length(_x81))))eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, _x41)))) → eq#(take(_x21, _x22), n__s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(n__s(_x51), n__length(_x81))))) → eq#(_x21, cons(s(_x51), n__take(n__length(_x71), n__length(_x81))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), _x71)))eq#(n__s(X), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(0, _x71)))
eq#(n__s(n__take(s(_x33), cons(_x32, n__inf(_x61)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), inf(_x61))), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__0), n__s(n__take(s(n__inf(_x71)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(0, cons(n__take(_x41, _x42), n__take(n__inf(_x71), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(s(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), _x71)))) → eq#(n__s(_x31), cons(take(_x51, _x52), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(s(_x21), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x41), n__length(_x81))))) → eq#(activate(X), cons(n__s(_x41), n__take(0, n__length(_x81))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x81))))) → eq#(cons(_x31, n__inf(s(_x31))), cons(_x51, n__take(length(_x61), n__s(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(inf(_x61), s(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(n__length(nil), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(0, n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__take(s(n__0), cons(n__s(_x41), _x31))), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(cons(s(_x41), n__take(0, activate(_x31))), cons(s(_x51), n__take(nil, _x71)))eq#(n__s(n__take(s(_x33), cons(_x32, n__take(_x61, _x62)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), take(_x61, _x62))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), n__length(nil))))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), 0)))eq#(n__s(_x21), n__s(n__take(s(n__0), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), s(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__take(0, _x31), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(nil, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, n__length(nil))))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, 0)))eq#(n__s(X), n__s(n__take(s(_x61), cons(n__s(_x41), n__length(_x81))))) → eq#(activate(X), cons(n__s(_x41), n__take(_x61, n__length(_x81))))
eq#(n__s(n__take(s(_x33), cons(_x32, n__0))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), 0)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__take(s(_x43), cons(_x42, _x41)), n__inf(_x71))))) → eq#(activate(X), cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(0, inf(_x71))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__take(0, _x41), n__inf(_x71))))) → eq#(0, cons(nil, n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__s(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x81))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), n__s(_x81))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x81))))) → eq#(length(_x21), cons(s(_x51), n__take(activate(_x43), n__length(_x81))))
eq#(n__s(n__length(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(length(_x21), s(n__length(activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x42, n__0)))) → eq#(_x21, cons(activate(_x42), n__take(0, 0)))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(_x61, inf(_x71))))eq#(n__s(n__0), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(length(_x61), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__take(s(_x93), cons(_x92, _x91)))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), s(n__length(cons(activate(_x92), n__take(activate(_x93), activate(_x91))))))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__s(_x41), n__length(_x81))))) → eq#(activate(X), cons(n__s(_x41), n__take(s(_x61), n__length(_x81))))
eq#(n__s(X), n__s(n__length(cons(_x42, _x41)))) → eq#(activate(X), n__s(n__length(activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(n__take(0, _x41), n__inf(_x81))))) → eq#(s(_x21), cons(nil, n__take(_x61, n__inf(_x81))))
eq#(n__s(n__take(s(_x33), cons(_x32, n__0))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), 0)), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, _x41)))) → eq#(n__s(_x31), cons(0, n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(n__take(s(n__0), cons(_x32, _x31))), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(0, activate(_x31))), cons(s(_x51), n__take(nil, _x71)))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(length(_x61), inf(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(n__s(_x51), n__s(_x71))))) → eq#(n__s(_x31), cons(s(_x51), n__take(0, s(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(n__s(_x31), cons(n__s(_x41), n__take(activate(_x43), _x71)))
eq#(n__s(n__take(s(_x33), cons(_x41, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(_x41, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__0), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(0, cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(n__0), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(0, cons(take(_x51, _x52), n__take(0, inf(_x71))))
eq#(n__s(n__take(0, _x31)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(nil, cons(s(_x51), n__take(length(_x61), n__length(_x81))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__s(_x41), n__length(_x81))))) → eq#(0, cons(n__s(_x41), n__take(activate(_x43), n__length(_x81))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(length(_x21), cons(n__take(_x41, _x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(0, _x41), n__inf(_x71))))) → eq#(s(_x21), cons(nil, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(_x41, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(_x41, n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(n__s(_x31), cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__0)))) → eq#(_x21, cons(_x51, n__take(length(_x61), 0)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__inf(_x51), _x71)))) → eq#(s(_x21), cons(inf(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(inf(_x61), inf(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(n__inf(_x31), cons(activate(_x42), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, n__take(_x71, _x72))))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), 0)))
eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__inf(_x61)), cons(n__0, _x41)))) → eq#(n__s(_x31), cons(0, n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(length(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__take(_x71, _x72))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(_x61, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), 0)))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(_x21, cons(_x51, n__take(length(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(activate(X), cons(_x51, n__take(activate(_x43), inf(_x71))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__0)))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), 0)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(inf(_x21), cons(take(_x51, _x52), n__take(inf(_x61), inf(_x71))))eq#(n__s(n__length(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x71))))) → eq#(length(_x21), cons(s(_x51), n__take(0, length(_x71))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(_x51, n__inf(_x71))))) → eq#(n__inf(_x31), cons(_x51, n__take(_x61, inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x71))))) → eq#(_x21, cons(inf(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(s(n__0), cons(n__0, n__0))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(0, n__take(0, 