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 (95ms).
 | – Problem 2 was processed with processor PolynomialLinearRange4iUR (2398ms).
 |    | – Problem 3 was processed with processor ForwardNarrowing (3ms).
 |    |    | – Problem 4 was processed with processor ForwardNarrowing (2ms).
 |    |    |    | – Problem 5 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    | – Problem 6 was processed with processor ForwardNarrowing (1ms).
 |    |    |    |    |    | – Problem 7 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    | – Problem 8 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    | – Problem 9 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (34ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (15ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (11ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (10ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (11ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (83ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (176ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (267ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 remains open; application of the following processors failed [ForwardNarrowing (143ms), ForwardNarrowing (235ms), ForwardNarrowing (163ms), ForwardNarrowing (69ms), ForwardNarrowing (95ms), ForwardNarrowing (76ms), ForwardNarrowing (265ms), ForwardNarrowing (176ms), ForwardNarrowing (96ms), ForwardNarrowing (71ms), ForwardNarrowing (149ms), ForwardNarrowing (236ms), ForwardNarrowing (179ms), ForwardNarrowing (207ms), ForwardNarrowing (204ms), ForwardNarrowing (290ms), ForwardNarrowing (188ms), ForwardNarrowing (169ms), ForwardNarrowing (78ms), ForwardNarrowing (244ms), ForwardNarrowing (188ms), ForwardNarrowing (243ms), ForwardNarrowing (218ms), ForwardNarrowing (290ms), ForwardNarrowing (209ms), ForwardNarrowing (220ms), ForwardNarrowing (202ms), ForwardNarrowing (283ms), ForwardNarrowing (177ms), ForwardNarrowing (194ms), ForwardNarrowing (202ms), ForwardNarrowing (182ms), ForwardNarrowing (timeout)].

The following open problems remain:

Open Dependency Pair Problem 3

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
activate#(n__incr(X)) → incr#(activate(X))activate#(n__adx(X)) → adx#(activate(X))
activate#(n__incr(X)) → activate#(X)incr#(cons(X, Y)) → activate#(Y)

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Problem 1: DependencyGraph

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
activate#(n__zeros) → zeros#activate#(n__adx(X)) → adx#(activate(X))
nats# → zeros#tl#(cons(X, Y)) → activate#(Y)
activate#(n__incr(X)) → activate#(X)hd#(cons(X, Y)) → activate#(X)
nats# → adx#(zeros)activate#(n__s(X)) → s#(X)
adx#(cons(X, Y)) → activate#(Y)activate#(n__incr(X)) → incr#(activate(X))
adx#(cons(X, Y)) → activate#(X)activate#(n__0) → 0#
incr#(cons(X, Y)) → activate#(Y)activate#(n__adx(X)) → activate#(X)

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The following SCCs where found

incr#(cons(X, Y)) → activate#(X)adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
adx#(cons(X, Y)) → activate#(Y)activate#(n__incr(X)) → incr#(activate(X))
activate#(n__adx(X)) → adx#(activate(X))adx#(cons(X, Y)) → activate#(X)
activate#(n__incr(X)) → activate#(X)incr#(cons(X, Y)) → activate#(Y)
activate#(n__adx(X)) → activate#(X)

Problem 2: PolynomialLinearRange4iUR

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
adx#(cons(X, Y)) → activate#(Y)activate#(n__incr(X)) → incr#(activate(X))
activate#(n__adx(X)) → adx#(activate(X))adx#(cons(X, Y)) → activate#(X)
activate#(n__incr(X)) → activate#(X)incr#(cons(X, Y)) → activate#(Y)
activate#(n__adx(X)) → activate#(X)

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

Polynomial Interpretation

Improved Usable rules

activate(n__zeros) → zeroszeros → cons(n__0, n__zeros)
activate(n__s(X)) → s(X)activate(n__0) → 0
zeros → n__zeros0 → n__0
activate(n__incr(X)) → incr(activate(X))s(X) → n__s(X)
activate(X) → Xactivate(n__adx(X)) → adx(activate(X))
adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))incr(X) → n__incr(X)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(X) → n__adx(X)

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

adx#(cons(X, Y)) → activate#(Y)adx#(cons(X, Y)) → activate#(X)
activate#(n__adx(X)) → activate#(X)

Problem 3: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
activate#(n__incr(X)) → incr#(activate(X))activate#(n__adx(X)) → adx#(activate(X))
activate#(n__incr(X)) → activate#(X)incr#(cons(X, Y)) → activate#(Y)

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__incr(X)) → incr#(activate(X)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
incr#(zeros) 
incr#(0) 
incr#(incr(activate(_x21))) 
incr#(_x21) 
incr#(s(_x21)) 
incr#(adx(activate(_x21))) 
Thus, the rule activate#(n__incr(X)) → incr#(activate(X)) is replaced by the following rules:
activate#(n__incr(n__s(_x21))) → incr#(s(_x21))activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))
activate#(n__incr(_x21)) → incr#(_x21)activate#(n__incr(n__0)) → incr#(0)

Problem 4: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
activate#(n__adx(X)) → adx#(activate(X))activate#(n__incr(n__s(_x21))) → incr#(s(_x21))
activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))activate#(n__incr(X)) → activate#(X)
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))
incr#(cons(X, Y)) → activate#(Y)activate#(n__incr(_x21)) → incr#(_x21)
activate#(n__incr(n__0)) → incr#(0)

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

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

Problem 5: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
activate#(n__adx(X)) → adx#(activate(X))activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__incr(X)) → activate#(X)
activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))incr#(cons(X, Y)) → activate#(Y)
activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))activate#(n__incr(n__0)) → incr#(0)
activate#(n__incr(_x21)) → incr#(_x21)

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(X)) → adx#(activate(X)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
adx#(s(_x21)) 
adx#(zeros) 
adx#(incr(activate(_x21))) 
adx#(_x21) 
adx#(adx(activate(_x21))) 
adx#(0) 
Thus, the rule activate#(n__adx(X)) → adx#(activate(X)) is replaced by the following rules:
activate#(n__adx(n__s(_x21))) → adx#(s(_x21))activate#(n__adx(_x21)) → adx#(_x21)
activate#(n__adx(n__incr(_x21))) → adx#(incr(activate(_x21)))activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))
activate#(n__adx(n__zeros)) → adx#(zeros)activate#(n__adx(n__0)) → adx#(0)

Problem 6: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__adx(n__s(_x21))) → adx#(s(_x21))
adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))activate#(n__adx(_x21)) → adx#(_x21)
activate#(n__adx(n__incr(_x21))) → adx#(incr(activate(_x21)))activate#(n__incr(X)) → activate#(X)
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__incr(n__0)) → incr#(0)
activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))activate#(n__adx(n__zeros)) → adx#(zeros)
activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))activate#(n__adx(n__0)) → adx#(0)
activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))incr#(cons(X, Y)) → activate#(Y)
activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))activate#(n__incr(_x21)) → incr#(_x21)

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

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

Problem 7: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
activate#(n__adx(_x21)) → adx#(_x21)activate#(n__adx(n__incr(_x21))) → adx#(incr(activate(_x21)))
activate#(n__incr(X)) → activate#(X)activate#(n__incr(n__zeros)) → incr#(zeros)
activate#(n__incr(n__0)) → incr#(0)activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))
activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))activate#(n__adx(n__zeros)) → adx#(zeros)
activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))activate#(n__adx(n__0)) → adx#(0)
activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))
incr#(cons(X, Y)) → activate#(Y)activate#(n__incr(_x21)) → incr#(_x21)

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(_x21))) → adx#(incr(activate(_x21))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
adx#(incr(zeros)) 
adx#(incr(_x41)) 
adx#(incr(adx(activate(_x41)))) 
adx#(incr(s(_x41))) 
adx#(incr(incr(activate(_x41)))) 
adx#(incr(0)) 
adx#(n__incr(activate(_x21))) 
Thus, the rule activate#(n__adx(n__incr(_x21))) → adx#(incr(activate(_x21))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41))))activate#(n__adx(n__incr(_x21))) → adx#(n__incr(activate(_x21)))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))
activate#(n__adx(n__incr(n__0))) → adx#(incr(0))

Problem 8: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
activate#(n__adx(_x21)) → adx#(_x21)activate#(n__adx(n__incr(_x21))) → adx#(n__incr(activate(_x21)))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))activate#(n__incr(X)) → activate#(X)
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))
activate#(n__incr(n__0)) → incr#(0)activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41))))
activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))
activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))activate#(n__adx(n__zeros)) → adx#(zeros)
activate#(n__adx(n__0)) → adx#(0)activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))incr#(cons(X, Y)) → activate#(Y)
activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))
activate#(n__incr(_x21)) → incr#(_x21)activate#(n__adx(n__incr(n__0))) → adx#(incr(0))

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(_x21))) → adx#(n__incr(activate(_x21))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
adx#(n__incr(0)) 
adx#(n__incr(incr(activate(_x41)))) 
adx#(n__incr(_x41)) 
adx#(n__incr(zeros)) 
adx#(n__incr(adx(activate(_x41)))) 
adx#(n__incr(s(_x41))) 
Thus, the rule activate#(n__adx(n__incr(_x21))) → adx#(n__incr(activate(_x21))) is replaced by the following rules:
activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))
activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(adx(activate(_x41))))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))

Problem 9: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__adx(_x21)) → adx#(_x21)
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(adx(activate(_x41))))activate#(n__incr(X)) → activate#(X)
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))
activate#(n__incr(n__0)) → incr#(0)activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41))))activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))
activate#(n__adx(n__0)) → adx#(0)activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))
incr#(cons(X, Y)) → activate#(Y)activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))
adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))
activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))
activate#(n__adx(n__zeros)) → adx#(zeros)activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))
activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))activate#(n__incr(_x21)) → incr#(_x21)
activate#(n__adx(n__incr(n__0))) → adx#(incr(0))

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(adx(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
adx#(n__incr(adx(0))) 
adx#(n__incr(adx(incr(activate(_x51))))) 
adx#(n__incr(n__adx(activate(_x41)))) 
adx#(n__incr(adx(adx(activate(_x51))))) 
adx#(n__incr(adx(_x51))) 
adx#(n__incr(adx(zeros))) 
adx#(n__incr(adx(s(_x51)))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(adx(activate(_x41)))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(0)))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))

Problem 10: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__adx(_x21)) → adx#(_x21)
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(adx(activate(_x51)))))activate#(n__incr(n__zeros)) → incr#(zeros)
activate#(n__incr(X)) → activate#(X)activate#(n__incr(n__0)) → incr#(0)
activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(0)))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41))))activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))
activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))activate#(n__adx(n__0)) → adx#(0)
activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))
incr#(cons(X, Y)) → activate#(Y)activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))
activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))
activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))
activate#(n__adx(n__zeros)) → adx#(zeros)activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))activate#(n__adx(n__incr(n__0))) → adx#(incr(0))
activate#(n__incr(_x21)) → incr#(_x21)

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(adx(activate(_x51))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
adx#(n__incr(adx(adx(incr(activate(_x61)))))) 
adx#(n__incr(adx(adx(zeros)))) 
adx#(n__incr(adx(adx(0)))) 
adx#(n__incr(n__adx(adx(activate(_x51))))) 
adx#(n__incr(adx(adx(_x61)))) 
adx#(n__incr(adx(adx(s(_x61))))) 
adx#(n__incr(adx(adx(adx(activate(_x61)))))) 
adx#(n__incr(adx(n__adx(activate(_x51))))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(adx(activate(_x51))))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(adx(incr(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(zeros))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(adx(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))
activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(adx(s(_x61)))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))

