TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60006 ms.

The following DP Processors were used


Problem 1 was processed with processor ForwardNarrowing (2ms).
 | – Problem 2 was processed with processor ForwardNarrowing (1ms).
 |    | – Problem 3 was processed with processor ForwardNarrowing (4ms).
 |    |    | – Problem 4 was processed with processor ForwardNarrowing (3ms).
 |    |    |    | – Problem 5 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    | – Problem 6 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    | – Problem 7 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    | – Problem 8 was processed with processor ForwardNarrowing (7ms).
 |    |    |    |    |    |    |    | – Problem 9 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (10ms).
 |    |    |    |    |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (16ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (18ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (18ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (21ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (25ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (58ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (23ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (87ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (139ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (263ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 remains open; application of the following processors failed [ForwardNarrowing (385ms), ForwardNarrowing (189ms), ForwardNarrowing (427ms), ForwardNarrowing (135ms), ForwardNarrowing (327ms), ForwardNarrowing (178ms), ForwardNarrowing (373ms), ForwardNarrowing (397ms), ForwardNarrowing (176ms), ForwardNarrowing (178ms), ForwardNarrowing (194ms), ForwardNarrowing (431ms), ForwardNarrowing (311ms), ForwardNarrowing (492ms), ForwardNarrowing (201ms), ForwardNarrowing (394ms), ForwardNarrowing (231ms), ForwardNarrowing (539ms), ForwardNarrowing (237ms), ForwardNarrowing (417ms), ForwardNarrowing (267ms), ForwardNarrowing (433ms), ForwardNarrowing (timeout)].

The following open problems remain:



Open Dependency Pair Problem 1

Dependency Pairs

s1#(s1(s0(s0(x))))s1#(x)s1#(s1(s0(s0(x))))s1#(s1(s1(x)))
s1#(s1(s0(s0(x))))s1#(s1(x))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1


Problem 1: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(x))))s1#(x)s1#(s1(s0(s0(x))))s1#(s1(s1(x)))
s1#(s1(s0(s0(x))))s1#(s1(x))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(x)))) → s1#(s1(s1(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
s1#(s1(s0(s0(s0(s1(s1(s1(_x31)))))))) 
s1#(s0(s0(s0(s1(s1(s1(_x21))))))) 
Thus, the rule s1#(s1(s0(s0(x)))) → s1#(s1(s1(x))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(_x21)))))) → s1#(s0(s0(s0(s1(s1(s1(_x21)))))))s1#(s1(s0(s0(s1(s0(s0(_x31))))))) → s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))

Problem 2: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(_x21))))))s1#(s0(s0(s0(s1(s1(s1(_x21)))))))s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))
s1#(s1(s0(s0(x))))s1#(x)s1#(s1(s0(s0(x))))s1#(s1(x))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(_x21)))))) → s1#(s0(s0(s0(s1(s1(s1(_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
s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81)))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x71))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(_x21)))))) → s1#(s0(s0(s0(s1(s1(s1(_x21))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(_x71)))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x71)))))))))))s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81))))))))) → s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))

Problem 3: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))s1#(s1(s0(s0(x))))s1#(x)
s1#(s1(s0(s0(s0(s0(s0(s0(_x71))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x71)))))))))))s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))
s1#(s1(s0(s0(x))))s1#(s1(x))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(_x71)))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x71))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x111))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x121)))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(_x71)))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x71))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x121))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x121))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x111)))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x111)))))))))))))))

Problem 4: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x121)))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x121))))))))))))))))s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))
s1#(s1(s0(s0(x))))s1#(x)s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x111))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x111)))))))))))))))
s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))s1#(s1(s0(s0(x))))s1#(s1(x))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x121))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_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
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x171))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161)))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x121)))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x121))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x121)))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171)))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x171)))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x121))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x121))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))

Problem 5: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x171)))))))))))))))))))))s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))
s1#(s1(s0(s0(x))))s1#(x)s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x111))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x111)))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x121)))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x121))))))))))))))))))s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))s1#(s1(s0(s0(x))))s1#(s1(x))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171)))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_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
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221)))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x171))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171)))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x171))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211)))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171)))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x171)))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171)))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))

Problem 6: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))
s1#(s1(s0(s0(x))))s1#(x)s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x111))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x111)))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x171)))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x121)))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x121))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))s1#(s1(s0(s0(x))))s1#(s1(x))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211)))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211))))))))))))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271)))))))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211)))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211))))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x271))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261)))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211)))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211)))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))

Problem 7: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x111))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x111)))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x171)))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x121)))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x121))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))s1#(s1(s0(s0(x))))s1#(x)
s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(x))))s1#(s1(x))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x111)))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_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
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x151))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x161)))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x111)))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x111))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x161))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x151)))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x151)))))))))))))))))))

Problem 8: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x171)))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x121)))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x121))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))s1#(s1(s0(s0(x))))s1#(x)
s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x151))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x151)))))))))))))))))))s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))
s1#(s1(s0(s0(x))))s1#(s1(x))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221)))))))))))))))))))))))))) 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
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x271)))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221)))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221)))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x281))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x221)))))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221)))))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x271))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x281)))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x281)))))))))))))))))))))))))))))))