0)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(0, s(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(n__inf(_x31), cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x61), cons(n__inf(_x51), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(inf(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(0, n__inf(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(inf(_x21), cons(n__take(_x41, _x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, n__take(_x71, _x72))))) → eq#(s(_x21), cons(0, n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x71)), cons(_x51, n__s(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(n__length(_x71), n__s(_x81))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(activate(X), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(n__0, _x41)))) → eq#(_x21, cons(0, n__take(0, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(n__inf(_x71), _x71)))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), _x71)))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), s(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__take(0, _x91))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), s(n__length(nil)))))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, _x41)))) → eq#(inf(_x21), n__s(n__length(activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(take(_x51, _x52), n__take(0, inf(_x71))))eq#(n__s(n__take(s(n__0), cons(_x32, n__inf(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(0, inf(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__0, n__length(_x71))))) → eq#(s(_x21), cons(0, n__take(nil, length(_x71))))eq#(n__s(n__length(cons(_x32, n__length(_x51)))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(length(_x51))), cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__take(0, _x31)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(nil, cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(s(_x61), activate(_x41))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(length(_x21), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__0, n__inf(_x71))))) → eq#(s(_x21), cons(0, n__take(nil, inf(_x71))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), _x71)))) → eq#(_x21, cons(s(_x51), n__take(s(_x61), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(activate(_x43), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__length(_x41))) → eq#(inf(_x21), n__length(_x41))
eq#(n__s(X), n__s(n__take(s(_x61), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(_x61, n__length(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(n__take(s(_x43), cons(_x42, _x41)), n__inf(_x81))))) → eq#(s(_x21), cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__0), cons(_x51, n__s(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(0, n__s(_x81))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x42, _x71)))) → eq#(_x21, cons(activate(_x42), n__take(0, _x71)))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(length(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__length(_x51), n__s(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(0, s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(0, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(s(_x43), cons(_x42, _x41)), n__take(_x71, _x72))))) → eq#(s(_x21), cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(0, take(_x71, _x72))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x51, n__s(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(s(_x61), s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), n__length(_x81))))) → eq#(activate(X), cons(n__s(_x41), n__take(length(_x61), n__length(_x81))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, n__s(_x71))))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), s(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), n__0))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), 0)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(s(n__s(_x51)), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(s(_x51), activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(X), n__s(n__take(0, _x41))) → eq#(activate(X), nil)eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__0, _x41)))) → eq#(s(_x21), cons(n__0, n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), n__0)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), 0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__s(_x61)), cons(_x51, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(_x51, n__take(s(_x61), n__inf(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x41), n__inf(_x71))))) → eq#(inf(_x21), cons(n__inf(_x41), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__0), n__s(n__take(s(n__s(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(0, cons(take(_x51, _x52), n__take(s(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(s(_x43), cons(_x42, _x41)), n__inf(_x71))))) → eq#(s(_x21), cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(s(n__0), cons(n__0, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(0, n__take(0, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x42, n__s(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(0, s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x41), n__s(_x71))))) → eq#(s(_x21), cons(n__s(_x41), n__take(0, s(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(n__0, n__s(_x81))))) → eq#(n__s(_x31), cons(n__0, n__take(0, n__s(_x81))))eq#(n__s(n__take(s(n__take(_x51, _x52)), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(take(_x51, _x52), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(_x21, cons(n__take(_x41, _x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(s(n__0), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(0, activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__0, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(0, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(0, n__take(n__0, s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), _x71)))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(inf(_x61), n__s(n__length(activate(_x81))))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(_x61, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, _x41)))) → eq#(s(_x21), cons(n__0, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x41), n__length(_x81))))) → eq#(s(_x21), cons(n__s(_x41), n__take(activate(_x43), n__length(_x81))))
eq#(n__s(n__take(s(n__0), cons(n__0, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(0, n__take(0, activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(length(_x21), cons(s(_x51), n__take(activate(_x43), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(inf(_x21), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__take(s(n__0), cons(_x32, n__length(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(0, length(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(length(_x21), cons(n__s(_x41), n__take(activate(_x43), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(inf(_x51), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__length(nil)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(0, cons(s(_x51), n__take(inf(_x61), _x71)))eq#(n__s(n__take(0, _x31)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__take(_x101, _x102))))))) → eq#(nil, cons(s(_x51), n__take(inf(_x61), s(n__length(take(_x101, _x102))))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(cons(_x71, n__inf(s(_x71))), length(_x71))))eq#(n__s(X), n__s(_x31)) → eq#(activate(X), _x31)