Problem 11: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__adx(_x21)) → adx#(_x21)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(adx(activate(_x61))))))activate#(n__incr(X)) → activate#(X)
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(adx(s(_x61)))))
activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))activate#(n__incr(n__0)) → incr#(0)
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(0)))activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(zeros))))
activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))
activate#(n__adx(n__0)) → adx#(0)activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))
activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))
activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))incr#(cons(X, Y)) → activate#(Y)
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(adx(incr(activate(_x61))))))activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))
activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))activate#(n__adx(n__zeros)) → adx#(zeros)
activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))
activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))
activate#(n__incr(_x21)) → incr#(_x21)activate#(n__adx(n__incr(n__0))) → adx#(incr(0))

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(adx(activate(_x61)))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
adx#(n__incr(adx(adx(adx(zeros))))) 
adx#(n__incr(adx(adx(adx(incr(activate(_x71))))))) 
adx#(n__incr(adx(adx(n__adx(activate(_x61)))))) 
adx#(n__incr(adx(adx(adx(0))))) 
adx#(n__incr(adx(n__adx(adx(activate(_x61)))))) 
adx#(n__incr(adx(adx(adx(adx(activate(_x71))))))) 
adx#(n__incr(adx(adx(adx(_x71))))) 
adx#(n__incr(adx(adx(adx(s(_x71)))))) 
adx#(n__incr(n__adx(adx(adx(activate(_x61)))))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(adx(activate(_x61)))))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(n__adx(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))

Problem 12: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__adx(_x21)) → adx#(_x21)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(adx(s(_x61)))))
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__incr(X)) → activate#(X)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(adx(activate(_x71)))))))activate#(n__incr(n__0)) → incr#(0)
activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(0)))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(zeros))))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41))))
activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))
activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))activate#(n__adx(n__0)) → adx#(0)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(n__adx(activate(_x61))))))activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))
activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))
activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))incr#(cons(X, Y)) → activate#(Y)
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))
activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))
activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(adx(incr(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(zeros)))))activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))
activate#(n__adx(n__zeros)) → adx#(zeros)activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))activate#(n__adx(n__incr(n__0))) → adx#(incr(0))
activate#(n__incr(_x21)) → incr#(_x21)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(incr(activate(_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
adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81)))))))) 
adx#(n__incr(adx(adx(adx(n__incr(activate(_x71))))))) 
adx#(n__incr(adx(adx(adx(incr(_x81)))))) 
adx#(n__incr(adx(adx(n__adx(incr(activate(_x71))))))) 
adx#(n__incr(adx(adx(adx(incr(0)))))) 
adx#(n__incr(n__adx(adx(adx(incr(activate(_x71))))))) 
adx#(n__incr(adx(adx(adx(incr(incr(activate(_x81)))))))) 
adx#(n__incr(adx(adx(adx(incr(zeros)))))) 
adx#(n__incr(adx(n__adx(adx(incr(activate(_x71))))))) 
adx#(n__incr(adx(adx(adx(incr(s(_x81))))))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(incr(activate(_x71))))))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(n__incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(adx(incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(adx(incr(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(adx(incr(zeros))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81))))))))

Problem 13: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(adx(activate(_x71)))))))
activate#(n__incr(X)) → activate#(X)activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(adx(s(_x61)))))
activate#(n__incr(n__0)) → incr#(0)activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(0)))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(zeros))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(n__adx(activate(_x61))))))activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))
activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(adx(incr(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__adx(incr(activate(_x71)))))))
activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(zeros)))))
activate#(n__adx(n__zeros)) → adx#(zeros)activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))activate#(n__adx(_x21)) → adx#(_x21)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(n__incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(adx(incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(adx(incr(zeros))))))activate#(n__incr(n__zeros)) → incr#(zeros)
activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))
activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(s(_x81)))))))
activate#(n__adx(n__0)) → adx#(0)incr#(cons(X, Y)) → activate#(Y)
activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))
adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(adx(incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))
activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))
activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))activate#(n__adx(n__incr(n__0))) → adx#(incr(0))
activate#(n__incr(_x21)) → incr#(_x21)

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(adx(activate(_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
adx#(n__incr(adx(adx(adx(adx(_x81)))))) 
adx#(n__incr(adx(adx(adx(n__adx(activate(_x71))))))) 
adx#(n__incr(adx(adx(adx(adx(adx(activate(_x81)))))))) 
adx#(n__incr(adx(adx(adx(adx(incr(activate(_x81)))))))) 
adx#(n__incr(n__adx(adx(adx(adx(activate(_x71))))))) 
adx#(n__incr(adx(n__adx(adx(adx(activate(_x71))))))) 
adx#(n__incr(adx(adx(n__adx(adx(activate(_x71))))))) 
adx#(n__incr(adx(adx(adx(adx(s(_x81))))))) 
adx#(n__incr(adx(adx(adx(adx(zeros)))))) 
adx#(n__incr(adx(adx(adx(adx(0)))))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(adx(activate(_x71))))))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(n__adx(adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x81))))))) → adx#(n__incr(adx(adx(adx(adx(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(n__adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__0))))))) → adx#(n__incr(adx(adx(adx(adx(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__zeros))))))) → adx#(n__incr(adx(adx(adx(adx(zeros))))))

Problem 14: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(s(_x81)))))))
activate#(n__incr(X)) → activate#(X)activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(adx(s(_x61)))))
activate#(n__incr(n__0)) → incr#(0)activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(0)))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(zeros))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(n__adx(activate(_x61))))))activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))
activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(n__adx(adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(adx(incr(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(zeros)))))
activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__adx(adx(activate(_x71)))))))
activate#(n__adx(n__zeros)) → adx#(zeros)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(incr(activate(_x81))))))))activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))activate#(n__adx(_x21)) → adx#(_x21)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(n__incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(adx(incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(n__adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(adx(incr(zeros))))))
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__0))))))) → adx#(n__incr(adx(adx(adx(adx(0))))))
activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))
activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(s(_x81)))))))
activate#(n__adx(n__0)) → adx#(0)incr#(cons(X, Y)) → activate#(Y)
activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__zeros))))))) → adx#(n__incr(adx(adx(adx(adx(zeros))))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x81))))))) → adx#(n__incr(adx(adx(adx(adx(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(adx(incr(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))
activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))
activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))
activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(adx(activate(_x81))))))))
activate#(n__incr(_x21)) → incr#(_x21)activate#(n__adx(n__incr(n__0))) → adx#(incr(0))

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(s(_x81))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
adx#(n__incr(adx(n__adx(adx(adx(s(_x81))))))) 
adx#(n__incr(n__adx(adx(adx(adx(s(_x81))))))) 
adx#(n__incr(adx(adx(adx(adx(n__s(_x71))))))) 
adx#(n__incr(adx(adx(n__adx(adx(s(_x81))))))) 
adx#(n__incr(adx(adx(adx(n__adx(s(_x81))))))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(s(_x81))))))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(adx(adx(n__s(_x71)))))))

Problem 15: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(adx(s(_x81)))))))
activate#(n__incr(X)) → activate#(X)activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(adx(s(_x61)))))
activate#(n__incr(n__0)) → incr#(0)activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(0)))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(zeros))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(n__adx(activate(_x61))))))activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))
activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(n__adx(adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(adx(adx(n__s(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(adx(incr(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__adx(incr(activate(_x71)))))))
activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__adx(adx(activate(_x71)))))))activate#(n__adx(n__zeros)) → adx#(zeros)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(incr(activate(_x81))))))))
activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))
activate#(n__adx(_x21)) → adx#(_x21)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(n__incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(adx(incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(n__adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(adx(incr(zeros))))))activate#(n__incr(n__zeros)) → incr#(zeros)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__0))))))) → adx#(n__incr(adx(adx(adx(adx(0))))))activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))
activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(s(_x81)))))))activate#(n__adx(n__0)) → adx#(0)
incr#(cons(X, Y)) → activate#(Y)activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__zeros))))))) → adx#(n__incr(adx(adx(adx(adx(zeros))))))activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))
adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x81))))))) → adx#(n__incr(adx(adx(adx(adx(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(adx(incr(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))
activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))
activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))
activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__0))) → adx#(incr(0))activate#(n__incr(_x21)) → incr#(_x21)

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(adx(s(_x81))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
adx#(n__incr(adx(n__adx(adx(n__adx(s(_x81))))))) 
adx#(n__incr(n__adx(n__adx(adx(adx(s(_x81))))))) 
adx#(n__incr(adx(n__adx(adx(adx(n__s(_x71))))))) 
adx#(n__incr(adx(n__adx(n__adx(adx(s(_x81))))))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(adx(s(_x81))))))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(n__adx(adx(adx(n__s(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__adx(s(_x81)))))))

Problem 16: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__incr(X)) → activate#(X)
activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(adx(s(_x61)))))activate#(n__incr(n__0)) → incr#(0)
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(0)))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(zeros))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(adx(incr(activate(_x71)))))))
activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(n__adx(activate(_x61))))))
activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(n__adx(adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(adx(adx(n__s(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(adx(incr(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(zeros)))))activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__adx(adx(activate(_x71)))))))activate#(n__adx(n__zeros)) → adx#(zeros)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(incr(activate(_x81))))))))
activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(n__adx(adx(adx(n__s(_x71)))))))activate#(n__adx(_x21)) → adx#(_x21)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(n__incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(adx(incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(n__adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(adx(incr(zeros))))))activate#(n__incr(n__zeros)) → incr#(zeros)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__0))))))) → adx#(n__incr(adx(adx(adx(adx(0))))))activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))
activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(s(_x81)))))))activate#(n__adx(n__0)) → adx#(0)
activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))incr#(cons(X, Y)) → activate#(Y)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__zeros))))))) → adx#(n__incr(adx(adx(adx(adx(zeros))))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))
adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x81))))))) → adx#(n__incr(adx(adx(adx(adx(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(adx(incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))
activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__adx(s(_x81)))))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))
activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(adx(activate(_x81))))))))activate#(n__incr(_x21)) → incr#(_x21)
activate#(n__adx(n__incr(n__0))) → adx#(incr(0))

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(adx(s(_x61))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
adx#(n__incr(adx(adx(n__s(_x51))))) 
adx#(n__incr(adx(n__adx(s(_x61))))) 
adx#(n__incr(n__adx(adx(s(_x61))))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(adx(s(_x61))))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(n__adx(adx(s(_x61)))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x51)))))) → adx#(n__incr(adx(adx(n__s(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(n__adx(s(_x61)))))

Problem 17: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__incr(X)) → activate#(X)
activate#(n__incr(n__0)) → incr#(0)activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(0)))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(zeros))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(n__adx(adx(s(_x61)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x51)))))) → adx#(n__incr(adx(adx(n__s(_x51)))))activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(n__adx(activate(_x61))))))activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))
activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(n__adx(adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(adx(adx(n__s(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(adx(incr(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__adx(incr(activate(_x71)))))))activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__adx(adx(activate(_x71)))))))
activate#(n__adx(n__zeros)) → adx#(zeros)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(incr(activate(_x81))))))))activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(n__adx(adx(adx(n__s(_x71)))))))
activate#(n__adx(_x21)) → adx#(_x21)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(n__incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(adx(incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(n__adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(adx(incr(zeros))))))
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__0))))))) → adx#(n__incr(adx(adx(adx(adx(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(n__adx(s(_x61)))))activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))
activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))
activate#(n__adx(n__0)) → adx#(0)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(s(_x81)))))))
incr#(cons(X, Y)) → activate#(Y)activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__zeros))))))) → adx#(n__incr(adx(adx(adx(adx(zeros))))))activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))
adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x81))))))) → adx#(n__incr(adx(adx(adx(adx(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(adx(incr(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))
activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__adx(s(_x81)))))))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))
activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(adx(activate(_x81))))))))activate#(n__adx(n__incr(n__0))) → adx#(incr(0))
activate#(n__incr(_x21)) → incr#(_x21)

