TIMEOUT

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

The following DP Processors were used


Problem 1 was processed with processor ForwardNarrowing (1ms).
 | – Problem 2 was processed with processor ForwardNarrowing (1ms).
 |    | – Problem 3 was processed with processor ForwardNarrowing (2ms).
 |    |    | – Problem 4 was processed with processor ForwardNarrowing (4ms).
 |    |    |    | – Problem 5 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    | – Problem 6 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    | – Problem 7 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    | – Problem 8 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    | – Problem 9 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (10ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (11ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (16ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (32ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (66ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (63ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (175ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (198ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 was processed with processor ForwardNarrowing (239ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 28 was processed with processor ForwardNarrowing (95ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 29 was processed with processor ForwardNarrowing (277ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 30 remains open; application of the following processors failed [ForwardNarrowing (83ms), ForwardNarrowing (268ms), ForwardNarrowing (106ms), ForwardNarrowing (96ms), ForwardNarrowing (97ms), ForwardNarrowing (82ms), ForwardNarrowing (93ms), ForwardNarrowing (79ms), ForwardNarrowing (81ms), ForwardNarrowing (267ms), ForwardNarrowing (92ms), ForwardNarrowing (83ms), ForwardNarrowing (97ms), ForwardNarrowing (122ms), ForwardNarrowing (94ms), ForwardNarrowing (94ms), ForwardNarrowing (110ms), ForwardNarrowing (107ms), ForwardNarrowing (92ms), ForwardNarrowing (timeout)].

The following open problems remain:



Open Dependency Pair Problem 1

Dependency Pairs

b#(c(x))a#(b(x))a#(d(x))b#(a(x))
b#(c(x))b#(x)a#(d(x))a#(x)

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a


Problem 1: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(d(x))b#(a(x))b#(c(x))a#(b(x))
b#(c(x))b#(x)a#(d(x))a#(x)

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(x)) → a#(b(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
a#(c(d(a(b(_x21))))) 
a#(_x21) 
Thus, the rule b#(c(x)) → a#(b(x)) is replaced by the following rules:
b#(c(c(_x21))) → a#(c(d(a(b(_x21)))))b#(c(d(_x21))) → a#(_x21)

Problem 2: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(_x21)))a#(c(d(a(b(_x21)))))b#(c(d(_x21)))a#(_x21)
a#(d(x))b#(a(x))b#(c(x))b#(x)
a#(d(x))a#(x)

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(_x21))) → a#(c(d(a(b(_x21))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(c(d(a(c(d(a(b(_x61)))))))) 
a#(c(d(a(_x61)))) 
Thus, the rule b#(c(c(_x21))) → a#(c(d(a(b(_x21))))) is replaced by the following rules:
b#(c(c(c(_x61)))) → a#(c(d(a(c(d(a(b(_x61))))))))b#(c(c(d(_x61)))) → a#(c(d(a(_x61))))

Problem 3: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(_x61))))a#(c(d(a(c(d(a(b(_x61))))))))b#(c(d(_x21)))a#(_x21)
b#(c(c(d(_x61))))a#(c(d(a(_x61))))a#(d(x))b#(a(x))
b#(c(x))b#(x)a#(d(x))a#(x)

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(_x61)))) → a#(c(d(a(c(d(a(b(_x61)))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(c(d(a(c(d(a(_x91))))))) 
a#(c(d(d(a(b(_x61)))))) 
a#(c(d(a(c(d(a(c(d(a(b(_x91))))))))))) 
Thus, the rule b#(c(c(c(_x61)))) → a#(c(d(a(c(d(a(b(_x61)))))))) is replaced by the following rules:
b#(c(c(c(_x61)))) → a#(c(d(d(a(b(_x61))))))b#(c(c(c(c(_x91))))) → a#(c(d(a(c(d(a(c(d(a(b(_x91)))))))))))
b#(c(c(c(d(_x91))))) → a#(c(d(a(c(d(a(_x91)))))))

Problem 4: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(_x61))))a#(c(d(d(a(b(_x61))))))b#(c(d(_x21)))a#(_x21)
b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(a(c(d(a(b(_x91)))))))))))b#(c(c(d(_x61))))a#(c(d(a(_x61))))
a#(d(x))b#(a(x))b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))
b#(c(x))b#(x)a#(d(x))a#(x)

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(_x61)))) → a#(c(d(d(a(b(_x61)))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(c(d(d(a(c(d(a(b(_x71))))))))) 
a#(c(d(d(a(_x71))))) 
Thus, the rule b#(c(c(c(_x61)))) → a#(c(d(d(a(b(_x61)))))) is replaced by the following rules:
b#(c(c(c(d(_x71))))) → a#(c(d(d(a(_x71)))))b#(c(c(c(c(_x71))))) → a#(c(d(d(a(c(d(a(b(_x71)))))))))

Problem 5: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(d(_x21)))a#(_x21)b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(a(c(d(a(b(_x91)))))))))))
b#(c(c(d(_x61))))a#(c(d(a(_x61))))b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))
b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))a#(d(x))b#(a(x))
b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))b#(c(x))b#(x)
a#(d(x))a#(x)

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(_x91))))) → a#(c(d(a(c(d(a(c(d(a(b(_x91))))))))))) 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
a#(c(d(a(c(d(a(c(d(a(_x121)))))))))) 
a#(c(d(a(c(d(a(c(d(a(c(d(a(b(_x121)))))))))))))) 
a#(c(d(a(c(d(d(a(b(_x91))))))))) 
a#(c(d(d(a(c(d(a(b(_x91))))))))) 
Thus, the rule b#(c(c(c(c(_x91))))) → a#(c(d(a(c(d(a(c(d(a(b(_x91))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(_x121)))))) → a#(c(d(a(c(d(a(c(d(a(c(d(a(b(_x121))))))))))))))b#(c(c(c(c(_x91))))) → a#(c(d(a(c(d(d(a(b(_x91)))))))))
b#(c(c(c(c(d(_x121)))))) → a#(c(d(a(c(d(a(c(d(a(_x121))))))))))b#(c(c(c(c(_x91))))) → a#(c(d(d(a(c(d(a(b(_x91)))))))))

Problem 6: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(b(_x121))))))))))))))b#(c(d(_x21)))a#(_x21)
b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))
b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))b#(c(c(d(_x61))))a#(c(d(a(_x61))))
b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))a#(d(x))b#(a(x))
b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))b#(c(x))b#(x)
b#(c(c(c(c(_x91)))))a#(c(d(d(a(c(d(a(b(_x91)))))))))a#(d(x))a#(x)

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(_x121)))))) → a#(c(d(a(c(d(a(c(d(a(c(d(a(b(_x121)))))))))))))) 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
a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x151))))))))))))))))) 
a#(c(d(d(a(c(d(a(c(d(a(b(_x121)))))))))))) 
a#(c(d(a(c(d(d(a(c(d(a(b(_x121)))))))))))) 
a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151))))))))))))) 
a#(c(d(a(c(d(a(c(d(d(a(b(_x121)))))))))))) 
Thus, the rule b#(c(c(c(c(c(_x121)))))) → a#(c(d(a(c(d(a(c(d(a(c(d(a(b(_x121)))))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(_x121)))))) → a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))b#(c(c(c(c(c(_x121)))))) → a#(c(d(a(c(d(a(c(d(d(a(b(_x121))))))))))))
b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))))b#(c(c(c(c(c(d(_x151))))))) → a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))
b#(c(c(c(c(c(_x121)))))) → a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))

Problem 7: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(a(c(d(d(a(b(_x121))))))))))))b#(c(d(_x21)))a#(_x21)
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))))b#(c(c(d(_x61))))a#(c(d(a(_x61))))
b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))a#(d(x))b#(a(x))
b#(c(c(c(c(_x91)))))a#(c(d(d(a(c(d(a(b(_x91)))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))
b#(c(c(c(c(c(d(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))
b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))b#(c(x))b#(x)
b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))a#(d(x))a#(x)

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(_x121)))))) → a#(c(d(a(c(d(a(c(d(d(a(b(_x121)))))))))))) 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
a#(c(d(d(a(c(d(d(a(b(_x121)))))))))) 
a#(c(d(a(c(d(a(c(d(d(a(_x131))))))))))) 
a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x131))))))))))))))) 
a#(c(d(a(c(d(d(d(a(b(_x121)))))))))) 
Thus, the rule b#(c(c(c(c(c(_x121)))))) → a#(c(d(a(c(d(a(c(d(d(a(b(_x121)))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))))b#(c(c(c(c(c(_x121)))))) → a#(c(d(a(c(d(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(_x121)))))) → a#(c(d(d(a(c(d(d(a(b(_x121))))))))))b#(c(c(c(c(c(d(_x131))))))) → a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))

Problem 8: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))))b#(c(d(_x21)))a#(_x21)
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))))b#(c(c(d(_x61))))a#(c(d(a(_x61))))
b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))a#(d(x))b#(a(x))
b#(c(c(c(c(_x91)))))a#(c(d(d(a(c(d(a(b(_x91)))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))
b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))b#(c(c(c(c(c(d(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))
b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))b#(c(x))b#(x)
b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(d(a(b(_x121))))))))))b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))
a#(d(x))a#(x)

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x131))))))))))))))) 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
a#(c(d(a(c(d(d(d(a(c(d(a(b(_x131))))))))))))) 
a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131))))))))))))) 
a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161)))))))))))))))))) 
a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161)))))))))))))) 
a#(c(d(a(c(d(a(c(d(d(d(a(b(_x131))))))))))))) 
Thus, the rule b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x131))))))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(a(c(d(a(c(d(d(d(a(b(_x131)))))))))))))b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(c(c(_x161)))))))) → a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))b#(c(c(c(c(c(c(d(_x161)))))))) → a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(a(c(d(d(d(a(c(d(a(b(_x131)))))))))))))

Problem 9: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(a(c(d(d(d(a(b(_x131)))))))))))))b#(c(d(_x21)))a#(_x21)
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))))b#(c(c(d(_x61))))a#(c(d(a(_x61))))
b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))a#(d(x))b#(a(x))
b#(c(c(c(c(_x91)))))a#(c(d(d(a(c(d(a(b(_x91)))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(d(a(b(_x121))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))
b#(c(c(c(c(c(d(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(d(a(b(_x121))))))))))b#(c(x))b#(x)
b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))
b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161))))))))))))))
a#(d(x))a#(x)

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(a(c(d(a(c(d(d(d(a(b(_x131))))))))))))) 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
a#(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x141)))))))))))))))) 
a#(c(d(a(c(d(a(c(d(d(d(a(_x141)))))))))))) 
a#(c(d(d(a(c(d(d(d(a(b(_x131))))))))))) 
a#(c(d(a(c(d(d(d(d(a(b(_x131))))))))))) 
Thus, the rule b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(a(c(d(a(c(d(d(d(a(b(_x131))))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(c(_x141)))))))) → a#(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x141))))))))))))))))b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(a(c(d(d(d(d(a(b(_x131)))))))))))
b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(d(a(c(d(d(d(a(b(_x131)))))))))))b#(c(c(c(c(c(c(d(_x141)))))))) → a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))

Problem 10: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(d(_x21)))a#(_x21)b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))))
b#(c(c(d(_x61))))a#(c(d(a(_x61))))b#(c(c(c(c(_x91)))))a#(c(d(d(a(c(d(a(b(_x91)))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(a(c(d(a(b(_x131)))))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(d(a(b(_x121))))))))))
b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))b#(c(x))b#(x)
b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))a#(d(x))a#(x)
b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))a#(d(x))b#(a(x))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(d(a(b(_x131)))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x141))))))))))))))))b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))
b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(d(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(d(a(b(_x131)))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161))))))))))))))b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x151))))))))))))))))) 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
a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x151))))))))))))))) 
a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151))))))))))))))) 
a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181)))))))))))))))))))) 
a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x181)))))))))))))))) 
a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151))))))))))))))) 
a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x151))))))))))))))) 
Thus, the rule b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x151))))))))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(d(_x181)))))))) → a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x181))))))))))))))))
b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(c(_x181)))))))) → a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))))

Problem 11: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(d(_x21)))a#(_x21)b#(c(c(d(_x61))))a#(c(d(a(_x61))))
b#(c(c(c(c(_x91)))))a#(c(d(d(a(c(d(a(b(_x91)))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(a(c(d(a(b(_x131)))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))b#(c(x))b#(x)
b#(c(c(c(c(c(c(d(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x181))))))))))))))))b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))
a#(d(x))a#(x)b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))
a#(d(x))b#(a(x))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(d(a(b(_x131)))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x141))))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))
b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(d(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(d(a(b(_x131)))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(c(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))))
b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(d(_x61)))) → a#(c(d(a(_x61)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(c(d(_x41))) 
a#(c(d(d(c(b(a(_x41))))))) 
Thus, the rule b#(c(c(d(_x61)))) → a#(c(d(a(_x61)))) is replaced by the following rules:
b#(c(c(d(c(_x41))))) → a#(c(d(_x41)))b#(c(c(d(d(_x41))))) → a#(c(d(d(c(b(a(_x41)))))))

Problem 12: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(d(_x21)))a#(_x21)b#(c(c(c(c(_x91)))))a#(c(d(d(a(c(d(a(b(_x91)))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(a(c(d(a(b(_x131)))))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))
b#(c(c(d(c(_x41)))))a#(c(d(_x41)))b#(c(c(c(c(c(c(d(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x181))))))))))))))))
b#(c(x))b#(x)b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))
a#(d(x))a#(x)b#(c(c(d(d(_x41)))))a#(c(d(d(c(b(a(_x41)))))))
b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))a#(d(x))b#(a(x))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(d(a(b(_x131)))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x141))))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))b#(c(c(c(c(c(d(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))
b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(d(a(b(_x131)))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(d(a(b(_x121))))))))))b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(c(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(_x91))))) → a#(c(d(d(a(c(d(a(b(_x91))))))))) 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
a#(c(d(d(a(c(d(a(c(d(a(b(_x101)))))))))))) 
a#(c(d(d(a(c(d(a(_x101)))))))) 
a#(c(d(d(d(a(b(_x91))))))) 
Thus, the rule b#(c(c(c(c(_x91))))) → a#(c(d(d(a(c(d(a(b(_x91))))))))) is replaced by the following rules:
b#(c(c(c(c(_x91))))) → a#(c(d(d(d(a(b(_x91)))))))b#(c(c(c(c(c(_x101)))))) → a#(c(d(d(a(c(d(a(c(d(a(b(_x101))))))))))))
b#(c(c(c(c(d(_x101)))))) → a#(c(d(d(a(c(d(a(_x101))))))))

