TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60008 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 (5ms).
 |    |    | – Problem 4 was processed with processor ForwardNarrowing (1ms).
 |    |    |    | – Problem 5 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    | – Problem 6 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    | – Problem 7 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    | – Problem 8 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    | – Problem 9 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (1ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (12ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (83ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (95ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (202ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (253ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (315ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 was processed with processor ForwardNarrowing (647ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 28 remains open; application of the following processors failed [ForwardNarrowing (375ms), ForwardNarrowing (378ms), ForwardNarrowing (389ms), ForwardNarrowing (400ms), ForwardNarrowing (423ms), ForwardNarrowing (421ms), ForwardNarrowing (609ms), ForwardNarrowing (395ms), ForwardNarrowing (406ms), ForwardNarrowing (395ms), ForwardNarrowing (420ms), ForwardNarrowing (timeout)].

The following open problems remain:



Open Dependency Pair Problem 1

Dependency Pairs

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

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a


Problem 1: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

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

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


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

Problem 2: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

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

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


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

Problem 3: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(a(_x21)))c#(a(c(c(_x21))))b#(c(v(_x21)))b#(_x21)
c#(a(x))c#(x)a#(b(x))a#(x)
b#(c(x))c#(b(b(x)))c#(a(w(_x21)))c#(_x21)
b#(c(x))b#(x)c#(a(x))a#(c(c(x)))
b#(c(c(_x21)))b#(c(b(b(_x21))))a#(b(x))a#(a(x))
a#(b(x))b#(a(a(x)))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


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

Problem 4: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(a(_x21)))c#(a(c(c(_x21))))b#(c(v(_x21)))b#(_x21)
c#(a(x))c#(x)a#(b(x))a#(x)
c#(a(w(_x21)))c#(_x21)b#(c(v(_x31)))c#(b(_x31))
c#(a(x))a#(c(c(x)))b#(c(x))b#(x)
b#(c(c(_x21)))b#(c(b(b(_x21))))a#(b(x))a#(a(x))
b#(c(c(_x31)))c#(b(c(b(b(_x31)))))a#(b(x))b#(a(a(x)))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule b#(c(v(_x31))) → c#(b(_x31)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
c#(c(b(b(_x21)))) 
c#(_x21) 
Thus, the rule b#(c(v(_x31))) → c#(b(_x31)) is replaced by the following rules:
b#(c(v(c(_x21)))) → c#(c(b(b(_x21))))b#(c(v(v(_x21)))) → c#(_x21)

Problem 5: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(x))c#(x)a#(b(x))a#(x)
c#(a(x))a#(c(c(x)))a#(b(x))a#(a(x))
c#(a(a(_x21)))c#(a(c(c(_x21))))b#(c(v(_x21)))b#(_x21)
c#(a(w(_x21)))c#(_x21)b#(c(x))b#(x)
b#(c(c(_x21)))b#(c(b(b(_x21))))b#(c(c(_x31)))c#(b(c(b(b(_x31)))))
b#(c(v(c(_x21))))c#(c(b(b(_x21))))b#(c(v(v(_x21))))c#(_x21)
a#(b(x))b#(a(a(x)))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


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

Problem 6: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(x))c#(x)a#(b(x))a#(x)
a#(b(x))a#(a(x))c#(a(a(_x21)))c#(a(c(c(_x21))))
c#(a(w(_x31)))a#(c(_x31))c#(a(a(_x31)))a#(c(a(c(c(_x31)))))
b#(c(v(_x21)))b#(_x21)c#(a(w(_x21)))c#(_x21)
b#(c(x))b#(x)b#(c(c(_x21)))b#(c(b(b(_x21))))
b#(c(c(_x31)))c#(b(c(b(b(_x31)))))b#(c(v(c(_x21))))c#(c(b(b(_x21))))
b#(c(v(v(_x21))))c#(_x21)a#(b(x))b#(a(a(x)))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