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__incr(n__0)) → incr#(0) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
incr#(n__0) 
Thus, the rule activate#(n__incr(n__0)) → incr#(0) is replaced by the following rules:
activate#(n__incr(n__0)) → incr#(n__0)

Problem 18: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__incr(X)) → activate#(X)
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(0)))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(zeros))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(n__adx(adx(s(_x61)))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x51)))))) → adx#(n__incr(adx(adx(n__s(_x51)))))
activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(n__adx(activate(_x61))))))
activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(n__adx(adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(adx(adx(n__s(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(adx(incr(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(zeros)))))activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__adx(adx(activate(_x71)))))))activate#(n__adx(n__zeros)) → adx#(zeros)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(incr(activate(_x81))))))))
activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(n__adx(adx(adx(n__s(_x71)))))))activate#(n__adx(_x21)) → adx#(_x21)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(n__incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(adx(incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(n__adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(adx(incr(zeros))))))activate#(n__incr(n__zeros)) → incr#(zeros)
activate#(n__incr(n__0)) → incr#(n__0)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__0))))))) → adx#(n__incr(adx(adx(adx(adx(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(n__adx(s(_x61)))))activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))
activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(s(_x81)))))))activate#(n__adx(n__0)) → adx#(0)
activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))incr#(cons(X, Y)) → activate#(Y)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__zeros))))))) → adx#(n__incr(adx(adx(adx(adx(zeros))))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))
adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x81))))))) → adx#(n__incr(adx(adx(adx(adx(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(adx(incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))
activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__adx(s(_x81)))))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))
activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(adx(activate(_x81))))))))activate#(n__incr(_x21)) → incr#(_x21)
activate#(n__adx(n__incr(n__0))) → adx#(incr(0))

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(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
adx#(n__incr(adx(n__0))) 
adx#(n__incr(n__adx(0))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(0))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(n__0)))activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(n__adx(0)))

Problem 19: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__incr(X)) → activate#(X)
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(n__0)))activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(n__adx(0)))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(zeros))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(n__adx(adx(s(_x61)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x51)))))) → adx#(n__incr(adx(adx(n__s(_x51)))))activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(n__adx(activate(_x61))))))activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))
activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(n__adx(adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(adx(adx(n__s(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(adx(incr(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__adx(incr(activate(_x71)))))))activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__adx(adx(activate(_x71)))))))
activate#(n__adx(n__zeros)) → adx#(zeros)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(incr(activate(_x81))))))))activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(n__adx(adx(adx(n__s(_x71)))))))
activate#(n__adx(_x21)) → adx#(_x21)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(n__incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(adx(incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(n__adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(adx(incr(zeros))))))
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__incr(n__0)) → incr#(n__0)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__0))))))) → adx#(n__incr(adx(adx(adx(adx(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(n__adx(s(_x61)))))
activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))
activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))activate#(n__adx(n__0)) → adx#(0)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(s(_x81)))))))incr#(cons(X, Y)) → activate#(Y)
activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__zeros))))))) → adx#(n__incr(adx(adx(adx(adx(zeros))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x81))))))) → adx#(n__incr(adx(adx(adx(adx(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(adx(incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__adx(s(_x81)))))))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))
activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))
activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__0))) → adx#(incr(0))activate#(n__incr(_x21)) → incr#(_x21)

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(n__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
adx#(n__incr(n__adx(n__0))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(n__0))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(n__adx(n__0)))

Problem 20: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__incr(X)) → activate#(X)
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(n__adx(0)))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(zeros))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(n__adx(adx(s(_x61)))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x51)))))) → adx#(n__incr(adx(adx(n__s(_x51)))))
activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(n__adx(activate(_x61))))))
activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(n__adx(adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(adx(adx(n__s(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(adx(incr(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(zeros)))))activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__adx(adx(activate(_x71)))))))activate#(n__adx(n__zeros)) → adx#(zeros)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(incr(activate(_x81))))))))
activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(n__adx(adx(adx(n__s(_x71)))))))activate#(n__adx(_x21)) → adx#(_x21)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(n__incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(adx(incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(n__adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(adx(incr(zeros))))))activate#(n__incr(n__zeros)) → incr#(zeros)
activate#(n__incr(n__0)) → incr#(n__0)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__0))))))) → adx#(n__incr(adx(adx(adx(adx(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(n__adx(s(_x61)))))activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))
activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(n__adx(n__0)))
activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(s(_x81)))))))
activate#(n__adx(n__0)) → adx#(0)activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))
incr#(cons(X, Y)) → activate#(Y)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__zeros))))))) → adx#(n__incr(adx(adx(adx(adx(zeros))))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x81))))))) → adx#(n__incr(adx(adx(adx(adx(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(adx(incr(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__adx(s(_x81)))))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))
activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))
activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(adx(activate(_x81))))))))
activate#(n__incr(_x21)) → incr#(_x21)activate#(n__adx(n__incr(n__0))) → adx#(incr(0))

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(n__adx(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
adx#(n__incr(n__adx(n__0))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(n__adx(0))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(n__adx(n__0)))

Problem 21: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__incr(X)) → activate#(X)
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(zeros))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(n__adx(adx(s(_x61)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x51)))))) → adx#(n__incr(adx(adx(n__s(_x51)))))activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(n__adx(activate(_x61))))))activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))
activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(n__adx(adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(adx(adx(n__s(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(adx(incr(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__adx(incr(activate(_x71)))))))activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__adx(adx(activate(_x71)))))))
activate#(n__adx(n__zeros)) → adx#(zeros)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(adx(adx(activate(_x71)))))))activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(n__adx(adx(adx(n__s(_x71)))))))
activate#(n__adx(_x21)) → adx#(_x21)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(n__incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(adx(incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(n__adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(adx(incr(zeros))))))
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__incr(n__0)) → incr#(n__0)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__0))))))) → adx#(n__incr(adx(adx(adx(adx(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(n__adx(s(_x61)))))
activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(n__adx(n__0)))activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))
activate#(n__adx(n__0)) → adx#(0)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(s(_x81)))))))
incr#(cons(X, Y)) → activate#(Y)activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__zeros))))))) → adx#(n__incr(adx(adx(adx(adx(zeros))))))activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))
adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x81))))))) → adx#(n__incr(adx(adx(adx(adx(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(adx(incr(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))
activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__adx(s(_x81)))))))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))
activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(adx(activate(_x81))))))))activate#(n__adx(n__incr(n__0))) → adx#(incr(0))
activate#(n__incr(_x21)) → incr#(_x21)

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(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
adx#(incr(n__adx(activate(_x41)))) 
adx#(incr(adx(_x51))) 
adx#(n__incr(adx(activate(_x41)))) 
adx#(incr(adx(0))) 
adx#(incr(adx(s(_x51)))) 
adx#(incr(adx(incr(activate(_x51))))) 
adx#(incr(adx(zeros))) 
adx#(incr(adx(adx(activate(_x51))))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(adx(activate(_x41)))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(incr(adx(0)))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(incr(adx(zeros)))
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(incr(adx(incr(activate(_x51)))))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(n__adx(activate(_x41))))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(incr(adx(_x51)))
activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(incr(adx(s(_x51))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(incr(adx(adx(activate(_x51)))))

Problem 22: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(adx(activate(_x41))))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(incr(n__adx(activate(_x41))))activate#(n__incr(X)) → activate#(X)
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(zeros))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(n__adx(adx(s(_x61)))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x51)))))) → adx#(n__incr(adx(adx(n__s(_x51)))))
activate#(n__adx(n__adx(_x21))) → adx#(adx(activate(_x21)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(adx(n__adx(activate(_x61))))))
activate#(n__adx(n__incr(n__zeros))) → adx#(incr(zeros))activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(n__adx(adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(incr(adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(adx(adx(n__s(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(adx(incr(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(zeros)))))
activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__adx(adx(activate(_x71)))))))
activate#(n__adx(n__zeros)) → adx#(zeros)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(adx(adx(activate(_x71)))))))activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(incr(adx(0)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(n__adx(adx(adx(n__s(_x71)))))))activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(incr(adx(incr(activate(_x51)))))
activate#(n__adx(_x21)) → adx#(_x21)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(n__incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(adx(incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(n__adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(adx(incr(zeros))))))
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__incr(n__0)) → incr#(n__0)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__0))))))) → adx#(n__incr(adx(adx(adx(adx(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(n__adx(s(_x61)))))
activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(n__adx(n__0)))activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))
activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(incr(adx(s(_x51))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(s(_x81)))))))
activate#(n__adx(n__0)) → adx#(0)activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))
incr#(cons(X, Y)) → activate#(Y)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__zeros))))))) → adx#(n__incr(adx(adx(adx(adx(zeros))))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(incr(adx(zeros)))
adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x81))))))) → adx#(n__incr(adx(adx(adx(adx(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(adx(incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))
activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__adx(s(_x81)))))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))
activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(incr(adx(_x51)))activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(adx(activate(_x81))))))))
activate#(n__incr(_x21)) → incr#(_x21)activate#(n__adx(n__incr(n__0))) → adx#(incr(0))

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(adx(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
adx#(n__incr(adx(0))) 
adx#(n__incr(adx(incr(activate(_x51))))) 
adx#(n__incr(n__adx(activate(_x41)))) 
adx#(n__incr(adx(adx(activate(_x51))))) 
adx#(n__incr(adx(_x51))) 
adx#(n__incr(adx(zeros))) 
adx#(n__incr(adx(s(_x51)))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(adx(activate(_x41)))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(adx(0)))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))
activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))

Problem 23: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

incr#(cons(X, Y)) → activate#(X)activate#(n__incr(X)) → activate#(X)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(incr(cons(n__0, n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(cons(n__0, n__zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(n__adx(adx(incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(incr(n__zeros)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(adx(adx(n__s(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(n__adx(n__adx(s(_x61)))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(adx(incr(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(n__zeros))))activate#(n__adx(n__adx(_x21))) → adx#(n__adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x91)))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(_x91)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(n__adx(zeros))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(incr(adx(0)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(n__adx(adx(adx(n__s(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(adx(incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__adx(s(_x81)))))))
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__adx(n__incr(n__zeros))) → adx#(incr(n__zeros))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x61))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(_x61))))))activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(n__adx(n__0)))
activate#(n__adx(n__adx(n__0))) → adx#(adx(0))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(0)))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(incr(adx(s(_x51))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(incr(0)))))))activate#(n__adx(n__0)) → adx#(0)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__s(_x91))))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(s(_x91))))))))activate#(n__adx(n__adx(n__s(_x31)))) → adx#(n__adx(n__s(_x31)))
activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))incr#(cons(X, Y)) → activate#(Y)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__zeros))))))) → adx#(n__incr(adx(adx(adx(adx(zeros))))))activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(incr(n__adx(incr(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(cons(_x62, _x61)))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(_x62)), n__incr(activate(_x61))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(n__incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(incr(cons(n__0, n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(n__adx(s(_x71))))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(n__adx(adx(n__adx(_x71)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(zeros)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(0)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(incr(adx(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x51)))))) → adx#(n__incr(n__adx(n__adx(n__s(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(n__adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(_x81))))))activate#(n__incr(_x21)) → incr#(_x21)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__incr(_x91))))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(incr(activate(_x91)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(incr(n__incr(zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(zeros)))))))
activate#(n__adx(n__adx(n__incr(_x41)))) → adx#(adx(incr(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(incr(zeros)))))))
activate#(n__adx(n__adx(n__adx(_x41)))) → adx#(adx(adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(incr(zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(n__adx(_x71)))))activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(incr(n__adx(_x51)))
activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(n__0)), n__incr(activate(n__zeros)))))))))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(n__adx(adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(n__adx(adx(n__adx(n__0)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(n__adx(n__adx(n__adx(0)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x61))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(incr(n__incr(0)))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(incr(adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(n__adx(0)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))activate#(n__adx(n__adx(n__zeros))) → adx#(adx(zeros))
activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__adx(adx(activate(_x71)))))))
activate#(n__adx(n__zeros)) → adx#(zeros)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(adx(incr(activate(_x71)))))))activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(n__adx(n__adx(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(n__adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(incr(adx(incr(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(n__incr(activate(_x71)))))))activate#(n__adx(_x21)) → adx#(_x21)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(cons(_x62, _x61)))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(_x62)), n__incr(activate(_x61))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(incr(n__adx(adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(n__adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(n__adx(adx(incr(zeros))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(adx(incr(zeros))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(n__adx(adx(n__adx(zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(n__incr(zeros)))))))activate#(n__adx(n__adx(cons(_x22, _x21)))) → adx#(incr(cons(activate(_x22), n__adx(activate(_x21)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__0))))))) → adx#(n__incr(adx(adx(adx(adx(0))))))activate#(n__incr(n__0)) → incr#(n__0)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(n__adx(zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(n__adx(s(_x61)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(n__adx(adx(n__adx(s(_x71))))))activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(n__adx(adx(zeros))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(incr(n__incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__adx(_x91))))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(adx(activate(_x91)))))))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(incr(adx(zeros)))activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))
adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x81))))))) → adx#(n__incr(adx(adx(adx(adx(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(adx(incr(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(incr(s(_x81)))))))
activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(n__zeros)))))))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))activate#(n__adx(n__incr(n__zeros))) → adx#(incr(cons(n__0, n__zeros)))
activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(incr(n__adx(zeros)))
activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(incr(n__adx(s(_x51))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(n__0)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(n__adx(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(incr(adx(_x51)))activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))
activate#(n__adx(n__adx(_x21))) → adx#(n__adx(_x21))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__0))) → adx#(incr(0))