Problem 13: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(c(c(_x101))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x101))))))))))))b#(c(d(_x21)))a#(_x21)
b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(d(a(b(_x121))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(d(c(_x41)))))a#(c(d(_x41)))
b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))b#(c(x))b#(x)
b#(c(c(c(c(c(c(d(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x181))))))))))))))))b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))
b#(c(c(d(d(_x41)))))a#(c(d(d(c(b(a(_x41)))))))a#(d(x))a#(x)
b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))a#(d(x))b#(a(x))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(d(a(b(_x131)))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(d(d(a(b(_x91)))))))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x141))))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))
b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(d(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))b#(c(c(c(c(d(_x101))))))a#(c(d(d(a(c(d(a(_x101))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(d(a(b(_x131)))))))))))b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(d(a(b(_x121))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(c(c(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))))b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(_x101)))))) → a#(c(d(d(a(c(d(a(c(d(a(b(_x101)))))))))))) 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
a#(c(d(d(a(c(d(d(a(b(_x101)))))))))) 
a#(c(d(d(d(a(c(d(a(b(_x101)))))))))) 
a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x131))))))))))))))) 
a#(c(d(d(a(c(d(a(c(d(a(_x131))))))))))) 
Thus, the rule b#(c(c(c(c(c(_x101)))))) → a#(c(d(d(a(c(d(a(c(d(a(b(_x101)))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x131)))))))))))))))b#(c(c(c(c(c(d(_x131))))))) → a#(c(d(d(a(c(d(a(c(d(a(_x131)))))))))))
b#(c(c(c(c(c(_x101)))))) → a#(c(d(d(a(c(d(d(a(b(_x101))))))))))b#(c(c(c(c(c(_x101)))))) → a#(c(d(d(d(a(c(d(a(b(_x101))))))))))

Problem 14: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(d(_x21)))a#(_x21)b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x131)))))))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(a(c(d(a(b(_x131)))))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(_x101))))))a#(c(d(d(a(c(d(d(a(b(_x101))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))b#(c(c(d(c(_x41)))))a#(c(d(_x41)))
b#(c(c(c(c(c(c(d(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x181))))))))))))))))b#(c(x))b#(x)
b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))b#(c(c(c(c(c(_x101))))))a#(c(d(d(d(a(c(d(a(b(_x101))))))))))
b#(c(c(d(d(_x41)))))a#(c(d(d(c(b(a(_x41)))))))a#(d(x))a#(x)
b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))a#(d(x))b#(a(x))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(d(a(b(_x131)))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(d(d(a(b(_x91)))))))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x141))))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))
b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(d(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))b#(c(c(c(c(c(d(_x131)))))))a#(c(d(d(a(c(d(a(c(d(a(_x131)))))))))))
b#(c(c(c(c(d(_x101))))))a#(c(d(d(a(c(d(a(_x101))))))))b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(d(a(b(_x131)))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(c(c(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x131))))))))))))))) 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
a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131))))))))))))) 
a#(c(d(d(a(c(d(a(c(d(d(a(b(_x131))))))))))))) 
a#(c(d(d(a(c(d(a(c(d(a(c(d(a(_x161)))))))))))))) 
a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x161)))))))))))))))))) 
a#(c(d(d(d(a(c(d(a(c(d(a(b(_x131))))))))))))) 
Thus, the rule b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x131))))))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(c(_x161)))))))) → a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(d(a(c(d(a(c(d(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))b#(c(c(c(c(c(c(d(_x161)))))))) → a#(c(d(d(a(c(d(a(c(d(a(c(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(d(d(a(c(d(a(c(d(a(b(_x131)))))))))))))

Problem 15: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(d(_x21)))a#(_x21)b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(a(c(d(a(b(_x131)))))))))))))b#(c(c(c(c(c(_x101))))))a#(c(d(d(a(c(d(d(a(b(_x101))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(d(c(_x41)))))a#(c(d(_x41)))
b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))b#(c(x))b#(x)
b#(c(c(c(c(c(c(d(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x181))))))))))))))))b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))
b#(c(c(c(c(c(_x101))))))a#(c(d(d(d(a(c(d(a(b(_x101))))))))))a#(d(x))a#(x)
b#(c(c(d(d(_x41)))))a#(c(d(d(c(b(a(_x41)))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))
b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))a#(d(x))b#(a(x))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(d(a(b(_x131)))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(d(d(a(b(_x91)))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(a(c(d(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x141))))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))
b#(c(c(c(c(c(d(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(d(_x131)))))))a#(c(d(d(a(c(d(a(c(d(a(_x131)))))))))))b#(c(c(c(c(d(_x101))))))a#(c(d(d(a(c(d(a(_x101))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(d(a(b(_x131)))))))))))b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(d(a(b(_x121))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161))))))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(a(c(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(c(c(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))))b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(a(c(d(d(d(a(c(d(a(b(_x131))))))))))))) 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
a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(b(_x141)))))))))))))))) 
a#(c(d(d(d(d(a(c(d(a(b(_x131))))))))))) 
a#(c(d(a(c(d(d(d(a(c(d(a(_x141)))))))))))) 
a#(c(d(a(c(d(d(d(d(a(b(_x131))))))))))) 
Thus, the rule b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(a(c(d(d(d(a(c(d(a(b(_x131))))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(d(_x141)))))))) → a#(c(d(a(c(d(d(d(a(c(d(a(_x141))))))))))))b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(a(c(d(d(d(d(a(b(_x131)))))))))))
b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(d(d(d(a(c(d(a(b(_x131)))))))))))b#(c(c(c(c(c(c(c(_x141)))))))) → a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(b(_x141))))))))))))))))

Problem 16: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(d(_x21)))a#(_x21)b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(d(d(a(c(d(a(_x141))))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(d(a(b(_x121))))))))))b#(c(c(c(c(c(_x101))))))a#(c(d(d(a(c(d(d(a(b(_x101))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(b(_x141))))))))))))))))
b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))b#(c(c(d(c(_x41)))))a#(c(d(_x41)))
b#(c(c(c(c(c(c(d(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x181))))))))))))))))b#(c(x))b#(x)
b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))b#(c(c(c(c(c(_x101))))))a#(c(d(d(d(a(c(d(a(b(_x101))))))))))
a#(d(x))a#(x)b#(c(c(d(d(_x41)))))a#(c(d(d(c(b(a(_x41)))))))
b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))
a#(d(x))b#(a(x))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(d(a(b(_x131)))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(d(a(c(d(a(b(_x131)))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(d(d(a(b(_x91)))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(a(c(d(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x141))))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))b#(c(c(c(c(c(d(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))
b#(c(c(c(c(c(d(_x131)))))))a#(c(d(d(a(c(d(a(c(d(a(_x131)))))))))))b#(c(c(c(c(d(_x101))))))a#(c(d(d(a(c(d(a(_x101))))))))
b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(d(a(b(_x131)))))))))))
b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(_x161))))))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(a(c(d(a(c(d(a(b(_x131)))))))))))))b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(c(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(c(d(_x141)))))))) → a#(c(d(a(c(d(d(d(a(c(d(a(_x141)))))))))))) 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
a#(c(d(a(c(d(d(d(d(a(_x141)))))))))) 
a#(c(d(a(c(d(d(d(a(c(d(d(c(b(a(_x121))))))))))))))) 
a#(c(d(a(c(d(d(d(a(c(d(_x121))))))))))) 
a#(c(d(d(d(d(a(c(d(a(_x141)))))))))) 
Thus, the rule b#(c(c(c(c(c(c(d(_x141)))))))) → a#(c(d(a(c(d(d(d(a(c(d(a(_x141)))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(d(d(_x121))))))))) → a#(c(d(a(c(d(d(d(a(c(d(d(c(b(a(_x121)))))))))))))))b#(c(c(c(c(c(c(d(c(_x121))))))))) → a#(c(d(a(c(d(d(d(a(c(d(_x121)))))))))))
b#(c(c(c(c(c(c(d(_x141)))))))) → a#(c(d(a(c(d(d(d(d(a(_x141))))))))))b#(c(c(c(c(c(c(d(_x141)))))))) → a#(c(d(d(d(d(a(c(d(a(_x141))))))))))

Problem 17: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(d(_x21)))a#(_x21)b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(d(d(d(a(_x141))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(d(a(b(_x121))))))))))b#(c(c(c(c(c(_x101))))))a#(c(d(d(a(c(d(d(a(b(_x101))))))))))
b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(d(d(d(a(c(d(a(_x141))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(b(_x141))))))))))))))))b#(c(c(c(c(c(c(d(d(_x121)))))))))a#(c(d(a(c(d(d(d(a(c(d(d(c(b(a(_x121)))))))))))))))
b#(c(c(d(c(_x41)))))a#(c(d(_x41)))b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))
b#(c(x))b#(x)b#(c(c(c(c(c(c(d(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x181))))))))))))))))
b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))b#(c(c(c(c(c(_x101))))))a#(c(d(d(d(a(c(d(a(b(_x101))))))))))
a#(d(x))a#(x)b#(c(c(d(d(_x41)))))a#(c(d(d(c(b(a(_x41)))))))
b#(c(c(c(c(c(c(d(c(_x121)))))))))a#(c(d(a(c(d(d(d(a(c(d(_x121)))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))
b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))a#(d(x))b#(a(x))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(d(a(b(_x131)))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(d(a(c(d(a(b(_x131)))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))b#(c(c(c(c(_x91)))))a#(c(d(d(d(a(b(_x91)))))))
b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x141))))))))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(a(c(d(d(a(b(_x131)))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))b#(c(c(c(c(c(d(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))b#(c(c(c(c(c(d(_x131)))))))a#(c(d(d(a(c(d(a(c(d(a(_x131)))))))))))
b#(c(c(c(c(d(_x101))))))a#(c(d(d(a(c(d(a(_x101))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(d(a(b(_x131)))))))))))
b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(_x161))))))))))))))b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(a(c(d(a(c(d(a(b(_x131)))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(c(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))))
b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


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

Problem 18: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(d(_x21)))a#(_x21)b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(c(d(d(_x101)))))))))a#(c(d(a(c(d(d(d(d(d(c(b(a(_x101)))))))))))))b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(d(d(d(a(c(d(a(_x141))))))))))
b#(c(c(c(c(c(_x101))))))a#(c(d(d(a(c(d(d(a(b(_x101))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(b(_x141))))))))))))))))b#(c(c(c(c(c(c(d(d(_x121)))))))))a#(c(d(a(c(d(d(d(a(c(d(d(c(b(a(_x121)))))))))))))))
b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))b#(c(c(d(c(_x41)))))a#(c(d(_x41)))
b#(c(c(c(c(c(c(d(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x181))))))))))))))))b#(c(x))b#(x)
b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))b#(c(c(c(c(c(_x101))))))a#(c(d(d(d(a(c(d(a(b(_x101))))))))))
a#(d(x))a#(x)b#(c(c(d(d(_x41)))))a#(c(d(d(c(b(a(_x41)))))))
b#(c(c(c(c(c(c(d(c(_x121)))))))))a#(c(d(a(c(d(d(d(a(c(d(_x121)))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))
b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))a#(d(x))b#(a(x))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(d(a(b(_x131)))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(d(a(c(d(a(b(_x131)))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))b#(c(c(c(c(_x91)))))a#(c(d(d(d(a(b(_x91)))))))
b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(d(d(d(d(a(_x141))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(a(c(d(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x141))))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))b#(c(c(c(c(c(c(d(c(_x101)))))))))a#(c(d(a(c(d(d(d(d(_x101)))))))))
b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(d(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))b#(c(c(c(c(c(d(_x131)))))))a#(c(d(d(a(c(d(a(c(d(a(_x131)))))))))))
b#(c(c(c(c(d(_x101))))))a#(c(d(d(a(c(d(a(_x101))))))))b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(d(a(b(_x131)))))))))))b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(_x161))))))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(d(a(b(_x121))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(a(c(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(c(c(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


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

Problem 19: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(c(c(_x101))))))a#(c(d(d(a(c(d(d(a(b(_x101))))))))))b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(d(d(d(a(c(d(a(_x141))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(b(_x141))))))))))))))))
b#(c(c(c(c(c(c(d(d(d(_x141))))))))))a#(c(d(a(c(d(d(d(d(d(c(b(d(c(b(a(_x141))))))))))))))))b#(c(c(c(c(c(c(d(d(_x121)))))))))a#(c(d(a(c(d(d(d(a(c(d(d(c(b(a(_x121)))))))))))))))
b#(c(c(d(c(_x41)))))a#(c(d(_x41)))b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))
b#(c(x))b#(x)b#(c(c(c(c(c(c(d(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x181))))))))))))))))
b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))b#(c(c(c(c(c(_x101))))))a#(c(d(d(d(a(c(d(a(b(_x101))))))))))
a#(d(x))a#(x)b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))
b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(d(a(b(_x131)))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(d(a(c(d(a(b(_x131)))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(c(c(d(d(c(_x141))))))))))a#(c(d(a(c(d(d(d(d(d(c(b(_x141))))))))))))b#(c(c(c(c(_x91)))))a#(c(d(d(d(a(b(_x91)))))))
b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(d(d(d(d(a(_x141))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(a(c(d(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(c(d(c(_x101)))))))))a#(c(d(a(c(d(d(d(d(_x101)))))))))b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))
b#(c(c(c(c(d(_x101))))))a#(c(d(d(a(c(d(a(_x101))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(d(a(b(_x131)))))))))))
b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(a(c(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(c(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))))
b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))b#(c(d(_x21)))a#(_x21)
b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(d(a(b(_x121))))))))))b#(c(c(c(c(c(c(d(d(_x101)))))))))a#(c(d(d(d(d(d(d(c(b(a(_x101)))))))))))
b#(c(c(d(d(_x41)))))a#(c(d(d(c(b(a(_x41)))))))b#(c(c(c(c(c(c(d(c(_x121)))))))))a#(c(d(a(c(d(d(d(a(c(d(_x121)))))))))))
a#(d(x))b#(a(x))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x141))))))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(d(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(d(_x131)))))))a#(c(d(d(a(c(d(a(c(d(a(_x131)))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(_x161))))))))))))))b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151)))))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(_x101)))))) → a#(c(d(d(a(c(d(d(a(b(_x101)))))))))) 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
a#(c(d(d(d(d(a(b(_x101)))))))) 
a#(c(d(d(a(c(d(d(a(c(d(a(b(_x111))))))))))))) 
a#(c(d(d(a(c(d(d(a(_x111))))))))) 
Thus, the rule b#(c(c(c(c(c(_x101)))))) → a#(c(d(d(a(c(d(d(a(b(_x101)))))))))) is replaced by the following rules:
b#(c(c(c(c(c(d(_x111))))))) → a#(c(d(d(a(c(d(d(a(_x111)))))))))b#(c(c(c(c(c(_x101)))))) → a#(c(d(d(d(d(a(b(_x101))))))))
b#(c(c(c(c(c(c(_x111))))))) → a#(c(d(d(a(c(d(d(a(c(d(a(b(_x111)))))))))))))

