TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60145 ms.

The following DP Processors were used


Problem 1 was processed with processor PolynomialLinearRange4iUR (806ms).
 | – Problem 2 was processed with processor PolynomialLinearRange4iUR (602ms).
 |    | – Problem 3 was processed with processor BackwardInstantiation (2ms).
 |    |    | – Problem 4 was processed with processor ForwardNarrowing (3ms).
 |    |    |    | – Problem 5 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    | – Problem 6 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    | – Problem 7 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    | – Problem 8 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    | – Problem 9 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (13ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (11ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (16ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (30ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (98ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (179ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (369ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 was processed with processor ForwardNarrowing (429ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 28 remains open; application of the following processors failed [ForwardNarrowing (270ms), ForwardNarrowing (265ms), ForwardNarrowing (269ms), ForwardNarrowing (196ms), ForwardNarrowing (216ms), ForwardNarrowing (214ms), ForwardNarrowing (239ms), ForwardNarrowing (422ms), ForwardNarrowing (217ms), ForwardNarrowing (195ms), ForwardNarrowing (195ms), ForwardNarrowing (201ms), ForwardNarrowing (200ms), ForwardNarrowing (283ms), ForwardNarrowing (241ms), ForwardNarrowing (342ms), ForwardNarrowing (321ms), ForwardNarrowing (229ms), ForwardNarrowing (246ms), ForwardNarrowing (222ms), ForwardNarrowing (228ms), ForwardNarrowing (240ms), ForwardNarrowing (258ms)].

The following open problems remain:



Open Dependency Pair Problem 3

Dependency Pairs

a#(0, x)c#(c(x))c#(c(b(c(x))))a#(0, c(x))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a


Problem 1: PolynomialLinearRange4iUR



Dependency Pair Problem

Dependency Pairs

a#(0, x)c#(c(x))c#(c(b(c(x))))c#(x)
c#(c(x))c#(b(c(x)))a#(0, x)c#(x)
c#(c(x))c#(x)c#(c(b(c(x))))a#(0, c(x))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


Polynomial Interpretation

Improved Usable rules

c(c(b(c(x))))b(a(0, c(x)))a(0, x)c(c(x))
c(c(x))b(c(b(c(x))))

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

c#(c(b(c(x))))c#(x)a#(0, x)c#(x)
c#(c(x))c#(x)

Problem 2: PolynomialLinearRange4iUR



Dependency Pair Problem

Dependency Pairs

a#(0, x)c#(c(x))c#(c(x))c#(b(c(x)))
c#(c(b(c(x))))a#(0, c(x))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


Polynomial Interpretation

Improved Usable rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))

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

c#(c(x))c#(b(c(x)))

Problem 3: BackwardInstantiation



Dependency Pair Problem

Dependency Pairs

a#(0, x)c#(c(x))c#(c(b(c(x))))a#(0, c(x))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


Instantiation

For all potential predecessors l → r of the rule a#(0, x) → c#(c(x)) on dependency pair chains it holds that: Thus, a#(0, x) → c#(c(x)) is replaced by instances determined through the above matching. These instances are:
a#(0, c(_x)) → c#(c(c(_x)))

Problem 4: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(_x))c#(c(c(_x)))c#(c(b(c(x))))a#(0, c(x))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(_x)) → c#(c(c(_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
c#(b(c(b(c(_x21))))) 
c#(c(b(c(b(c(_x31)))))) 
c#(c(b(a(0, c(_x31))))) 
c#(b(a(0, c(_x21)))) 
Thus, the rule a#(0, c(_x)) → c#(c(c(_x))) is replaced by the following rules:
a#(0, c(_x21)) → c#(b(c(b(c(_x21)))))a#(0, c(c(_x31))) → c#(c(b(c(b(c(_x31))))))
a#(0, c(c(b(c(_x31))))) → c#(c(b(a(0, c(_x31)))))a#(0, c(b(c(_x21)))) → c#(b(a(0, c(_x21))))

Problem 5: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(_x21))c#(b(c(b(c(_x21)))))a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))
a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))c#(c(b(c(x))))a#(0, c(x))
a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(_x21)) → c#(b(c(b(c(_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
c#(b(c(b(b(c(b(c(_x61)))))))) 
c#(b(c(b(b(a(0, c(_x61))))))) 
Thus, the rule a#(0, c(_x21)) → c#(b(c(b(c(_x21))))) is replaced by the following rules:
a#(0, c(c(_x61))) → c#(b(c(b(b(c(b(c(_x61))))))))a#(0, c(c(b(c(_x61))))) → c#(b(c(b(b(a(0, c(_x61)))))))

Problem 6: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))
a#(0, c(c(_x61)))c#(b(c(b(b(c(b(c(_x61))))))))a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))
c#(c(b(c(x))))a#(0, c(x))a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(_x61))) → c#(b(c(b(b(c(b(c(_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
c#(b(c(b(b(c(b(b(a(0, c(_x91)))))))))) 
c#(b(c(b(b(c(b(b(c(b(c(_x91))))))))))) 
Thus, the rule a#(0, c(c(_x61))) → c#(b(c(b(b(c(b(c(_x61)))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(_x91)))))) → c#(b(c(b(b(c(b(b(a(0, c(_x91))))))))))a#(0, c(c(c(_x91)))) → c#(b(c(b(b(c(b(b(c(b(c(_x91)))))))))))

Problem 7: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(a(0, c(_x91))))))))))a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))
a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))
a#(0, c(c(c(_x91))))c#(b(c(b(b(c(b(b(c(b(c(_x91)))))))))))c#(c(b(c(x))))a#(0, c(x))
a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(_x91)))))) → c#(b(c(b(b(c(b(b(a(0, c(_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
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(_x121))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(a(0, c(_x121)))))))))))) 
c#(b(c(b(b(c(b(b(c(c(c(_x91))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(_x91)))))) → c#(b(c(b(b(c(b(b(a(0, c(_x91)))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(_x91)))))) → c#(b(c(b(b(c(b(b(c(c(c(_x91)))))))))))a#(0, c(c(c(b(c(c(b(c(_x121))))))))) → c#(b(c(b(b(c(b(b(a(0, b(a(0, c(_x121))))))))))))
a#(0, c(c(c(b(c(c(_x121))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(_x121)))))))))))))

Problem 8: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(c(c(c(_x91)))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, c(_x121))))))))))))
a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))
a#(0, c(c(c(_x91))))c#(b(c(b(b(c(b(b(c(b(c(_x91)))))))))))a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))
c#(c(b(c(x))))a#(0, c(x))a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))
a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(_x121)))))))))))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(_x91)))))) → c#(b(c(b(b(c(b(b(c(c(c(_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
c#(b(c(b(b(c(b(b(c(b(c(b(c(_x111))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121)))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121))))))))))))) 
c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111)))))))))))) 
c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(_x91)))))) → c#(b(c(b(b(c(b(b(c(c(c(_x91))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(b(c(_x111)))))))) → c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))a#(0, c(c(c(b(c(_x111)))))) → c#(b(c(b(b(c(b(b(c(b(c(b(c(_x111)))))))))))))
a#(0, c(c(c(b(c(c(_x121))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))a#(0, c(c(c(b(c(_x91)))))) → c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121))))))))) → c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))