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(incr(cons(n__0, n__zeros)))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(activate(n__0)), n__incr(activate(n__zeros))))))))) 
adx#(n__incr(n__adx(n__adx(n__adx(n__incr(incr(cons(n__0, n__zeros)))))))) 
adx#(n__incr(n__adx(n__adx(n__adx(incr(n__incr(cons(n__0, n__zeros)))))))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(incr(cons(n__0, n__zeros)))))))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(activate(n__0)), n__incr(activate(n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(n__incr(cons(n__0, n__zeros))))))))

Problem 24: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

activate#(n__incr(X)) → activate#(X)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__adx(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(adx(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(s(_x101)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(_x101))), n__incr(activate(n__incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(n__adx(zeros))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x91), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(n__s(_x91))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(activate(n__0)), n__incr(n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(incr(adx(0)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(n__adx(adx(adx(n__s(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(n__adx(adx(adx(adx(n__s(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(activate(_x71)))))))))activate#(n__adx(n__adx(n__zeros))) → adx#(n__adx(zeros))
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(activate(_x71)))))))))activate#(n__adx(n__adx(_x41))) → adx#(n__adx(_x41))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x61))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(_x61))))))activate#(n__adx(n__adx(n__0))) → adx#(adx(0))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(0)))))))activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(incr(adx(s(_x51))))
activate#(n__adx(n__0)) → adx#(0)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__s(_x91))))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(s(_x91))))))))incr#(cons(X, Y)) → activate#(Y)
activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(zeros), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__zeros))))))) → adx#(n__incr(adx(adx(adx(adx(zeros))))))
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(incr(n__adx(incr(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(n__incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__incr(_x91))))))))) → adx#(n__incr(adx(adx(adx(incr(incr(incr(activate(_x91)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(n__adx(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(zeros)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(adx(activate(_x101))), n__incr(0))))))))
activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(n__incr(n__zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x61))))))) → adx#(n__incr(adx(adx(n__incr(n__s(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x51)))))) → adx#(n__incr(n__adx(n__adx(n__s(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(0))))))))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(n__0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(activate(_x72)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(n__adx(incr(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(activate(_x72)))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__adx(n__incr(_x41)))) → adx#(n__adx(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__s(_x91))))))))) → adx#(n__incr(adx(adx(adx(incr(incr(s(_x91))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(activate(_x72)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__0)))))) → adx#(n__incr(adx(adx(incr(0)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__zeros)))))) → adx#(n__incr(adx(adx(incr(zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(n__zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(n__adx(incr(zeros))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__0), n__incr(activate(n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(n__adx(n__incr(activate(_x61))))))activate#(n__adx(n__adx(n__incr(_x41)))) → adx#(adx(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(incr(zeros)))))))activate#(n__adx(n__adx(n__adx(_x41)))) → adx#(adx(adx(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(incr(zeros)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(_x101), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(_x101), n__incr(n__0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x71))))))) → adx#(n__incr(adx(n__adx(incr(s(_x71))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))
activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(incr(n__adx(_x51)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(n__adx(incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(n__adx(adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(n__incr(cons(n__0, n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x61))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(incr(adx(adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(n__adx(0)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__0))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(n__0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(activate(n__0)), n__incr(n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(activate(_x72)), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(n__s(_x111))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(s(_x101)), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))
activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(incr(activate(_x111)))), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(n__adx(incr(activate(_x71)))))))activate#(n__adx(_x21)) → adx#(_x21)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(n__incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(cons(_x62, _x61)))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(_x62)), n__incr(activate(_x61))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x111)), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(s(_x111))), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(incr(n__adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(0)))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(s(_x101)))))))))
activate#(n__adx(n__adx(cons(_x22, _x21)))) → adx#(incr(cons(activate(_x22), n__adx(activate(_x21)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__0))))))) → adx#(n__incr(adx(adx(adx(adx(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(n__adx(s(_x61)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(n__adx(adx(n__adx(s(_x71))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(n__adx(adx(zeros))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(n__adx(adx(n__s(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__incr(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x71)))))))) → adx#(n__incr(adx(n__adx(adx(incr(n__incr(_x71)))))))
adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x81))))))) → adx#(n__incr(adx(adx(adx(adx(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__adx(n__incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(s(_x81)))))))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(0), n__incr(activate(n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(incr(n__adx(zeros)))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))
activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(incr(n__adx(s(_x51))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(n__0), n__incr(activate(n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(incr(cons(activate(n__0), n__adx(activate(n__zeros)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(n__0)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(incr(cons(n__0, n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(incr(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(n__incr(cons(n__0, n__zeros))))))))activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(incr(adx(_x51)))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__incr(adx(activate(_x71)))))))activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x61))))))) → adx#(n__incr(n__adx(adx(incr(n__s(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(activate(_x72)))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))
activate#(n__adx(n__adx(n__s(_x41)))) → adx#(n__adx(s(_x41)))incr#(cons(X, Y)) → activate#(X)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(s(_x101)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__0))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(n__adx(incr(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(adx(activate(_x111)))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__s(_x111)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x131)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(_x131)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x111))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(zeros), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(s(_x101)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x91)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(_x91)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(adx(activate(_x101))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__0)))))) → adx#(n__incr(adx(adx(n__incr(0)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(n__adx(adx(n__incr(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(n__adx(adx(incr(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x71)))))) → adx#(n__incr(adx(adx(incr(_x71)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(activate(_x72)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(activate(n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(n__zeros))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(n__adx(cons(n__0, n__zeros)))))activate#(n__adx(n__adx(n__adx(_x41)))) → adx#(n__adx(adx(activate(_x41))))
activate#(n__adx(n__adx(n__0))) → adx#(n__adx(0))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__0))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(_x101), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(adx(activate(_x101))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(incr(activate(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x91)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(_x91)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(zeros), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(adx(incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x71))))))) → adx#(n__incr(adx(adx(n__incr(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(zeros))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__adx(s(_x81)))))))
activate#(n__adx(n__incr(n__zeros))) → adx#(incr(n__zeros))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(activate(_x81))))))))
activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(n__adx(n__0)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(_x101), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(incr(0)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__adx(n__s(_x31)))) → adx#(n__adx(n__s(_x31)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(activate(_x72)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(n__0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(incr(activate(_x101))), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(cons(_x62, _x61)))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(_x62)), n__incr(activate(_x61))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(incr(n__zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(activate(n__0)))), n__incr(activate(n__incr(activate(n__zeros))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x71)))))) → adx#(n__incr(adx(adx(n__incr(_x71)))))activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(incr(n__zeros)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(n__adx(adx(n__adx(_x71)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(activate(n__0)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(activate(_x72)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(0)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(incr(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x111), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(_x111)), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(n__adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(n__0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(_x81))))))
activate#(n__incr(_x21)) → incr#(_x21)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__incr(_x91))))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(incr(activate(_x91)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(n__adx(adx(zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(incr(incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(incr(n__incr(zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x91)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(_x91)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x91)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(incr(_x91)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(zeros), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(n__adx(_x71)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(zeros)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(adx(activate(_x81))))))))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(n__0)), n__incr(activate(n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(n__incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(n__adx(adx(n__adx(n__0)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(n__adx(n__adx(n__adx(0)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__adx(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(adx(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(n__adx(adx(cons(n__0, n__zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__zeros)))))) → adx#(n__incr(adx(adx(n__incr(zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(zeros)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(incr(n__incr(0)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(incr(activate(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(adx(activate(_x131)))))))))))activate#(n__adx(n__adx(n__zeros))) → adx#(adx(zeros))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__zeros)) → adx#(zeros)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(n__adx(n__adx(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x61))))))) → adx#(n__incr(adx(n__adx(incr(n__s(_x61))))))activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(incr(adx(incr(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(cons(n__0, n__zeros))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(n__0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(n__adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(n__adx(adx(incr(zeros))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(adx(incr(zeros))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(n__adx(adx(n__adx(zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(n__0)), n__incr(activate(n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(n__incr(zeros)))))))
activate#(n__incr(n__0)) → incr#(n__0)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(n__adx(zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x101))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(_x101))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(n__incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(adx(n__adx(n__s(_x71)))))))activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__adx(_x71))))))) → adx#(n__incr(adx(adx(incr(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x101))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(_x101))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(incr(n__incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__adx(_x91))))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(adx(activate(_x91)))))))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(incr(adx(zeros)))
activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(adx(activate(_x101))), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(adx(incr(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(incr(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(n__zeros)))))))activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(incr(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(activate(n__0)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__zeros))) → adx#(incr(cons(n__0, n__zeros)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__adx(_x91))))))))) → adx#(n__incr(adx(adx(adx(incr(incr(adx(activate(_x91)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(incr(activate(_x101))))), n__incr(activate(n__incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(n__incr(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(incr(activate(_x131)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(n__adx(adx(adx(zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(n__adx(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x71))))))) → adx#(n__incr(n__adx(adx(incr(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(n__s(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(s(_x131))))))))))
activate#(n__adx(n__adx(_x21))) → adx#(n__adx(_x21))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__0))) → adx#(incr(0))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__incr(_x71))))))) → adx#(n__incr(adx(adx(incr(incr(activate(_x71)))))))

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(activate(_x111)))))))))) 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
adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(_x121))))))))) 
adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(0))))))))) 
adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(_x101), n__incr(incr(activate(_x111)))))))))) 
adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(activate(_x111)))))))))) 
adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(incr(activate(_x121))))))))))) 
adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(n__incr(activate(_x111)))))))))) 
adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(zeros))))))))) 
adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(_x101), n__incr(incr(activate(_x111)))))))))) 
adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(_x101))), n__incr(activate(n__incr(incr(activate(_x111))))))))))) 
adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(adx(activate(_x121))))))))))) 
adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(s(_x121)))))))))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(activate(_x111)))))))))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(n__adx(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(adx(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(n__s(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(s(_x121))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(_x101))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(incr(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(_x101), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(_x101), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(_x121)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(activate(_x111), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(n__incr(activate(_x111))))))))))