Problem 20: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(c(c(c(_x111)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x111)))))))))))))b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(d(d(d(a(c(d(a(_x141))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(b(_x141))))))))))))))))
b#(c(c(c(c(c(c(d(d(d(_x141))))))))))a#(c(d(a(c(d(d(d(d(d(c(b(d(c(b(a(_x141))))))))))))))))b#(c(c(c(c(c(c(d(d(_x121)))))))))a#(c(d(a(c(d(d(d(a(c(d(d(c(b(a(_x121)))))))))))))))
b#(c(c(d(c(_x41)))))a#(c(d(_x41)))b#(c(c(c(c(_x71)))))a#(c(d(d(a(c(d(a(b(_x71)))))))))
b#(c(x))b#(x)b#(c(c(c(c(c(c(d(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x181))))))))))))))))
b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))b#(c(c(c(c(c(_x101))))))a#(c(d(d(d(a(c(d(a(b(_x101))))))))))
a#(d(x))a#(x)b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))
b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(d(a(b(_x131)))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(d(a(c(d(a(b(_x131)))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(d(d(a(b(_x91)))))))b#(c(c(c(c(c(c(d(d(c(_x141))))))))))a#(c(d(a(c(d(d(d(d(d(c(b(_x141))))))))))))
b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(d(d(d(d(a(_x141))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(a(c(d(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(c(d(c(_x101)))))))))a#(c(d(a(c(d(d(d(d(_x101)))))))))b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))
b#(c(c(c(c(d(_x101))))))a#(c(d(d(a(c(d(a(_x101))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(d(a(b(_x131)))))))))))
b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(a(c(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(c(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))))
b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))b#(c(d(_x21)))a#(_x21)
b#(c(c(c(c(c(d(_x111)))))))a#(c(d(d(a(c(d(d(a(_x111)))))))))b#(c(c(c(c(c(_x101))))))a#(c(d(d(d(d(a(b(_x101))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(d(a(b(_x121))))))))))b#(c(c(c(c(c(c(d(d(_x101)))))))))a#(c(d(d(d(d(d(d(c(b(a(_x101)))))))))))
b#(c(c(d(d(_x41)))))a#(c(d(d(c(b(a(_x41)))))))b#(c(c(c(c(c(c(d(c(_x121)))))))))a#(c(d(a(c(d(d(d(a(c(d(_x121)))))))))))
a#(d(x))b#(a(x))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x141))))))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(d(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(d(_x131)))))))a#(c(d(d(a(c(d(a(c(d(a(_x131)))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(_x161))))))))))))))b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151)))))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(c(_x111))))))) → a#(c(d(d(a(c(d(d(a(c(d(a(b(_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
a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(b(_x141)))))))))))))))) 
a#(c(d(d(a(c(d(d(a(c(d(a(_x141)))))))))))) 
a#(c(d(d(d(d(a(c(d(a(b(_x111))))))))))) 
a#(c(d(d(a(c(d(d(d(a(b(_x111))))))))))) 
Thus, the rule b#(c(c(c(c(c(c(_x111))))))) → a#(c(d(d(a(c(d(d(a(c(d(a(b(_x111))))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(_x111))))))) → a#(c(d(d(a(c(d(d(d(a(b(_x111)))))))))))b#(c(c(c(c(c(c(c(_x141)))))))) → a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(b(_x141))))))))))))))))
b#(c(c(c(c(c(c(d(_x141)))))))) → a#(c(d(d(a(c(d(d(a(c(d(a(_x141))))))))))))b#(c(c(c(c(c(c(_x111))))))) → a#(c(d(d(d(d(a(c(d(a(b(_x111)))))))))))

Problem 21: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(c(c(c(c(c(c(_x141))))))))))a#(c(d(a(c(d(d(d(d(d(d(a(c(d(a(b(_x141))))))))))))))))b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(c(d(a(b(_x191)))))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))b#(c(c(c(c(c(c(d(d(d(c(_x171)))))))))))a#(c(d(a(c(d(d(d(d(d(c(b(d(c(b(_x171)))))))))))))))
b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x191)))))))))))))))))))b#(c(c(c(c(c(c(d(d(_x121)))))))))a#(c(d(d(d(d(a(c(d(d(c(b(a(_x121)))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(_x171)))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(a(_x171)))))))))))))))))))b#(c(c(c(c(c(c(d(d(c(_x141))))))))))a#(c(d(a(c(d(d(d(d(d(c(b(_x141))))))))))))
b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x191)))))))))))))))))b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x191)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(a(c(d(d(d(d(d(d(a(_x201))))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(_x191)))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(d(c(b(a(_x191)))))))))))))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(a(c(d(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(c(d(c(_x101)))))))))a#(c(d(a(c(d(d(d(d(_x101)))))))))b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x191)))))))))))))))))))
b#(c(c(c(c(d(_x121))))))a#(c(d(a(c(d(a(c(d(a(_x121))))))))))b#(c(c(c(c(d(_x101))))))a#(c(d(d(a(c(d(a(_x101))))))))
b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(a(c(d(a(_x201))))))))))))))))b#(c(c(c(d(_x91)))))a#(c(d(a(c(d(a(_x91)))))))
b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(d(a(c(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(a(c(d(a(c(d(a(b(_x131)))))))))))))b#(c(c(c(c(c(c(d(_x91))))))))a#(c(d(d(d(d(d(a(_x91))))))))
b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))b#(c(c(c(c(c(c(d(d(d(_x161))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(c(b(d(c(b(a(_x161))))))))))))))))))
b#(c(c(c(c(c(_x101))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x101))))))))))))b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(_x201))))))))))))))))))
b#(c(c(c(c(c(c(c(d(d(_x131))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(c(b(a(_x131))))))))))))))))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(d(d(d(d(d(a(b(_x141))))))))))
b#(c(c(c(c(c(c(c(c(d(d(_x171)))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(a(c(d(d(c(b(a(_x171)))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(c(_x151)))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(_x151)))))))))))))
b#(c(c(c(c(c(_x101))))))a#(c(d(d(d(d(a(b(_x101))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(b(_x141))))))))))))))))b#(c(c(c(c(c(c(d(d(c(_x161))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(c(b(_x161))))))))))))))
b#(c(c(c(c(c(c(d(d(d(_x141))))))))))a#(c(d(d(d(d(d(d(c(b(d(c(b(a(_x141))))))))))))))b#(c(c(c(c(c(c(c(d(_x151)))))))))a#(c(d(d(d(d(d(a(c(d(a(_x151)))))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(a(c(d(_x171)))))))))))))))b#(c(c(c(c(c(c(c(d(d(_x111))))))))))a#(c(d(d(d(d(d(d(d(c(b(a(_x111))))))))))))
b#(c(c(c(c(c(c(c(d(_x151)))))))))a#(c(d(d(d(d(d(d(a(_x151)))))))))b#(c(c(c(c(c(c(c(d(c(_x111))))))))))a#(c(d(a(c(d(d(d(d(d(_x111))))))))))
b#(c(c(d(d(_x41)))))a#(c(d(d(c(b(a(_x41)))))))b#(c(c(c(c(c(c(c(c(d(d(_x151)))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(a(_x151)))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(a(_x201))))))))))))))b#(c(c(c(c(c(c(c(_x91))))))))a#(c(d(d(d(d(d(a(c(d(a(b(_x91))))))))))))
b#(c(c(c(c(c(c(d(c(_x101)))))))))a#(c(d(d(d(d(a(c(d(_x101)))))))))b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(c(d(a(_x201))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x221))))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x221))))))))))))))))))))))))b#(c(c(c(c(c(c(c(d(_x171)))))))))a#(c(d(d(a(c(d(a(c(d(d(a(c(d(a(_x171)))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(d(a(c(d(d(a(b(_x151)))))))))))b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(a(c(d(d(d(a(c(d(a(c(d(a(b(_x191)))))))))))))))))
b#(c(c(c(c(c(c(d(_x131))))))))a#(c(d(d(a(c(d(a(c(d(d(a(_x131))))))))))))b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(b(_x191)))))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(_x171)))))))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(c(c(c(d(_x161))))))))))a#(c(d(a(c(d(d(d(d(d(a(c(d(a(_x161))))))))))))))b#(c(c(c(c(c(d(_x131)))))))a#(c(d(d(a(c(d(a(c(d(a(_x131)))))))))))
b#(c(c(c(c(c(c(c(d(d(d(_x151)))))))))))a#(c(d(a(c(d(d(d(d(d(d(c(b(d(c(b(a(_x151)))))))))))))))))b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(c(d(d(d(d(_x171)))))))))))a#(c(d(a(c(d(d(d(d(d(c(b(d(c(b(d(c(b(a(_x171)))))))))))))))))))b#(c(c(c(c(c(c(d(d(d(_x141))))))))))a#(c(d(a(c(d(d(d(d(d(c(c(b(a(_x141))))))))))))))
b#(c(c(c(c(c(c(c(_x131))))))))a#(c(d(d(a(c(d(a(c(d(d(d(a(b(_x131))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(a(_x201))))))))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x191)))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(_x191)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(a(c(d(d(d(a(_x201))))))))))))
b#(c(c(c(c(c(c(c(_x131))))))))a#(c(d(d(a(c(d(d(d(a(c(d(a(b(_x131))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x221))))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x221))))))))))))))))))))
b#(c(c(c(c(c(c(d(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x181))))))))))))))))b#(c(x))b#(x)
b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))b#(c(c(c(c(c(c(d(d(_x101)))))))))a#(c(d(d(d(d(a(c(d(d(c(b(a(_x101)))))))))))))
b#(c(c(c(c(c(_x101))))))a#(c(d(d(d(a(c(d(a(b(_x101))))))))))a#(d(x))a#(x)
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(c(d(a(b(_x171)))))))))))))))))b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(c(d(a(b(_x191)))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(a(b(_x171)))))))))))))))))b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))
b#(c(c(c(c(c(c(c(d(c(_x131))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(_x131))))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(d(a(b(_x131)))))))))))
b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(a(c(d(d(d(d(d(a(c(d(a(_x201))))))))))))))b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(d(d(a(b(_x191)))))))))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(d(a(c(d(a(b(_x131)))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(d(a(b(_x161))))))))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))b#(c(c(c(c(_x91)))))a#(c(d(d(d(a(b(_x91)))))))
b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(d(d(d(d(a(_x141))))))))b#(c(c(c(c(c(c(c(c(_x151)))))))))a#(c(d(a(c(d(d(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(a(b(_x171)))))))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(d(a(b(_x131)))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(d(a(b(_x121))))))))))b#(c(c(c(c(c(c(c(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(d(_x21)))a#(_x21)
b#(c(c(c(c(c(c(c(d(_x171)))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(_x171)))))))))))))))b#(c(c(c(c(c(c(c(d(_x121)))))))))a#(c(d(d(d(d(d(d(a(_x121)))))))))
b#(c(c(c(c(c(c(_x111)))))))a#(c(d(d(a(c(d(d(d(a(b(_x111)))))))))))b#(c(c(c(c(c(d(_x111)))))))a#(c(d(d(a(c(d(d(a(_x111)))))))))
b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(a(c(d(a(c(d(d(a(c(d(a(b(_x161))))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x121)))))))))a#(c(d(d(d(d(d(d(d(a(b(_x121)))))))))))b#(c(c(c(c(c(c(c(c(c(_x181))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(d(d(_x101)))))))))a#(c(d(d(d(d(d(d(c(b(a(_x101)))))))))))
b#(c(c(c(c(c(c(c(c(d(_x181))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(a(c(d(a(_x181))))))))))))))))b#(c(c(c(c(c(c(c(_x131))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(b(_x131))))))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(a(c(d(d(d(d(a(c(d(a(c(d(a(b(_x171)))))))))))))))))b#(c(c(c(c(c(c(d(d(_x121)))))))))a#(c(d(a(c(d(d(d(d(d(c(b(a(_x121)))))))))))))
b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(d(d(a(c(d(d(a(b(_x141))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(d(a(c(d(a(_x201))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(_x141))))))))))a#(c(d(a(c(d(d(d(d(d(d(a(_x141))))))))))))b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(d(a(c(d(d(a(c(d(a(_x141))))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(d(d(d(a(c(d(d(a(c(d(a(b(_x171)))))))))))))))b#(c(c(c(c(c(c(d(c(_x121)))))))))a#(c(d(a(c(d(d(d(a(c(d(_x121)))))))))))
b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(d(a(b(_x191)))))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))
a#(d(x))b#(a(x))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(b(_x141))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x161))))))))))a#(c(d(a(c(d(d(d(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))
b#(c(c(c(c(c(c(c(_x121))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(a(_x201))))))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x171)))))))))))))))))))b#(c(c(c(c(c(c(c(c(_x121)))))))))a#(c(d(d(d(d(d(d(a(c(d(a(b(_x121)))))))))))))
b#(c(c(c(c(c(c(d(_x121))))))))a#(c(d(d(d(d(a(c(d(a(_x121))))))))))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x141))))))))))))))))
b#(c(c(c(c(c(d(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(_x151)))))))))))))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(d(d(d(d(a(c(d(a(b(_x141))))))))))))
b#(c(c(c(c(c(c(c(d(d(c(_x151)))))))))))a#(c(d(a(c(d(d(d(d(d(d(c(b(_x151)))))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(d(d(a(b(_x151)))))))))))b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(a(c(d(d(d(d(d(a(c(d(a(b(_x171)))))))))))))))
b#(c(c(c(c(_x71)))))a#(c(d(d(d(a(b(_x71)))))))b#(c(c(c(c(c(c(c(d(_x191)))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x191)))))))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(c(c(c(c(_x141)))))))))) → a#(c(d(a(c(d(d(d(d(d(d(a(c(d(a(b(_x141)))))))))))))))) 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
a#(c(d(a(c(d(d(d(d(d(d(d(a(b(_x141)))))))))))))) 
a#(c(d(d(d(d(d(d(d(a(c(d(a(b(_x141)))))))))))))) 
a#(c(d(a(c(d(d(d(d(d(d(a(c(d(a(c(d(a(b(_x171))))))))))))))))))) 
a#(c(d(a(c(d(d(d(d(d(d(a(c(d(a(_x171))))))))))))))) 
Thus, the rule b#(c(c(c(c(c(c(c(c(c(_x141)))))))))) → a#(c(d(a(c(d(d(d(d(d(d(a(c(d(a(b(_x141)))))))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(c(c(c(d(_x171))))))))))) → a#(c(d(a(c(d(d(d(d(d(d(a(c(d(a(_x171)))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x141)))))))))) → a#(c(d(d(d(d(d(d(d(a(c(d(a(b(_x141))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x171))))))))))) → a#(c(d(a(c(d(d(d(d(d(d(a(c(d(a(c(d(a(b(_x171)))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x141)))))))))) → a#(c(d(a(c(d(d(d(d(d(d(d(a(b(_x141))))))))))))))