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

Problem 7: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(b(u(_x21)))a#(_x21)c#(a(x))c#(x)
a#(b(x))a#(x)a#(b(b(_x21)))a#(b(a(a(_x21))))
c#(a(a(_x21)))c#(a(c(c(_x21))))c#(a(w(_x31)))a#(c(_x31))
c#(a(a(_x31)))a#(c(a(c(c(_x31)))))b#(c(v(_x21)))b#(_x21)
c#(a(w(_x21)))c#(_x21)b#(c(x))b#(x)
b#(c(c(_x21)))b#(c(b(b(_x21))))b#(c(c(_x31)))c#(b(c(b(b(_x31)))))
b#(c(v(c(_x21))))c#(c(b(b(_x21))))b#(c(v(v(_x21))))c#(_x21)
a#(b(x))b#(a(a(x)))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(_x31))) → a#(c(_x31)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(_x21) 
a#(a(c(c(_x21)))) 
Thus, the rule c#(a(w(_x31))) → a#(c(_x31)) is replaced by the following rules:
c#(a(w(w(_x21)))) → a#(_x21)c#(a(w(a(_x21)))) → a#(a(c(c(_x21))))

Problem 8: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(b(u(_x21)))a#(_x21)c#(a(w(w(_x21))))a#(_x21)
c#(a(x))c#(x)c#(a(w(a(_x21))))a#(a(c(c(_x21))))
a#(b(x))a#(x)a#(b(b(_x21)))a#(b(a(a(_x21))))
c#(a(a(_x21)))c#(a(c(c(_x21))))c#(a(a(_x31)))a#(c(a(c(c(_x31)))))
b#(c(v(_x21)))b#(_x21)c#(a(w(_x21)))c#(_x21)
b#(c(x))b#(x)b#(c(c(_x21)))b#(c(b(b(_x21))))
b#(c(v(c(_x21))))c#(c(b(b(_x21))))b#(c(c(_x31)))c#(b(c(b(b(_x31)))))
b#(c(v(v(_x21))))c#(_x21)a#(b(x))b#(a(a(x)))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(_x21)))) → a#(a(c(c(_x21)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(a(c(a(c(c(_x51)))))) 
a#(a(c(_x51))) 
Thus, the rule c#(a(w(a(_x21)))) → a#(a(c(c(_x21)))) is replaced by the following rules:
c#(a(w(a(w(_x51))))) → a#(a(c(_x51)))c#(a(w(a(a(_x51))))) → a#(a(c(a(c(c(_x51))))))

Problem 9: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(b(u(_x21)))a#(_x21)c#(a(w(w(_x21))))a#(_x21)
c#(a(x))c#(x)a#(b(x))a#(x)
a#(b(b(_x21)))a#(b(a(a(_x21))))c#(a(w(a(w(_x51)))))a#(a(c(_x51)))
c#(a(a(_x21)))c#(a(c(c(_x21))))c#(a(w(a(a(_x51)))))a#(a(c(a(c(c(_x51))))))
c#(a(a(_x31)))a#(c(a(c(c(_x31)))))b#(c(v(_x21)))b#(_x21)
c#(a(w(_x21)))c#(_x21)b#(c(x))b#(x)
b#(c(c(_x21)))b#(c(b(b(_x21))))b#(c(c(_x31)))c#(b(c(b(b(_x31)))))
b#(c(v(c(_x21))))c#(c(b(b(_x21))))b#(c(v(v(_x21))))c#(_x21)
a#(b(x))b#(a(a(x)))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(_x51))))) → a#(a(c(_x51))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(a(_x31)) 
a#(a(a(c(c(_x31))))) 
Thus, the rule c#(a(w(a(w(_x51))))) → a#(a(c(_x51))) is replaced by the following rules:
c#(a(w(a(w(w(_x31)))))) → a#(a(_x31))c#(a(w(a(w(a(_x31)))))) → a#(a(a(c(c(_x31)))))

Problem 10: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(b(u(_x21)))a#(_x21)c#(a(w(w(_x21))))a#(_x21)
c#(a(x))c#(x)a#(b(x))a#(x)
c#(a(w(a(w(a(_x31))))))a#(a(a(c(c(_x31)))))a#(b(b(_x21)))a#(b(a(a(_x21))))
c#(a(w(a(w(w(_x31))))))a#(a(_x31))c#(a(a(_x21)))c#(a(c(c(_x21))))
c#(a(w(a(a(_x51)))))a#(a(c(a(c(c(_x51))))))c#(a(a(_x31)))a#(c(a(c(c(_x31)))))
b#(c(v(_x21)))b#(_x21)c#(a(w(_x21)))c#(_x21)
b#(c(x))b#(x)b#(c(c(_x21)))b#(c(b(b(_x21))))
b#(c(v(c(_x21))))c#(c(b(b(_x21))))b#(c(c(_x31)))c#(b(c(b(b(_x31)))))
b#(c(v(v(_x21))))c#(_x21)a#(b(x))b#(a(a(x)))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(a(_x31)))))) → a#(a(a(c(c(_x31))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(a(a(c(a(c(c(_x61))))))) 
a#(a(a(c(_x61)))) 
Thus, the rule c#(a(w(a(w(a(_x31)))))) → a#(a(a(c(c(_x31))))) is replaced by the following rules:
c#(a(w(a(w(a(w(_x61))))))) → a#(a(a(c(_x61))))c#(a(w(a(w(a(a(_x61))))))) → a#(a(a(c(a(c(c(_x61)))))))