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(0, _x41), _x71)))) → eq#(s(_x21), cons(nil, n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(s(_x33), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__s(_x61)), cons(_x51, n__inf(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(s(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, n__take(_x81, _x82))))) → eq#(s(_x21), cons(activate(_x42), n__take(0, n__take(_x81, _x82))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(nil, activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), n__length(_x81))))eq#(n__s(_x21), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(s(n__length(activate(_x71))), activate(_x41))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__take(s(_x43), cons(_x42, _x41)), n__inf(_x71))))) → eq#(0, cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, _x101)))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), s(n__length(_x101)))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x81))))) → eq#(inf(_x21), cons(s(_x51), n__take(activate(_x43), n__length(_x81))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, _x41)))) → eq#(activate(X), cons(_x51, n__take(s(_x61), activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__s(_x81))))) → eq#(n__s(_x31), cons(n__0, n__take(inf(_x61), n__s(_x81))))eq#(n__s(n__take(s(n__0), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(0, activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x41), n__length(_x81))))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(activate(_x43), n__length(_x81))))eq#(n__s(n__take(s(n__take(_x51, _x52)), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(take(_x51, _x52), activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x61), cons(n__0, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(0, n__take(_x61, n__inf(_x81))))eq#(n__s(n__take(s(n__take(_x51, _x52)), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(take(_x51, _x52), activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(cons(_x71, n__inf(s(_x71))), s(n__length(activate(_x81))))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__take(_x71, _x72))))) → eq#(s(_x21), cons(0, n__take(inf(_x61), take(_x71, _x72))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__length(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(length(_x51), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), n__length(_x81))))) → eq#(length(_x21), cons(n__s(_x41), n__take(length(_x61), n__length(_x81))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(activate(_x42), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__0, n__take(_x71, _x72))))) → eq#(s(_x21), cons(0, n__take(nil, take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, n__inf(_x71))))) → eq#(s(_x21), cons(0, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(s(n__0), cons(n__s(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(cons(s(_x41), n__take(0, activate(_x31))), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(s(n__0), cons(_x32, n__take(_x61, _x62)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(0, take(_x61, _x62))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__s(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(take(_x61, _x62), s(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(_x21, cons(take(_x51, _x52), n__take(0, inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__length(cons(_x42, n__s(_x61))))) → eq#(inf(_x21), s(n__length(s(_x61))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(length(_x51), n__take(take(_x61, _x62), n__inf(_x81))))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(activate(_x42), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, _x41)))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, _x41)))) → eq#(n__s(_x31), cons(_x51, n__take(nil, activate(_x41))))
eq#(n__s(n__take(s(n__0), cons(_x32, n__0))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(cons(activate(_x32), n__take(0, 0)), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(nil, _x71)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(_x61), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(n__s(_x31), cons(take(_x51, _x52), n__take(_x61, n__inf(_x81))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x81))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(activate(_x43), n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(_x61, inf(_x71))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__0), cons(_x51, n__inf(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(0, inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__0, n__take(_x71, _x72))))) → eq#(s(_x21), cons(0, n__take(n__take(_x71, _x72), take(_x71, _x72))))
eq#(n__s(n__length(nil)), n__s(n__take(s(n__length(_x71)), cons(n__s(_x51), n__length(_x81))))) → eq#(0, cons(s(_x51), n__take(n__length(_x71), n__length(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(take(_x61, _x62), s(_x71))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__length(cons(_x72, _x71))), cons(n__length(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(length(_x51), n__take(s(n__length(activate(_x71))), n__inf(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), 0)))
eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), n__length(_x81))))) → eq#(s(n__length(activate(_x31))), cons(n__s(_x41), n__take(length(_x61), n__length(_x81))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__s(_x61)), cons(_x51, n__s(_x71))))) → eq#(n__inf(_x31), cons(_x51, n__take(s(_x61), s(_x71))))
eq#(n__s(n__inf(_x31)), n__s(n__length(nil))) → eq#(cons(_x31, n__inf(s(_x31))), 0)eq#(n__s(X), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x71))))) → eq#(activate(X), cons(inf(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, n__length(_x81))))) → eq#(_x21, cons(_x51, n__take(activate(_x43), n__length(_x81))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__length(_x91))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), s(n__length(n__length(_x91))))))eq#(n__s(n__take(s(n__0), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(cons(activate(_x32), n__take(0, activate(_x31))), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(0, _x41), n__inf(_x81))))) → eq#(s(_x21), cons(nil, n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(s(_x21), cons(n__take(_x41, _x42), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__0), n__s(n__take(s(_x61), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(0, cons(take(_x51, _x52), n__take(_x61, inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(take(_x61, _x62), inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__inf(_x51), _x41)))) → eq#(_x21, cons(inf(_x51), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__0), cons(_x42, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(0, n__inf(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(inf(_x21), cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x41, _x42), _x41)))) → eq#(s(_x21), cons(n__take(_x41, _x42), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__0), cons(_x42, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(activate(_x42), n__take(0, n__inf(_x81))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(0, cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x41), n__take(_x71, _x72))))) → eq#(s(_x21), cons(n__length(_x41), n__take(take(_x61, _x62), take(_x71, _x72))))
eq#(n__s(n__take(s(n__0), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(nil))))) → eq#(cons(activate(_x32), n__take(0, activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), 0)))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, n__s(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(n__take(_x71, _x72), s(_x71))))