Problem 9: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(_x111))))))c#(b(c(b(b(c(b(b(c(b(c(b(c(_x111)))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, c(_x121))))))))))))
a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))
a#(0, c(c(c(_x91))))c#(b(c(b(b(c(b(b(c(b(c(_x91)))))))))))c#(c(b(c(x))))a#(0, c(x))
a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))
a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))
a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))
a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(_x111)))))) → c#(b(c(b(b(c(b(b(c(b(c(b(c(_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
c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141)))))))))))))))) 
c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(_x111)))))) → c#(b(c(b(b(c(b(b(c(b(c(b(c(_x111))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(_x141))))))))) → c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141)))))))))))))))a#(0, c(c(c(b(c(c(_x141))))))) → c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141))))))))))))))))

Problem 10: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, c(_x121))))))))))))a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))
a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))a#(0, c(c(c(_x91))))c#(b(c(b(b(c(b(b(c(b(c(_x91)))))))))))
a#(0, c(c(c(b(c(c(_x141)))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141))))))))))))))))c#(c(b(c(x))))a#(0, c(x))
a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))
a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141)))))))))))))))
a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))
a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(_x121))))))))) → c#(b(c(b(b(c(b(b(a(0, b(a(0, c(_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
c#(b(c(b(b(c(b(b(a(0, b(c(c(c(_x121))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x151))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x151)))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(_x121))))))))) → c#(b(c(b(b(c(b(b(a(0, b(a(0, c(_x121)))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(_x121))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(c(c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151)))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x151))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151)))))))))) → c#(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x151)))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121))))))))) → c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))

Problem 11: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(c(_x121)))))))))))))a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))
a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))a#(0, c(c(c(_x91))))c#(b(c(b(b(c(b(b(c(b(c(_x91)))))))))))
a#(0, c(c(c(b(c(c(_x141)))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141))))))))))))))))c#(c(b(c(x))))a#(0, c(x))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x151)))))))))))))))a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141)))))))))))))))a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))
a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x151))))))))))))))a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(_x121))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(c(c(_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
c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x121))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(c(c(c(_x121)))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_x141))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x141)))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x151))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x151)))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(_x121))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(c(c(_x121))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(_x141))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_x141)))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(c(c(_x121))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151)))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x151)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151)))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(_x141))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x141))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121))))))))) → c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x121)))))))))))))))

Problem 12: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(c(_x121))))))))))))))a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x141))))))))))))))a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))
a#(0, c(c(c(_x91))))c#(b(c(b(b(c(b(b(c(b(c(_x91)))))))))))a#(0, c(c(c(b(c(c(_x141)))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141))))))))))))))))
c#(c(b(c(x))))a#(0, c(x))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x151)))))))))))))))
a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_x141)))))))))))))))a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141)))))))))))))))a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))
a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x151)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x151))))))))))))))))a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x151))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x121)))))))))))))))
a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(_x121))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(c(c(_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
c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(c(_x151))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x141)))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(c(c(b(a(0, c(_x151)))))))))))))))) 
c#(b(c(b(b(c(b(b(b(a(0, c(c(c(_x121))))))))))))) 
c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(c(_x121)))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(c(b(a(0, c(_x141))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(c(_x121)))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(_x121))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(c(c(_x121)))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(_x121))))))))) → c#(b(c(b(b(c(b(b(b(a(0, c(c(c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151)))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(c(b(a(0, c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x141))))))))))))))))a#(0, c(c(c(b(c(c(b(c(b(c(_x141))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(b(a(0, c(_x141)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151)))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(c(_x151)))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(c(_x121))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121))))))))) → c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(c(_x121))))))))))))))))

Problem 13: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(c(_x151)))))))))))))))))a#(0, c(c(c(_x91))))c#(b(c(b(b(c(b(b(c(b(c(_x91)))))))))))
a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_x141)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141)))))))))))))))a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x151)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x121)))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(a(0, c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x141))))))))))))))))
a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x141))))))))))))))
a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))a#(0, c(c(c(b(c(c(_x141)))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141))))))))))))))))
c#(c(b(c(x))))a#(0, c(x))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x151)))))))))))))))a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))
a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(a(0, c(_x141)))))))))))))))
a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(c(_x121))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x151))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(c(_x121))))))))))))))))
a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(c(_x151)))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(c(_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
c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(c(_x151)))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(c(_x181)))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x151))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(a(0, c(_x181))))))))))))))))))) 
c#(b(c(b(b(c(b(b(b(a(0, c(c(b(c(b(c(_x151)))))))))))))))) 
c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(c(_x151))))))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(c(_x151)))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(c(_x151))))))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(c(_x151)))))))))) → c#(b(c(b(b(c(b(b(b(a(0, c(c(b(c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151)))))))))) → c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(c(_x151)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x181))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(a(0, c(_x181)))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151)))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x151)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(_x181))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(c(_x181))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151)))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(c(_x151))))))))))))))))

Problem 14: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(_x91))))c#(b(c(b(b(c(b(b(c(b(c(_x91)))))))))))a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_x141)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x181)))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(a(0, c(_x181)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x151)))))))))))))))a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))
a#(0, c(c(c(b(c(c(b(c(c(c(_x181)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(c(_x181))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x121)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(a(0, c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(c(_x151)))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x141))))))))))))))))
a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x141))))))))))))))
a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))a#(0, c(c(c(b(c(c(_x141)))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141))))))))))))))))
c#(c(b(c(x))))a#(0, c(x))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x151)))))))))))))))a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(a(0, c(_x141)))))))))))))))a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))
a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x151)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(c(_x121))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x151))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(c(_x121))))))))))))))))a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(_x91)))) → c#(b(c(b(b(c(b(b(c(b(c(_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
c#(b(c(b(b(c(b(b(c(b(b(c(b(c(_x121)))))))))))))) 
c#(b(c(b(b(c(b(b(c(b(b(a(0, c(_x121))))))))))))) 
Thus, the rule a#(0, c(c(c(_x91)))) → c#(b(c(b(b(c(b(b(c(b(c(_x91))))))))))) is replaced by the following rules:
a#(0, c(c(c(c(b(c(_x121))))))) → c#(b(c(b(b(c(b(b(c(b(b(a(0, c(_x121)))))))))))))a#(0, c(c(c(c(_x121))))) → c#(b(c(b(b(c(b(b(c(b(b(c(b(c(_x121))))))))))))))

Problem 15: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_x141)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x181)))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(a(0, c(_x181)))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141)))))))))))))))
a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x151)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x151))))))))))))))))a#(0, c(c(c(c(_x121)))))c#(b(c(b(b(c(b(b(c(b(b(c(b(c(_x121))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(_x181)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(c(_x181))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x121)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(c(_x121)))))))))))))a#(0, c(c(c(c(b(c(_x121)))))))c#(b(c(b(b(c(b(b(c(b(b(a(0, c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(a(0, c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(c(_x151)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x141))))))))))))))))a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x141))))))))))))))a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))
a#(0, c(c(c(b(c(c(_x141)))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141))))))))))))))))c#(c(b(c(x))))a#(0, c(x))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x151)))))))))))))))
a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(a(0, c(_x141)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x151)))))))))))))))))))
a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(c(_x121))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x151))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(c(_x121))))))))))))))))
a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(_x121))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(_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
c#(b(c(b(b(c(b(b(a(0, b(c(b(b(a(0, c(_x151))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(_x151)))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121)))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(_x121))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(_x121))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(c(_x151)))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(c(b(c(_x151)))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(b(a(0, c(_x151)))))))))))))))
a#(0, c(c(c(b(c(c(_x121))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))