Problem 11: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(b(u(_x21)))a#(_x21)c#(a(w(w(_x21))))a#(_x21)
c#(a(x))c#(x)a#(b(x))a#(x)
a#(b(b(_x21)))a#(b(a(a(_x21))))c#(a(w(a(w(w(_x31))))))a#(a(_x31))
c#(a(a(_x21)))c#(a(c(c(_x21))))c#(a(w(a(w(a(w(_x61)))))))a#(a(a(c(_x61))))
c#(a(w(a(a(_x51)))))a#(a(c(a(c(c(_x51))))))c#(a(a(_x31)))a#(c(a(c(c(_x31)))))
b#(c(v(_x21)))b#(_x21)c#(a(w(_x21)))c#(_x21)
b#(c(x))b#(x)b#(c(c(_x21)))b#(c(b(b(_x21))))
c#(a(w(a(w(a(a(_x61)))))))a#(a(a(c(a(c(c(_x61)))))))b#(c(c(_x31)))c#(b(c(b(b(_x31)))))
b#(c(v(c(_x21))))c#(c(b(b(_x21))))b#(c(v(v(_x21))))c#(_x21)
a#(b(x))b#(a(a(x)))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(w(_x31)))))) → a#(a(_x31)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(b(a(a(_x21)))) 
a#(_x21) 
Thus, the rule c#(a(w(a(w(w(_x31)))))) → a#(a(_x31)) is replaced by the following rules:
c#(a(w(a(w(w(b(_x21))))))) → a#(b(a(a(_x21))))c#(a(w(a(w(w(u(_x21))))))) → a#(_x21)

Problem 12: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(b(u(_x21)))a#(_x21)c#(a(w(w(_x21))))a#(_x21)
c#(a(x))c#(x)a#(b(x))a#(x)
c#(a(w(a(w(w(u(_x21)))))))a#(_x21)c#(a(w(a(w(w(b(_x21)))))))a#(b(a(a(_x21))))
a#(b(b(_x21)))a#(b(a(a(_x21))))c#(a(a(_x21)))c#(a(c(c(_x21))))
c#(a(w(a(w(a(w(_x61)))))))a#(a(a(c(_x61))))c#(a(w(a(a(_x51)))))a#(a(c(a(c(c(_x51))))))
c#(a(a(_x31)))a#(c(a(c(c(_x31)))))b#(c(v(_x21)))b#(_x21)
c#(a(w(_x21)))c#(_x21)b#(c(x))b#(x)
c#(a(w(a(w(a(a(_x61)))))))a#(a(a(c(a(c(c(_x61)))))))b#(c(c(_x21)))b#(c(b(b(_x21))))
b#(c(v(c(_x21))))c#(c(b(b(_x21))))b#(c(c(_x31)))c#(b(c(b(b(_x31)))))
b#(c(v(v(_x21))))c#(_x21)a#(b(x))b#(a(a(x)))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