Problem 22: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x131)))))))))))))))b#(c(c(c(c(c(c(c(d(d(_x131))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(c(b(a(_x131))))))))))))))))
b#(c(c(c(c(d(_x101))))))a#(c(d(d(d(a(_x101))))))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(d(d(d(d(d(a(b(_x141))))))))))
b#(c(c(c(c(c(c(c(c(d(d(_x171)))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(a(c(d(d(c(b(a(_x171)))))))))))))))))))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(d(a(c(d(d(d(a(c(d(a(b(_x141))))))))))))))
b#(c(c(c(c(c(_x101))))))a#(c(d(d(d(d(a(b(_x101))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(c(c(_x131))))))))a#(c(d(d(d(d(a(c(d(d(a(b(_x131))))))))))))b#(c(c(c(c(c(c(c(c(c(d(_x211)))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(c(d(a(c(d(a(_x211)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x141))))))))))a#(c(d(d(d(d(d(d(d(d(a(b(_x141))))))))))))b#(c(c(c(c(c(c(c(d(_x151)))))))))a#(c(d(d(d(d(d(a(c(d(a(_x151)))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(d(d(a(c(d(a(b(_x151)))))))))))b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x171)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x151)))))))))a#(c(d(d(d(d(d(d(a(c(d(a(b(_x151)))))))))))))b#(c(c(c(c(c(c(c(c(c(_x181))))))))))a#(c(d(d(d(d(a(c(d(d(a(c(d(d(a(b(_x181))))))))))))))))
b#(c(c(d(d(_x41)))))a#(c(d(d(c(b(a(_x41)))))))b#(c(c(c(c(c(c(c(c(d(d(_x191)))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(c(d(d(c(b(a(_x191)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(_x211)))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(b(d(c(b(a(_x211)))))))))))))))))))))))b#(c(c(c(c(d(d(c(c(_x121)))))))))a#(c(d(a(c(d(a(c(d(d(c(c(d(a(b(_x121)))))))))))))))
b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(a(_x201))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x181))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(_x191)))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(c(d(d(a(_x191)))))))))))))))))b#(c(c(c(c(c(c(c(c(c(d(_x171)))))))))))a#(c(d(a(c(d(d(d(d(d(d(a(c(d(a(_x171)))))))))))))))
b#(c(c(c(c(d(d(_x81)))))))a#(c(d(d(a(c(d(d(c(b(a(_x81)))))))))))b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(c(d(a(_x201))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(a(c(d(d(c(b(d(c(b(d(c(b(a(_x261)))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(_x201))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x181))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(b(_x181))))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(d(a(c(d(d(a(b(_x151)))))))))))
b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(a(c(d(d(d(a(c(d(a(c(d(a(b(_x191)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(d(_x291))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(d(c(b(d(c(b(d(c(b(d(c(b(a(_x291))))))))))))))))))))))))))))))
b#(c(c(c(c(c(c(d(_x131))))))))a#(c(d(d(a(c(d(a(c(d(d(a(_x131))))))))))))b#(c(c(c(c(c(c(c(c(c(_x151))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(b(_x151))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(b(_x191)))))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(d(a(c(d(a(c(d(a(c(d(d(a(b(_x191)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(_x171)))))))))))a#(c(d(d(d(d(a(c(d(d(d(d(c(b(a(_x171)))))))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))b#(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(_x171)))))))))))))))
b#(c(c(c(c(c(c(d(d(c(d(_x121)))))))))))a#(c(d(a(c(d(d(d(d(d(c(_x121)))))))))))b#(c(c(c(c(c(c(d(d(c(_x121))))))))))a#(c(d(d(d(d(d(d(c(b(_x121))))))))))
b#(c(c(c(c(c(c(d(d(d(_x161))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(c(c(b(a(_x161))))))))))))))))b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(_x181))))))))))))a#(c(d(d(d(d(a(c(d(d(d(d(c(b(d(c(b(a(_x181))))))))))))))))))
b#(c(c(c(c(c(c(d(d(d(d(_x171)))))))))))a#(c(d(a(c(d(d(d(d(d(c(b(d(c(b(d(c(b(a(_x171)))))))))))))))))))b#(c(c(c(c(c(c(d(d(d(_x141))))))))))a#(c(d(a(c(d(d(d(d(d(c(c(b(a(_x141))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(c(_x181))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(_x181))))))))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))
b#(c(c(c(c(c(c(_x111)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x111)))))))))))))b#(c(c(c(c(c(c(c(_x131))))))))a#(c(d(d(a(c(d(a(c(d(d(d(a(b(_x131))))))))))))))
b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(a(_x201))))))))))))))b#(c(c(c(c(c(c(c(c(d(c(_x191)))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(_x191)))))))))))))))))
b#(c(c(c(c(d(_x121))))))a#(c(d(d(a(c(d(a(_x121))))))))b#(c(c(c(c(c(c(c(d(_x151)))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(_x151)))))))))))))
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b#(c(c(c(c(c(c(d(c(_x101)))))))))a#(c(d(d(d(d(a(c(d(_x101)))))))))b#(c(c(c(c(c(c(c(_x131))))))))a#(c(d(d(a(c(d(d(d(d(a(b(_x131))))))))))))
b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(d(a(c(d(a(c(d(d(a(b(_x161))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x221))))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x221))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(d(_x171)))))))))a#(c(d(d(a(c(d(a(c(d(d(a(c(d(a(_x171)))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(_x151)))))))))))a#(c(d(d(d(d(d(d(d(d(d(a(b(_x151)))))))))))))
b#(c(c(c(c(d(d(_x101)))))))a#(c(d(a(c(d(d(d(c(b(a(_x101)))))))))))b#(c(c(c(c(c(c(c(c(d(_x151))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(a(_x151))))))))))))))
b#(c(c(c(c(c(c(d(d(c(c(_x101)))))))))))a#(c(d(d(d(d(d(d(c(c(d(a(b(_x101)))))))))))))b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))
b#(c(c(c(c(c(c(c(c(d(_x161))))))))))a#(c(d(a(c(d(d(d(d(d(a(c(d(a(_x161))))))))))))))b#(c(c(c(c(c(d(_x131)))))))a#(c(d(d(a(c(d(a(c(d(a(_x131)))))))))))
b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(d(d(d(a(c(d(d(a(b(_x191)))))))))))))b#(c(c(c(c(c(c(c(c(d(_x181))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(c(d(a(_x181))))))))))))))))
b#(c(c(c(c(c(c(c(d(d(d(_x151)))))))))))a#(c(d(a(c(d(d(d(d(d(d(c(b(d(c(b(a(_x151)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(d(c(b(d(c(b(d(c(b(a(_x261)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(c(_x261)))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(d(c(b(d(c(b(_x261)))))))))))))))))))))))b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(c(_x181))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(_x181))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(d(_x181))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(a(c(d(a(_x181))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(_x191)))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(a(_x191)))))))))))))))))b#(c(c(c(c(d(d(d(_x121))))))))a#(c(d(d(a(c(d(d(c(b(d(c(b(a(_x121))))))))))))))
b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(a(c(d(a(c(d(d(a(c(d(d(a(b(_x191)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(a(c(d(d(d(a(_x201))))))))))))
b#(c(c(c(c(c(c(d(d(d(c(c(_x151))))))))))))a#(c(d(a(c(d(d(d(d(d(c(b(d(c(c(d(a(b(_x151))))))))))))))))))b#(c(c(c(c(c(c(c(_x131))))))))a#(c(d(d(a(c(d(d(d(a(c(d(a(b(_x131))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x171)))))))))))a#(c(d(a(c(d(d(d(d(d(d(a(c(d(a(c(d(a(b(_x171)))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(c(_x211)))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(b(_x211)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(_x221))))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x221))))))))))))))))))))b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))
b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(b(_x191)))))))))))))))))b#(c(c(c(c(c(_x101))))))a#(c(d(d(d(a(c(d(a(b(_x101))))))))))
b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(d(d(a(c(d(d(d(a(b(_x141))))))))))))b#(c(c(c(c(c(c(c(c(c(c(_x191)))))))))))a#(c(d(d(a(c(d(d(d(d(a(c(d(a(c(d(a(c(d(a(b(_x191)))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(d(c(c(b(d(c(b(a(_x261)))))))))))))))))))))))))b#(c(c(c(c(d(d(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(c(b(d(c(b(a(_x141))))))))))))))))
b#(c(c(c(c(c(c(d(d(d(c(_x171)))))))))))a#(c(d(a(c(d(d(d(d(d(c(c(b(_x171)))))))))))))b#(c(c(c(c(d(_x121))))))a#(c(d(d(d(a(_x121))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(a(b(_x171)))))))))))))))))b#(c(c(c(c(c(c(c(d(_x171)))))))))a#(c(d(d(d(a(c(d(a(c(d(a(c(d(a(_x171)))))))))))))))
b#(c(c(c(d(_x71)))))a#(c(d(d(a(_x71)))))b#(c(c(c(c(c(c(c(d(c(_x131))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(_x131))))))))))))
b#(c(c(c(c(c(c(d(_x131))))))))a#(c(d(d(a(c(d(d(d(a(_x131))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(a(c(d(d(d(a(b(_x131)))))))))))
b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(a(c(d(d(d(d(d(a(c(d(a(_x201))))))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(b(_x161))))))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(d(a(c(d(a(b(_x131)))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(d(_x241))))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(b(d(c(b(d(c(b(a(_x241))))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(_x181))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(d(a(b(_x161))))))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(d(d(a(b(_x91)))))))b#(c(c(c(c(c(c(c(c(c(d(_x191)))))))))))a#(c(d(d(a(c(d(d(d(d(a(c(d(a(c(d(a(_x191)))))))))))))))))
b#(c(c(c(c(c(c(c(_x131))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(b(_x131))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(d(d(d(a(_x201))))))))))
b#(c(c(c(c(c(c(c(c(_x151)))))))))a#(c(d(a(c(d(d(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(_x181))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(b(a(_x181))))))))))))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(a(c(d(d(d(d(a(b(_x131)))))))))))b#(c(c(c(c(d(c(_x101)))))))a#(c(d(a(c(d(a(c(d(_x101)))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(d(d(d(d(a(c(d(a(b(_x191)))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(c(_x201))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(_x201))))))))))))))))))b#(c(d(_x21)))a#(_x21)
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x171)))))))))))))))))))b#(c(c(c(c(c(c(c(d(_x171)))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(_x171)))))))))))))))
b#(c(c(c(c(c(c(c(d(_x121)))))))))a#(c(d(d(d(d(d(d(a(_x121)))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(c(b(d(c(b(a(_x261)))))))))))))))))))))
b#(c(c(c(c(c(c(_x111)))))))a#(c(d(d(a(c(d(d(d(a(b(_x111)))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(c(b(d(c(b(d(c(b(a(_x261)))))))))))))))))))))
b#(c(c(c(c(d(d(c(_x121))))))))a#(c(d(d(a(c(d(d(c(b(_x121))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(a(c(d(d(a(b(_x131)))))))))))
b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(d(d(_x101)))))))))a#(c(d(d(d(d(d(d(c(b(a(_x101)))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(a(c(d(d(d(d(a(c(d(a(c(d(a(b(_x171)))))))))))))))))b#(c(c(c(c(c(c(c(c(_x151)))))))))a#(c(d(d(d(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(d(d(a(c(d(d(a(b(_x141))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(d(a(c(d(a(_x201))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(_x181))))))))))))a#(c(d(d(d(d(d(d(d(d(c(b(d(c(b(a(_x181))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(a(c(d(d(c(b(d(c(b(d(c(b(a(_x261)))))))))))))))))))))))))
b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(d(a(c(d(d(a(c(d(a(_x141))))))))))))b#(c(c(c(c(c(c(d(d(d(_x121))))))))))a#(c(d(d(d(d(d(d(c(b(d(c(b(a(_x121))))))))))))))
b#(c(c(c(c(d(d(c(d(_x121)))))))))a#(c(d(a(c(d(a(c(d(d(c(_x121)))))))))))b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(d(a(b(_x191)))))))))))))))))
a#(d(x))b#(a(x))b#(c(c(c(c(c(c(d(d(c(_x141))))))))))a#(c(d(d(d(d(a(c(d(d(c(b(_x141))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(d(_x151)))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(a(_x151)))))))))))))
b#(c(c(c(c(c(c(c(_x121))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(a(_x201))))))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x171)))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(_x191)))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(a(c(d(d(c(b(a(_x191)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(d(_x161))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(a(_x161))))))))))))))b#(c(c(c(c(c(c(d(d(d(c(_x191)))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(c(b(d(c(b(_x191)))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(c(d(d(c(b(d(c(b(d(c(b(a(_x261)))))))))))))))))))))))))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(d(d(d(d(a(c(d(a(b(_x141))))))))))))
b#(c(c(c(c(c(c(c(d(d(c(_x151)))))))))))a#(c(d(a(c(d(d(d(d(d(d(c(b(_x151)))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(d(d(a(b(_x151)))))))))))
b#(c(c(c(c(_x71)))))a#(c(d(d(d(a(b(_x71)))))))b#(c(c(c(c(c(c(d(d(d(_x161))))))))))a#(c(d(a(c(d(d(d(d(d(c(b(d(c(b(a(_x161))))))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x131))))))))))))))) 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
a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131))))))))))))) 
a#(c(d(d(a(c(d(a(c(d(d(a(b(_x131))))))))))))) 
a#(c(d(d(a(c(d(a(c(d(a(c(d(a(_x161)))))))))))))) 
a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x161)))))))))))))))))) 
a#(c(d(d(d(a(c(d(a(c(d(a(b(_x131))))))))))))) 
Thus, the rule b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x131))))))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(c(_x161)))))))) → a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(d(a(c(d(a(c(d(d(a(b(_x131)))))))))))))
b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))b#(c(c(c(c(c(c(d(_x161)))))))) → a#(c(d(d(a(c(d(a(c(d(a(c(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(_x131))))))) → a#(c(d(d(d(a(c(d(a(c(d(a(b(_x131)))))))))))))