Problem 16: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_x141)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x181)))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(a(0, c(_x181)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141)))))))))))))))a#(0, c(c(c(c(_x121)))))c#(b(c(b(b(c(b(b(c(b(b(c(b(c(_x121))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x151)))))))))))))))
a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))a#(0, c(c(c(b(c(c(b(c(c(c(_x181)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(c(_x181))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x121)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(b(c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(c(_x151))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(c(_x121)))))))))))))a#(0, c(c(c(c(b(c(_x121)))))))c#(b(c(b(b(c(b(b(c(b(b(a(0, c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(a(0, c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(c(_x151)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x141))))))))))))))))a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x141))))))))))))))a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))
a#(0, c(c(c(b(c(c(_x141)))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141))))))))))))))))c#(c(b(c(x))))a#(0, c(x))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x151)))))))))))))))
a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))a#(0, c(c(c(b(c(c(c(b(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(b(a(0, c(_x151)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(a(0, c(_x141)))))))))))))))a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))
a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x151)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(c(_x121))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x151))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(c(_x121))))))))))))))))a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(_x141))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_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
c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x141)))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(b(c(_x171)))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, c(_x171))))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(_x141))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_x141))))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(_x141))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x141))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171)))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, c(_x171)))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x171)))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(b(c(_x171))))))))))))))))))

Problem 17: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, c(_x171)))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x181)))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(a(0, c(_x181)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141)))))))))))))))a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x151)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(c(_x121)))))c#(b(c(b(b(c(b(b(c(b(b(c(b(c(_x121))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(_x181)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(c(_x181))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x121)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(b(c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(c(_x151))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(c(_x121)))))))))))))a#(0, c(c(c(c(b(c(_x121)))))))c#(b(c(b(b(c(b(b(c(b(b(a(0, c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(a(0, c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(c(_x151)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x141))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x171))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(b(c(_x171))))))))))))))))))
a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x141))))))))))))))
a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))a#(0, c(c(c(b(c(c(_x141)))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141))))))))))))))))
c#(c(b(c(x))))a#(0, c(x))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x151)))))))))))))))a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))
a#(0, c(c(c(b(c(c(c(b(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(b(a(0, c(_x151)))))))))))))))a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(a(0, c(_x141)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x151)))))))))))))))))))
a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(c(_x121))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x151))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(c(_x121))))))))))))))))
a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171)))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, c(_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
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(c(_x201)))))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(c(_x171)))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(a(0, c(_x201))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, c(_x171)))))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171)))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, c(_x171))))))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(c(_x201))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171)))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(c(_x171))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171)))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, c(_x171))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x201))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(a(0, c(_x201)))))))))))))))))))

Problem 18: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(c(_x201))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x181)))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(a(0, c(_x181)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141)))))))))))))))a#(0, c(c(c(c(_x121)))))c#(b(c(b(b(c(b(b(c(b(b(c(b(c(_x121))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x151)))))))))))))))
a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))a#(0, c(c(c(b(c(c(b(c(c(c(_x181)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(c(_x181))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x121)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(b(c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(c(_x151))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(c(_x121)))))))))))))a#(0, c(c(c(c(b(c(_x121)))))))c#(b(c(b(b(c(b(b(c(b(b(a(0, c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(a(0, c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(c(_x151)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x141))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x171))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(b(c(_x171))))))))))))))))))
a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x141))))))))))))))
a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))a#(0, c(c(c(b(c(c(_x141)))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, c(_x171))))))))))))))))))c#(c(b(c(x))))a#(0, c(x))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x151)))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x201)))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(a(0, c(_x201)))))))))))))))))))a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))
a#(0, c(c(c(b(c(c(c(b(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(b(a(0, c(_x151)))))))))))))))a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(a(0, c(_x141)))))))))))))))
a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x151)))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(c(_x121))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x151))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(c(_x171))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(c(_x121))))))))))))))))a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(c(_x201)))))))))))))))))))) 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
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(c(_x201))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(b(c(_x241))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, c(_x241)))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(c(_x201))))))))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(c(_x201)))))))))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, c(_x241))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(_x241)))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(b(c(_x241)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(c(_x201)))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(c(_x201)))))))))))))))))))))

Problem 19: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, c(_x241))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(c(_x201)))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(_x241))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(b(c(_x241)))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x181)))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(a(0, c(_x181)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141)))))))))))))))a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x151)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(c(_x121)))))c#(b(c(b(b(c(b(b(c(b(b(c(b(c(_x121))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(_x181)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(c(_x181))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x121)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(b(c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(c(_x151))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(c(_x121)))))))))))))a#(0, c(c(c(c(b(c(_x121)))))))c#(b(c(b(b(c(b(b(c(b(b(a(0, c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(a(0, c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(c(_x151)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x141))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(c(_x201)))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x171))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(b(c(_x171))))))))))))))))))a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x141))))))))))))))a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))
a#(0, c(c(c(b(c(c(_x141)))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141))))))))))))))))c#(c(b(c(x))))a#(0, c(x))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, c(_x171))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x201)))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(a(0, c(_x201)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x151)))))))))))))))
a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))a#(0, c(c(c(b(c(c(c(b(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(b(a(0, c(_x151)))))))))))))))
a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(a(0, c(_x141)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x151)))))))))))))))))))a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(c(_x121))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(c(_x171))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x151))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(c(_x121))))))))))))))))
a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, 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
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(a(0, c(_x241))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(a(0, c(_x271)))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(c(b(c(_x271))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(b(a(0, c(_x241))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(c(c(_x241))))))))))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, c(_x241)))))))))))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(b(a(0, c(_x241)))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271))))))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(a(0, c(_x271))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x271))))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(c(b(c(_x271)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(a(0, c(_x241)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(c(c(_x241)))))))))))))))))))))))

Problem 20: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(a(0, c(_x241)))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(c(_x201)))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(_x241))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(b(c(_x241)))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x181)))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(a(0, c(_x181)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141)))))))))))))))a#(0, c(c(c(c(_x121)))))c#(b(c(b(b(c(b(b(c(b(b(c(b(c(_x121))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x151)))))))))))))))
a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))a#(0, c(c(c(b(c(c(b(c(c(c(_x181)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(c(_x181))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(c(c(_x241)))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x121)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(b(a(0, c(_x241)))))))))))))))))))))))a#(0, c(c(c(b(c(c(c(_x151))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(c(_x121)))))))))))))a#(0, c(c(c(c(b(c(_x121)))))))c#(b(c(b(b(c(b(b(c(b(b(a(0, c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(a(0, c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(a(0, c(_x271))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(c(_x151)))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x141))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(c(_x201)))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x171))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(b(c(_x171))))))))))))))))))
a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x141))))))))))))))
a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))a#(0, c(c(c(b(c(c(_x141)))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, c(_x171))))))))))))))))))c#(c(b(c(x))))a#(0, c(x))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x151)))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x201)))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(a(0, c(_x201)))))))))))))))))))a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))
a#(0, c(c(c(b(c(c(c(b(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(b(a(0, c(_x151)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(c(b(c(_x271)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(a(0, c(_x141)))))))))))))))a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))
a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x151)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(c(_x121))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x151))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(c(_x171))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(c(_x121))))))))))))))))
a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(a(0, 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
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(c(c(c(_x241)))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(c(b(c(b(c(b(b(a(0, c(_x241))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(a(0, b(a(0, c(_x271))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(c(c(b(c(b(b(a(0, c(_x241)))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(a(0, b(c(b(c(_x271)))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(a(0, c(b(b(a(0, c(_x241)))))))))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(a(0, c(_x241))))))))))))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(c(c(b(c(b(b(a(0, c(_x241))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x271))))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(a(0, b(c(b(c(_x271))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(c(b(c(b(c(b(b(a(0, c(_x241)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(c(c(c(_x241))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(a(0, c(b(b(a(0, c(_x241))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271))))))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(a(0, b(a(0, c(_x271)))))))))))))))))))))))))