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

Problem 13: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(b(u(_x21)))a#(_x21)c#(a(w(w(_x21))))a#(_x21)
c#(a(x))c#(x)a#(b(x))a#(x)
c#(a(w(a(w(a(w(w(_x41))))))))a#(a(a(_x41)))c#(a(w(a(w(w(u(_x21)))))))a#(_x21)
c#(a(w(a(w(a(w(a(_x41))))))))a#(a(a(a(c(c(_x41))))))c#(a(w(a(w(w(b(_x21)))))))a#(b(a(a(_x21))))
a#(b(b(_x21)))a#(b(a(a(_x21))))c#(a(a(_x21)))c#(a(c(c(_x21))))
c#(a(w(a(a(_x51)))))a#(a(c(a(c(c(_x51))))))c#(a(a(_x31)))a#(c(a(c(c(_x31)))))
b#(c(v(_x21)))b#(_x21)c#(a(w(_x21)))c#(_x21)
b#(c(x))b#(x)b#(c(c(_x21)))b#(c(b(b(_x21))))
c#(a(w(a(w(a(a(_x61)))))))a#(a(a(c(a(c(c(_x61)))))))b#(c(c(_x31)))c#(b(c(b(b(_x31)))))
b#(c(v(c(_x21))))c#(c(b(b(_x21))))b#(c(v(v(_x21))))c#(_x21)
a#(b(x))b#(a(a(x)))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(a(w(w(_x41)))))))) → a#(a(a(_x41))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(a(b(a(a(_x31))))) 
a#(a(_x31)) 
Thus, the rule c#(a(w(a(w(a(w(w(_x41)))))))) → a#(a(a(_x41))) is replaced by the following rules:
c#(a(w(a(w(a(w(w(b(_x31))))))))) → a#(a(b(a(a(_x31)))))c#(a(w(a(w(a(w(w(u(_x31))))))))) → a#(a(_x31))

Problem 14: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(w(a(w(a(w(w(b(_x31)))))))))a#(a(b(a(a(_x31)))))a#(b(u(_x21)))a#(_x21)
c#(a(w(w(_x21))))a#(_x21)c#(a(x))c#(x)
a#(b(x))a#(x)c#(a(w(a(w(w(u(_x21)))))))a#(_x21)
c#(a(w(a(w(a(w(a(_x41))))))))a#(a(a(a(c(c(_x41))))))c#(a(w(a(w(a(w(w(u(_x31)))))))))a#(a(_x31))
c#(a(w(a(w(w(b(_x21)))))))a#(b(a(a(_x21))))a#(b(b(_x21)))a#(b(a(a(_x21))))
c#(a(a(_x21)))c#(a(c(c(_x21))))b#(c(v(_x21)))b#(_x21)
c#(a(w(a(a(_x51)))))a#(a(c(a(c(c(_x51))))))c#(a(a(_x31)))a#(c(a(c(c(_x31)))))
c#(a(w(_x21)))c#(_x21)b#(c(x))b#(x)
c#(a(w(a(w(a(a(_x61)))))))a#(a(a(c(a(c(c(_x61)))))))b#(c(c(_x21)))b#(c(b(b(_x21))))
b#(c(v(c(_x21))))c#(c(b(b(_x21))))b#(c(c(_x31)))c#(b(c(b(b(_x31)))))
b#(c(v(v(_x21))))c#(_x21)a#(b(x))b#(a(a(x)))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(a(w(w(b(_x31))))))))) → a#(a(b(a(a(_x31))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(a(b(a(_x61)))) 
a#(b(a(a(a(a(_x31)))))) 
a#(a(b(a(b(a(a(_x61))))))) 
Thus, the rule c#(a(w(a(w(a(w(w(b(_x31))))))))) → a#(a(b(a(a(_x31))))) is replaced by the following rules:
c#(a(w(a(w(a(w(w(b(u(_x61)))))))))) → a#(a(b(a(_x61))))c#(a(w(a(w(a(w(w(b(b(_x61)))))))))) → a#(a(b(a(b(a(a(_x61)))))))
c#(a(w(a(w(a(w(w(b(_x31))))))))) → a#(b(a(a(a(a(_x31))))))

Problem 15: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

a#(b(u(_x21)))a#(_x21)c#(a(w(a(w(a(w(w(b(u(_x61))))))))))a#(a(b(a(_x61))))
c#(a(w(w(_x21))))a#(_x21)c#(a(x))c#(x)
a#(b(x))a#(x)c#(a(w(a(w(w(u(_x21)))))))a#(_x21)
c#(a(w(a(w(a(w(w(b(b(_x61))))))))))a#(a(b(a(b(a(a(_x61)))))))c#(a(w(a(w(a(w(a(_x41))))))))a#(a(a(a(c(c(_x41))))))
c#(a(w(a(w(a(w(w(u(_x31)))))))))a#(a(_x31))c#(a(w(a(w(w(b(_x21)))))))a#(b(a(a(_x21))))
a#(b(b(_x21)))a#(b(a(a(_x21))))c#(a(a(_x21)))c#(a(c(c(_x21))))
c#(a(a(_x31)))a#(c(a(c(c(_x31)))))c#(a(w(a(a(_x51)))))a#(a(c(a(c(c(_x51))))))
b#(c(v(_x21)))b#(_x21)c#(a(w(_x21)))c#(_x21)
b#(c(x))b#(x)b#(c(c(_x21)))b#(c(b(b(_x21))))
c#(a(w(a(w(a(a(_x61)))))))a#(a(a(c(a(c(c(_x61)))))))b#(c(c(_x31)))c#(b(c(b(b(_x31)))))
b#(c(v(c(_x21))))c#(c(b(b(_x21))))b#(c(v(v(_x21))))c#(_x21)
c#(a(w(a(w(a(w(w(b(_x31)))))))))a#(b(a(a(a(a(_x31))))))a#(b(x))b#(a(a(x)))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