Problem 23: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x281)))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x181))))))))))a#(c(d(d(d(d(a(c(d(d(a(c(d(d(a(b(_x181))))))))))))))))
b#(c(c(c(c(c(c(_x101)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x101)))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x211)))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(b(d(c(b(a(_x211)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(_x191)))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(c(d(d(c(b(a(_x191)))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(d(_x191)))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(c(d(d(a(_x191)))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(c(d(a(_x201))))))))))))))))b#(c(c(c(c(c(c(d(_x111))))))))a#(c(d(d(d(d(a(c(d(a(_x111))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x241)))))))))))a#(c(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x241)))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(a(c(d(d(c(b(d(c(b(d(c(b(a(_x261)))))))))))))))))))))))))
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b#(c(c(c(c(c(c(c(c(d(d(c(_x181))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(_x181))))))))))))))))b#(c(c(c(c(c(c(c(c(c(d(d(_x201))))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(c(d(a(c(d(d(c(b(a(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(_x191)))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(a(_x191)))))))))))))))))b#(c(c(c(c(c(c(c(c(c(d(_x211)))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(d(a(c(d(a(_x211)))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(a(c(d(d(d(a(_x201))))))))))))b#(c(c(c(c(c(c(c(c(c(c(_x241)))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x241)))))))))))))))))))))
b#(c(c(c(c(c(c(c(_x131))))))))a#(c(d(d(a(c(d(d(d(a(c(d(a(b(_x131))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(_x251))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x251))))))))))))))))))))))))
b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))b#(c(c(c(c(c(_x101))))))a#(c(d(d(d(a(c(d(a(b(_x101))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(_x311))))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x311))))))))))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x181))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(_x181))))))))))))))))
b#(c(c(c(c(c(c(d(d(d(c(_x171)))))))))))a#(c(d(a(c(d(d(d(d(d(c(c(b(_x171)))))))))))))b#(c(c(c(c(d(d(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(c(b(d(c(b(a(_x141))))))))))))))))
b#(c(c(c(c(d(_x121))))))a#(c(d(d(d(a(_x121))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(_x281)))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(a(b(_x171)))))))))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(b(_x161))))))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(d(d(a(b(_x91)))))))b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(d(d(d(a(_x201))))))))))
b#(c(c(c(c(c(c(c(c(d(_x131))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(_x131))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(_x181))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(b(a(_x181))))))))))))))))))))
b#(c(c(c(c(d(c(_x101)))))))a#(c(d(a(c(d(a(c(d(_x101)))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x271))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(b(_x271))))))))))))))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(c(_x201))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(_x201))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x171)))))))))))))))))))b#(c(c(c(c(c(c(c(d(_x171)))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(_x171)))))))))))))))
b#(c(c(c(c(c(d(_x81)))))))a#(c(d(d(d(d(a(_x81)))))))b#(c(c(c(c(c(c(c(d(d(d(_x171)))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(c(b(d(c(b(a(_x171)))))))))))))))))))
b#(c(c(c(c(d(d(c(_x121))))))))a#(c(d(d(a(c(d(d(c(b(_x121))))))))))b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(a(c(d(d(a(b(_x131)))))))))))
b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(a(c(d(d(d(d(a(c(d(a(c(d(a(b(_x171)))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x271))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(d(a(b(_x271))))))))))))))))))))))))))b#(c(c(c(c(d(d(c(d(_x121)))))))))a#(c(d(a(c(d(a(c(d(d(c(_x121)))))))))))
b#(c(c(c(c(c(c(d(d(d(_x121))))))))))a#(c(d(d(d(d(d(d(c(b(d(c(b(a(_x121))))))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(d(d(a(b(_x121))))))))
b#(c(c(c(c(c(c(c(d(d(c(d(_x151))))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(c(_x151))))))))))))))b#(c(c(c(c(c(c(c(d(_x121)))))))))a#(c(d(d(d(d(a(c(d(d(a(_x121)))))))))))
a#(d(x))b#(a(x))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(_x151)))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(a(_x151)))))))))))))b#(c(c(c(c(c(c(c(c(c(c(d(_x161))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(_x261)))))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x261)))))))))))))))))))))))))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(d(d(d(d(a(c(d(a(b(_x141))))))))))))
b#(c(c(c(c(c(c(c(d(d(c(_x151)))))))))))a#(c(d(a(c(d(d(d(d(d(d(c(b(_x151)))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(d(d(a(b(_x151)))))))))))
b#(c(c(c(c(c(c(d(d(d(_x161))))))))))a#(c(d(a(c(d(d(d(d(d(c(b(d(c(b(a(_x161))))))))))))))))b#(c(c(c(c(c(c(c(c(c(d(c(_x201))))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(d(a(c(d(_x201))))))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


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

Problem 24: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(_x251))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x251))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(_x281)))))))))))))))))))))))b#(c(c(c(c(c(c(c(d(d(_x131))))))))))a#(c(d(d(d(d(d(a(c(d(d(c(b(a(_x131))))))))))))))
b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(_x281)))))))))))))))))))
b#(c(c(c(c(c(c(c(d(d(c(c(_x151))))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(c(c(d(a(b(_x151))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(c(_x191)))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(_x191)))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(d(a(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x201))))))))))))))))))))b#(c(c(c(c(d(_x121))))))a#(c(d(d(a(c(d(a(_x121))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(a(c(d(d(a(c(d(a(_x281)))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(_x261)))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(d(a(c(d(d(a(c(d(a(b(_x261)))))))))))))))))))))))
a#(d(x))a#(x)b#(c(c(c(c(c(c(c(c(c(c(_x161)))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(a(b(_x161)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x211)))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x211)))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(b(a(_x261)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(c(d(a(b(_x191)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(c(_x251))))))))))))))a#(c(d(d(d(d(a(c(d(d(d(d(c(c(c(b(_x251))))))))))))))))
b#(c(c(c(c(c(c(d(d(d(c(_x171)))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(c(c(b(_x171)))))))))))))))b#(c(c(c(c(c(c(c(c(_x151)))))))))a#(c(d(d(a(c(d(d(d(d(d(a(b(_x151)))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(_x191)))))))))))a#(c(d(d(d(d(a(c(d(d(a(c(d(d(a(_x191)))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(_x191)))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(a(c(d(d(c(b(a(_x191)))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(b(d(c(b(a(_x261)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x131)))))))))))a#(c(d(a(c(d(d(d(d(d(d(_x131)))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))a#(c(d(a(c(d(d(d(d(d(d(_x171)))))))))))b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(d(d(d(d(a(_x141))))))))
b#(c(c(c(c(c(c(d(d(d(_x161))))))))))a#(c(d(d(d(d(a(c(d(d(c(b(d(c(b(a(_x161))))))))))))))))b#(c(c(c(c(c(c(c(d(d(_x131))))))))))a#(c(d(d(d(d(d(d(d(c(b(a(_x131))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(a(c(d(d(c(b(d(c(c(b(a(_x261)))))))))))))))))))))))b#(c(c(c(c(c(c(c(d(d(c(c(d(_x171)))))))))))))a#(c(d(d(d(d(d(a(c(d(d(c(c(d(a(_x171)))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x271))))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(b(_x271))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(_x251))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x251))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x271))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(d(d(a(c(d(a(c(d(a(c(d(a(b(_x271))))))))))))))))))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(a(c(d(d(d(a(b(_x121))))))))))
b#(c(c(c(c(c(c(c(_x181))))))))a#(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(_x211)))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x211)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(_x171)))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(a(c(d(d(d(d(d(a(c(d(d(c(b(d(c(b(d(c(b(a(_x261)))))))))))))))))))))))
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b#(c(c(c(c(d(d(_x101)))))))a#(c(d(a(c(d(d(d(c(b(a(_x101)))))))))))b#(c(c(c(c(c(c(c(c(d(_x151))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(a(_x151))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x241)))))))))))a#(c(d(d(d(a(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x241)))))))))))))))))))))))b#(c(c(c(c(c(c(_x101)))))))a#(c(d(d(d(d(a(c(d(a(b(_x101)))))))))))
b#(c(c(c(c(_x91)))))a#(c(d(a(c(d(d(a(b(_x91)))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(_x261)))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(a(b(_x261)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(_x161))))))))))a#(c(d(a(c(d(d(d(d(d(a(c(d(a(_x161))))))))))))))b#(c(c(c(c(c(d(_x131)))))))a#(c(d(d(a(c(d(a(c(d(a(_x131)))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x171)))))))))))a#(c(d(d(d(d(d(d(a(c(d(d(a(c(d(a(b(_x171)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(c(_x261)))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(d(c(b(d(c(b(_x261)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(d(d(d(_x151)))))))))))a#(c(d(a(c(d(d(d(d(d(d(c(b(d(c(b(a(_x151)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(c(_x181))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(_x181))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(_x171)))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(c(d(d(c(b(a(_x171)))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x241))))))))))))))a#(c(d(d(d(a(c(d(d(d(a(c(d(a(c(d(d(a(c(d(d(c(b(a(_x241))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(d(_x201))))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(c(d(a(c(d(d(c(b(a(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(_x191)))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(a(_x191)))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(c(d(_x191)))))))))))))))a#(c(d(d(d(d(d(d(d(d(c(c(c(_x191)))))))))))))b#(c(c(c(c(c(c(c(c(c(_x181))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(a(b(_x181))))))))))))))
b#(c(c(c(c(c(c(c(d(d(c(c(_x131))))))))))))a#(c(d(d(d(d(d(d(d(c(c(d(a(b(_x131))))))))))))))b#(c(c(c(c(c(c(c(c(c(d(_x211)))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(d(a(c(d(a(_x211)))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(c(c(_x211)))))))))))))))a#(c(d(d(d(d(a(c(d(d(d(d(c(b(d(c(b(d(c(c(d(a(b(_x211)))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x171))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(_x171))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(a(c(d(d(d(a(_x201))))))))))))b#(c(c(c(c(c(c(c(c(c(c(_x241)))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x241)))))))))))))))))))))
b#(c(c(c(c(c(c(c(_x131))))))))a#(c(d(d(a(c(d(d(d(a(c(d(a(b(_x131))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(_x251))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x251))))))))))))))))))))))))
b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))b#(c(c(c(c(c(_x101))))))a#(c(d(d(d(a(c(d(a(b(_x101))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(_x311))))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x311))))))))))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x181))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(_x181))))))))))))))))
b#(c(c(c(c(c(c(d(d(d(c(_x171)))))))))))a#(c(d(a(c(d(d(d(d(d(c(c(b(_x171)))))))))))))b#(c(c(c(c(d(d(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(c(b(d(c(b(a(_x141))))))))))))))))
b#(c(c(c(c(d(_x121))))))a#(c(d(d(d(a(_x121))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(_x281)))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(a(b(_x171)))))))))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(b(_x161))))))))))))))
b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x161))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(a(c(d(a(_x281)))))))))))))))))
b#(c(c(c(c(c(c(d(d(d(c(d(_x131))))))))))))a#(c(d(d(d(d(a(c(d(d(c(c(_x131))))))))))))b#(c(c(c(c(_x91)))))a#(c(d(d(d(a(b(_x91)))))))
b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(d(d(d(a(_x201))))))))))b#(c(c(c(c(c(c(c(c(d(_x131))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(_x131))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(_x181))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(b(a(_x181))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(c(d(_x211)))))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(c(b(d(c(_x211)))))))))))))))))))
b#(c(c(c(c(d(c(_x101)))))))a#(c(d(a(c(d(a(c(d(_x101)))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x271))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(b(_x271))))))))))))))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(c(_x201))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(_x201))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x171)))))))))))))))))))b#(c(c(c(c(c(c(c(d(_x171)))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(_x171)))))))))))))))
b#(c(c(c(c(c(d(_x81)))))))a#(c(d(d(d(d(a(_x81)))))))b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(a(c(d(d(a(c(d(a(_x201))))))))))))))
b#(c(c(c(c(c(c(c(d(d(d(_x171)))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(c(b(d(c(b(a(_x171)))))))))))))))))))b#(c(c(c(c(d(d(c(_x121))))))))a#(c(d(d(a(c(d(d(c(b(_x121))))))))))
b#(c(c(c(c(c(c(_x131)))))))a#(c(d(d(d(a(c(d(d(a(b(_x131)))))))))))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(a(c(d(d(d(d(a(c(d(a(c(d(a(b(_x171)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))a#(c(d(d(d(d(d(a(c(d(d(_x171)))))))))))
b#(c(c(c(c(c(c(c(c(c(d(_x191)))))))))))a#(c(d(d(d(d(a(c(d(d(d(d(a(_x191)))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x271))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(d(a(b(_x271))))))))))))))))))))))))))
b#(c(c(c(c(d(d(c(d(_x121)))))))))a#(c(d(a(c(d(a(c(d(d(c(_x121)))))))))))b#(c(c(c(c(c(c(d(d(d(_x121))))))))))a#(c(d(d(d(d(d(d(c(b(d(c(b(a(_x121))))))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(d(d(d(a(b(_x121))))))))b#(c(c(c(c(c(c(c(d(d(c(d(_x151))))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(c(_x151))))))))))))))
b#(c(c(c(c(c(c(c(d(_x121)))))))))a#(c(d(d(d(d(a(c(d(d(a(_x121)))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(c(_x261))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(_x261))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x241))))))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(a(c(d(d(d(c(b(a(_x241))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(d(_x251))))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(b(d(c(b(d(c(b(a(_x251))))))))))))))))))))))))))
a#(d(x))b#(a(x))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(_x151)))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(a(_x151)))))))))))))b#(c(c(c(c(c(c(c(c(c(c(d(_x161))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(_x261)))))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x261)))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x171))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x171))))))))))))))))))))
b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(d(d(d(d(a(c(d(a(b(_x141))))))))))))b#(c(c(c(c(c(c(c(d(d(c(_x151)))))))))))a#(c(d(a(c(d(d(d(d(d(d(c(b(_x151)))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(d(d(a(b(_x151)))))))))))b#(c(c(c(c(c(c(d(d(d(_x161))))))))))a#(c(d(a(c(d(d(d(d(d(c(b(d(c(b(a(_x161))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(c(_x201))))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(d(a(c(d(_x201))))))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151))))))))))))))) 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
a#(c(d(a(c(d(d(a(c(d(d(a(b(_x151))))))))))))) 
a#(c(d(a(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x161)))))))))))))))))) 
a#(c(d(a(c(d(a(c(d(a(c(d(d(a(_x161)))))))))))))) 
a#(c(d(a(c(d(a(c(d(d(d(a(b(_x151))))))))))))) 
a#(c(d(d(a(c(d(a(c(d(d(a(b(_x151))))))))))))) 
Thus, the rule b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(a(c(d(a(c(d(a(c(d(d(a(b(_x151))))))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(c(_x161)))))))) → a#(c(d(a(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x161))))))))))))))))))b#(c(c(c(c(c(c(d(_x161)))))))) → a#(c(d(a(c(d(a(c(d(a(c(d(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(a(c(d(d(a(c(d(d(a(b(_x151)))))))))))))b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(d(a(c(d(a(c(d(d(a(b(_x151)))))))))))))
b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(a(c(d(a(c(d(d(d(a(b(_x151)))))))))))))

