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 PolynomialLinearRange4iUR (420ms).
 | – Problem 2 was processed with processor ForwardNarrowing (2ms).
 |    | – Problem 3 was processed with processor ForwardNarrowing (1ms).
 |    |    | – Problem 4 was processed with processor ForwardNarrowing (1ms).
 |    |    |    | – Problem 5 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    | – Problem 6 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    | – Problem 7 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    | – Problem 8 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    | – Problem 9 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (11ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (26ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (79ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (135ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (227ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (382ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 was processed with processor ForwardNarrowing (493ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 28 remains open; application of the following processors failed [ForwardNarrowing (512ms), ForwardNarrowing (480ms), ForwardNarrowing (timeout)].

The following open problems remain:



Open Dependency Pair Problem 2

Dependency Pairs

f#(a, f(a, x))f#(a, f(f(a, x), f(a, a)))f#(a, f(a, x))f#(a, a)
f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a


Problem 1: PolynomialLinearRange4iUR



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, x))f#(a, f(f(a, x), f(a, a)))f#(a, f(a, x))f#(f(a, x), f(a, a))
f#(a, f(a, x))f#(a, a)f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


Polynomial Interpretation

Improved Usable rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

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

f#(a, f(a, x))f#(f(a, x), f(a, a))

Problem 2: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, x))f#(a, f(f(a, x), f(a, a)))f#(a, f(a, x))f#(a, a)
f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, x)) → f#(a, f(f(a, x), f(a, a))) 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
f#(a, f(f(a, f(f(a, _x41), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, x)) → f#(a, f(f(a, x), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, _x41))) → f#(a, f(f(a, f(f(a, _x41), f(a, a))), f(a, a)))

Problem 3: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, _x41)))f#(a, f(f(a, f(f(a, _x41), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, a)
f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, _x41))) → f#(a, f(f(a, f(f(a, _x41), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, _x81), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, _x41))) → f#(a, f(f(a, f(f(a, _x41), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, _x81)))) → f#(a, f(f(a, f(f(a, f(f(a, _x81), f(a, a))), f(a, a))), f(a, a)))

Problem 4: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, x))f#(a, a)f#(a, f(a, x))f#(a, x)
f#(a, f(a, f(a, f(a, _x81))))f#(a, f(f(a, f(f(a, f(f(a, _x81), f(a, a))), f(a, a))), f(a, a)))

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, x)) → f#(a, a) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
Thus, the rule f#(a, f(a, x)) → f#(a, a) is deleted.

Problem 5: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, x))f#(a, x)f#(a, f(a, f(a, f(a, _x81))))f#(a, f(f(a, f(f(a, f(f(a, _x81), f(a, a))), f(a, a))), f(a, a)))

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, _x81)))) → f#(a, f(f(a, f(f(a, f(f(a, _x81), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, _x101), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, _x81)))) → f#(a, f(f(a, f(f(a, f(f(a, _x81), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, _x101))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, _x101), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 6: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, _x101)))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, _x101), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, _x101))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, _x101), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x141), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, _x101))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, _x101), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, _x141)))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x141), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 7: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, _x141))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x141), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, _x141)))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x141), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x161), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, _x141)))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x141), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, _x161))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x161), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 8: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, _x161)))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x161), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, _x161))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x161), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x201), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, _x161))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x161), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x201)))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x201), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 9: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x201))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x201), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x201)))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x201), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x221), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x201)))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x201), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x221))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x221), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 10: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, x))f#(a, x)f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x221)))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x221), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x221))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x221), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x261), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x221))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x221), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x261)))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x261), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 11: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x261))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x261), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x261)))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x261), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x281), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x261)))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x261), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x281))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x281), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 12: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, x))f#(a, x)f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x281)))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x281), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x281))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x281), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x321), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x281))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x281), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x321)))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x321), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 13: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x321))))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x321), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x321)))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x321), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x361), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x321)))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x321), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x361))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x361), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 14: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x361)))))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x361), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x361))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x361), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x381), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x361))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x361), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x381)))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x381), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 15: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x381))))))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x381), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x381)))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x381), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x421), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x381)))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x381), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x421))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x421), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 16: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x421)))))))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x421), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x421))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x421), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x441), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x421))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x421), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x441)))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x441), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 17: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, x))f#(a, x)f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x441))))))))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x441), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x441)))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x441), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x441)))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x441), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x481))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 18: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, x))f#(a, x)f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x481)))))))))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x481))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x481))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x501)))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 19: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x501))))))))))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x501)))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x501)))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x521))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 20: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x521)))))))))))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x521))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x561), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x521))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x561)))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x561), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 21: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x561))))))))))))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x561), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x561)))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x561), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x581), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x561)))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x561), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x581))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x581), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 22: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x1481)))))))))))))))))))))))))))))))))))))))))))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x1481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x1481))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x1481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x1521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x1481))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x1481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x1521)))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x1521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 23: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x2981)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x2981), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x2981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x2981), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x3021), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x2981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x2981), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x3021)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x3021), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 24: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x4501)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x4501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x4501))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x4501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x4521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x4501))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x4501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x4521)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x4521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 25: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x5981)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x5981), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x5981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x5981), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x6021), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x5981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x5981), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x6021)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x6021), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 26: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x7501)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, 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f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x7501))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, 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f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x7521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x7501))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, 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f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x7521)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x7521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))

Problem 27: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, 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f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, 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a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a)))f#(a, f(a, x))f#(a, x)

Rewrite Rules

f(a, f(a, x))f(a, f(f(a, x), f(a, a)))

Original Signature

Termination of terms over the following signature is verified: f, a

Strategy


The right-hand side of the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x8981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, 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f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 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
f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, 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f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) 
Thus, the rule f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x8981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x8981), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
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