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 (434ms).
 | – Problem 2 was processed with processor ForwardNarrowing (1ms).
 |    | – Problem 3 was processed with processor ForwardNarrowing (0ms).
 |    |    | – Problem 4 was processed with processor ForwardInstantiation (1ms).
 |    |    |    | – Problem 5 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    | – Problem 6 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    | – Problem 7 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    | – Problem 8 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    | – Problem 9 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (10ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (10ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (14ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (61ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (14ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (64ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (424ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 remains open; application of the following processors failed [ForwardNarrowing (234ms), ForwardNarrowing (481ms), ForwardNarrowing (411ms), ForwardNarrowing (516ms), ForwardNarrowing (603ms), ForwardNarrowing (275ms), ForwardNarrowing (472ms), ForwardNarrowing (406ms), ForwardNarrowing (357ms), ForwardNarrowing (372ms), ForwardNarrowing (386ms), ForwardNarrowing (448ms), ForwardNarrowing (530ms), ForwardNarrowing (298ms), ForwardNarrowing (674ms), ForwardNarrowing (686ms), ForwardNarrowing (705ms), ForwardNarrowing (859ms), ForwardNarrowing (343ms), ForwardNarrowing (968ms), ForwardNarrowing (491ms), ForwardNarrowing (837ms), ForwardNarrowing (738ms), ForwardNarrowing (946ms), ForwardNarrowing (561ms), ForwardNarrowing (969ms), ForwardNarrowing (988ms), ForwardNarrowing (773ms), ForwardNarrowing (1018ms), ForwardNarrowing (315ms), ForwardNarrowing (423ms), ForwardNarrowing (579ms), ForwardNarrowing (977ms), ForwardNarrowing (923ms), ForwardNarrowing (562ms), ForwardNarrowing (461ms), ForwardNarrowing (1182ms), ForwardNarrowing (996ms), ForwardNarrowing (828ms), ForwardNarrowing (864ms), ForwardNarrowing (1175ms), ForwardNarrowing (1334ms), ForwardNarrowing (417ms), ForwardNarrowing (1090ms), ForwardNarrowing (1010ms), ForwardNarrowing (360ms), ForwardNarrowing (timeout)].

The following open problems remain:

Open Dependency Pair Problem 2

Dependency Pairs

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

Rewrite Rules

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

Original Signature

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

Problem 1: PolynomialLinearRange4iUR

Dependency Pair Problem

Dependency Pairs

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

Rewrite Rules

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

Original Signature

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

Strategy

Polynomial Interpretation

Improved Usable rules

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

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

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

Problem 2: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

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

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, 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(f(a, a), x)) → f#(a, a) is deleted.

Problem 3: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

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

Rewrite Rules

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

Original Signature

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

Strategy

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

Problem 4: ForwardInstantiation

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), x)) → f#(a, x)f#(a, f(f(a, a), f(f(a, a), _x31))) → f#(a, f(f(a, a), f(a, f(a, _x31))))

Rewrite Rules

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

Original Signature

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

Strategy

Instantiation

For all potential successors l → r of the rule f#(a, f(f(a, a), x)) → f#(a, x) on dependency pair chains it holds that: Thus, f#(a, f(f(a, a), x)) → f#(a, x) is replaced by instances determined through the above matching. These instances are:
f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Problem 5: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), _x31))) → f#(a, f(f(a, a), f(a, f(a, _x31))))f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), _x31))) → f#(a, f(f(a, a), f(a, f(a, _x31)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x81)))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), _x31))) → f#(a, f(f(a, a), f(a, f(a, _x31)))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x81))))))

Problem 6: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x81))))))f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x81)))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x111)))))))) 
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x81)))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x111))))))))

Problem 7: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x111))))))))
f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x111)))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x111)))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x111)))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))

Problem 8: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x111)))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))
f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191)))))))))))) 
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))

Problem 9: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x111)))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111)))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181)))))))))))

Problem 10: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))) 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, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181)))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))

Problem 11: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))
f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))) 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, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))) 
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261))))))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261)))))))))))))))

Problem 12: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261)))))))))))))))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))) 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, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x181))))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x181)))))))))))))

Problem 13: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x181)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))) 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, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))) 
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281)))))))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))

Problem 14: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))
f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x181)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261)))))))))))))))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))) 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, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))) 
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))

Problem 15: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x181)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))) 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, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321)))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))

Problem 16: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x181)))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))) 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, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x281)))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211))))))))))))))) 
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211))))))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))

Problem 17: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x181)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))) 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, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281)))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))) 
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))

Problem 18: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x181)))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))) 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, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))) 
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231))))))))))))))))

Problem 19: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x181)))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))) 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, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321)))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))

Problem 20: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x181)))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))) 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, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x231))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231))))))))))))))))) 
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321)))))))))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))

Problem 21: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x181)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))) 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, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x351))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))) 
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301)))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x351))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x351)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))

Problem 22: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x181)))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x351))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x351)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))) 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, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x371)))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))) 
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x371))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x371))))))))))))))))))))

Problem 23: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x181)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x371))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x371))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x351))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x351)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))) 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, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))) 
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301)))))))))))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x391)))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))))