Problem 21: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(c(_x201)))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(a(0, c(b(b(a(0, c(_x241))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x181)))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(a(0, c(_x181)))))))))))))))))))a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x151))))))))))))))))a#(0, c(c(c(c(_x121)))))c#(b(c(b(b(c(b(b(c(b(b(c(b(c(_x121))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(c(c(_x241)))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(c(_x151)))))))))))))))))))a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x141))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(c(b(c(b(c(b(b(a(0, c(_x241)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(_x141)))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, c(_x171))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x201)))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(a(0, c(_x201)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(a(0, b(a(0, c(_x271)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(a(0, c(_x141)))))))))))))))
a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x151))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(c(_x171))))))))))))))))))a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(a(0, b(c(b(c(_x271))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(c(c(b(c(b(b(a(0, c(_x241))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(_x241))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(b(c(_x241)))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x151)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(_x181)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(c(_x181))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x121)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(c(_x151))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(b(a(0, c(_x241)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(a(0, c(_x151))))))))))))))))
a#(0, c(c(c(c(b(c(_x121)))))))c#(b(c(b(b(c(b(b(c(b(b(a(0, c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(a(0, c(_x271))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x141))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(c(_x201)))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x171))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(b(c(_x171))))))))))))))))))a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))
c#(c(b(c(x))))a#(0, c(x))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x151)))))))))))))))
a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(c(b(c(_x271)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(c(b(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(b(a(0, c(_x151)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x151)))))))))))))))))))
a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(c(_x121))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(c(c(c(_x241))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(c(_x121))))))))))))))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(c(_x201))))))))))))))))))))) 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
c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(b(c(b(c(_x241)))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(b(a(0, c(b(c(b(b(a(0, b(c(b(c(_x201)))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(c(c(b(c(b(c(_x201)))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(b(a(0, c(_x241))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(b(c(b(c(b(c(b(c(b(b(a(0, b(c(b(c(_x201))))))))))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(c(_x201))))))))))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(c(c(b(c(b(c(_x201))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(b(a(0, c(_x241)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201))))))))))))) → c#(b(c(b(b(c(b(b(b(a(0, c(b(c(b(b(a(0, b(c(b(c(_x201))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201))))))))))))) → c#(b(c(b(b(c(b(b(b(c(b(c(b(c(b(c(b(b(a(0, b(c(b(c(_x201)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(_x241)))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(b(c(b(c(_x241))))))))))))))))))))))))

Problem 22: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(a(0, c(b(b(a(0, c(_x241))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x181)))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(a(0, c(_x181)))))))))))))))))))
a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(c(_x121)))))c#(b(c(b(b(c(b(b(c(b(b(c(b(c(_x121))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(c(c(_x241)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(c(_x151)))))))))))))))))))
a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x141))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(c(b(c(b(c(b(b(a(0, c(_x241)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(_x141)))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, c(_x171))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(a(0, b(a(0, c(_x271)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x201)))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(a(0, c(_x201)))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(a(0, c(_x121)))))))))))))
a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(a(0, c(_x141)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(c(_x171))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x151))))))))))))))
a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(a(0, b(c(b(c(_x271))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(c(c(b(c(b(c(_x201))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(_x241))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(b(c(_x241)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(c(c(b(c(b(b(a(0, c(_x241))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x151)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(_x181)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(c(_x181))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x121)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(c(_x151))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(b(a(0, c(_x241)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(a(0, c(_x151))))))))))))))))
a#(0, c(c(c(c(b(c(_x121)))))))c#(b(c(b(b(c(b(b(c(b(b(a(0, c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(a(0, c(_x271))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x141))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(_x241))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(b(c(b(c(_x241))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(b(c(b(b(a(0, b(c(b(c(_x201)))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(c(_x201)))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x171))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(b(c(_x171))))))))))))))))))a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))
c#(c(b(c(x))))a#(0, c(x))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x151)))))))))))))))
a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(b(a(0, c(b(c(b(b(a(0, b(c(b(c(_x201))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(c(b(c(_x271)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(c(b(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(b(a(0, c(_x151)))))))))))))))
a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x151)))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(c(_x121))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(c(c(c(_x241))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(c(_x121))))))))))))))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(a(0, c(b(b(a(0, 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
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(a(0, c(b(b(c(c(c(_x241))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(c(c(c(b(b(a(0, c(_x241))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(a(0, c(b(b(a(0, b(c(b(c(_x271))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(b(a(0, c(b(b(a(0, c(_x241))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(a(0, c(b(b(a(0, b(a(0, c(_x271)))))))))))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(a(0, c(b(b(a(0, c(_x241)))))))))))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271))))))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(a(0, c(b(b(a(0, b(a(0, c(_x271))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(c(c(c(b(b(a(0, c(_x241)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x271))))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(a(0, c(b(b(a(0, b(c(b(c(_x271)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(a(0, c(b(b(c(c(c(_x241)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(b(a(0, c(b(b(a(0, c(_x241)))))))))))))))))))))))