Problem 9: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x171)))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x121)))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x121))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))
s1#(s1(s0(s0(x))))s1#(x)s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x151))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x151)))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(x))))s1#(s1(x))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x281))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x281)))))))))))))))))))))))))))))))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171)))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_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
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241)))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x231))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171)))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x171))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171)))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x231)))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x231)))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))

Problem 10: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x121)))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x121))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x231))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x231)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))
s1#(s1(s0(s0(x))))s1#(x)s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x151))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x151)))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x281))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x281)))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))
s1#(s1(s0(s0(x))))s1#(s1(x))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_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
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x291)))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x301))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241)))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241)))))))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241)))))))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x301)))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x291))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x291))))))))))))))))))))))))))))))))

Problem 11: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x121)))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x121))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x291)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x291))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x231))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x231)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))
s1#(s1(s0(s0(x))))s1#(x)s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x151))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x151)))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))
s1#(s1(s0(s0(x))))s1#(s1(x))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x281))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x281)))))))))))))))))))))))))))))))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_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
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x311)))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241)))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241)))))))))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241)))))))))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321)))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x311))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))

Problem 12: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x121)))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x121))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x231))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x231)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(x))))s1#(x)
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x311)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x291)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x291))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x151))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x151)))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(x))))s1#(s1(x))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x281))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x281)))))))))))))))))))))))))))))))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x121))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_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
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x181)))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x191))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x121))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x121)))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x191)))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x191)))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x181))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x181))))))))))))))))))))))

Problem 13: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x231))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x231)))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))s1#(s1(s0(s0(x))))s1#(x)
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x191))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x191)))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x311)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x181)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x181))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x291)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x291))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x151))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x151)))))))))))))))))))s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x281))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x281)))))))))))))))))))))))))))))))s1#(s1(s0(s0(x))))s1#(s1(x))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261)))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261))))))))))))))))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x301))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x311)))))))))))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261)))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261))))))))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261)))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x301)))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261)))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x311))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))

Problem 14: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x231))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x231)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x191))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x191)))))))))))))))))))))))
s1#(s1(s0(s0(x))))s1#(x)s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x311)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x311)))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x181)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x181))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x291)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x291))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x151))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x151)))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(x))))s1#(s1(x))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x281))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x281)))))))))))))))))))))))))))))))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321)))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321))))))))))))))))))))))))))))))))))) 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
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x321))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x371)))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321))))))))))))))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321)))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321))))))))))))))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x371))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x371))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321)))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321)))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321)))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361)))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))

Problem 15: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x231))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x231)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x371)))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x371))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(x))))s1#(x)s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x191))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x191)))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x311)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x311)))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x181)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x181))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x291)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x291))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x151))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x151)))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x281))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x281)))))))))))))))))))))))))))))))
s1#(s1(s0(s0(x))))s1#(s1(x))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361)))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361))))))))))))))))))))))))))))))))))))))) 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
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x361))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x411)))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401))))))))))))))))))))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361)))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361)))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x411))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x411))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361)))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401)))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361)))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))

Problem 16: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x371)))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x371))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x231))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x231)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x411)))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x411))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(x))))s1#(x)
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x191))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x191)))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x311)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x311)))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x291)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x291))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x181)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x181))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x151))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x151)))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(x))))s1#(s1(x))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x281))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x281)))))))))))))))))))))))))))))))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401)))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401))))))))))))))))))))))))))))))))))))))))))) 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
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x451)))))))))))))))))))))))))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401)))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441)))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x451))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x451))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401)))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401)))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401)))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))

Problem 17: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x231))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x231)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x371)))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x371))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x411)))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x411))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(x))))s1#(x)s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x191))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x191)))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x311)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x451)))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x451))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x311)))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x181)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x181))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x291)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x291))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x151))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x151)))))))))))))))))))s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x281))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x281)))))))))))))))))))))))))))))))
s1#(s1(s0(s0(x))))s1#(s1(x))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441)))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441))))))))))))))))))))))))))))))))))))))))))))))) 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
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x491)))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x481))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441))))))))))))))))))))))))))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441)))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441)))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x491))))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x491))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441)))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x481)))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x481)))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441)))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))

Problem 18: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x371)))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x371))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x231))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x231)))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x411)))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x411))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x491)))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x491))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(x))))s1#(x)
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x191))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x191)))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x481))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x481)))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x311)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x451)))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x451))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x311)))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x291)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x291))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x181)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x181))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x151))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x151)))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(x))))s1#(s1(x))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x281))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x281)))))))))))))))))))))))))))))))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441)))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441))))))))))))))))))))))))))))))))))))))))))))))))) 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
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x501))))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x511)))))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441))))))))))))))))))))))))))))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441)))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x501)))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x501)))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441)))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441)))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x511))))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x511))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441)))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))))