Problem 24: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541)))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x371))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x371))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x421)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x421)))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x181))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x461)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x461))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391)))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x461)))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x461))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391)))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x351))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x351)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x391)))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x261)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x331))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x331)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x411))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x411)))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x431))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x431))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x261))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x341)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x341)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x461)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x461))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x461)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x461)))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x441)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x441))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x371))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x371)))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x311))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x311)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x401)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x401))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x431))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x431))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x391)))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x371))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x371)))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x351))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x351)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x181))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x311))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x311)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x391))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x461)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x461))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x371))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x371)))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x421)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x421)))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x461)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x461))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x261))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x311))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x311)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x441)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x441))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x161))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x211)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391)))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x361)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x361))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x481)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x481))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x391))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x311))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x311)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x301))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x431))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x431))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x371))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x371)))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x311))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x311))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301)))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x211)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x391)))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391)))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x561)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x561))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x261))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x211)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x371))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x371)))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x391)))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x411))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x411)))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x431))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x431))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x461)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x461))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x251))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x251)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x441)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x441))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391)))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x281)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x361)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x361))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x501)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x501)))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x261))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x311))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x311)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x291))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x291)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x261))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x261))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x411))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x411)))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x331))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x331)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x411))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x411)))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x391))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x391)))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x211))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x261))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391)))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x281)))))))))))))))))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x561)))))))))))))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))) 
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x561)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x561))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))

Problem 25: ForwardNarrowing

Dependency Pair Problem

Dependency Pairs

f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x461)))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x461))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x261))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x691))))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x641)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x641))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x481)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x481))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621)))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x311))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x311)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x661)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x661)))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x501)))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x501))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x311))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x311)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x391))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x371))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x371)))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x351))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x351))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x421)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x421))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621)))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x211)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391)))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x721)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x721))))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x621)))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x391))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x301))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x701)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x701)))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x671))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x671))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x641)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x641))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x431))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x431))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x311))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x311))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x351))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x351))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x661)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x661)))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391)))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x561)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x561))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x421)))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x421))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x541)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x251))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x251)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x611))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x611))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x441)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x441))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x391))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x361)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x361))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x551))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x551)))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x621))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x691)))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x581)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x581)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x291))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x291)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x621)))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x621)))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x591))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x591)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x631))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x631)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x501)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x501))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x701)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x701)))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621)))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x621)))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x351))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x351))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x601)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x601))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x621)))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x691))))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x371))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x371))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x461)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x461))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x691)))))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x461)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x461)))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x621)))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x31)))) → f#(a, f(f(a, a), f(f(a, a), _x31)))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x391)))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x411))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x411)))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x461)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x461)))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x441)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x441))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x541))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x601)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x601))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x711))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x711))))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x321)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x321))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x351))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x351)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x181))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x651))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x651)))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x261))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x621)))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x601)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x601))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621)))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x621))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x711))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x711))))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x561)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x561))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x421)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x421))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x391)))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x691))))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x381)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x381)))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x391)))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x621))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x261))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x541))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x351))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x351))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x501)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x501))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x281)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391)))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x411))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x411)))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x661)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x661)))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x261))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x501)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x501))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x621))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x261))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x421)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x421))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x691))))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x601)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x601))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x741)))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x741)))))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x181))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391)))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x431))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x431))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x461)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x461))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x181)))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x621)))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x691))))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x541)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x441)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x441))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x311))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x311)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x161))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x691)))))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x391)))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621)))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x621)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x111)))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x161))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x211)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x161)))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x161)))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x391)))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x411))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x411)))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x461)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x461))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x691)))))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x311))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x311)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x261))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x501)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x501))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x641)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x641))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x581)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x581)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x501)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x501))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x281)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x331))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x331)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x411))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x411)))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x761)))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x761))))))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), _x))) → f#(a, f(f(a, a), _x))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x391))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x621)))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x211))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x281)))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x281)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x281))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x621))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x391))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x111))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x111))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x211))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x351))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x351))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x621)))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x691))))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x621)))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x621)))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x181)))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x181))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x691))))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x261)))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x541))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x331))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x331)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x231))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x691)))))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x341)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x341)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x231))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x621))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x371))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x371)))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x621)))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x401)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x401))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x431))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x431))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x211)))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x391)))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x371))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x371)))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x691)))))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x211))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x461)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x461))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x421)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x421)))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x631))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x631)))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x661)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x661)))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x461)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x461))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x681)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x681))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x391)))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x301))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), _x81)))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x81)))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x361)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x361))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x691)))))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x641)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x641))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x481)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x481))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x311))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x311)))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x601)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x601))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x371))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x371)))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301)))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x211))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x211)))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x421)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x421))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x701)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x701)))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x371))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x371)))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x301)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x301))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x681)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x681))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x431))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x431))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x691)))))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x501)))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x501)))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491)))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x621))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x391))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x261))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x191))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x191))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x261)))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x261))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x391)))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, _x621))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x691))))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x691)))))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x451))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x451)))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x491))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x701)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x701)))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x601)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, _x601))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x621)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x621))))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x391)))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x541)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x541))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x231))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x231)))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x391))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x391)))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))

Rewrite Rules

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

Original Signature

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

Strategy

The right-hand side of the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))) 
f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x661))))))))))))))))))))))))))))))))))) 
f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491)))))))))))))))))))))))))))))))))) 
Thus, the rule f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))) is replaced by the following rules:
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x661)))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, _x661)))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(f(a, a), f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))
f#(a, f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), f(f(a, a), _x491))))))))))) → f#(a, f(f(a, a), f(a, f(f(a, a), f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(a, f(a, f(f(a, a), f(a, f(a, f(f(a, a), f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x491))))))))))))))))))))))))))))))))))