Problem 23: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(a(0, c(_x201))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x251)))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(c(c(_x251)))))))))))))))))))))))))
a#(0, c(c(c(c(c(c(c(b(c(c(b(c(_x271)))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_x271)))))))))))))))))))))))))))a#(0, c(c(c(c(c(c(c(b(c(_x241))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(c(b(c(_x241)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x311)))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(a(0, c(_x311)))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x141))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(c(b(c(b(c(b(b(a(0, c(_x241)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x251)))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(c(c(b(c(c(c(_x251)))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(a(0, c(b(b(c(c(c(_x241)))))))))))))))))))))))a#(0, c(c(c(b(c(c(_x141)))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(c(b(c(_x141))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(_x211))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(b(c(_x211))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(_x281))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(_x281)))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(_x251)))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(c(b(c(_x251)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, c(_x171))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(b(c(c(b(c(_x311)))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(b(b(a(0, b(a(0, c(_x311))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(a(0, b(a(0, c(_x271)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x201)))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(a(0, c(_x201)))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(a(0, c(_x271)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(b(c(_x261))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(b(a(0, c(_x261))))))))))))))))))))))))a#(0, c(c(c(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(c(c(b(c(c(c(_x281))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(a(0, c(_x141)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x171))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(c(_x171))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(c(c(b(c(b(c(_x281))))))))))))))))))))))))))))a#(0, c(b(c(_x21))))c#(b(a(0, c(_x21))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(a(0, c(b(b(a(0, b(a(0, c(_x271))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(_x181)))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(c(_x181))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x251)))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x251))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(b(c(c(c(_x241))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(b(c(b(c(b(c(b(a(0, c(_x271))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(a(0, b(c(b(c(_x271))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(_x321)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(c(b(b(c(b(c(_x321))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(c(_x151)))))))))))))))))
a#(0, c(c(c(c(c(c(c(b(c(b(c(_x241))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(a(0, c(_x241))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(c(c(b(a(0, c(_x281)))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(_x321)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(c(b(c(b(b(c(b(c(_x321))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(c(c(b(c(b(c(_x201))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(c(c(b(c(b(b(a(0, c(_x241))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(_x241))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(b(c(_x241)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(b(c(b(b(a(0, c(_x141)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(c(_x211))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(a(0, b(c(b(c(_x211))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(c(c(c(b(b(a(0, c(_x241)))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x181)))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(b(a(0, c(_x181))))))))))))))))))
a#(0, c(c(c(c(c(c(b(c(_x181)))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(c(c(_x181))))))))))))))))))))a#(0, c(c(c(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x281))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(b(c(_x331)))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(b(b(a(0, c(_x331)))))))))))))))))))))))))))))))a#(0, c(c(c(c(c(c(c(b(c(c(b(c(_x251)))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x251)))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(_x211))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(c(_x211))))))))))))))))))))))a#(0, c(c(c(c(c(c(c(b(c(c(b(c(_x251)))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(c(b(a(0, c(_x251)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x121)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(_x211))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, c(_x211))))))))))))))))))))))
a#(0, c(c(c(c(c(c(c(b(c(c(b(c(b(c(_x271)))))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x271))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(_x251)))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(c(_x251)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(_x271)))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(c(c(b(c(b(c(_x271)))))))))))))))))))))))))))a#(0, c(c(c(c(c(c(b(c(c(_x211))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(c(b(c(_x211))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(a(0, c(_x271))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(_x141)))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x141))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(b(c(b(b(a(0, b(c(b(c(_x201)))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(c(_x201)))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(c(b(c(_x301))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(c(b(a(0, b(a(0, c(_x301))))))))))))))))))))))))))))a#(0, c(c(c(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x281)))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x281)))))))))))))))))))))))))))c#(c(b(c(x))))a#(0, c(x))
a#(0, c(c(c(c(c(c(c(b(c(c(_x251)))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(c(b(c(b(c(_x251))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(c(_x151))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x281))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(b(c(_x321)))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(a(0, b(c(b(b(a(0, c(_x321))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(c(b(c(b(c(_x271)))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x251)))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(c(c(_x251))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(b(a(0, c(b(c(b(b(a(0, b(c(b(c(_x201))))))))))))))))))))a#(0, c(c(c(c(c(b(c(_x151))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(b(a(0, c(b(b(a(0, b(c(b(c(_x271)))))))))))))))))))))))))a#(0, c(c(b(c(_x31)))))c#(c(b(a(0, c(_x31)))))
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a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x151)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(c(b(c(b(c(_x271))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x251)))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(b(a(0, c(c(c(_x251))))))))))))))))))))))))
a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(_x181)))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(c(_x181)))))))))))))))))))))
a#(0, c(c(c(b(c(c(c(b(c(_x151))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(b(a(0, c(_x151)))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(c(b(c(_x271)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(_x181)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(b(c(b(c(_x181)))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x281))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x151)))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(c(b(a(0, c(_x271)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x281)))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(b(c(b(c(c(_x241)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(c(b(c(_x361))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(a(0, b(c(b(b(c(b(b(a(0, c(_x361)))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x261))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(b(c(b(c(_x261)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(c(_x121))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x281)))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x181)))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(a(0, c(_x181))))))))))))))))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x201))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(a(0, c(_x201)))))))))))))))))))) 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
c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(a(0, b(c(b(c(_x241))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(c(c(c(_x201))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(a(0, c(_x201))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(a(0, b(a(0, c(_x241)))))))))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x201))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(a(0, c(_x201)))))))))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x241)))))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(a(0, b(a(0, c(_x241))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(c(_x241)))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(a(0, b(c(b(c(_x241)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x201))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(a(0, c(_x201)))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x201))))))))))))) → c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(c(c(c(_x201)))))))))))))))))))))

Problem 24: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(c(c(_x281)))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(b(c(_x141)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(c(c(_x141)))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, c(_x281))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x181)))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(b(a(0, c(_x181))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x251)))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(c(c(_x251)))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x311)))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(b(c(b(c(c(_x311)))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x311)))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(b(c(b(c(c(_x311)))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x281))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(a(0, c(_x271))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(b(c(_x331)))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(c(b(a(0, c(_x331)))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x341))))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(c(c(b(c(c(b(c(b(c(_x341)))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x331)))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, b(a(0, c(_x331)))))))))))))))))))))))))))))))
a#(0, c(c(c(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x281)))))))))))))))))))))))))))a#(0, c(c(c(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(c(c(_x281))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(b(c(_x331)))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(b(c(c(b(c(b(c(b(c(b(b(a(0, c(_x331)))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x281)))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(_x281))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(_x281))))))))))))))))))))))))))))a#(0, c(c(c(c(c(b(c(_x151))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x341))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(b(c(b(c(b(a(0, b(c(c(b(c(b(c(_x341)))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x251)))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(c(c(_x251)))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(c(c(_x271))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x341))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(c(b(a(0, b(c(c(b(c(b(c(_x341)))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(b(c(c(c(_x271))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(_x331)))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(b(a(0, b(c(b(c(b(c(b(b(c(b(c(_x331)))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(b(c(_x261))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(c(b(a(0, c(_x261)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(c(b(c(c(c(_x271)))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(c(_x301))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(c(b(a(0, b(c(b(c(_x301)))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x341))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(b(c(b(c(b(c(b(c(_x341))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_x271)))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, c(_x281)))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(_x371)))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(c(b(a(0, b(c(b(b(c(b(c(_x371))))))))))))))))))))))))))))))))))))a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(_x321)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(c(c(b(a(0, b(c(b(b(c(b(c(_x321))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(_x291)))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(c(b(a(0, c(_x291))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(c(c(b(c(_x371)))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(b(c(b(b(a(0, c(_x371))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x341))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(c(b(a(0, b(b(c(b(c(b(c(b(c(_x341))))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(c(b(c(_x361))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(b(c(c(b(c(b(c(b(c(b(b(c(b(b(a(0, c(_x361)))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(b(c(_x241))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(a(0, b(a(0, c(_x241)))))))))))))))))))))
a#(0, c(c(c(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(a(0, c(_x281)))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x181)))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(b(a(0, c(_x181)))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x201)))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(a(0, c(_x201))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(b(c(_x351)))))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(b(c(b(b(a(0, c(_x351))))))))))))))))))))))))))))))))
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a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(c(b(c(_x361))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(a(0, b(c(b(b(c(b(b(a(0, c(_x361)))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(_x311)))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(c(_x311)))))))))))))))))))))))))))))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281)))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(c(c(_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
c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(c(c(_x281))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(c(b(c(b(c(_x311)))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(b(c(b(c(_x301))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, b(c(b(c(c(_x281))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(b(a(0, c(_x301)))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(c(c(c(c(c(_x281)))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(c(b(a(0, c(_x311))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(c(c(_x281))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(c(c(b(b(a(0, c(c(c(_x281)))))))))))))))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281)))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(c(c(_x281))))))))))))))))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281)))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, b(c(b(c(c(_x281)))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x301)))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(b(c(b(c(_x301)))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(_x311))))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(c(b(c(b(c(_x311))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(b(c(_x301)))))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(b(a(0, c(_x301))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281)))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(c(c(b(b(a(0, c(c(c(_x281))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281)))))))))))))))))))) → c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(c(c(_x281)))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281)))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(c(c(c(c(c(_x281))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281)))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(c(c(_x281)))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x311))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(c(b(a(0, c(_x311)))))))))))))))))))))))))))))