eq#(n__s(n__take(s(n__0), cons(n__s(_x41), n__length(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(s(_x41), n__take(0, length(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(0, _x31)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(nil, cons(s(_x51), n__take(inf(_x61), s(n__length(activate(_x81))))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x42, n__s(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(length(_x61), s(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(n__0, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(0, n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(n__take(s(_x33), cons(_x32, n__take(_x61, _x62)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), take(_x61, _x62))), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(cons(_x31, n__inf(s(_x31))), cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__take(s(n__length(_x51)), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(length(_x51), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(take(_x61, _x62), length(_x71))))eq#(n__s(n__take(s(_x51), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(_x51, activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(n__0, n__inf(_x71))))) → eq#(_x21, cons(0, n__take(_x61, inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(_x21, cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(inf(_x21), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__take(s(n__0), cons(_x32, _x31))), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(0, activate(_x31))), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x41, _x42), n__take(_x71, _x72))))) → eq#(s(_x21), cons(n__take(_x41, _x42), n__take(0, take(_x71, _x72))))eq#(n__s(X), n__s(n__take(s(_x43), cons(n__take(s(_x43), cons(_x42, _x41)), n__inf(_x71))))) → eq#(activate(X), cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(nil))))) → eq#(activate(X), cons(s(_x51), n__take(activate(_x43), 0)))eq#(n__s(n__0), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(0, cons(take(_x51, _x52), n__take(take(_x61, _x62), inf(_x71))))
eq#(n__s(n__take(s(n__0), cons(n__s(_x41), n__s(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(s(_x41), n__take(0, s(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__0, _x41)))) → eq#(_x21, cons(0, n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__take(s(_x33), cons(n__0, _x31))), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(0, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(cons(_x71, n__inf(s(_x71))), length(_x71))))eq#(n__s(X), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(cons(_x71, n__inf(s(_x71))), length(_x71))))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(length(_x61), inf(_x71))))eq#(n__s(n__take(s(n__0), cons(n__s(_x41), _x31))), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(cons(s(_x41), n__take(0, activate(_x31))), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(nil, 0)))
eq#(n__s(X), n__s(n__length(cons(_x42, n__0)))) → eq#(activate(X), s(n__length(0)))eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), n__length(_x81))))) → eq#(activate(X), cons(n__s(_x41), n__take(take(_x61, _x62), n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(0, activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(_x71))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(cons(_x71, n__inf(s(_x71))), length(_x71))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(0, n__inf(_x81))))eq#(n__s(n__take(s(n__take(_x51, _x52)), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(take(_x51, _x52), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(take(_x51, _x52), n__take(activate(_x43), n__inf(_x81))))
eq#(n__s(X), n__s(n__take(_x41, _x42))) → eq#(activate(X), n__take(_x41, _x42))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(n__take(_x51, _x52), _x41)))) → eq#(_x21, cons(take(_x51, _x52), n__take(0, activate(_x41))))
eq#(n__s(n__take(s(_x51), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(_x51, activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__s(_x61)), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(s(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), _x71)))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(inf(_x61), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(s(_x61), s(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__s(_x41), _x71)))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(activate(_x43), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, n__length(nil))))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), 0)))eq#(n__s(n__take(s(n__s(_x51)), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(s(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(s(n__length(activate(_x31))), cons(s(_x51), n__take(inf(_x61), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__0, _x41)))) → eq#(s(_x21), cons(n__0, n__take(nil, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), n__0)))) → eq#(activate(X), cons(s(_x51), n__take(take(_x61, _x62), 0)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(0, inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), n__inf(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), inf(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__length(nil))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), 0)))
eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(_x21, cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(s(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), s(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), n__length(_x81))))) → eq#(_x21, cons(s(_x51), n__take(0, n__length(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), _x71)))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(n__s(_x41), _x71)))) → eq#(_x21, cons(n__s(_x41), n__take(_x61, _x71)))
eq#(n__s(n__take(s(n__0), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(0, activate(_x31))), cons(n__s(_x41), n__take(cons(_x71, n__inf(s(_x71))), length(_x71))))eq#(n__s(n__length(_x21)), n__s(Y)) → eq#(length(_x21), activate(Y))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__0, n__inf(_x71))))) → eq#(s(_x21), cons(0, n__take(n__take(_x71, _x72), inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(cons(_x71, n__inf(s(_x71))), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(inf(_x21), cons(activate(_x42), n__take(_x61, n__inf(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(inf(_x21), cons(activate(_x42), n__take(_x61, cons(_x81, n__inf(s(_x81))))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x51, _x41)))) → eq#(s(_x21), cons(_x51, n__take(n__take(_x71, _x72), activate(_x41))))eq#(n__s(n__take(s(n__inf(_x51)), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(inf(_x51), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(cons(_x82, n__0)))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(n__inf(_x71), s(n__length(0)))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(inf(_x21), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x51, n__s(_x81))))) → eq#(n__inf(_x31), cons(_x51, n__take(activate(_x43), n__s(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(inf(_x61), n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(n__0, n__take(n__inf(_x71), s(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x41), _x71)))) → eq#(inf(_x21), cons(n__s(_x41), n__take(nil, _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(_x42, _x41)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__0, activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(0, inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x71))))) → eq#(inf(_x21), cons(s(_x51), n__take(0, length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(_x81))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__0, _x71)))) → eq#(s(_x21), cons(0, n__take(n__take(_x71, _x72), _x71)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x51, n__inf(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(length(_x61), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x71)), cons(_x51, _x71)))) → eq#(_x21, cons(_x51, n__take(n__length(_x71), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__length(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(length(_x51), n__take(0, take(_x71, _x72))))