Problem 25: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(d(x))a#(x)b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(b(a(_x261)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(c(d(a(b(_x191)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(c(_x251))))))))))))))a#(c(d(d(d(d(a(c(d(d(d(d(c(c(c(b(_x251))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x151)))))))))a#(c(d(d(a(c(d(d(d(d(d(a(b(_x151)))))))))))))b#(c(c(c(c(c(c(d(d(d(c(_x171)))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(c(c(b(_x171)))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(_x191)))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(a(c(d(d(c(b(a(_x191)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(_x191)))))))))))a#(c(d(d(d(d(a(c(d(d(a(c(d(d(a(_x191)))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(b(d(c(b(a(_x261)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x131)))))))))))a#(c(d(a(c(d(d(d(d(d(d(_x131)))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x241)))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(a(c(d(a(c(d(a(_x241)))))))))))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(d(a(c(d(a(c(d(a(b(_x121))))))))))))b#(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))a#(c(d(a(c(d(d(d(d(d(d(_x171)))))))))))
b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(d(d(d(d(a(_x141))))))))b#(c(c(c(c(c(c(d(d(d(_x161))))))))))a#(c(d(d(d(d(a(c(d(d(c(b(d(c(b(a(_x161))))))))))))))))
b#(c(c(c(c(c(c(c(d(d(_x131))))))))))a#(c(d(d(d(d(d(d(d(c(b(a(_x131))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(a(c(d(d(c(b(d(c(c(b(a(_x261)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(d(d(c(c(d(_x171)))))))))))))a#(c(d(d(d(d(d(a(c(d(d(c(c(d(a(_x171)))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(_x251))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x251))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x271))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(d(d(a(c(d(a(c(d(a(c(d(a(b(_x271))))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x271))))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(b(_x271))))))))))))))))))))))))
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b#(c(c(c(c(c(c(c(c(c(c(c(d(c(_x261))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(_x261))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x201))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(d(d(c(b(a(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x241))))))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(a(c(d(d(d(c(b(a(_x241))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(d(_x251))))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(b(d(c(b(d(c(b(a(_x251))))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(_x241)))))))))))))a#(c(d(d(d(d(d(d(d(d(a(c(d(d(a(_x241)))))))))))))))a#(d(x))b#(a(x))
b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(d(_x151)))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(a(_x151)))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(d(d(d(a(c(d(a(c(d(a(_x281)))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(d(_x161))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(a(_x161))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x201))))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(_x261)))))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x261)))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(d(_x201))))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(d(d(a(c(d(a(_x201))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x241)))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(a(c(d(a(_x241)))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x171))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x171))))))))))))))))))))b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(d(d(d(d(a(c(d(a(b(_x141))))))))))))
b#(c(c(c(c(c(c(c(d(d(c(_x151)))))))))))a#(c(d(a(c(d(d(d(d(d(d(c(b(_x151)))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(d(d(a(b(_x151)))))))))))
b#(c(c(c(c(c(c(d(d(d(_x161))))))))))a#(c(d(a(c(d(d(d(d(d(c(b(d(c(b(a(_x161))))))))))))))))b#(c(c(c(c(c(c(c(c(c(d(c(_x201))))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(d(a(c(d(_x201))))))))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261))))))))))))) → a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(b(a(_x261))))))))))))))))))))))) 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
a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(c(b(a(_x261))))))))))))))))))))) 
a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(c(c(b(a(_x261))))))))))))))))))))) 
a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(b(_x241)))))))))))))))))))))) 
a#(c(d(a(c(d(d(d(d(a(c(d(d(d(c(b(d(c(c(b(a(_x261))))))))))))))))))))) 
a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(b(d(c(b(a(_x241)))))))))))))))))))))))))) 
a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(b(a(_x261))))))))))))))))))))) 
Thus, the rule b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261))))))))))))) → a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(b(a(_x261))))))))))))))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261))))))))))))) → a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(c(c(b(a(_x261)))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261))))))))))))) → a#(c(d(a(c(d(d(d(d(a(c(d(d(d(c(b(d(c(c(b(a(_x261)))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261))))))))))))) → a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(c(b(a(_x261)))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(c(_x241)))))))))))))) → a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(b(_x241))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(d(_x241)))))))))))))) → a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(b(d(c(b(a(_x241))))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261))))))))))))) → a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(b(a(_x261)))))))))))))))))))))

Problem 26: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(c(c(c(c(c(c(c(_x171)))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(d(a(b(_x171)))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(d(c(_x211)))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(d(d(_x211)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(c(_x241))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(d(_x241))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(_x171))))))))))))a#(c(d(d(d(d(a(c(d(d(d(a(c(d(d(a(c(d(a(b(_x171))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(_x251))))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x251))))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(a(c(d(d(a(_x281)))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(_x211)))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(d(a(c(d(a(c(d(a(b(_x211)))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(c(d(_x231)))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(a(c(d(d(c(b(d(c(c(_x231)))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(d(_x221))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(d(d(d(a(c(d(a(_x221))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x191)))))))))))a#(c(d(d(d(a(c(d(d(d(d(d(d(a(b(_x191)))))))))))))))b#(c(c(c(c(d(c(_x81)))))))a#(c(d(d(a(c(d(_x81)))))))
b#(c(c(c(c(c(c(c(c(c(_x181))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(d(d(a(b(_x181))))))))))))))))b#(c(c(c(c(c(c(d(d(_x121)))))))))a#(c(d(d(a(c(d(d(a(c(d(d(c(b(a(_x121)))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x221))))))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(a(c(d(d(a(c(d(d(c(b(a(_x221))))))))))))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(d(a(c(d(a(b(_x151)))))))))))))
b#(c(c(c(c(c(c(d(d(d(_x111))))))))))a#(c(d(d(d(d(d(d(c(b(d(c(b(a(_x111))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(_x241)))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(a(c(d(d(a(b(_x241)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(d(d(a(c(d(d(d(a(c(d(a(b(_x171)))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x151))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(d(a(_x151))))))))))))))
b#(c(c(c(c(c(c(c(d(d(c(d(_x131))))))))))))a#(c(d(d(d(d(d(a(c(d(d(c(_x131))))))))))))b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(d(a(c(d(d(a(c(d(a(_x161))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x241)))))))))))a#(c(d(d(d(a(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x241)))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(c(d(_x231)))))))))))))))a#(c(d(d(d(d(a(c(d(d(d(d(c(b(d(c(b(d(c(_x231)))))))))))))))))))
b#(c(c(c(c(d(d(c(_x141))))))))a#(c(d(a(c(d(d(d(c(b(_x141))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(_x161))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(a(c(d(a(b(_x161))))))))))))))))))
b#(c(c(c(c(c(c(c(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x141))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(_x201))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(d(c(d(_x241))))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(c(_x241))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(d(a(b(_x201))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x101)))))))))a#(c(d(d(d(d(d(d(a(c(d(a(b(_x101)))))))))))))b#(c(c(c(c(c(c(c(c(c(d(d(c(_x211)))))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(c(d(d(d(c(b(_x211)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(_x201))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(d(a(c(d(a(b(_x201))))))))))))))))))))b#(c(c(c(c(d(d(_x81)))))))a#(c(d(a(c(d(d(d(c(b(a(_x81)))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(_x231))))))))))))a#(c(d(d(d(a(c(d(d(d(d(a(c(d(a(c(d(a(c(d(a(b(_x231))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x261)))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(d(a(_x261)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(_x241)))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(d(a(c(d(a(c(d(a(b(_x241)))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(c(_x191)))))))))))a#(c(d(d(d(d(d(d(d(_x191)))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))a#(c(d(d(d(d(a(c(d(d(d(_x171)))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(d(d(_x171)))))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(d(d(d(c(b(a(_x171)))))))))))))))))))
b#(c(c(c(c(c(c(c(d(d(c(c(c(_x191)))))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(c(c(d(a(c(d(a(b(_x191)))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x181))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(_x181))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(d(_x271))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x271))))))))))))))))))))))))b#(c(c(c(c(c(c(d(d(c(d(_x121)))))))))))a#(c(d(d(d(d(d(d(c(_x121)))))))))
b#(c(c(c(c(d(d(c(_x141))))))))a#(c(d(d(a(c(d(d(c(b(_x141))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(c(_x191)))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(c(b(d(c(b(_x191)))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(c(_x241))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(c(b(_x241))))))))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(d(a(b(_x151)))))))))))))
b#(c(c(c(c(c(c(d(d(d(c(c(_x131))))))))))))a#(c(d(d(d(d(a(c(d(d(c(c(c(d(a(b(_x131))))))))))))))))b#(c(c(c(c(c(c(c(c(c(d(_x171)))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(a(_x171)))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x211)))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(b(_x211)))))))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(d(d(_x191)))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(d(c(b(d(c(b(a(_x191)))))))))))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(a(c(d(d(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))b#(c(c(c(c(c(c(d(c(_x121)))))))))a#(c(d(d(a(c(d(d(a(c(d(_x121)))))))))))
b#(c(c(c(c(c(c(c(c(c(_x181))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(a(b(_x181))))))))))))))b#(c(c(c(c(c(c(c(c(d(c(_x191)))))))))))a#(c(d(a(c(d(d(d(d(d(d(_x191)))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x201))))))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(d(a(c(d(d(c(b(a(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(_x111))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(b(_x111))))))))))))))
b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(_x151)))))))))))a#(c(d(d(d(d(d(d(d(d(a(c(d(a(b(_x151)))))))))))))))
b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))b#(c(c(c(c(c(c(c(c(d(d(_x191)))))))))))a#(c(d(a(c(d(d(d(d(d(a(c(d(d(c(b(a(_x191)))))))))))))))))
b#(c(c(c(c(c(c(d(d(c(c(_x121)))))))))))a#(c(d(a(c(d(d(d(d(d(c(c(d(a(b(_x121)))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(d(a(_x281)))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(c(d(_x231)))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(c(_x231)))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(c(_x151)))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(_x151)))))))))))))
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b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x201))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(d(d(c(b(a(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(_x151)))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(a(_x151)))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(d(d(d(a(c(d(a(c(d(a(_x281)))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(d(c(c(d(_x281)))))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(c(c(d(a(_x281)))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x201))))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(_x261)))))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x261)))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(d(d(_x281)))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(b(d(c(b(d(c(b(a(_x281)))))))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(c(d(_x231)))))))))))))))a#(c(d(d(d(d(a(c(d(d(d(d(c(c(c(_x231)))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x171))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x171))))))))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(d(d(a(b(_x151)))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(c(c(c(c(c(_x171))))))))))) → a#(c(d(d(d(d(d(d(a(c(d(a(c(d(d(a(b(_x171))))))))))))))))) 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
a#(c(d(d(d(d(d(d(a(c(d(d(d(a(b(_x171))))))))))))))) 
a#(c(d(d(d(d(d(d(a(c(d(a(c(d(d(a(c(d(a(b(_x181)))))))))))))))))))) 
a#(c(d(d(d(d(d(d(a(c(d(a(c(d(d(a(_x181)))))))))))))))) 
a#(c(d(d(d(d(d(d(d(a(c(d(d(a(b(_x171))))))))))))))) 
Thus, the rule b#(c(c(c(c(c(c(c(c(c(c(_x171))))))))))) → a#(c(d(d(d(d(d(d(a(c(d(a(c(d(d(a(b(_x171))))))))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(c(c(c(c(d(_x181)))))))))))) → a#(c(d(d(d(d(d(d(a(c(d(a(c(d(d(a(_x181))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(_x171))))))))))) → a#(c(d(d(d(d(d(d(a(c(d(d(d(a(b(_x171)))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(_x181)))))))))))) → a#(c(d(d(d(d(d(d(a(c(d(a(c(d(d(a(c(d(a(b(_x181))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(_x171))))))))))) → a#(c(d(d(d(d(d(d(d(a(c(d(d(a(b(_x171)))))))))))))))