Problem 25: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x331)))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, b(a(0, c(_x331))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x361))))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, b(a(0, b(c(b(c(_x361))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x281)))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x291))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(b(c(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x291)))))))))))))))))))))))))))))))))
a#(0, c(c(c(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(c(c(_x281))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(b(c(_x331)))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(b(c(c(b(c(b(c(b(c(b(b(a(0, c(_x331)))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x331)))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(c(b(a(0, c(_x331)))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x281)))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(_x281))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(_x281))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x341))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(b(c(b(c(b(a(0, b(c(c(b(c(b(c(_x341)))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(c(c(b(c(_x151))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x251)))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(c(c(_x251)))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x341))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(c(b(a(0, b(c(c(b(c(b(c(_x341)))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(c(c(_x271))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(b(c(c(c(_x271))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(_x331)))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(b(a(0, b(c(b(c(b(c(b(b(c(b(c(_x331)))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(b(c(_x261))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(c(b(a(0, c(_x261)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x341))))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(c(c(b(b(c(b(c(b(c(b(c(_x341)))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(c(b(c(_x171))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(c(b(a(0, c(_x171))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x361)))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(b(c(b(b(c(b(c(_x361)))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(c(_x301))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(c(b(a(0, b(c(b(c(_x301)))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(c(b(c(c(c(_x271)))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(c(b(c(_x321))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(c(c(b(c(b(a(0, b(a(0, c(_x321)))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x341))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(b(c(b(c(b(c(b(c(_x341))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_x271)))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, c(_x281)))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(b(c(_x401))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(c(c(b(b(c(b(c(b(c(b(c(b(c(_x401)))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(_x371)))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(c(b(a(0, b(c(b(b(c(b(c(_x371))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(_x161)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(c(b(c(_x161)))))))))))))))))a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(c(b(c(b(c(_x201)))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(_x321)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(c(c(b(a(0, b(c(b(b(c(b(c(_x321))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(_x291)))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(c(b(a(0, c(_x291))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(c(c(b(c(_x371)))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(b(c(b(b(a(0, c(_x371))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x341))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(c(b(a(0, b(b(c(b(c(b(c(b(c(_x341))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(c(b(c(_x361))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(b(c(c(b(c(b(c(b(c(b(b(c(b(b(a(0, c(_x361)))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(b(c(_x241))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(a(0, b(a(0, c(_x241)))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(c(_x211))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(b(a(0, b(c(b(c(_x211)))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(a(0, c(_x281))))))))))))))))))))))))))))))))))a#(0, c(c(c(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(a(0, c(_x281)))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(b(c(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x281)))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x291))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x291))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x181)))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(b(a(0, c(_x181)))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x201)))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(a(0, c(_x201))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(b(c(_x201)))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(b(a(0, c(b(b(c(b(a(0, c(_x201)))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(b(c(_x351)))))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(b(c(b(b(a(0, c(_x351))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(c(b(c(_x281)))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(_x311)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(c(b(c(b(c(_x311)))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(c(_x171))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(a(0, b(c(b(c(_x171)))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(b(c(_x231)))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(c(b(a(0, c(_x231))))))))))))))))))))))
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a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(b(c(_x371)))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(c(b(a(0, b(c(b(b(a(0, c(_x371)))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(_x371)))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(c(b(c(c(b(c(b(b(c(b(c(_x371)))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(c(_x371)))))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(c(c(b(c(b(b(c(b(c(_x371)))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(b(c(b(c(_x151))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x311)))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(b(c(b(c(c(_x311)))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x411)))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(c(c(b(b(c(b(c(b(c(c(b(c(b(c(_x411))))))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x251)))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(a(0, c(_x251)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(a(0, c(_x151))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(c(b(c(_x331)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(b(b(c(b(b(a(0, c(_x331)))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x341))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(b(c(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(b(c(_x341))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(c(_x321))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(b(c(b(c(_x321))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x341))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(a(0, b(b(a(0, c(b(c(_x341)))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(_x341))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(b(c(b(c(b(c(_x341))))))))))))))))))))))))))))))))))))
a#(0, c(c(b(c(_x61)))))c#(b(c(b(b(a(0, c(_x61)))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(b(c(_x371))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(b(c(b(c(b(a(0, c(_x371)))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(b(c(_x201)))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(c(b(a(0, c(_x201))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x371))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(b(c(b(c(b(c(b(c(_x371))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(a(0, b(a(0, c(_x241))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(c(_x281))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(b(c(_x111))))))))c#(b(c(b(b(c(b(b(c(b(a(0, c(_x111))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(b(c(_x301))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(b(a(0, c(_x301))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(c(b(c(_x271)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x321))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(b(c(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x321))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x311)))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(a(0, b(c(c(b(b(c(b(c(c(_x311))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(b(a(0, c(c(b(a(0, c(_x281))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(b(c(c(_x381))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(c(c(b(a(0, b(a(0, b(c(b(a(0, b(c(b(c(_x381)))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(b(c(c(b(c(_x171))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(c(b(a(0, c(_x171)))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(b(c(c(b(c(_x241))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(a(0, b(a(0, c(_x241)))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(c(c(b(c(c(b(c(b(c(_x281))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(c(b(a(0, c(_x271)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(b(c(b(c(c(_x241)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(c(b(c(_x361))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(a(0, b(c(b(b(c(b(b(a(0, c(_x361)))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(_x311)))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(c(_x311)))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x381))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(c(b(a(0, b(c(b(b(a(0, c(_x381))))))))))))))))))))))))))))))))))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x331))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, b(a(0, c(_x331)))))))))))))))))))))))))))))))))) 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
c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(c(b(a(0, c(_x331))))))))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, b(a(0, b(c(b(c(_x371))))))))))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, b(c(c(c(_x331))))))))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, b(a(0, b(a(0, c(_x371)))))))))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(a(0, b(a(0, c(_x331)))))))))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, b(a(0, c(_x331)))))))))))))))))))))))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x331))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, b(a(0, c(_x331)))))))))))))))))))))))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(b(c(_x371)))))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, b(a(0, b(a(0, c(_x371))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x331))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(a(0, b(a(0, c(_x331))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x371)))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, b(a(0, b(c(b(c(_x371)))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x331))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(c(b(a(0, c(_x331)))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x331))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, b(c(c(c(_x331)))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x331))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, b(a(0, c(_x331))))))))))))))))))))))))))))))))))))