eq#(n__s(n__length(cons(_x32, _x31))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(n__s(n__length(activate(_x31))), cons(s(_x51), n__take(length(_x61), n__length(_x81))))eq#(n__s(X), n__s(n__take(s(n__length(_x61)), cons(_x42, _x41)))) → eq#(activate(X), cons(activate(_x42), n__take(length(_x61), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(n__inf(_x71), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(activate(_x43), length(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__s(_x61)), cons(_x51, n__length(_x71))))) → eq#(_x21, cons(_x51, n__take(s(_x61), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(inf(_x61), n__inf(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x51, n__inf(_x81))))) → eq#(inf(_x21), cons(_x51, n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__0)))) → eq#(s(_x21), cons(0, n__take(n__inf(_x71), 0)))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), length(_x71))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(n__0, n__inf(_x71))))) → eq#(_x21, cons(0, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), n__take(_x61, _x62)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), take(_x61, _x62))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x31)), n__s(n__0)) → eq#(n__s(_x31), 0)
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__0)))) → eq#(take(_x21, _x22), s(n__length(0)))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, n__0)))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, n__s(_x81))))) → eq#(s(_x21), cons(n__0, n__take(n__inf(_x71), n__s(_x81))))eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x41), n__length(_x81))))) → eq#(take(_x21, _x22), cons(n__s(_x41), n__take(length(_x61), n__length(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(cons(_x71, n__inf(s(_x71))), activate(_x41))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x61)), cons(_x51, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(_x51, n__take(inf(_x61), n__inf(_x81))))eq#(n__s(n__length(cons(_x32, n__inf(_x51)))), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(s(n__length(inf(_x51))), cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(_x21), n__s(Y)) → eq#(_x21, activate(Y))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__0)))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), s(n__length(0)))))
eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x42, n__length(_x71))))) → eq#(_x21, cons(activate(_x42), n__take(0, length(_x71))))eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(cons(_x82, _x81)))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), s(n__length(activate(_x81))))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(0, cons(activate(_x42), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x71))))) → eq#(inf(_x21), cons(s(_x51), n__take(activate(_x43), length(_x71))))
eq#(n__s(n__take(s(n__take(_x51, _x52)), cons(n__0, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(0, n__take(take(_x51, _x52), activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(_x42, n__inf(_x71))))) → eq#(cons(_x31, n__inf(s(_x31))), cons(activate(_x42), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(activate(X), cons(s(_x51), n__take(0, s(n__length(activate(_x81))))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(_x42, _x41)))) → eq#(_x21, cons(activate(_x42), n__take(n__0, activate(_x41))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), _x41)))) → eq#(n__s(_x31), cons(length(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(s(_x61), n__length(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(cons(_x42, _x41)), _x41)))) → eq#(s(_x21), cons(s(n__length(activate(_x41))), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(0, activate(_x41))))
eq#(n__s(n__0), n__s(Y)) → eq#(0, activate(Y))eq#(n__s(n__take(s(_x51), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(_x51, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(s(_x43), cons(_x42, _x41)), _x41)))) → eq#(s(_x21), cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__0, n__0)))) → eq#(s(_x21), cons(0, n__take(inf(_x61), 0)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__length(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(length(_x51), n__take(nil, take(_x71, _x72))))eq#(n__s(_x21), n__s(n__take(s(n__0), cons(n__s(_x51), _x71)))) → eq#(_x21, cons(s(_x51), n__take(0, _x71)))
eq#(n__s(n__0), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(0, cons(n__take(_x41, _x42), n__take(inf(_x61), n__inf(_x81))))eq#(n__s(n__take(s(_x51), cons(_x32, _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(_x51, activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x41)))) → eq#(_x21, cons(s(_x51), n__take(length(_x61), activate(_x41))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(inf(_x61), activate(_x41))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(inf(_x21), cons(take(_x51, _x52), n__take(0, inf(_x71))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(activate(X), cons(s(_x51), n__take(inf(_x61), s(n__length(activate(_x81))))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__take(_x51, _x52), _x71)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(nil, _x71)))eq#(n__s(n__take(_x31, _x32)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__take(_x31, _x32), s(n__length(activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(_x21, cons(activate(_x42), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__take(0, _x31)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(nil, cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(activate(X), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(_x71))))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(X), n__s(n__length(cons(_x42, _x61)))) → eq#(activate(X), s(n__length(_x61)))eq#(n__s(n__length(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), _x71)))) → eq#(length(_x21), cons(s(_x51), n__take(n__inf(_x71), _x71)))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__length(_x51), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(length(_x51), n__take(activate(_x43), n__inf(_x81))))eq#(n__s(n__take(s(_x33), cons(_x32, _x61))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), _x61)), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__s(_x101))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(inf(_x61), s(n__length(s(_x101))))))eq#(n__s(n__take(s(n__0), cons(n__inf(_x41), n__0))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(inf(_x41), n__take(0, 0)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, n__take(_x71, _x72))))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), take(_x71, _x72))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x81))))) → eq#(activate(X), cons(n__s(_x41), n__take(inf(_x61), n__length(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(n__0), n__s(n__take(s(n__inf(_x71)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(0, cons(n__take(_x41, _x42), n__take(cons(_x71, n__inf(s(_x71))), inf(_x71))))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x42, _x71)))) → eq#(_x21, cons(activate(_x42), n__take(length(_x61), _x71)))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(_x61, activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), _x41)))) → eq#(_x21, cons(s(_x51), n__take(0, activate(_x41))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__s(_x51), n__length(_x81))))) → eq#(0, cons(s(_x51), n__take(activate(_x43), n__length(_x81))))eq#(n__s(n__take(s(_x33), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__take(s(_x33), cons(n__0, n__inf(_x61)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(0, n__take(activate(_x33), inf(_x61))), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(X), n__s(n__take(s(_x43), cons(n__0, n__inf(_x71))))) → eq#(activate(X), cons(0, n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(cons(_x82, _x81)))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(n__inf(_x71), s(n__length(activate(_x81))))))