Problem 25: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x111), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(_x111)), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(s(_x101)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(incr(activate(_x111)))), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(adx(activate(_x111)))), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(0)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(activate(_x121)))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(activate(_x71)))))))
activate#(n__adx(n__0)) → adx#(0)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(activate(_x71)))))))))
activate#(n__incr(n__s(_x31))) → incr#(n__s(_x31))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(zeros), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(n__s(_x101)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(n__incr(cons(n__0, n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(s(_x101)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(_x121)))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(n__adx(s(_x71))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(zeros)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x101))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(_x101))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(_x121)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(adx(activate(_x101))), n__incr(0))))))))
activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x51)))))) → adx#(n__incr(n__adx(n__adx(n__s(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(n__s(n__incr(0)))), n__adx(activate(n__incr(n__incr(incr(incr(activate(_x121)))))))))))))
activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(activate(_x72)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(n__0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(0))))), n__adx(activate(n__incr(n__incr(activate(_x71)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(incr(0))), n__incr(zeros))))))))activate#(n__adx(n__adx(n__incr(_x41)))) → adx#(n__adx(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(activate(_x72)))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(activate(_x72)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__0)))))) → adx#(n__incr(adx(adx(incr(0)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__zeros)))))) → adx#(n__incr(adx(adx(incr(zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(_x121))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(n__adx(incr(zeros))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(n__adx(n__incr(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(0)), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(n__incr(incr(activate(_x121)))))))))))
activate#(n__adx(n__adx(n__incr(_x41)))) → adx#(adx(incr(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(0))), n__incr(cons(n__0, n__zeros)))))))))
activate#(n__adx(n__adx(n__adx(_x41)))) → adx#(adx(adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(incr(zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(incr(activate(_x111)))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(incr(zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(_x101), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(_x101), n__incr(n__0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))
activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(incr(n__adx(_x51)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(n__s(_x131)))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(incr(s(_x131)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(_x121)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(_x121)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(incr(0)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(0)), n__incr(adx(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(0)), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(n__incr(incr(activate(_x121)))))))))))activate#(n__adx(n__adx(n__0))) → adx#(adx(n__0))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__0))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(activate(_x72)), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(n__s(_x111))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(zeros))))))))
activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(incr(activate(_x111)))), n__incr(0))))))))activate#(n__adx(n__adx(n__zeros))) → adx#(n__adx(cons(n__0, n__zeros)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(adx(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(activate(_x111)))), n__incr(cons(n__0, n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(incr(activate(s(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(_x121)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(n__incr(activate(_x71)))))))
activate#(n__adx(_x21)) → adx#(_x21)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(cons(_x62, _x61)))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(_x62)), n__incr(activate(_x61))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x111)), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(s(_x111))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x111), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(_x111)), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(_x121))), n__incr(cons(n__0, n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(n__0))), n__incr(incr(activate(n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(incr(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(activate(_x71)))))))))activate#(n__adx(n__adx(cons(_x22, _x21)))) → adx#(incr(cons(activate(_x22), n__adx(activate(_x21)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(incr(activate(_x101))))), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(n__adx(adx(n__adx(s(_x71))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x101)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(n__adx(_x101))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(n__incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__adx(_x121))), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(adx(activate(_x121))))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(n__adx(adx(n__s(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__incr(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x71)))))))) → adx#(n__incr(adx(n__adx(adx(incr(n__incr(_x71)))))))
adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x81))))))) → adx#(n__incr(adx(adx(adx(adx(_x81))))))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))
activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(incr(n__adx(zeros)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(zeros)), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(n__adx(_x121))), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(adx(activate(_x121))))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(zeros)))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(n__0)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(cons(n__0, n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x101))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(_x101))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__incr(adx(activate(_x71)))))))
activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(s(_x101)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(zeros)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(n__0)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(adx(activate(_x121)))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(0))))), n__adx(activate(n__incr(activate(n__incr(activate(_x71))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(n__adx(incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(adx(activate(_x111)))), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x101))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(_x101))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(n__0))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__s(_x111)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(n__incr(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(0), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(_x101), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x111))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(_x111))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(zeros)), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__adx(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(0), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__s(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(s(_x121))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(0), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x61))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__0)))))) → adx#(n__incr(adx(adx(n__incr(0)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(incr(activate(_x101))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(n__incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x71)))))) → adx#(n__incr(adx(adx(incr(_x71)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(activate(_x72)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(activate(n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(0)), n__incr(zeros))))))))activate#(n__adx(n__adx(n__0))) → adx#(n__adx(0))
activate#(n__adx(n__adx(n__adx(_x41)))) → adx#(n__adx(adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(activate(_x111)))), n__incr(n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(n__incr(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(adx(activate(_x101))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(s(_x121))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(incr(activate(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(0), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(_x121))), n__incr(n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(adx(incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x71))))))) → adx#(n__incr(adx(adx(n__incr(s(_x71))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(incr(0)), n__incr(_x111))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(n__s(_x101)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(incr(activate(_x101))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(n__adx(n__0)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(_x101), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(incr(0)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__adx(n__s(_x31)))) → adx#(n__adx(n__s(_x31)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(activate(_x72)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(n__0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(incr(activate(_x101))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(activate(n__0)))), n__incr(activate(n__incr(activate(n__zeros))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(0)))), n__adx(activate(n__incr(activate(n__incr(s(_x111))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(0))))), n__adx(activate(n__incr(n__incr(incr(activate(_x101))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(incr(0)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__adx(s(_x81)))))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x71)))))) → adx#(n__incr(adx(adx(n__incr(_x71)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(activate(_x111)))), n__incr(n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(n__adx(activate(_x111)))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(0), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(activate(n__0)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(activate(_x72)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(n__adx(_x131)))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(incr(adx(activate(_x131))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(0)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(n__0)), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(_x121)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x111), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(_x111)), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(n__0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(s(_x101)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(n__0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(zeros)), n__incr(zeros))))))))
activate#(n__incr(_x21)) → incr#(_x21)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__incr(_x91))))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(incr(activate(_x91)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(n__adx(adx(zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(incr(n__incr(zeros)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x91)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(incr(_x91)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x91)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(_x91)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(s(_x121))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(zeros), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x101))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(_x101))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(incr(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(zeros)), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(n__incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(_x121))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__adx(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(adx(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(n__adx(adx(cons(n__0, n__zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__zeros)))))) → adx#(n__incr(adx(adx(n__incr(zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(activate(_x101)))))), n__adx(activate(n__incr(activate(n__incr(activate(_x71))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(n__0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(incr(activate(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(incr(activate(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__zeros)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(zeros))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__zeros)) → adx#(zeros)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(_x131))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(n__incr(0))))))))activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(n__adx(n__adx(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x61))))))) → adx#(n__incr(adx(n__adx(incr(n__s(_x61))))))activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(incr(adx(incr(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(cons(_x102, _x101))), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(incr(cons(activate(_x102), n__adx(activate(_x101)))))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(n__adx(adx(incr(zeros))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(adx(incr(zeros))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(incr(0)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(n__adx(adx(n__adx(zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(incr(incr(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(cons(n__0, n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x101))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(_x101))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(n__incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x101))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(_x101))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(_x111))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x111))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(incr(n__incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__incr(_x121))), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(incr(activate(_x121))))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__adx(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(adx(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(incr(adx(zeros)))
activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(incr(s(_x81)))))))
activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__incr(_x121))), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(incr(activate(_x121))))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(activate(n__incr(zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(activate(_x111)))), n__incr(n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(n__adx(adx(adx(zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__zeros)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(zeros))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(0))))), n__adx(activate(n__incr(n__incr(incr(0)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(n__adx(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(n__s(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(s(_x131))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x71))))))) → adx#(n__incr(n__adx(adx(incr(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(n__0))), n__incr(n__incr(incr(incr(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__incr(_x71))))))) → adx#(n__incr(adx(adx(incr(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(s(_x111))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__adx(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(adx(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(s(_x111))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x111), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(_x111)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(n__incr(_x131)))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(incr(incr(activate(_x131))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(incr(incr(activate(_x121))))))))))))activate#(n__incr(X)) → activate#(X)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(n__0)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(n__0))), n__incr(n__incr(incr(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(adx(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(incr(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x101))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(n__incr(_x101))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(incr(0)), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(s(_x121))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(incr(activate(_x101))), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(0), n__incr(incr(incr(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x91), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x91))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(incr(activate(_x111)))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(n__s(n__incr(0)))), n__adx(activate(n__incr(n__incr(incr(activate(_x101))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__adx(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(adx(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(adx(activate(_x121)))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(_x101))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__adx(_x121))), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(adx(activate(_x121))))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(n__adx(zeros))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x91), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(n__s(_x91))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(activate(_x111)))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(cons(n__0, n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__s(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(s(_x121))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(n__adx(adx(adx(n__s(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(incr(adx(0)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(n__adx(adx(adx(adx(n__s(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(0)), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(incr(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(0))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(n__incr(0))), n__incr(zeros))))))))
activate#(n__incr(n__zeros)) → incr#(zeros)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__0))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(0), n__incr(0))))))))activate#(n__adx(n__adx(_x41))) → adx#(n__adx(_x41))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(n__incr(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(incr(activate(_x111)))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(_x121)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__0))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(incr(adx(s(_x51))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__s(_x91))))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(s(_x91))))))))
incr#(cons(X, Y)) → activate#(Y)activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__zeros))))))) → adx#(n__incr(adx(adx(adx(adx(zeros))))))activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(incr(n__adx(incr(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(activate(_x111), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(n__incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__incr(_x91))))))))) → adx#(n__incr(adx(adx(adx(incr(incr(incr(activate(_x91)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(s(_x121))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(n__incr(s(_x101)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__adx(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(n__incr(adx(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(n__incr(n__zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x61))))))) → adx#(n__incr(adx(adx(n__incr(n__s(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x111))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(0), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(n__adx(incr(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(0)), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__s(_x91))))))))) → adx#(n__incr(adx(adx(adx(incr(incr(s(_x91))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x111), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(_x111)), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(incr(activate(_x121)))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__0), n__incr(activate(n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(n__zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(0)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(activate(_x101)))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__0))), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(adx(activate(_x111)))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x71))))))) → adx#(n__incr(adx(n__adx(incr(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(0)))), n__adx(activate(n__incr(activate(n__incr(activate(_x71))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(n__adx(incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(n__adx(adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(n__incr(cons(n__0, n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x61))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(incr(adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(0)), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(adx(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(n__adx(0)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(n__0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(activate(n__0)), n__incr(n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(s(_x101)), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(n__zeros)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(zeros))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(adx(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x111)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(s(_x111))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(n__adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(0)))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(incr(n__adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(n__s(_x101)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(s(_x101)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(n__s(_x121))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(_x101), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__0))))))) → adx#(n__incr(adx(adx(adx(adx(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(0))), n__incr(n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(n__adx(s(_x61)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(0)), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(incr(activate(_x101))))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(0)), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(n__adx(adx(zeros))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(s(n__0)), n__incr(activate(n__incr(n__zeros)))))))))activate#(n__adx(n__adx(n__zeros))) → adx#(n__adx(n__zeros))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(incr(activate(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(cons(n__0, n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__adx(n__incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(incr(activate(_x101))))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(0), n__incr(activate(n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__adx(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(adx(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(0)), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(incr(n__adx(s(_x51))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(n__0), n__incr(activate(n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(incr(activate(_x121)))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(incr(cons(activate(n__0), n__adx(activate(n__zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(n__incr(cons(n__0, n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(incr(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(incr(0)))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(incr(adx(_x51)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x111), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(_x111)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x61))))))) → adx#(n__incr(n__adx(adx(incr(n__s(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__adx(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(adx(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(activate(_x72)))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__adx(n__s(_x41)))) → adx#(n__adx(s(_x41)))
incr#(cons(X, Y)) → activate#(X)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x111)), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(s(_x111))), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__0))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__0))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(0)), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x131)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(_x131)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(0), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(zeros), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(s(_x101)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(n__0))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(0))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x91)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(_x91)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(adx(activate(_x101))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x111))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(_x111))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(incr(0)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(n__adx(adx(n__incr(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(n__adx(adx(incr(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(n__zeros))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(s(_x111))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(n__adx(cons(n__0, n__zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(incr(_x131))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__0))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(_x101), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(n__adx(_x131)))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(adx(activate(_x131))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(0), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(activate(n__0)))), n__incr(activate(n__incr(n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(cons(n__0, n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x91)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(_x91)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(zeros), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__s(_x121))), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(s(_x121)))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(adx(activate(_x111)))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(zeros))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(incr(activate(activate(_x71))))))))))activate#(n__adx(n__incr(n__zeros))) → adx#(incr(n__zeros))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(adx(activate(_x121)))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(incr(activate(_x121)))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(n__zeros))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(incr(zeros))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(0)), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(incr(n__zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(cons(_x62, _x61)))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(_x62)), n__incr(activate(_x61))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(n__incr(_x121))), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(incr(activate(_x121))))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(incr(n__zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(n__adx(adx(n__adx(_x71)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(n__0)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(0))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(0)), n__incr(_x111))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(incr(adx(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x91), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__s(_x91)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(_x121)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(n__adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(n__0))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(incr(0))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(zeros)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__s(_x121))), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(s(_x121)))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(_x121))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(activate(_x111)))), n__incr(cons(n__0, n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(n__s(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(s(_x121))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(n__zeros))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(zeros))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(zeros)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(incr(0)))), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(zeros)), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__incr(incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(adx(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(n__incr(activate(_x111)))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(incr(activate(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(n__adx(_x71)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(n__incr(_x131)))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(incr(activate(_x131))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(n__s(n__0)), n__incr(activate(n__incr(n__zeros)))))))))
activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(n__0)), n__incr(activate(n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(incr(0)))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(n__adx(adx(n__adx(n__0)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(n__adx(n__adx(n__adx(0)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(n__incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(n__s(_x131)))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(s(_x131)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(0)), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x101))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(0))))), n__adx(activate(n__incr(n__incr(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(incr(n__incr(0)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(n__adx(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(adx(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(adx(activate(_x131)))))))))))
activate#(n__adx(n__adx(n__zeros))) → adx#(adx(zeros))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(activate(_x101)))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(s(n__incr(0)))), n__adx(activate(n__incr(n__incr(incr(activate(_x101))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(cons(n__0, n__zeros))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(n__s(_x121))), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(s(_x121)))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(n__0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(n__adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(n__0))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(_x101))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(activate(_x111)))), n__incr(cons(n__0, n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x101))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(_x101))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(n__0)), n__incr(activate(n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(incr(incr(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__s(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(s(_x121))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(n__incr(zeros)))))))
activate#(n__incr(n__0)) → incr#(n__0)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(n__adx(zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__s(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(s(_x121))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(adx(n__adx(n__s(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(zeros)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__adx(_x71))))))) → adx#(n__incr(adx(adx(incr(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(n__0))), n__incr(n__incr(n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__adx(_x91))))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(adx(activate(_x91)))))))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(n__incr(activate(_x111)))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(adx(activate(_x101))), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(adx(incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(0)), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(_x111))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(n__zeros)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(incr(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(activate(n__0)), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__zeros))) → adx#(incr(cons(n__0, n__zeros)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__adx(_x91))))))))) → adx#(n__incr(adx(adx(adx(incr(incr(adx(activate(_x91)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(incr(activate(_x101))))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(adx(activate(_x121)))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(n__incr(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(incr(activate(_x131)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(n__0)), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(_x121)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__adx(_x21))) → adx#(n__adx(_x21))activate#(n__adx(n__incr(n__0))) → adx#(incr(0))