Problem 27: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(c(c(c(c(c(d(d(d(d(d(c(d(_x241))))))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(c(_x241))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(d(c(d(_x241))))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(c(c(_x241))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(c(_x201))))))))))))))a#(c(d(d(d(d(d(d(a(c(d(d(a(c(d(d(_x201))))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(d(a(b(_x201))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x101)))))))))a#(c(d(d(d(d(d(d(a(c(d(a(b(_x101)))))))))))))b#(c(c(c(c(c(c(c(c(c(d(d(c(_x211)))))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(c(d(d(d(c(b(_x211)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(_x201))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(d(a(c(d(a(b(_x201))))))))))))))))))))b#(c(c(c(c(d(d(_x81)))))))a#(c(d(a(c(d(d(d(c(b(a(_x81)))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(_x231))))))))))))a#(c(d(d(d(a(c(d(d(d(d(a(c(d(a(c(d(a(c(d(a(b(_x231))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x261)))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(d(a(_x261)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(_x241)))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(d(a(c(d(a(c(d(a(b(_x241)))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(c(_x191)))))))))))a#(c(d(d(d(d(d(d(d(_x191)))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))a#(c(d(d(d(d(a(c(d(d(d(_x171)))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(d(_x261)))))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(a(c(d(d(d(a(_x261)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(d(d(_x171)))))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(d(d(d(c(b(a(_x171)))))))))))))))))))b#(c(c(c(c(c(c(c(d(d(c(c(c(_x191)))))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(c(c(d(a(c(d(a(b(_x191)))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(d(_x251))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(a(c(d(d(a(_x251))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x181))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(_x181))))))))))))))))
b#(c(c(c(c(c(c(d(d(c(d(_x121)))))))))))a#(c(d(d(d(d(d(d(c(_x121)))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(d(_x271))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(_x271))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(c(_x191)))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(c(b(d(c(b(_x191)))))))))))))))))b#(c(c(c(c(d(d(c(_x141))))))))a#(c(d(d(a(c(d(d(c(b(_x141))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(c(_x241))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(c(b(_x241))))))))))))))))))))b#(c(c(c(c(c(c(d(d(d(c(c(_x131))))))))))))a#(c(d(d(d(d(a(c(d(d(c(c(c(d(a(b(_x131))))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(d(a(b(_x151)))))))))))))b#(c(c(c(c(c(c(c(c(c(d(_x171)))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(a(_x171)))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x211)))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(b(_x211)))))))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(d(d(_x191)))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(d(c(b(d(c(b(a(_x191)))))))))))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))
b#(c(c(c(c(c(c(d(c(_x121)))))))))a#(c(d(d(a(c(d(d(a(c(d(_x121)))))))))))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(a(c(d(d(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x181))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(a(b(_x181))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x201))))))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(d(a(c(d(d(c(b(a(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x191)))))))))))a#(c(d(a(c(d(d(d(d(d(d(_x191)))))))))))b#(c(c(c(c(c(c(c(_x111))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(b(_x111))))))))))))))
b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(d(_x261)))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(d(d(d(d(a(_x261)))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x151)))))))))))a#(c(d(d(d(d(d(d(d(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(_x191)))))))))))a#(c(d(a(c(d(d(d(d(d(a(c(d(d(c(b(a(_x191)))))))))))))))))b#(c(c(c(c(c(c(d(d(c(c(_x121)))))))))))a#(c(d(a(c(d(d(d(d(d(c(c(d(a(b(_x121)))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(d(a(_x281)))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(c(d(_x231)))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(c(_x231)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x151)))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(_x151)))))))))))))b#(c(c(c(c(c(c(c(c(c(c(_x211)))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(d(d(a(c(d(a(b(_x211)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x221))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(d(d(d(a(c(d(a(b(_x221))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x241))))))))))))))a#(c(d(d(d(a(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(a(_x241))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(c(c(_x211)))))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(c(b(d(c(c(d(a(b(_x211)))))))))))))))))))))))b#(c(c(c(c(c(c(c(d(_x151)))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(_x151)))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(d(a(_x281)))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(_x251))))))))))))a#(c(d(d(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x251))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(d(d(d(a(c(d(d(a(c(d(d(c(b(d(c(c(b(a(_x261)))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))a#(c(d(d(d(d(d(d(a(c(d(_x171)))))))))))
b#(c(c(c(c(c(c(c(d(_x151)))))))))a#(c(d(d(d(d(d(d(a(_x151)))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(_x261)))))))))))))a#(c(d(d(d(d(d(d(d(d(d(d(a(c(d(a(b(_x261)))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(_x151)))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(a(_x151)))))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x181))))))))))a#(c(d(d(d(d(a(c(d(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))
b#(c(c(c(c(c(c(c(_x181))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(d(d(a(c(d(d(d(a(b(_x191)))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(d(d(d(a(b(_x151)))))))))b#(c(c(c(c(c(c(c(_x131))))))))a#(c(d(d(a(c(d(d(d(d(a(b(_x131))))))))))))
b#(c(c(c(c(c(c(d(d(_x141)))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(d(c(b(a(_x141)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(d(_x241))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(b(d(c(b(d(c(b(a(_x241))))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(d(_x171)))))))))a#(c(d(d(a(c(d(a(c(d(d(a(c(d(a(_x171)))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(c(_x281)))))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x281)))))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(c(_x201))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(d(d(_x201))))))))))))))b#(c(c(c(c(c(c(d(d(c(c(_x101)))))))))))a#(c(d(d(d(d(d(d(c(c(d(a(b(_x101)))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(c(_x241))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(_x241))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(a(c(d(d(c(c(b(d(c(b(a(_x261)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(d(d(c(d(_x131))))))))))))a#(c(d(d(d(d(d(d(d(c(_x131))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(d(d(a(_x281)))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x201))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(d(d(d(c(_x221))))))))))))))a#(c(d(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(b(_x221))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(d(c(_x261)))))))))))))))a#(c(d(d(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(d(d(c(b(_x261)))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(d(c(c(c(_x281)))))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(c(c(d(a(c(d(a(b(_x281)))))))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x151)))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(a(c(d(a(b(_x151)))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(_x241)))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(d(a(b(_x241)))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x181))))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(d(d(d(a(c(d(a(b(_x181))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x221))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(d(a(c(d(d(a(c(d(a(b(_x221))))))))))))))))))))))
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b#(c(c(c(c(c(c(c(d(_x171)))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(_x171)))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(_x231))))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x231))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(a(c(d(d(a(c(d(a(_x201))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(_x221))))))))))))a#(c(d(d(d(a(c(d(a(c(d(a(c(d(d(d(a(c(d(a(c(d(a(b(_x221))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(_x241)))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(d(d(a(_x241)))))))))))))))))b#(c(c(c(c(c(c(c(d(d(d(_x171)))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(c(b(d(c(b(a(_x171)))))))))))))))))))
b#(c(c(c(c(d(d(c(_x121))))))))a#(c(d(d(a(c(d(d(c(b(_x121))))))))))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(a(c(d(d(d(d(a(c(d(a(c(d(a(b(_x171)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))a#(c(d(d(d(d(d(a(c(d(d(_x171)))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(d(_x261)))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(d(a(c(d(d(a(c(d(a(_x261)))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(d(d(_x171)))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(d(_x221))))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(d(d(a(c(d(a(_x221))))))))))))))))))b#(c(c(c(c(c(c(_x101)))))))a#(c(d(a(c(d(d(d(a(c(d(a(b(_x101)))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(d(_x251))))))))))))))a#(c(d(d(d(d(d(d(d(d(d(d(d(a(_x251))))))))))))))b#(c(c(c(c(c(c(d(d(d(_x121))))))))))a#(c(d(d(d(d(d(d(c(b(d(c(b(a(_x121))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(b(_x201))))))))))))))))b#(c(c(c(c(c(_x121))))))a#(c(d(d(d(d(a(b(_x121))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(_x241)))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(a(c(d(d(a(c(d(a(b(_x241)))))))))))))))))))))b#(c(c(c(c(c(c(c(d(d(c(d(_x151))))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(c(_x151))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(c(_x261))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(_x261))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x201))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(d(d(c(b(a(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(d(_x151)))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(a(_x151)))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(d(d(d(a(c(d(a(c(d(a(_x281)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(d(c(c(d(_x281)))))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(c(c(d(a(_x281)))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x201))))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(_x261)))))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x261)))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(d(d(_x281)))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(b(d(c(b(d(c(b(a(_x281)))))))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(c(d(_x231)))))))))))))))a#(c(d(d(d(d(a(c(d(d(d(d(c(c(c(_x231)))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x171))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x171))))))))))))))))))))b#(c(c(c(c(c(c(d(d(_x121)))))))))a#(c(d(d(a(c(d(d(d(d(c(b(a(_x121)))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(d(d(a(b(_x151)))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(c(c(c(d(d(d(d(d(c(d(_x241)))))))))))))))) → a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(c(_x241)))))))))))))))))))) 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
a#(c(d(d(d(d(a(c(d(d(d(d(c(b(d(c(c(c(_x241)))))))))))))))))) 
a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(c(c(c(_x241)))))))))))))))))) 
a#(c(d(d(d(d(d(a(c(d(d(d(c(b(d(c(c(c(_x241)))))))))))))))))) 
Thus, the rule b#(c(c(c(c(c(c(c(c(d(d(d(d(d(c(d(_x241)))))))))))))))) → a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(c(_x241)))))))))))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(c(c(d(d(d(d(d(c(d(_x241)))))))))))))))) → a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(c(c(c(_x241))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(d(c(d(_x241)))))))))))))))) → a#(c(d(d(d(d(d(a(c(d(d(d(c(b(d(c(c(c(_x241))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(d(c(d(_x241)))))))))))))))) → a#(c(d(d(d(d(a(c(d(d(d(d(c(b(d(c(c(c(_x241))))))))))))))))))