eq#(n__s(n__inf(_x21)), n__s(Y)) → eq#(inf(_x21), activate(Y))eq#(n__s(n__take(s(n__0), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(cons(_x82, _x81)))))) → eq#(cons(activate(_x32), n__take(0, activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), s(n__length(activate(_x81))))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x61), cons(_x51, n__s(_x71))))) → eq#(s(_x21), cons(_x51, n__take(_x61, s(_x71))))eq#(n__s(n__take(s(_x33), cons(n__length(_x41), _x61))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), _x61)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(s(n__0), cons(n__0, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(0, n__take(0, activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), length(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__0, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(cons(0, n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(inf(_x61), n__length(_x81))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, _x71)))) → eq#(n__s(_x31), cons(_x51, n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__take(_x51, _x52), _x71)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(_x42, _x71)))) → eq#(s(_x21), cons(activate(_x42), n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(n__take(s(_x33), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(nil, _x71)))eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__inf(_x81))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x81))))) → eq#(inf(_x21), cons(inf(_x51), n__take(activate(_x43), cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__take(_x71, _x72))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), take(_x71, _x72))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(length(_x21), cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71))))eq#(n__s(n__take(s(_x33), cons(n__length(_x41), n__length(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), length(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(s(_x33), cons(_x32, n__s(_x61)))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), s(_x61))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(_x61), cons(_x42, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(activate(_x42), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x61)), cons(_x42, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(inf(_x61), n__inf(_x81))))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(_x21, cons(n__take(_x41, _x42), n__take(_x61, inf(_x71))))
eq#(n__s(n__inf(_x31)), n__s(n__length(_x31))) → eq#(n__inf(_x31), length(_x31))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(s(_x21), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(s(n__take(_x51, _x52)), cons(n__length(_x41), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(take(_x51, _x52), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(activate(X), cons(s(_x51), n__take(inf(_x61), n__length(_x81))))
eq#(n__s(n__take(s(_x33), cons(n__take(s(_x33), cons(_x32, _x31)), _x31))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(s(n__0), cons(_x32, n__take(_x61, _x62)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(0, take(_x61, _x62))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(activate(_x42), n__take(take(_x61, _x62), n__inf(_x81))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(_x61, inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__length(nil)), cons(n__s(_x51), n__length(_x81))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(0, n__length(_x81))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(0, _x71)), cons(_x51, n__s(_x71))))) → eq#(n__s(_x31), cons(_x51, n__take(nil, s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__length(nil))))) → eq#(s(_x21), cons(_x51, n__take(take(_x61, _x62), 0)))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(s(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x71))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(0, length(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, _x41)))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(0, cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__length(_x71))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), length(_x71))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), _x71)))) → eq#(length(_x21), cons(s(_x51), n__take(length(_x61), _x71)))eq#(n__s(n__take(s(n__inf(_x51)), cons(n__0, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(0, n__take(inf(_x51), activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(s(_x51), n__take(0, take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__s(_x61)), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(s(_x61), n__inf(_x81))))
eq#(n__s(X), n__s(n__0)) → eq#(activate(X), 0)eq#(n__s(n__take(s(_x33), cons(n__0, n__s(_x61)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(0, n__take(activate(_x33), s(_x61))), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(_x51, _x52), n__length(_x71))))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(take(_x61, _x62), length(_x71))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(nil))))) → eq#(n__s(_x31), cons(activate(_x42), n__take(take(_x61, _x62), 0)))
eq#(n__s(X), n__s(n__take(s(_x43), cons(_x42, n__length(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(activate(_x43), length(_x71))))eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), _x61))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), _x61)), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x42, n__take(_x71, _x72))))) → eq#(_x21, cons(activate(_x42), n__take(length(_x61), take(_x71, _x72))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(activate(_x42), n__take(length(_x61), n__inf(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__length(_x61)), cons(_x42, n__inf(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(length(_x61), inf(_x71))))eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), n__s(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), s(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__length(cons(_x42, _x41)))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), s(n__length(activate(_x41))))eq#(n__s(n__take(s(_x33), cons(n__inf(_x41), _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(inf(_x41), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(take(_x21, _x22), s(n__length(take(_x61, _x62))))eq#(n__s(n__take(0, _x31)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__length(_x101))))))) → eq#(nil, cons(s(_x51), n__take(inf(_x61), s(n__length(length(_x101))))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x61), cons(_x51, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(_x51, n__take(_x61, n__inf(_x81))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__length(_x61)), cons(n__length(cons(_x42, _x41)), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(s(n__length(activate(_x41))), n__take(length(_x61), n__inf(_x81))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(_x42, _x41)))) → eq#(inf(_x21), cons(activate(_x42), n__take(inf(_x61), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(_x42, n__length(_x71))))) → eq#(s(_x21), cons(activate(_x42), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), length(_x71))))