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(0))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
adx#(n__incr(adx(n__adx(adx(n__incr(n__incr(0))))))) 
adx#(n__incr(adx(n__adx(n__adx(n__incr(incr(0))))))) 
adx#(n__incr(n__adx(n__adx(adx(n__incr(incr(0))))))) 
adx#(n__incr(adx(n__adx(adx(n__incr(incr(n__0))))))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(0))))))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(n__0)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(n__incr(0)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(incr(0)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(incr(0)))))))

Problem 26: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x111), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(_x111)), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(s(_x101)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(incr(activate(_x111)))), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(adx(activate(_x111)))), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(n__0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(activate(_x72)), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(0))))), n__adx(activate(n__incr(n__incr(activate(_x71)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(_x141))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(adx(_x141)))))))))))activate#(n__adx(n__adx(n__incr(_x41)))) → adx#(n__adx(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(activate(_x72)))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(_x121))))), n__adx(activate(n__incr(activate(n__incr(activate(_x71))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__zeros)))))) → adx#(n__incr(adx(adx(incr(zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(_x121))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(n__adx(n__adx(s(_x71))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(0)), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(adx(incr(activate(_x121)))))))))))
activate#(n__adx(n__adx(n__adx(_x41)))) → adx#(adx(adx(activate(_x41))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(incr(zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(incr(activate(_x111)))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(incr(0)))))), n__adx(activate(n__incr(activate(n__incr(adx(activate(_x111)))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(incr(activate(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(_x121)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(incr(0)))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(0)), n__incr(adx(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__0))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(0))))))))
activate#(n__adx(n__adx(n__0))) → adx#(adx(n__0))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__adx(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(incr(adx(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(activate(_x72)), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(n__s(_x111))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(s(_x101)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__s(_x31))) → adx#(n__s(_x31))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(incr(activate(_x111)))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__adx(n__zeros))) → adx#(n__adx(cons(n__0, n__zeros)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(adx(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(n__0))))), n__incr(activate(n__incr(adx(adx(activate(_x131))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(n__adx(activate(_x131))))))))))))activate#(n__adx(n__adx(cons(_x22, _x21)))) → adx#(incr(cons(activate(_x22), n__adx(activate(_x21)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(n__adx(adx(n__adx(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(adx(activate(_x101))), n__incr(n__0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(adx(activate(_x101))), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(n__incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__adx(_x121))), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(adx(activate(_x121))))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(activate(_x71)))))))))adx#(cons(X, Y)) → incr#(cons(activate(X), n__adx(activate(Y))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x81))))))) → adx#(n__incr(adx(adx(adx(adx(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(adx(_x121)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(0)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(n__incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(_x121))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(zeros)), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(zeros)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(n__0)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__incr(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x101))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(_x101))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(activate(_x101)))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(s(_x101)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(0))))), n__adx(activate(n__incr(activate(n__incr(activate(_x71))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(incr(activate(_x121))))))), n__adx(activate(n__incr(activate(n__incr(activate(_x71))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(_x121))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(adx(activate(_x111)))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(n__0))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x101))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(_x101))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__adx(_x131))), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(adx(activate(_x131))))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(zeros)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(0), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x61))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__0)))))) → adx#(n__incr(adx(adx(n__incr(0)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(n__incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x71)))))) → adx#(n__incr(adx(adx(incr(_x71)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(n__0))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(activate(n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(n__incr(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(adx(activate(_x101))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(adx(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(0), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(_x121))), n__incr(n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(adx(incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(n__incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(n__adx(adx(_x61))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(n__s(_x101)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x121)), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(s(_x121))))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(n__incr(n__adx(n__0)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(_x101), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(incr(0)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__adx(n__s(_x31)))) → adx#(n__adx(n__s(_x31)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(activate(_x72)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(n__0))))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(activate(n__0)))), n__incr(activate(n__incr(activate(n__zeros))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(incr(0)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(adx(0)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(zeros), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(n__adx(_x131)))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(incr(adx(activate(_x131))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(0)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x91))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(_x121)))), n__incr(incr(activate(_x91)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x111), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(_x111)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__incr(n__s(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(incr(s(_x131)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(zeros)), n__incr(zeros))))))))
activate#(n__incr(_x21)) → incr#(_x21)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(incr(n__incr(zeros)))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(n__adx(n__adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(_x111))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x91)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(_x91)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x101))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(_x101))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(incr(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__incr(0))))), n__incr(activate(n__incr(adx(adx(activate(_x131))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(adx(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(_x121)))), n__incr(activate(n__incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(n__0))))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(n__incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(_x121))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__adx(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(adx(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(n__adx(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(adx(adx(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x111))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(_x121))))), n__adx(activate(n__incr(activate(n__incr(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(n__adx(adx(cons(n__0, n__zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__zeros)))))) → adx#(n__incr(adx(adx(n__incr(zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(activate(_x101)))))), n__adx(activate(n__incr(activate(n__incr(activate(_x71))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(_x121)))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__zeros)) → adx#(zeros)activate#(n__incr(n__adx(_x21))) → incr#(adx(activate(_x21)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(n__adx(n__adx(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(cons(_x102, _x101))), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(incr(cons(activate(_x102), n__adx(activate(_x101)))))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(n__adx(adx(n__adx(zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(incr(0)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(incr(incr(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(n__incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(adx(zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x101))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(_x101))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(incr(n__incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x111))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(n__s(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(adx(s(_x121))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__adx(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(adx(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(s(n__incr(_x121)))), n__adx(activate(n__incr(activate(n__incr(activate(_x71))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(adx(adx(0))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(s(_x121))))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(incr(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(0))))))))))activate#(n__adx(n__incr(n__0))) → adx#(n__incr(0))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__incr(_x121))), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(incr(activate(_x121))))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(activate(n__incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(activate(_x111)))), n__incr(n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(n__adx(adx(adx(zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(_x111))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(_x131))))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(adx(activate(_x131))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__zeros)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(zeros))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(0))))), n__adx(activate(n__incr(n__incr(incr(0)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(n__s(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(s(_x131))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x71))))))) → adx#(n__incr(n__adx(adx(incr(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(n__0))), n__incr(n__incr(incr(incr(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(activate(_x121)))))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(incr(activate(_x121)))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(zeros))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__adx(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(adx(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x111), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(_x111)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(n__incr(_x131)))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(incr(incr(activate(_x131))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(incr(incr(activate(_x121))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(n__incr(adx(adx(activate(_x131)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(s(_x121))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(0), n__incr(incr(incr(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x91), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x91))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(n__s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(n__s(n__incr(0)))), n__adx(activate(n__incr(n__incr(incr(activate(_x101))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), 0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__incr(0))))), n__incr(activate(n__incr(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(incr(0)))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(adx(activate(_x121)))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(_x101))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__adx(_x121))), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(adx(activate(_x121))))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__0))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(activate(_x111)))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__s(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(s(_x121))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(n__adx(adx(adx(n__s(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(adx(zeros))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(0))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(n__incr(0))), n__incr(zeros))))))))activate#(n__incr(n__zeros)) → incr#(zeros)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(n__0))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(activate(_x101)))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__0))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(0), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(n__incr(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(incr(activate(_x111)))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__0))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__s(_x91))))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(s(_x91))))))))
incr#(cons(X, Y)) → activate#(Y)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(incr(activate(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(activate(_x111), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(n__incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(incr(n__adx(incr(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(n__incr(adx(incr(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__incr(_x91))))))))) → adx#(n__incr(adx(adx(adx(incr(incr(incr(activate(_x91)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(n__incr(s(_x101)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(n__incr(_x111)), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(adx(incr(activate(_x111)))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(n__incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(n__incr(n__zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x61))))))) → adx#(n__incr(adx(adx(n__incr(n__s(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(incr(0)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(zeros), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x111))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(0), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(adx(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(0)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__s(_x91))))))))) → adx#(n__incr(adx(adx(adx(incr(incr(s(_x91))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(n__zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__0), n__incr(activate(n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__0))))) → adx#(n__incr(n__adx(adx(0))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(0)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__incr(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__0))), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(_x121))), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x71))))))) → adx#(n__incr(adx(n__adx(incr(s(_x71))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x131)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(adx(_x131))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(adx(n__adx(incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(n__incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(0)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(adx(adx(n__adx(0)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(n__incr(n__0)), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(activate(_x121)))))), n__incr(activate(n__incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(s(_x101)), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(n__adx(adx(adx(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(adx(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x111))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(n__adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(incr(zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(incr(n__adx(adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(0)))))))activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(adx(activate(_x51)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(s(n__incr(_x121))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(n__0)), n__incr(_x111))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(n__s(_x121))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(0))), n__incr(n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__0))))))) → adx#(n__incr(adx(adx(adx(adx(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(_x101), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(adx(n__adx(s(_x61)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__zeros), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(incr(activate(_x101))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(s(n__0)), n__incr(activate(n__incr(n__zeros)))))))))
activate#(n__adx(n__adx(n__zeros))) → adx#(n__adx(n__zeros))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(n__0))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__zeros)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(zeros))))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(incr(activate(_x101))))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__adx(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(adx(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(0)), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(_x121))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(incr(cons(activate(n__0), n__adx(activate(n__zeros)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(incr(0)))), n__incr(activate(n__incr(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(n__incr(cons(n__0, n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(incr(activate(adx(adx(activate(_x131))))))))))))
activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(incr(adx(_x51)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(n__zeros))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(adx(zeros)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x111), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(_x111)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__adx(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(adx(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x111)), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(s(_x111))), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(n__0), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(adx(0)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(0)), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(_x121))), n__incr(activate(n__incr(zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__0))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(incr(activate(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x131)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(_x131)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__incr(0))))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x91)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(_x91)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(adx(activate(_x101))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(incr(0)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(n__adx(adx(incr(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(zeros))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(adx(n__zeros))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(incr(_x131))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(n__adx(_x131)))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(adx(activate(_x131))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__0))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(_x101), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(activate(n__0)))), n__incr(activate(n__incr(n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(n__adx(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__s(_x121))), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(s(_x121)))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(zeros))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(incr(0)))), n__incr(activate(n__incr(adx(adx(activate(_x131))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(incr(activate(incr(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(0)), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(incr(0))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(incr(activate(_x121)))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(n__zeros))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(incr(zeros))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x61))))) → adx#(n__incr(adx(adx(_x61))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(n__incr(_x121))), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(incr(activate(_x121))))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(s(_x101)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__s(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(s(_x131)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(incr(n__zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(cons(n__0, n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(n__0)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(0))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(zeros)))))))))activate#(n__adx(n__0)) → adx#(n__0)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(adx(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x91), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__s(_x91)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(incr(adx(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(s(_x101)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(activate(_x101)))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(n__adx(_x141)))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(adx(adx(activate(_x141)))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(_x121)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(n__adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(n__0))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(incr(0))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(n__zeros))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(zeros))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(n__s(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(s(_x121))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(zeros)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(incr(0)))), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(n__incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(adx(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(activate(_x101)))))), n__adx(activate(n__incr(activate(n__incr(adx(activate(_x111)))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(incr(activate(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(_x121))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(n__incr(_x131)))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(incr(activate(_x131))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(n__s(n__0)), n__incr(activate(n__incr(n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(n__adx(_x111)), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(adx(adx(activate(_x111)))), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(n__0)), n__incr(activate(n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(n__incr(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x91))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(incr(activate(_x91)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x101))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(0))))), n__adx(activate(n__incr(n__incr(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(incr(_x121)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(n__adx(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(adx(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(n__0)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(adx(cons(n__0, n__zeros))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(n__s(_x121))), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(s(_x121)))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(adx(n__adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(_x101))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(activate(_x111)))), n__incr(cons(n__0, n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(n__0)), n__incr(activate(n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__s(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(s(_x121))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(n__incr(zeros)))))))activate#(n__incr(n__0)) → incr#(n__0)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(adx(n__adx(zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__s(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(s(_x121))))))))))
activate#(n__adx(n__incr(n__zeros))) → adx#(n__incr(zeros))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__adx(_x71))))))) → adx#(n__incr(adx(adx(incr(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__adx(_x91))))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(adx(activate(_x91)))))))))
activate#(n__adx(n__incr(n__s(_x41)))) → adx#(n__incr(s(_x41)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(adx(activate(_x101))), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(incr(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(activate(n__0)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__zeros))) → adx#(incr(cons(n__0, n__zeros)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(incr(activate(_x101))))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(n__incr(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(incr(activate(_x131)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(incr(0)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(incr(0)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(n__0)), n__incr(_x111))))))))