Problem 19: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x231))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x231)))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x491)))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x491))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x191))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x191)))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x451)))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x451))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x181)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x181))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))))
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s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x511)))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x511))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))
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s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))s1#(s1(s0(s0(x))))s1#(x)
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x481))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x481)))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x311)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x501))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x501)))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x311)))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x291)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x291))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(x))))s1#(s1(x))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x281))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x281)))))))))))))))))))))))))))))))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361)))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361))))))))))))))))))))))))))))))))))))))))) 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
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x431)))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x361))))))))))))))))))))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361)))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x421)))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421)))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x431))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x431))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361)))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361)))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361)))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))))

Problem 20: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x421))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421)))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x231))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x231)))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x491)))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x491))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x191))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x191)))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x261))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x261)))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x451)))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x451))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x181)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x181))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))))s1#(s1(s0(s0(s1(s0(s0(_x31)))))))s1#(s1(s0(s0(s0(s1(s1(s1(_x31))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x151))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x151)))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x511)))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x511))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s1(s0(s0(_x81)))))))))s1#(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x81))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x431)))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x431))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x161)))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x161))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x301))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x301)))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x371)))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x371))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x411)))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x411))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x241)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x241))))))))))))))))))))))))))))))))s1#(s1(s0(s0(x))))s1#(x)
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x481))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x481)))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x311)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x171))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x171)))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x501))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x501)))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x311)))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x291)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x291))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x271)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x271))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x281))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x281)))))))))))))))))))))))))))))))
s1#(s1(s0(s0(x))))s1#(s1(x))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x421)))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421))))))))))))))))))))))))))))))))))))))))))))) 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
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x471)))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x461))))))))))))))))))))))))))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x421)))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x421)))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421)))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x421)))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421)))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x421)))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421)))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x461)))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x461)))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x471))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x471))))))))))))))))))))))))))))))))))))))))))))))))))

Problem 21: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

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s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x541))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x541)))))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x491)))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x491))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s0(s0(_x501))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x501)))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x281))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x281)))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x311)))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x311))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x291)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x291))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x451)))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x451))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x421))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421)))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x451)))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x451))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x561))))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x561)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x441))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x441)))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x421))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421)))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x291)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x291))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x471)))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x471))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x401))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x411)))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x411))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(x))))s1#(s1(x))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x541)))))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x601))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x611)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x541)))))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x541)))))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x541)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x541)))))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x541)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x541)))))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x541)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x541)))))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x541)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x601)))))))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x601)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x541)))))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x541)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x611))))))))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x611))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Problem 22: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x331)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x331))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x521))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x521)))))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x211))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x211)))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x681))))))))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x681)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x541))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x541)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x761))))))))))))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x761)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x421))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421)))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x661))))))))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x661)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x771)))))))))))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x771))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x581))))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x581)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x291)))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x291))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x491)))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x491))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x551)))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x551))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
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s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x591)))))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x591))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x561))))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x561)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x421))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421)))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x501))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x501)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x671)))))))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x671))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x331))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_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
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x401))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x331)))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x391)))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x331)))))))))))))))))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x331))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x331)))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s1(s0(s0(_x401)))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x401)))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x331))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x331))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x391))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x391))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x331))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x331))))))))))))))))))))))))))))))))))))))))

Problem 23: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x471)))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x471))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x431)))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x431))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x581))))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x581)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x221)))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x221))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(_x321))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x321)))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s0(s0(_x771)))))))))))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x771))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x361))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s1(s1(_x361)))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(_x581))))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x581)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
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s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x521))))))))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x521)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(_x421))))))))))))))))))))))))s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s1(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x421)))))))))))))))))))))))))))))))))))))))))))))))))

Rewrite Rules

s1(s1(s0(s0(x))))s0(s0(s0(s1(s1(s1(x))))))

Original Signature

Termination of terms over the following signature is verified: s0, s1

Strategy


The right-hand side of the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x471))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x471)))))))))))))))))))))))))))))))))))))))))))))))))))) 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
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x471)))))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x541))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x471)))))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x531)))))))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x471)))))))))))))))))))))))))))))))))))))))))))))))))))))) 
s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x471)))))))))))))))))))))))))))))))))))))))))))))))))))))) 
Thus, the rule s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x471))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x471)))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x471))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x471))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x471))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s1(_x471))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(_x541)))))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x541)))))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x471))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x471))))))))))))))))))))))))))))))))))))))))))))))))))))))
s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(_x471))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s1(s1(_x471))))))))))))))))))))))))))))))))))))))))))))))))))))))s1#(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s0(_x531))))))))))))))))))))))))))))) → s1#(s0(s0(s0(s1(s0(s0(s0(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(s0(s0(s1(s1(s1(s0(s0(s0(s0(s1(s1(s1(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s0(s0(s0(s1(s0(s0(s0(s1(s1(s1(_x531))))))))))))))))))))))))))))))))))))))))))))))))))))))))