Problem 26: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(_x371)))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(b(c(b(a(0, b(c(b(b(c(b(c(_x371))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(_x371)))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(b(a(0, c(b(c(b(a(0, b(c(b(b(c(b(c(_x371))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(_x161)))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(c(b(c(_x161)))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_x271)))))))))))))))))))))))))))))
a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x201)))))))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(c(b(c(b(c(_x201)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(_x321)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(c(c(b(a(0, b(c(b(b(c(b(c(_x321))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(b(c(_x331)))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(b(b(a(0, c(b(c(b(c(b(b(a(0, c(_x331))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(_x291)))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(c(b(a(0, c(_x291))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x411)))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(c(b(c(c(b(c(b(b(a(0, c(_x411))))))))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(c(c(b(c(_x371)))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(b(c(b(b(a(0, c(_x371))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(c(b(c(_x361))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(b(c(c(b(c(b(c(b(c(b(b(c(b(b(a(0, c(_x361)))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(a(0, c(_x281))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(b(c(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x281)))))))))))))))))))))))))))))))))))
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a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x291))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(b(c(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(a(0, c(_x291)))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(_x91))))))c#(b(c(b(b(c(b(b(b(c(b(c(c(_x91)))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(b(c(_x261))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(b(c(b(a(0, c(_x261)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x311)))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(b(c(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(b(c(b(c(c(_x311)))))))))))))))))))))))))))))))))))
a#(0, c(c(c(c(c(c(c(b(c(c(b(c(c(c(b(c(_x311)))))))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(c(b(a(0, b(c(b(b(a(0, c(_x311))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x331)))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(a(0, b(a(0, c(_x331))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(b(c(_x201)))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(a(0, c(_x201)))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(_x211))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(c(c(c(_x211))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, c(_x271))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(a(0, b(a(0, c(_x151))))))))))))))
a#(0, c(c(c(c(c(c(c(b(c(c(_x251)))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(c(b(c(_x251)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(_x231)))))))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(c(b(c(b(c(_x231)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x341))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(b(c(b(c(b(c(c(b(a(0, b(c(c(b(c(b(c(_x341))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(_x311)))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(b(c(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x311))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(b(c(_x361)))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(b(c(b(b(a(0, c(_x361))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x351)))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(b(c(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, b(a(0, c(_x351)))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(_x281)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x281))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(_x331)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(b(a(0, b(c(b(c(b(c(b(b(c(b(c(_x331))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x251)))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(b(c(b(c(c(_x251)))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x291))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(c(b(c(b(c(_x291))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x281)))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_x281)))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(b(b(c(b(c(b(c(b(c(b(c(b(c(_x281)))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(b(c(c(b(c(c(b(c(_x221)))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(c(b(b(c(b(c(b(c(c(b(c(c(c(_x221))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(b(c(b(c(_x401))))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(c(c(b(b(c(b(c(b(c(b(a(0, c(_x401))))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(b(c(_x371))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(c(b(a(0, b(b(c(b(c(b(c(c(c(_x371)))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(c(c(b(a(0, c(_x241)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(c(_x401))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(b(c(b(a(0, b(c(b(b(c(b(b(c(b(c(_x401))))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(b(c(_x331)))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(b(b(c(b(c(b(c(b(c(b(c(b(b(a(0, c(_x331)))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(c(c(b(c(b(c(b(c(b(c(_x281)))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x441))))))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(b(c(b(c(b(a(0, b(c(c(b(c(b(b(a(0, b(a(0, c(_x441)))))))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(c(_x371)))))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(c(c(b(c(b(b(c(b(c(_x371)))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(_x371)))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(c(c(b(c(b(c(b(a(0, b(c(b(b(c(b(c(_x371)))))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(_x121)))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(c(_x121)))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x251)))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(a(0, c(_x251)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x411)))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(c(b(c(c(b(c(b(b(c(c(c(_x411)))))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x341))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(b(c(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(b(c(_x341))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x341))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(a(0, b(b(a(0, c(b(c(_x341)))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(c(_x321))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(b(c(b(c(_x321))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(_x341))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(b(c(b(c(b(c(_x341))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(_x281))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(c(c(b(c(b(b(c(b(c(_x281)))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(b(c(_x201)))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(c(b(a(0, c(_x201))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x371))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(b(c(b(c(b(c(b(c(_x371))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(c(b(c(_x331))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(c(b(c(c(b(a(0, c(_x331)))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(a(0, b(a(0, c(_x241))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x311))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(c(_x311))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(c(_x281))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(b(c(_x301))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(b(a(0, c(_x301))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(c(b(c(_x271)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(b(c(c(_x291)))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(c(b(a(0, b(c(b(c(_x291))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x311)))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(a(0, b(c(c(b(b(c(b(c(c(_x311))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(b(c(c(_x381))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(c(c(b(a(0, b(a(0, b(c(b(a(0, b(c(b(c(_x381)))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(b(a(0, c(c(b(a(0, c(_x281))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(b(c(c(b(c(_x241))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(a(0, b(a(0, c(_x241)))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x341))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(c(b(b(c(b(c(b(c(b(c(_x341))))))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(c(b(a(0, c(_x271)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(b(c(b(c(c(_x241)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(c(b(c(_x361))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(a(0, b(c(b(b(c(b(b(a(0, c(_x361)))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_x271)))))))))))))))))))))))))))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(_x371))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(b(c(b(a(0, b(c(b(b(c(b(c(_x371)))))))))))))))))))))))))))))))))))))) 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
c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(b(c(b(a(0, b(c(b(b(c(b(b(a(0, c(_x421)))))))))))))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(b(c(b(a(0, b(c(b(b(c(b(b(c(b(c(_x421))))))))))))))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(c(c(b(c(b(c(b(a(0, b(c(b(b(c(b(c(_x371))))))))))))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(b(c(b(c(c(b(c(b(b(c(b(c(_x371))))))))))))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(b(c(b(c(b(b(c(b(b(a(0, b(c(b(c(b(a(0, b(c(b(b(c(b(c(_x371)))))))))))))))))))))))))))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(_x371))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(b(c(b(a(0, b(c(b(b(c(b(c(_x371)))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(_x371))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(b(c(b(c(c(b(c(b(b(c(b(c(_x371)))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(_x371))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(c(c(b(c(b(c(b(a(0, b(c(b(b(c(b(c(_x371)))))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(_x371))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(b(c(b(c(b(b(c(b(b(a(0, b(c(b(c(b(a(0, b(c(b(b(c(b(c(_x371))))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(c(_x421)))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(b(c(b(a(0, b(c(b(b(c(b(b(c(b(c(_x421)))))))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(c(b(c(_x421)))))))))))))))))))))))))) → c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(b(c(b(a(0, b(c(b(b(c(b(b(a(0, c(_x421))))))))))))))))))))))))))))))))))))))))