eq#(n__s(n__0), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(n__0, cons(s(_x51), n__take(activate(_x43), _x71)))eq#(n__s(n__take(s(_x33), cons(n__s(_x41), _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(s(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__take(s(n__s(_x51)), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(s(_x51), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))eq#(n__s(X), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(inf(_x61), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__0, _x71)))) → eq#(s(_x21), cons(0, n__take(nil, _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__inf(_x51), _x41)))) → eq#(s(_x21), cons(inf(_x51), n__take(activate(_x43), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__inf(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(inf(_x51), n__take(0, take(_x71, _x72))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__take(_x51, _x52), _x41)))) → eq#(s(_x21), cons(take(_x51, _x52), n__take(nil, activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(_x21, cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(inf(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__s(_x61)), cons(_x42, n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(activate(_x42), n__take(s(_x61), n__inf(_x81))))eq#(n__s(X), n__s(n__take(s(_x61), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(_x61, _x71)))
eq#(n__s(n__take(s(n__length(_x51)), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(length(_x51), activate(_x31))), cons(s(_x51), n__take(inf(_x61), length(_x71))))eq#(n__s(n__take(s(_x33), cons(_x32, n__s(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(activate(_x33), s(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(X), n__s(n__take(s(n__inf(_x71)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(n__inf(_x71), inf(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__0, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(0, n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__s(_x51), n__length(_x71))))) → eq#(activate(X), cons(s(_x51), n__take(s(_x61), length(_x71))))eq#(n__s(n__take(s(_x33), cons(_x32, n__take(_x61, _x62)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), take(_x61, _x62))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, _x41)))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), activate(_x41))))eq#(n__s(n__0), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(n__0, cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(_x32, n__inf(_x61)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), inf(_x61))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__length(nil)), cons(n__length(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(length(_x51), n__take(0, n__inf(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__length(_x51), n__take(s(_x83), cons(_x82, _x81)))))) → eq#(s(_x21), cons(length(_x51), n__take(take(_x61, _x62), cons(activate(_x82), n__take(activate(_x83), activate(_x81))))))eq#(n__s(n__s(_x31)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__0, n__inf(_x71))))) → eq#(n__s(_x31), cons(0, n__take(n__take(_x71, _x72), inf(_x71))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x51), n__length(cons(_x82, n__length(_x101))))))) → eq#(take(_x21, _x22), cons(s(_x51), n__take(cons(_x71, n__inf(s(_x71))), s(n__length(length(_x101))))))eq#(n__s(n__take(s(_x33), cons(n__length(_x41), n__take(_x61, _x62)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), take(_x61, _x62))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(s(_x33), cons(_x32, _x31))), n__s(n__take(s(_x61), cons(n__s(_x41), n__inf(_x81))))) → eq#(cons(activate(_x32), n__take(activate(_x33), activate(_x31))), cons(n__s(_x41), n__take(_x61, n__inf(_x81))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(take(_x21, _x22), cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__0, _x71)))) → eq#(s(_x21), cons(0, n__take(n__inf(_x71), _x71)))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__take(_x51, _x52), _x41)))) → eq#(_x21, cons(take(_x51, _x52), n__take(length(_x61), activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), _x71)))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__inf(_x81))))) → eq#(take(_x21, _x22), cons(_x51, n__take(take(_x61, _x62), n__inf(_x81))))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(_x21, cons(n__take(_x41, _x42), n__take(_x61, n__inf(_x81))))eq#(n__s(_x21), n__s(n__take(s(_x61), cons(n__take(s(_x43), cons(_x42, _x41)), n__inf(_x81))))) → eq#(_x21, cons(cons(activate(_x42), n__take(activate(_x43), activate(_x41))), n__take(_x61, n__inf(_x81))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__length(_x61)), cons(_x51, n__s(_x71))))) → eq#(n__inf(_x31), cons(_x51, n__take(length(_x61), s(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(_x31, _x32))) → eq#(inf(_x21), take(_x31, _x32))
eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x51), n__length(cons(_x82, n__length(_x101))))))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(inf(_x61), s(n__length(length(_x101))))))eq#(n__s(X), n__s(n__take(s(n__0), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(0, _x71)))
eq#(n__s(n__length(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(length(_x21), cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__0), n__s(n__take(s(n__0), cons(n__s(_x51), n__length(_x71))))) → eq#(0, cons(s(_x51), n__take(0, length(_x71))))
eq#(n__s(n__take(s(n__0), cons(_x32, n__s(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(activate(_x32), n__take(0, s(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(X), n__s(n__take(s(n__take(0, _x71)), cons(n__s(_x51), _x41)))) → eq#(activate(X), cons(s(_x51), n__take(nil, activate(_x41))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, _x41)))) → eq#(s(_x21), cons(0, n__take(0, activate(_x41))))eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__inf(_x71))))) → eq#(_x21, cons(s(_x51), n__take(length(_x61), inf(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(cons(_x82, _x81)))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), s(n__length(activate(_x81))))))eq#(n__s(n__take(s(_x33), cons(n__length(_x41), _x31))), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x81))))) → eq#(cons(length(_x41), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(_x61, n__inf(_x81))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(_x51, n__s(_x71))))) → eq#(activate(X), cons(_x51, n__take(take(_x61, _x62), s(_x71))))eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x43), cons(_x51, n__inf(_x71))))) → eq#(take(_x21, _x22), cons(_x51, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(_x32, n__length(_x61)))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(activate(_x33), length(_x61))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__s(_x51), n__s(_x81))))) → eq#(s(_x21), cons(s(_x51), n__take(0, n__s(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__length(nil))))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), n__0)))eq#(n__s(_x21), n__s(n__take(s(n__length(nil)), cons(n__inf(_x51), _x41)))) → eq#(_x21, cons(inf(_x51), n__take(0, activate(_x41))))
eq#(n__s(X), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x41), _x71)))) → eq#(activate(X), cons(n__s(_x41), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__take(s(n__0), cons(_x41, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(_x41, n__take(0, activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(inf(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(n__0, n__inf(_x71))))) → eq#(inf(_x21), cons(0, n__take(activate(_x43), inf(_x71))))
eq#(n__s(n__take(s(_x33), cons(n__length(_x41), n__inf(_x61)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(length(_x41), n__take(activate(_x33), inf(_x61))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), n__0)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), 0)))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__0), cons(n__inf(_x51), n__inf(_x71))))) → eq#(inf(_x21), cons(inf(_x51), n__take(0, inf(_x71))))eq#(n__s(n__s(_x31)), n__s(Y)) → eq#(n__s(_x31), activate(Y))