activate#(n__adx(n__adx(_x21))) → adx#(n__adx(_x21))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__incr(n__0))) → adx#(incr(0))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x61))))))) → adx#(n__incr(adx(adx(n__adx(n__s(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(n__0))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(n__s(_x141)))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(adx(s(_x141))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__incr(_x131)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(incr(_x131))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(n__s(_x101)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(n__incr(cons(n__0, n__zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(activate(_x121)))))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(_x111))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(_x121))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(_x121)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x101))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(_x101))))))))activate#(n__adx(n__incr(_x41))) → adx#(n__incr(_x41))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(n__s(n__incr(0)))), n__adx(activate(n__incr(n__incr(incr(incr(activate(_x121)))))))))))))activate#(n__adx(n__incr(n__adx(_x41)))) → adx#(n__incr(n__adx(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(incr(0))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__s(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(incr(s(_x121))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(activate(_x72)))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__0)))))) → adx#(n__incr(adx(adx(incr(0)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(n__adx(incr(zeros))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(n__adx(n__incr(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(0))), n__incr(cons(n__0, n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(n__incr(incr(activate(_x121)))))))))))activate#(n__adx(n__adx(n__incr(_x41)))) → adx#(adx(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(activate(_x121)))))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(_x101), n__incr(n__0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(_x101), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(incr(zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(incr(activate(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(n__zeros), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(adx(zeros)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(incr(n__adx(_x51)))activate#(n__adx(n__incr(n__adx(_x51)))) → adx#(n__incr(adx(_x51)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(activate(_x111)), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(n__incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(n__s(_x131)))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(incr(s(_x131)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(_x121)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(0)), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(n__incr(incr(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(activate(_x101)))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(adx(n__adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(n__adx(adx(adx(adx(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(adx(adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(incr(activate(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(activate(_x111)))), n__incr(cons(n__0, n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(_x121)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__s(_x71))))))) → adx#(n__incr(adx(adx(adx(s(_x71))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(adx(_x71)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(adx(n__incr(activate(_x71)))))))
activate#(n__adx(_x21)) → adx#(_x21)activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(cons(_x62, _x61)))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(_x62)), n__incr(activate(_x61))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x111)), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(s(_x111))), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x111), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(_x111)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(_x121))), n__incr(cons(n__0, n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(n__0))), n__incr(incr(activate(n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(activate(_x101)))))), n__adx(activate(n__incr(n__incr(activate(_x71)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(incr(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(incr(zeros))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(incr(activate(_x101))))), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x101)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(n__adx(_x101))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(n__0))))), n__adx(activate(n__incr(activate(n__incr(incr(activate(_x111)))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(n__adx(adx(n__s(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__incr(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(zeros), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x71)))))))) → adx#(n__incr(adx(n__adx(adx(incr(n__incr(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(incr(n__adx(zeros)))
activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(n__incr(adx(zeros)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(n__adx(_x121))), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(adx(activate(_x121))))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(cons(n__0, n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(incr(activate(_x121))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__incr(n__incr(_x21))) → incr#(incr(activate(_x21)))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(n__incr(adx(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__0), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(zeros)), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(n__0)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(adx(activate(_x121)))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(incr(zeros))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(n__adx(incr(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(_x121)))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__s(_x111)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(n__incr(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(0), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(n__adx(adx(activate(_x131))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__s(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(incr(s(_x131)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(_x101), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x111))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(_x111))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__adx(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(0), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__s(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(s(_x121))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(n__s(n__incr(_x121)))), n__adx(activate(n__incr(activate(n__incr(activate(_x71))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(incr(activate(_x101))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(_x121)))), n__incr(incr(activate(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(activate(_x72)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(0)), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(activate(_x111)))), n__incr(n__zeros))))))))activate#(n__adx(n__adx(n__adx(_x41)))) → adx#(n__adx(adx(activate(_x41))))
activate#(n__adx(n__adx(n__0))) → adx#(n__adx(0))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(n__incr(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(adx(incr(activate(_x131))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(s(_x121))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(incr(activate(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__incr(0))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x71))))))) → adx#(n__incr(adx(adx(n__incr(s(_x71))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(incr(0)), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(_x121)))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), n__0))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(adx(activate(_x101))), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x111), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(adx(_x111)), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(adx(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(adx(0))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x101)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(s(_x101)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(incr(activate(_x101))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(n__s(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(adx(s(_x131)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(zeros), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(incr(activate(_x101))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(n__0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(0)))), n__adx(activate(n__incr(activate(n__incr(s(_x111))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(0))))), n__adx(activate(n__incr(n__incr(incr(activate(_x101))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(n__adx(adx(n__adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x71)))))) → adx#(n__incr(adx(adx(n__incr(_x71)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(adx(adx(activate(_x131))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(n__adx(activate(_x111)))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(activate(_x111)))), n__incr(n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(0), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(activate(n__0)), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(activate(_x72)))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(n__0)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(n__0)), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(_x121)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(_x121)))), n__incr(activate(n__incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x131)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(_x131))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(n__0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(n__0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(s(_x101)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(incr(adx(activate(_x131))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(n__0))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(adx(0)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__incr(_x91))))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(incr(activate(_x91)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(n__s(_x111)), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(adx(s(_x111))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__zeros)))))) → adx#(n__incr(adx(n__adx(adx(zeros)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(adx(activate(_x121)))))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x91)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(incr(_x91)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(s(_x121))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__incr(activate(_x121)))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(incr(0)))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(incr(activate(_x121))))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(zeros), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(0))))), n__adx(activate(n__incr(n__incr(s(_x101)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(zeros)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(n__incr(_x141)))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(adx(incr(activate(_x141)))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(incr(0))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(cons(n__0, n__zeros)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(n__0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__adx(activate(_x101))), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(incr(activate(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(_x131)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(_x131))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(incr(activate(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__zeros)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(zeros))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(_x131))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(zeros)))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(n__incr(adx(n__adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x61))))))) → adx#(n__incr(adx(n__adx(incr(n__s(_x61))))))
activate#(n__adx(n__incr(n__adx(n__incr(_x51))))) → adx#(incr(adx(incr(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__incr(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(incr(activate(_x131))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(adx(s(_x81)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(n__adx(adx(incr(zeros))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__zeros))))))) → adx#(n__incr(adx(adx(adx(incr(zeros))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(incr(incr(activate(_x131))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(activate(_x101))), n__incr(cons(n__0, n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x101))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(_x101))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__incr(_x121))), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(incr(activate(_x121))))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(_x121)))), n__incr(n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__zeros)))) → adx#(incr(adx(zeros)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(incr(0)))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(zeros), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(incr(0)))), n__incr(activate(n__incr(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x61)))))) → adx#(n__incr(adx(n__adx(n__adx(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(activate(_x72)), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(adx(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__incr(_x71))))))) → adx#(n__incr(adx(adx(incr(incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(s(_x111))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(s(_x111))), n__incr(zeros))))))))activate#(n__incr(X)) → activate#(X)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(n__incr(_x121))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(n__0))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(n__0)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(n__0))))), n__incr(activate(n__incr(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x101))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(n__incr(_x101))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(incr(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(n__0)), n__incr(_x111))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(incr(0)), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(incr(activate(_x101))), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(incr(activate(_x111)))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__adx(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(s(_x101))), n__incr(n__incr(adx(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__s(_x131))), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(s(_x131)))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(n__adx(zeros))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x91), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(s(n__s(_x91))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x111))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(incr(0)))))), n__adx(activate(n__incr(activate(n__incr(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__incr(_x81)))))))) → adx#(n__incr(adx(adx(adx(adx(incr(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(cons(n__0, n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__0)))) → adx#(incr(adx(0)))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(n__adx(adx(adx(adx(n__s(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(0), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(incr(incr(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(0)), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(_x81))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x71))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(incr(0)))))), n__adx(activate(n__incr(activate(n__incr(activate(_x71))))))))))))
activate#(n__adx(n__adx(_x41))) → adx#(n__adx(_x41))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(incr(_x121)))))))))activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(incr(adx(s(_x51))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__zeros))))))) → adx#(n__incr(adx(adx(adx(adx(zeros))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(s(_x121))))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__adx(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(n__incr(adx(activate(_x101))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(n__incr(adx(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(n__incr(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(adx(n__adx(incr(activate(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(adx(activate(_x131))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__s(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x111), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(_x111)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(_x121)))), n__incr(activate(n__incr(s(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(incr(activate(_x121)))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(n__0))))), n__adx(activate(n__incr(activate(n__incr(activate(_x71))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(activate(_x101)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(adx(activate(_x111)))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(incr(0)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(0)))), n__adx(activate(n__incr(activate(n__incr(activate(_x71))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(_x71))))))) → adx#(n__incr(adx(n__adx(adx(adx(activate(_x71)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x61))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(_x61))))))
activate#(n__adx(n__incr(n__adx(n__adx(_x51))))) → adx#(incr(adx(adx(activate(_x51)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(incr(activate(adx(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(activate(n__0)), n__incr(activate(n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(adx(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(n__0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(incr(0)))), n__incr(activate(n__incr(adx(adx(activate(_x131))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(activate(n__0)), n__incr(n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(n__adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(n__zeros)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(zeros))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(zeros)))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x111)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(s(_x111))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(_x121))), n__incr(incr(activate(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(activate(_x121)))))), n__incr(incr(activate(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(n__s(_x101)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(n__incr(s(_x101)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(s(_x101)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x111))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(s(_x101)))), n__incr(activate(n__incr(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(0)), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(0)), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(n__adx(adx(zeros))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(0)), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(incr(0)))))), n__adx(activate(n__incr(activate(n__incr(adx(adx(activate(_x131))))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(incr(activate(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(n__s(n__incr(_x121)))), n__adx(activate(n__incr(activate(n__incr(incr(activate(_x111)))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x71))))))) → adx#(n__incr(adx(adx(n__adx(n__incr(activate(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), _x71))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(n__s(_x111)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(cons(n__s(0), n__incr(activate(n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x101, n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(_x101), n__incr(incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(n__0), n__incr(activate(n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(incr(n__adx(s(_x51))))
activate#(n__adx(n__incr(n__adx(n__s(_x51))))) → adx#(n__incr(adx(s(_x51))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(incr(activate(_x121)))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x111))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(_x121)))), n__incr(activate(n__incr(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(n__incr(incr(cons(n__0, n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(zeros))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(incr(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(n__s(_x61))))))) → adx#(n__incr(n__adx(adx(incr(n__s(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__incr(_x131))), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(incr(activate(_x131))))))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(activate(_x72)))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))
activate#(n__adx(n__adx(n__s(_x41)))) → adx#(n__adx(s(_x41)))incr#(cons(X, Y)) → activate#(X)
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(n__incr(0)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__0))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(0))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(0)), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(0)), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__s(_x61)))))) → adx#(n__incr(n__adx(adx(s(_x61)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(0), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(s(_x101)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(zeros), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(n__0))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(0))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x111))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(0), n__incr(_x111))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__incr(_x61)))))) → adx#(n__incr(n__adx(adx(n__incr(activate(_x61))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(0)), n__incr(n__adx(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(n__0)), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__s(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(s(_x111))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__zeros))))) → adx#(n__incr(adx(n__adx(cons(n__0, n__zeros)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(0), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(activate(_x121)))))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(activate(_x101))), n__incr(cons(n__0, n__zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__adx(_x81)))))))) → adx#(n__incr(adx(adx(adx(incr(adx(activate(_x81))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(zeros), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x91)))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(incr(_x91)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(activate(_x121)))))), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x81)))))))) → adx#(n__incr(adx(adx(n__adx(adx(s(_x81)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(adx(activate(_x111)))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(incr(activate(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(activate(_x121)))))), n__incr(activate(n__incr(zeros)))))))))activate#(n__adx(n__incr(n__zeros))) → adx#(incr(n__zeros))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(adx(activate(_x121)))), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x111), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(n__s(_x111))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(_x41))) → adx#(incr(_x41))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(_x121)))), n__incr(n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(activate(_x101))), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__0), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(n__incr(0)), n__incr(s(_x111)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(incr(n__zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(cons(_x62, _x61)))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(_x62)), n__incr(activate(_x61))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(n__adx(adx(n__adx(_x71)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(0)), n__incr(_x111))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__s(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(n__s(s(_x101))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(incr(activate(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(zeros)), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__s(_x121))), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(s(_x121)))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(_x121))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x101))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(n__incr(_x101))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(adx(activate(_x121)))))), n__incr(activate(n__incr(adx(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(n__adx(n__incr(cons(n__s(n__incr(adx(activate(_x111)))), n__incr(cons(n__0, n__zeros)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(incr(zeros)), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(_x121)))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(activate(n__incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(n__incr(activate(_x111)))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(_x71)))))) → adx#(n__incr(adx(adx(n__adx(_x71)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(cons(n__s(incr(activate(_x101))), n__incr(s(_x111)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(n__incr(s(_x101)))))))))activate#(n__adx(n__incr(n__incr(_x41)))) → adx#(incr(incr(activate(_x41))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x121)), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(activate(_x121)))))), n__incr(activate(n__incr(incr(activate(_x111)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(activate(_x101))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(_x81)))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(incr(activate(_x81))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__incr(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(incr(adx(activate(_x131))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(incr(0)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(n__adx(adx(n__adx(n__0)))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__0)))))) → adx#(n__incr(n__adx(n__adx(n__adx(0)))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(n__s(_x131)))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(0))), n__incr(n__incr(incr(incr(s(_x131)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(0)), n__incr(activate(n__incr(s(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(adx(adx(incr(incr(zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__0)))))))) → adx#(n__incr(adx(n__adx(adx(incr(n__incr(0)))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(_x72, n__incr(n__adx(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(activate(_x72)), n__incr(incr(adx(activate(_x131)))))))))))
activate#(n__adx(n__adx(n__zeros))) → adx#(adx(zeros))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(activate(_x101)))), n__incr(activate(n__incr(activate(_x71))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x101)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(s(n__incr(0)))), n__adx(activate(n__incr(n__incr(incr(activate(_x101))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(n__adx(n__adx(n__adx(incr(0))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__0))))))) → adx#(n__incr(n__adx(n__adx(adx(incr(n__0))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), n__zeros))))))))) → adx#(n__incr(adx(n__adx(adx(n__incr(cons(n__s(n__incr(incr(n__0))), n__incr(zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(_x121)))), n__incr(activate(n__incr(activate(_x71))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), _x101))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(0)))), n__incr(n__incr(_x101))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__0), n__incr(incr(incr(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(zeros), n__incr(adx(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__adx(n__s(_x71)))))))) → adx#(n__incr(adx(adx(adx(n__adx(n__s(_x71)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__zeros), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(zeros)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(n__adx(n__adx(n__adx(cons(n__s(activate(n__s(n__0))), n__incr(n__incr(n__zeros))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x131)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(activate(n__incr(incr(_x131))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x101), n__adx(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(activate(_x101))))), n__incr(n__incr(adx(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(_x111)), n__zeros))))))))) → adx#(n__incr(n__adx(n__adx(adx(n__incr(cons(n__s(n__incr(n__incr(activate(_x111)))), n__incr(zeros))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(_x81))))))) → adx#(n__incr(adx(adx(adx(incr(_x81))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__0))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(incr(0)), n__incr(0))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__zeros)))))))) → adx#(n__incr(adx(n__adx(adx(incr(incr(n__zeros)))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__s(_x101)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(0))), n__incr(n__incr(s(_x101)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__0, _x71))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(0))), n__incr(n__incr(activate(_x71)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__adx(_x101), n__0))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(adx(activate(_x101))))), n__incr(activate(n__incr(0)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(n__adx(_x91))))))))) → adx#(n__incr(adx(adx(adx(incr(incr(adx(activate(_x91)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__adx(_x121)), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(adx(activate(_x121)))), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__incr(n__0)), _x111))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(incr(0))))), n__incr(n__incr(_x111))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), _x71))))))))) → adx#(n__incr(adx(n__adx(adx(incr(cons(n__s(n__incr(_x121)), n__incr(activate(_x71)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(_x121), n__incr(n__incr(_x131))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(_x121))), n__incr(activate(n__incr(incr(incr(activate(_x131))))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__zeros, n__s(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(incr(cons(n__s(zeros), n__incr(s(_x111)))))))))