Problem 27: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(b(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(b(b(a(0, c(_x281))))))))))))))))))))))))))))a#(0, c(c(_x31)))c#(c(b(c(b(c(_x31))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(b(c(_x371)))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(b(c(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(a(0, c(_x371)))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x251)))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(b(c(b(c(b(c(c(c(_x251)))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(c(c(_x271)))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(c(_x411)))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(b(c(b(c(b(a(0, b(c(c(b(c(b(b(c(b(c(_x411))))))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(b(c(b(c(b(c(b(c(b(c(_x271))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(_x121)))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(_x121))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x431)))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(a(0, b(c(c(b(c(b(b(a(0, c(_x431))))))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x311)))))))))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, b(a(0, c(_x311)))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x331)))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(a(0, b(a(0, c(_x331)))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x411)))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(b(c(b(c(b(a(0, b(b(a(0, c(b(b(a(0, c(_x411))))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(c(c(_x281)))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(b(c(_x401))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(b(c(b(c(b(b(c(b(c(b(c(b(c(b(c(_x401)))))))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(_x281)))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(c(b(c(c(c(_x281)))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x301))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x301))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x311)))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(c(c(c(_x311))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(b(c(_x331)))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(b(b(b(c(b(b(a(0, c(b(c(b(b(a(0, c(_x331))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(_x331)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(b(a(0, b(c(b(c(b(c(b(b(c(b(c(_x331)))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(b(c(_x331)))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(b(b(b(c(b(b(a(0, c(b(c(b(b(c(c(c(_x331)))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(_x311)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(c(b(a(0, c(_x311))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(b(c(c(_x361))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(b(c(c(b(c(b(c(b(c(b(b(a(0, b(c(b(c(_x361))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(c(_x371)))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(b(c(b(c(b(c(b(c(b(a(0, b(c(b(b(c(b(c(_x371)))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(_x281)))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(c(c(b(c(b(a(0, c(_x281)))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(b(c(c(b(c(_x411)))))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(b(c(b(c(b(c(c(b(a(0, c(_x411))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x341))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(c(b(c(b(b(c(b(b(c(b(c(_x341))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x251)))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(c(c(c(_x251)))))))))))))))))))))))))))a#(0, c(c(c(c(c(c(b(c(c(b(c(_x211))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(a(0, c(_x211)))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(b(c(_x301))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(b(b(a(0, c(_x301))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(b(a(0, c(_x271)))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x211))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(a(0, b(a(0, c(_x211)))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(_x151))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(a(0, c(_x151)))))))))))))))
a#(0, c(c(c(c(c(b(c(c(_x181)))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(c(b(c(_x181)))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(c(_x211))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(b(c(c(b(c(b(c(_x211))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(b(c(c(b(c(_x241))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(c(b(c(b(b(c(b(a(0, b(a(0, c(_x241))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(c(_x431)))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(a(0, b(c(c(b(c(b(b(c(b(c(_x431)))))))))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(_x151))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(c(_x151)))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x481))))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(a(0, b(b(c(b(c(b(c(b(b(a(0, b(c(b(c(_x481)))))))))))))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(b(c(b(c(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(c(_x281)))))))))))))))))))))))))))))))))))a#(0, c(c(c(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x331)))))))))))))))))))c#(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(c(b(a(0, c(_x331))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(b(c(b(b(a(0, b(c(b(b(a(0, c(_x241)))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(c(b(c(_x361))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, c(_x361))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(b(c(_x331)))))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(a(0, b(c(c(b(a(0, b(c(b(a(0, c(_x331))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x311)))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(c(c(b(a(0, b(a(0, b(b(c(b(c(c(_x311))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(b(c(_x331)))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(b(b(c(c(c(b(c(b(c(b(b(a(0, c(_x331)))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x291))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(c(_x291))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x351)))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(c(b(c(b(b(c(b(c(b(a(0, c(_x351))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(b(c(_x201)))))))))))))))c#(b(c(b(b(c(b(b(b(a(0, c(c(b(c(b(b(c(b(a(0, c(_x201))))))))))))))))))))
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a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(c(_x321))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(b(c(b(c(b(c(b(c(_x321))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(b(c(c(_x341))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(b(c(b(c(b(c(_x341))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(b(c(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(b(a(0, c(b(b(c(b(a(0, b(c(b(c(_x241))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(_x281))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(c(c(b(c(b(b(c(b(c(_x281)))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(b(c(b(c(_x201)))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(c(b(a(0, c(_x201))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x371))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(a(0, b(a(0, b(b(c(b(c(b(c(b(c(_x371))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(b(c(c(b(c(_x331))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(c(b(c(c(b(a(0, c(_x331)))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(b(a(0, b(a(0, c(_x241))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x311))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(b(c(_x311))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(_x281))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(b(c(b(c(b(c(c(b(c(b(c(_x281))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(b(c(_x301))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(a(0, c(b(a(0, c(_x301))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(a(0, b(c(b(c(_x271)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(b(c(c(_x291)))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(c(c(b(c(b(b(c(b(a(0, b(c(b(c(_x291))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(_x311)))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(a(0, b(c(c(b(b(c(b(c(c(_x311))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(b(c(c(_x381))))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(c(c(b(a(0, b(a(0, b(c(b(a(0, b(c(b(c(_x381)))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x281))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(b(a(0, c(c(b(a(0, c(_x281))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(b(c(_x341))))))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(c(b(c(b(b(c(b(b(a(0, c(_x341)))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(b(c(b(c(c(b(c(_x241))))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(c(c(b(c(b(b(c(b(a(0, b(a(0, c(_x241)))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(c(b(c(c(_x341))))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(a(0, b(b(c(b(c(b(c(c(b(b(c(b(c(b(c(b(c(_x341))))))))))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(b(c(_x361))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(c(c(b(b(c(b(c(b(b(c(b(b(c(b(c(_x361))))))))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(c(b(c(_x271)))))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(c(c(b(a(0, c(_x271)))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(b(c(c(c(b(c(_x241))))))))))))))))c#(b(c(b(b(c(b(b(a(0, b(c(b(c(b(b(a(0, b(c(b(b(b(c(b(c(c(_x241)))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(c(c(c(b(c(_x361))))))))))))))))))))))c#(b(c(b(b(c(b(b(b(c(b(c(b(b(a(0, c(b(b(c(b(b(a(0, b(a(0, b(c(b(b(c(b(b(a(0, c(_x361)))))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(b(c(_x271)))))))))))))))))c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(a(0, b(c(b(c(b(c(_x271)))))))))))))))))))))))))))))

Rewrite Rules

c(c(b(c(x))))b(a(0, c(x)))c(c(x))b(c(b(c(x))))
a(0, x)c(c(x))

Original Signature

Termination of terms over the following signature is verified: 0, b, c, a

Strategy


The right-hand side of the rule a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(b(c(_x281)))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(b(b(a(0, c(_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
c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(b(a(0, c(b(b(a(0, c(_x281))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(b(b(a(0, b(a(0, c(_x311)))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(c(c(b(c(b(b(a(0, c(_x281)))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(b(b(c(c(c(_x281))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(c(c(b(c(b(b(a(0, c(_x281)))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(b(b(a(0, c(_x281)))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(b(c(b(c(b(c(b(b(a(0, c(_x281)))))))))))))))))))))))))))))) 
c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(b(b(a(0, b(c(b(c(_x311))))))))))))))))))))))))))))))) 
Thus, the rule a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(b(c(_x281)))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(b(b(a(0, c(_x281)))))))))))))))))))))))))))) is replaced by the following rules:
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(b(c(c(b(c(_x311))))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(b(b(a(0, b(a(0, c(_x311))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(b(c(_x281)))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(b(c(b(c(b(c(b(b(a(0, c(_x281))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(b(c(_x281)))))))))))))))))) → c#(b(c(b(b(c(b(b(b(c(b(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(b(b(a(0, c(_x281))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(b(c(_x281)))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(b(b(c(c(c(_x281)))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(b(c(_x281)))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(b(a(0, c(b(b(a(0, c(_x281)))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(b(c(_x281)))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(c(c(b(c(b(b(a(0, c(_x281))))))))))))))))))))))))))))))
a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(b(c(c(_x311))))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(c(c(b(b(c(b(b(c(c(b(c(b(b(a(0, b(c(b(c(_x311)))))))))))))))))))))))))))))))a#(0, c(c(c(b(c(c(b(c(c(c(c(b(c(c(c(b(c(_x281)))))))))))))))))) → c#(b(c(b(b(c(b(b(c(c(b(b(c(b(c(b(c(b(b(c(b(b(c(c(b(c(b(b(a(0, c(_x281))))))))))))))))))))))))))))))