Problem 28: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(c(c(c(_x151)))))))a#(c(d(a(c(d(d(a(c(d(d(a(b(_x151)))))))))))))b#(c(c(c(c(c(c(d(d(d(c(c(_x131))))))))))))a#(c(d(d(d(d(a(c(d(d(c(c(c(d(a(b(_x131))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(_x171)))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(a(_x171)))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(c(_x241))))))))))))))a#(c(d(d(d(d(a(c(d(d(d(d(c(b(d(c(c(b(_x241))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x211)))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(b(_x211)))))))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(d(a(c(d(a(b(_x151)))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(d(d(_x191)))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(d(c(b(d(c(b(a(_x191)))))))))))))))))))b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))
b#(c(c(c(c(c(c(d(c(_x121)))))))))a#(c(d(d(a(c(d(d(a(c(d(_x121)))))))))))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(a(c(d(d(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x181))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(a(b(_x181))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x201))))))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(d(a(c(d(d(c(b(a(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x191)))))))))))a#(c(d(a(c(d(d(d(d(d(d(_x191)))))))))))b#(c(c(c(c(c(c(c(_x111))))))))a#(c(d(d(d(d(a(c(d(a(c(d(a(b(_x111))))))))))))))
b#(c(c(c(c(c(c(c(_x161))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x161))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(d(_x261)))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(d(d(d(d(a(_x261)))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x151)))))))))))a#(c(d(d(d(d(d(d(d(d(a(c(d(a(b(_x151)))))))))))))))b#(c(c(c(c(c(c(d(_x141))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x141))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(_x191)))))))))))a#(c(d(a(c(d(d(d(d(d(a(c(d(d(c(b(a(_x191)))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(d(a(_x281)))))))))))))))))))))
b#(c(c(c(c(c(c(d(d(c(c(_x121)))))))))))a#(c(d(a(c(d(d(d(d(d(c(c(d(a(b(_x121)))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(c(d(_x231)))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(c(_x231)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x151)))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(_x151)))))))))))))b#(c(c(c(c(c(c(c(c(d(d(_x141)))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(d(d(c(b(a(_x141)))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(d(d(_x241)))))))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(a(c(d(d(d(c(b(d(c(b(a(_x241)))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(_x211)))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(d(d(a(c(d(a(b(_x211)))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x221))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(d(d(d(a(c(d(a(b(_x221))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x241))))))))))))))a#(c(d(d(d(a(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(a(_x241))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(c(c(_x211)))))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(c(b(d(c(c(d(a(b(_x211)))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(d(a(_x281)))))))))))))))))))))
b#(c(c(c(c(c(c(c(d(_x151)))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(_x151)))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(_x251))))))))))))a#(c(d(d(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x251))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x221))))))))))))))a#(c(d(d(d(a(c(d(d(d(a(c(d(d(a(c(d(d(d(c(b(a(_x221))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(d(d(d(a(c(d(d(a(c(d(d(c(b(d(c(c(b(a(_x261)))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))a#(c(d(d(d(d(d(d(a(c(d(_x171)))))))))))b#(c(c(c(c(c(c(c(d(_x151)))))))))a#(c(d(d(d(d(d(d(a(_x151)))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(_x261)))))))))))))a#(c(d(d(d(d(d(d(d(d(d(d(a(c(d(a(b(_x261)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(_x151)))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(a(_x151)))))))))))))))))
b#(c(c(c(c(c(c(c(_x181))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x181))))))))))a#(c(d(d(d(d(a(c(d(d(a(c(d(a(c(d(a(b(_x181))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x191)))))))))a#(c(d(d(d(d(a(c(d(d(d(a(b(_x191)))))))))))))b#(c(c(c(c(c(c(c(_x131))))))))a#(c(d(d(a(c(d(d(d(d(a(b(_x131))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(d(d(d(a(b(_x151)))))))))b#(c(c(c(c(c(c(d(d(_x141)))))))))a#(c(d(a(c(d(a(c(d(d(a(c(d(d(c(b(a(_x141)))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(_x231))))))))))))a#(c(d(d(d(a(c(d(d(d(d(a(c(d(a(c(d(d(a(b(_x231))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(d(_x241))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(b(d(c(b(d(c(b(a(_x241))))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(d(_x171)))))))))a#(c(d(d(a(c(d(a(c(d(d(a(c(d(a(_x171)))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(c(_x281)))))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x281)))))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(c(_x201))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(d(d(_x201))))))))))))))b#(c(c(c(c(c(c(d(d(c(c(_x101)))))))))))a#(c(d(d(d(d(d(d(c(c(d(a(b(_x101)))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(c(_x241))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(_x241))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(a(c(d(d(c(c(b(d(c(b(a(_x261)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(d(d(c(d(_x131))))))))))))a#(c(d(d(d(d(d(d(d(c(_x131))))))))))b#(c(c(c(c(c(c(c(c(d(_x141))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(_x141))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(d(d(a(_x281)))))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(a(c(d(a(c(d(d(d(a(c(d(a(b(_x201))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(d(d(c(_x221))))))))))))))a#(c(d(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(b(_x221))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(d(c(_x261)))))))))))))))a#(c(d(d(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(d(d(c(b(_x261)))))))))))))))))))))))
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b#(c(c(c(c(c(c(c(c(d(d(d(c(_x261)))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(d(c(b(d(c(b(_x261)))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(_x171)))))))))))a#(c(d(d(d(d(d(d(a(c(d(d(a(c(d(a(b(_x171)))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(_x241)))))))))))a#(c(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(_x241)))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(d(d(c(_x171)))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(d(c(b(_x171)))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(d(_x161))))))))))))))a#(c(d(d(d(d(d(d(d(d(d(d(d(a(_x161))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(d(c(_x191)))))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(d(d(_x191)))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(d(_x261)))))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(d(d(d(a(_x261)))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x261)))))))))))))a#(c(d(d(d(a(c(d(d(d(d(a(c(d(a(c(d(d(a(_x261)))))))))))))))))))
b#(c(c(c(c(c(c(d(d(d(c(c(_x151))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(c(c(c(d(a(b(_x151))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(c(c(_x211)))))))))))))))a#(c(d(d(d(d(a(c(d(d(d(d(c(b(d(c(b(d(c(c(d(a(b(_x211)))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(_x211)))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(d(a(c(d(a(_x211)))))))))))))))))b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(a(c(d(d(d(a(_x201))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(d(_x251))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(d(d(d(a(_x251))))))))))))))))))b#(c(c(c(c(c(c(c(_x131))))))))a#(c(d(d(a(c(d(d(d(a(c(d(a(b(_x131))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(_x251))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(d(a(c(d(a(b(_x251))))))))))))))))))))))))b#(c(c(c(c(c(d(_x131)))))))a#(c(d(a(c(d(a(c(d(d(a(_x131)))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x161)))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(a(c(d(a(b(_x161)))))))))))))))))b#(c(c(c(c(c(_x101))))))a#(c(d(d(d(a(c(d(a(b(_x101))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(c(c(_x311))))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x311))))))))))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(_x241)))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(d(d(a(b(_x241)))))))))))))))))))))
b#(c(c(c(c(c(c(d(d(d(c(_x171)))))))))))a#(c(d(a(c(d(d(d(d(d(c(c(b(_x171)))))))))))))b#(c(c(c(c(d(_x121))))))a#(c(d(d(d(a(_x121))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(_x191)))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(a(c(d(a(_x191)))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(_x281)))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(a(b(_x171)))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(d(_x261)))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(d(a(c(d(d(d(a(_x261)))))))))))))))))))
b#(c(c(c(c(c(c(d(_x161))))))))a#(c(d(a(c(d(a(c(d(d(d(a(_x161))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(a(c(d(a(_x281)))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(d(d(d(a(_x201))))))))))b#(c(c(c(c(c(c(c(c(d(_x131))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(_x131))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(_x181))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(b(a(_x181))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(d(c(_x241)))))))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(a(c(d(d(d(c(b(_x241)))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x271))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(b(_x271))))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(a(c(d(d(d(d(d(d(d(c(b(d(c(b(d(c(b(a(_x261)))))))))))))))))))))
b#(c(c(c(c(d(d(d(d(c(_x161))))))))))a#(c(d(d(d(d(c(b(d(c(b(d(c(b(_x161))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(d(_x241))))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(b(d(c(b(a(_x241))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(c(_x201))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(_x201))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(c(_x201))))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(a(c(d(d(_x201))))))))))))))))
b#(c(c(c(c(c(c(c(d(_x171)))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(_x171)))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(_x231))))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x231))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(_x201))))))))))a#(c(d(d(d(d(a(c(d(d(a(c(d(a(_x201))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(_x221))))))))))))a#(c(d(d(d(a(c(d(a(c(d(a(c(d(d(d(a(c(d(a(c(d(a(b(_x221))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(_x241)))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(d(d(a(_x241)))))))))))))))))b#(c(c(c(c(c(c(c(d(d(d(_x171)))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(c(b(d(c(b(a(_x171)))))))))))))))))))
b#(c(c(c(c(d(d(c(_x121))))))))a#(c(d(d(a(c(d(d(c(b(_x121))))))))))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(_x171)))))))))a#(c(d(a(c(d(d(d(d(a(c(d(a(c(d(a(b(_x171)))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x261)))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(d(d(a(_x261)))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))a#(c(d(d(d(d(d(a(c(d(d(_x171)))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(d(_x261)))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(d(a(c(d(d(a(c(d(a(_x261)))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(d(d(_x171)))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(d(_x221))))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(d(d(a(c(d(a(_x221))))))))))))))))))
b#(c(c(c(c(c(c(_x101)))))))a#(c(d(a(c(d(d(d(a(c(d(a(b(_x101)))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(d(_x251))))))))))))))a#(c(d(d(d(d(d(d(d(d(d(d(d(a(_x251))))))))))))))
b#(c(c(c(c(c(c(d(d(d(_x121))))))))))a#(c(d(d(d(d(d(d(c(b(d(c(b(a(_x121))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(b(_x201))))))))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(d(d(d(a(b(_x121))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(_x241)))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(a(c(d(d(a(c(d(a(b(_x241)))))))))))))))))))))
b#(c(c(c(c(c(c(c(d(d(c(d(_x151))))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(c(_x151))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(c(_x261))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(_x261))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x201))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(d(d(c(b(a(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(_x151)))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(a(_x151)))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(d(d(d(a(c(d(a(c(d(a(_x281)))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(d(d(c(c(_x201))))))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(c(d(d(d(c(c(d(a(b(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(d(c(c(d(_x281)))))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(c(c(d(a(_x281)))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x201))))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(_x261)))))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x261)))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(d(d(_x281)))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(b(d(c(b(d(c(b(a(_x281)))))))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(c(d(_x231)))))))))))))))a#(c(d(d(d(d(a(c(d(d(d(d(c(c(c(_x231)))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x171))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x171))))))))))))))))))))b#(c(c(c(c(c(c(d(d(_x121)))))))))a#(c(d(d(a(c(d(d(d(d(c(b(a(_x121)))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(d(_x221))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(d(a(c(d(a(c(d(a(_x221))))))))))))))))))))b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(d(d(a(b(_x151)))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(a(c(d(d(a(c(d(d(a(b(_x151))))))))))))) 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
a#(c(d(a(c(d(d(d(d(a(b(_x151))))))))))) 
a#(c(d(d(d(a(c(d(d(a(b(_x151))))))))))) 
a#(c(d(a(c(d(d(a(c(d(d(a(c(d(a(b(_x131)))))))))))))))) 
a#(c(d(a(c(d(d(a(c(d(d(a(_x131)))))))))))) 
Thus, the rule b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(a(c(d(d(a(c(d(d(a(b(_x151))))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(d(_x131)))))))) → a#(c(d(a(c(d(d(a(c(d(d(a(_x131))))))))))))b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(a(c(d(d(d(d(a(b(_x151)))))))))))
b#(c(c(c(c(c(c(c(_x131)))))))) → a#(c(d(a(c(d(d(a(c(d(d(a(c(d(a(b(_x131))))))))))))))))b#(c(c(c(c(c(c(_x151))))))) → a#(c(d(d(d(a(c(d(d(a(b(_x151)))))))))))

Problem 29: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

b#(c(c(c(c(c(c(c(c(d(d(_x191)))))))))))a#(c(d(a(c(d(d(d(d(d(a(c(d(d(c(b(a(_x191)))))))))))))))))b#(c(c(c(c(c(c(d(d(c(c(_x121)))))))))))a#(c(d(a(c(d(d(d(d(d(c(c(d(a(b(_x121)))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(d(a(_x281)))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(c(d(_x231)))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(d(c(b(d(c(c(_x231)))))))))))))))))))
b#(c(c(c(c(c(c(c(_x131))))))))a#(c(d(a(c(d(d(a(c(d(d(d(a(b(_x131))))))))))))))b#(c(c(c(c(c(c(c(c(d(c(_x151)))))))))))a#(c(d(a(c(d(d(d(a(c(d(d(d(_x151)))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(_x141)))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(d(d(c(b(a(_x141)))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(d(d(_x241)))))))))))))))a#(c(d(d(d(d(d(d(a(c(d(a(c(d(a(c(d(d(d(c(b(d(c(b(a(_x241)))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(_x211)))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(d(d(a(c(d(a(b(_x211)))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x221))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(d(d(d(a(c(d(a(b(_x221))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(c(c(_x211)))))))))))))))a#(c(d(d(d(d(a(c(d(a(c(d(d(d(c(c(b(d(c(c(d(a(b(_x211)))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x241))))))))))))))a#(c(d(d(d(a(c(d(d(d(d(a(c(d(a(c(d(d(d(c(b(a(_x241))))))))))))))))))))))
b#(c(c(c(c(c(c(c(d(_x151)))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(_x151)))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(d(a(_x281)))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(_x251))))))))))))a#(c(d(d(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x251))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x221))))))))))))))a#(c(d(d(d(a(c(d(d(d(a(c(d(d(a(c(d(d(d(c(b(a(_x221))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(_x261)))))))))))))a#(c(d(d(d(d(a(c(d(d(a(c(d(d(c(b(d(c(c(b(a(_x261)))))))))))))))))))))b#(c(c(c(c(c(c(c(d(_x151)))))))))a#(c(d(d(d(d(d(d(a(_x151)))))))))
b#(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))a#(c(d(d(d(d(d(d(a(c(d(_x171)))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(_x261)))))))))))))a#(c(d(d(d(d(d(d(d(d(d(d(a(c(d(a(b(_x261)))))))))))))))))
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b#(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))a#(c(d(d(d(d(d(a(c(d(d(_x171)))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(d(_x261)))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(d(a(c(d(d(a(c(d(a(_x261)))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(d(c(_x171)))))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(d(d(_x171)))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(d(_x221))))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(d(d(a(c(d(a(_x221))))))))))))))))))
b#(c(c(c(c(c(c(_x101)))))))a#(c(d(a(c(d(d(d(a(c(d(a(b(_x101)))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(d(_x251))))))))))))))a#(c(d(d(d(d(d(d(d(d(d(d(d(a(_x251))))))))))))))
b#(c(c(c(c(c(c(d(d(d(_x121))))))))))a#(c(d(d(d(d(d(d(c(b(d(c(b(a(_x121))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(b(_x201))))))))))))))))
b#(c(c(c(c(c(_x121))))))a#(c(d(d(d(d(a(b(_x121))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(d(d(c(_x271))))))))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(d(a(c(d(d(c(b(d(c(b(_x271))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(_x241)))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(a(c(d(d(a(c(d(a(b(_x241)))))))))))))))))))))b#(c(c(c(c(c(c(c(d(d(c(d(_x151))))))))))))a#(c(d(a(c(d(d(d(d(a(c(d(d(c(_x151))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(c(_x261))))))))))))))a#(c(d(d(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(c(d(_x261))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(d(d(_x201))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(d(d(c(b(a(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(_x201))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(d(_x151)))))))))))a#(c(d(d(d(d(d(d(d(a(c(d(a(_x151)))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(d(_x281)))))))))))))a#(c(d(d(d(d(d(d(d(d(a(c(d(a(c(d(a(_x281)))))))))))))))))b#(c(c(c(c(c(c(c(c(c(d(d(c(c(_x201))))))))))))))a#(c(d(d(a(c(d(d(a(c(d(d(a(c(d(d(d(c(c(d(a(b(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(d(c(c(d(_x281)))))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(c(c(d(a(_x281)))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(c(_x201))))))))))))))a#(c(d(d(d(d(d(a(c(d(d(d(d(d(a(c(d(a(c(d(a(b(_x201))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(c(c(c(c(_x261)))))))))))))a#(c(d(d(d(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(c(d(a(b(_x261)))))))))))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(d(d(d(_x281)))))))))))))))a#(c(d(a(c(d(d(d(a(c(d(a(c(d(d(d(c(b(d(c(c(b(d(c(b(d(c(b(a(_x281)))))))))))))))))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(d(d(c(d(_x231)))))))))))))))a#(c(d(d(d(d(a(c(d(d(d(d(c(c(c(_x231)))))))))))))))b#(c(c(c(c(c(c(c(c(c(_x171))))))))))a#(c(d(d(d(a(c(d(a(c(d(d(a(c(d(a(c(d(a(b(_x171))))))))))))))))))))
b#(c(c(c(c(c(c(d(d(_x121)))))))))a#(c(d(d(a(c(d(d(d(d(c(b(a(_x121)))))))))))))b#(c(c(c(c(c(c(c(c(c(c(c(c(d(_x221))))))))))))))a#(c(d(d(a(c(d(d(d(d(d(d(d(a(c(d(a(c(d(a(_x221))))))))))))))))))))
b#(c(c(c(c(c(c(_x151)))))))a#(c(d(d(a(c(d(d(d(a(b(_x151)))))))))))

Rewrite Rules

a(d(x))d(c(b(a(x))))b(c(x))c(d(a(b(x))))
a(c(x))xb(d(x))x

Original Signature

Termination of terms over the following signature is verified: d, b, c, a

Strategy


The right-hand side of the rule b#(c(c(c(c(c(c(c(c(d(d(_x191))))))))))) → a#(c(d(a(c(d(d(d(d(d(a(c(d(d(c(b(a(_x191))))))))))))))))) 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
a#(c(d(a(c(d(d(d(d(d(a(c(d(d(c(b(d(c(b(a(_x171)))))))))))))))))))) 
a#(c(d(a(c(d(d(d(d(d(d(d(c(b(a(_x191))))))))))))))) 
a#(c(d(a(c(d(d(d(d(d(a(c(d(d(c(b(_x171)))))))))))))))) 
a#(c(d(d(d(d(d(d(a(c(d(d(c(b(a(_x191))))))))))))))) 
Thus, the rule b#(c(c(c(c(c(c(c(c(d(d(_x191))))))))))) → a#(c(d(a(c(d(d(d(d(d(a(c(d(d(c(b(a(_x191))))))))))))))))) is replaced by the following rules:
b#(c(c(c(c(c(c(c(c(d(d(c(_x171)))))))))))) → a#(c(d(a(c(d(d(d(d(d(a(c(d(d(c(b(_x171))))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(_x191))))))))))) → a#(c(d(d(d(d(d(d(a(c(d(d(c(b(a(_x191)))))))))))))))
b#(c(c(c(c(c(c(c(c(d(d(_x191))))))))))) → a#(c(d(a(c(d(d(d(d(d(d(d(c(b(a(_x191)))))))))))))))b#(c(c(c(c(c(c(c(c(d(d(d(_x171)))))))))))) → a#(c(d(a(c(d(d(d(d(d(a(c(d(d(c(b(d(c(b(a(_x171))))))))))))))))))))