eq#(n__s(_x21), n__s(n__take(s(n__length(_x61)), cons(_x42, n__0)))) → eq#(_x21, cons(activate(_x42), n__take(length(_x61), 0)))eq#(n__s(n__take(s(_x33), cons(n__take(_x41, _x42), _x31))), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(cons(take(_x41, _x42), n__take(activate(_x33), activate(_x31))), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x61), cons(n__s(_x51), n__inf(_x71))))) → eq#(n__inf(_x31), cons(s(_x51), n__take(_x61, inf(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__length(_x71)), cons(n__length(_x51), n__inf(_x81))))) → eq#(n__take(_x31, _x32), cons(length(_x51), n__take(n__length(_x71), n__inf(_x81))))
eq#(n__s(n__length(_x21)), n__s(n__take(s(_x43), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(length(_x21), cons(take(_x51, _x52), n__take(activate(_x43), inf(_x71))))eq#(n__s(n__take(_x31, _x32)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(n__take(_x31, _x32), cons(s(_x51), n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__take(0, _x41), _x41)))) → eq#(s(_x21), cons(nil, n__take(take(_x61, _x62), activate(_x41))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(s(_x73), cons(_x72, _x71))), cons(n__length(_x51), n__take(_x71, _x72))))) → eq#(s(_x21), cons(length(_x51), n__take(cons(activate(_x72), n__take(activate(_x73), activate(_x71))), take(_x71, _x72))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x43), cons(_x42, n__s(_x71))))) → eq#(inf(_x21), cons(activate(_x42), n__take(activate(_x43), s(_x71))))eq#(n__s(X), n__s(n__length(cons(_x42, n__take(_x61, _x62))))) → eq#(activate(X), s(n__length(take(_x61, _x62))))
eq#(n__s(X), n__s(n__take(s(n__inf(_x71)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(activate(X), cons(n__take(_x41, _x42), n__take(cons(_x71, n__inf(s(_x71))), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(_x61), cons(_x51, n__s(_x71))))) → eq#(inf(_x21), cons(_x51, n__take(_x61, s(_x71))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__s(_x51), _x41)))) → eq#(s(_x21), cons(s(_x51), n__take(activate(_x43), activate(_x41))))eq#(n__s(n__inf(_x31)), n__s(n__length(cons(_x42, _x41)))) → eq#(n__inf(_x31), s(n__length(activate(_x41))))
eq#(n__s(X), n__s(n__take(s(_x61), cons(n__s(_x51), _x71)))) → eq#(activate(X), cons(s(_x51), n__take(_x61, _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(_x43), cons(n__0, n__0)))) → eq#(s(_x21), cons(0, n__take(activate(_x43), 0)))
eq#(n__s(n__take(s(n__length(_x51)), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(length(_x51), activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(0, n__take(n__take(_x71, _x72), s(_x71))))
eq#(n__s(n__s(_x31)), n__s(n__take(s(n__0), cons(n__0, n__s(_x71))))) → eq#(n__s(_x31), cons(0, n__take(0, s(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__0), cons(n__0, n__s(_x81))))) → eq#(s(_x21), cons(n__0, n__take(n__0, n__s(_x81))))
eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__s(_x51), _x71)))) → eq#(s(_x21), cons(s(_x51), n__take(n__take(_x71, _x72), _x71)))eq#(n__s(n__inf(_x31)), n__s(n__take(s(_x43), cons(n__inf(_x51), n__inf(_x71))))) → eq#(cons(_x31, n__inf(s(_x31))), cons(inf(_x51), n__take(activate(_x43), inf(_x71))))
eq#(n__s(X), n__s(n__take(s(n__0), cons(_x42, n__inf(_x71))))) → eq#(activate(X), cons(activate(_x42), n__take(0, inf(_x71))))eq#(n__s(_x21), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x41)))) → eq#(_x21, cons(s(_x51), n__take(take(_x61, _x62), activate(_x41))))
eq#(n__s(_x21), n__s(n__take(s(_x61), cons(n__take(0, _x41), n__inf(_x81))))) → eq#(_x21, cons(nil, n__take(_x61, n__inf(_x81))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x71, _x72)), cons(n__length(_x51), _x41)))) → eq#(s(_x21), cons(length(_x51), n__take(n__take(_x71, _x72), activate(_x41))))
eq#(n__s(n__take(_x21, _x22)), n__s(n__take(s(_x61), cons(n__take(_x51, _x52), n__inf(_x81))))) → eq#(take(_x21, _x22), cons(take(_x51, _x52), n__take(_x61, n__inf(_x81))))eq#(n__s(X), n__s(n__take(s(n__s(_x61)), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(s(_x61), inf(_x71))))
eq#(n__s(X), n__s(n__inf(_x31))) → eq#(activate(X), inf(_x31))eq#(n__s(n__length(_x31)), n__s(n__take(s(n__length(_x61)), cons(n__s(_x51), n__length(_x81))))) → eq#(n__length(_x31), cons(s(_x51), n__take(length(_x61), n__length(_x81))))
eq#(n__s(X), n__s(n__length(nil))) → eq#(activate(X), 0)eq#(n__s(X), n__s(n__take(s(_x61), cons(n__take(_x51, _x52), n__inf(_x71))))) → eq#(activate(X), cons(take(_x51, _x52), n__take(_x61, inf(_x71))))
eq#(n__s(n__take(s(n__0), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x61)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(n__0, activate(_x31))), cons(n__s(_x41), n__take(inf(_x61), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(n__0, _x71)))) → eq#(s(_x21), cons(0, n__take(take(_x61, _x62), _x71)))
eq#(n__s(n__take(s(n__0), cons(n__s(_x41), n__take(_x61, _x62)))), n__s(n__take(s(n__take(_x61, _x62)), cons(n__s(_x51), _x71)))) → eq#(cons(s(_x41), n__take(0, take(_x61, _x62))), cons(s(_x51), n__take(take(_x61, _x62), _x71)))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(0, _x71)), cons(n__0, n__s(_x71))))) → eq#(s(_x21), cons(0, n__take(nil, s(_x71))))
eq#(n__s(n__take(s(n__0), cons(_x32, _x31))), n__s(n__take(s(n__inf(_x71)), cons(n__s(_x41), n__length(_x71))))) → eq#(cons(activate(_x32), n__take(0, activate(_x31))), cons(n__s(_x41), n__take(n__inf(_x71), length(_x71))))eq#(n__s(n__s(_x21)), n__s(n__take(s(n__take(_x61, _x62)), cons(_x42, n__0)))) → eq#(s(_x21), cons(activate(_x42), n__take(take(_x61, _x62), 0)))

Rewrite Rules

eq(n__0, n__0) → trueeq(n__s(X), n__s(Y)) → eq(activate(X), activate(Y))
eq(X, Y) → falseinf(X) → cons(X, n__inf(s(X)))
take(0, X) → niltake(s(X), cons(Y, L)) → cons(activate(Y), n__take(activate(X), activate(L)))
length(nil) → 0length(cons(X, L)) → s(n__length(activate(L)))
0 → n__0s(X) → n__s(X)
inf(X) → n__inf(X)take(X1, X2) → n__take(X1, X2)
length(X) → n__length(X)activate(n__0) → 0
activate(n__s(X)) → s(X)activate(n__inf(X)) → inf(X)
activate(n__take(X1, X2)) → take(X1, X2)activate(n__length(X)) → length(X)
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__inf, n__length, inf, true, n__take, activate, n__s, n__0, 0, s, take, length, false, nil, cons, eq

Strategy

The right-hand side of the rule eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(inf(_x21), cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
eq#(inf(_x21), cons(n__take(_x41, _x42), n__take(inf(_x61), n__inf(_x81)))) 
eq#(inf(_x21), cons(n__take(_x41, _x42), n__take(cons(_x71, n__inf(s(_x71))), inf(_x71)))) 
eq#(n__inf(_x31), cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71)))) 
eq#(cons(_x31, n__inf(s(_x31))), cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71)))) 
eq#(inf(_x21), cons(n__take(_x41, _x42), n__take(n__inf(_x71), inf(_x71)))) 
eq#(inf(_x21), cons(n__take(_x41, _x42), n__take(inf(_x61), cons(_x81, n__inf(s(_x81)))))) 
Thus, the rule eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(inf(_x21), cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71)))) is replaced by the following rules:
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(inf(_x21), cons(n__take(_x41, _x42), n__take(inf(_x61), cons(_x81, n__inf(s(_x81))))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(inf(_x21), cons(n__take(_x41, _x42), n__take(n__inf(_x71), inf(_x71))))
eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x71)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(inf(_x21), cons(n__take(_x41, _x42), n__take(cons(_x71, n__inf(s(_x71))), inf(_x71))))eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(cons(_x31, n__inf(s(_x31))), cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71))))
eq#(n__s(n__inf(_x31)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x71))))) → eq#(n__inf(_x31), cons(n__take(_x41, _x42), n__take(inf(_x61), inf(_x71))))eq#(n__s(n__inf(_x21)), n__s(n__take(s(n__inf(_x61)), cons(n__take(_x41, _x42), n__inf(_x81))))) → eq#(inf(_x21), cons(n__take(_x41, _x42), n__take(inf(_x61), n__inf(_x81))))