Rewrite Rules

nats → adx(zeros)zeros → cons(n__0, n__zeros)
incr(cons(X, Y)) → cons(n__s(activate(X)), n__incr(activate(Y)))adx(cons(X, Y)) → incr(cons(activate(X), n__adx(activate(Y))))
hd(cons(X, Y)) → activate(X)tl(cons(X, Y)) → activate(Y)
0 → n__0zeros → n__zeros
s(X) → n__s(X)incr(X) → n__incr(X)
adx(X) → n__adx(X)activate(n__0) → 0
activate(n__zeros) → zerosactivate(n__s(X)) → s(X)
activate(n__incr(X)) → incr(activate(X))activate(n__adx(X)) → adx(activate(X))
activate(X) → X

Original Signature

Termination of terms over the following signature is verified: n__incr, tl, hd, n__adx, activate, n__s, nats, 0, n__0, s, zeros, adx, incr, n__zeros, cons

Strategy

The right-hand side of the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(activate(_x111)))))))))) 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
adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(incr(activate(_x121))))))))))) 
adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(n__0))), n__incr(n__incr(incr(activate(_x111)))))))))) 
adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(activate(_x111)))))))))) 
adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(zeros))))))))) 
adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(0))))))))) 
adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(activate(_x111)))))))))) 
adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(_x121))))))))) 
adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(adx(activate(_x121))))))))))) 
adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(s(_x121)))))))))) 
adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(n__incr(activate(_x111)))))))))) 
adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(n__0))))), n__adx(activate(n__incr(n__incr(incr(activate(_x111)))))))))))) 
adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(n__0))), n__incr(n__incr(incr(activate(_x111)))))))))) 
Thus, the rule activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(activate(_x111)))))))))) is replaced by the following rules:
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__zeros)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(zeros)))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(n__adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__incr(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(incr(activate(_x121)))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__0)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(0)))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(n__incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(n__s(n__incr(n__0))), n__incr(n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(incr(cons(activate(n__s(activate(n__s(n__incr(n__0))))), n__adx(activate(n__incr(n__incr(incr(activate(_x111))))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__adx(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(adx(activate(_x121)))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(n__s(_x121))))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(s(_x121))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(n__adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(activate(_x111))))))))))
activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x111)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(s(n__incr(n__0))), n__incr(n__incr(incr(activate(_x111))))))))))activate#(n__adx(n__incr(n__adx(n__adx(n__adx(n__incr(n__incr(cons(n__incr(n__0), n__incr(_x121)))))))))) → adx#(n__incr(adx(n__adx(adx(cons(n__s(activate(n__s(n__incr(n__0)))), n__incr(n__incr(incr(_x121)))))))))