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

Problem 16: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(w(a(w(a(w(w(b(u(u(_x41)))))))))))a#(a(b(_x41)))c#(a(w(a(w(a(w(w(b(u(b(_x41)))))))))))a#(a(b(b(a(a(_x41))))))
c#(a(w(a(w(a(w(w(b(u(_x61))))))))))a#(b(a(a(a(_x61)))))c#(a(w(a(w(a(w(w(b(b(_x61))))))))))a#(a(b(a(b(a(a(_x61)))))))
c#(a(w(a(w(a(w(w(u(_x31)))))))))a#(a(_x31))c#(a(w(a(w(w(b(_x21)))))))a#(b(a(a(_x21))))
c#(a(a(_x31)))a#(c(a(c(c(_x31)))))c#(a(w(a(a(_x51)))))a#(a(c(a(c(c(_x51))))))
b#(c(v(_x21)))b#(_x21)c#(a(w(_x21)))c#(_x21)
b#(c(x))b#(x)b#(c(c(_x21)))b#(c(b(b(_x21))))
c#(a(w(a(w(a(a(_x61)))))))a#(a(a(c(a(c(c(_x61)))))))c#(a(w(a(w(a(w(w(b(_x31)))))))))a#(b(a(a(a(a(_x31))))))
a#(b(x))b#(a(a(x)))a#(b(u(_x21)))a#(_x21)
c#(a(x))c#(x)c#(a(w(w(_x21))))a#(_x21)
a#(b(x))a#(x)c#(a(w(a(w(w(u(_x21)))))))a#(_x21)
c#(a(w(a(w(a(w(a(_x41))))))))a#(a(a(a(c(c(_x41))))))a#(b(b(_x21)))a#(b(a(a(_x21))))
c#(a(a(_x21)))c#(a(c(c(_x21))))b#(c(v(c(_x21))))c#(c(b(b(_x21))))
b#(c(c(_x31)))c#(b(c(b(b(_x31)))))b#(c(v(v(_x21))))c#(_x21)

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(a(w(w(b(u(u(_x41))))))))))) → a#(a(b(_x41))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(b(a(a(_x21)))) 
a#(a(c(b(b(_x31))))) 
a#(a(_x31)) 
Thus, the rule c#(a(w(a(w(a(w(w(b(u(u(_x41))))))))))) → a#(a(b(_x41))) is replaced by the following rules:
c#(a(w(a(w(a(w(w(b(u(u(v(_x31)))))))))))) → a#(a(_x31))c#(a(w(a(w(a(w(w(b(u(u(_x21))))))))))) → a#(b(a(a(_x21))))
c#(a(w(a(w(a(w(w(b(u(u(c(_x31)))))))))))) → a#(a(c(b(b(_x31)))))

Problem 17: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(w(a(w(a(w(w(b(u(b(_x41)))))))))))a#(a(b(b(a(a(_x41))))))c#(a(w(a(w(a(w(w(b(u(_x61))))))))))a#(b(a(a(a(_x61)))))
c#(a(w(a(w(a(w(w(b(b(_x61))))))))))a#(a(b(a(b(a(a(_x61)))))))c#(a(w(a(w(a(w(w(u(_x31)))))))))a#(a(_x31))
c#(a(w(a(w(w(b(_x21)))))))a#(b(a(a(_x21))))b#(c(v(_x21)))b#(_x21)
c#(a(w(a(a(_x51)))))a#(a(c(a(c(c(_x51))))))c#(a(a(_x31)))a#(c(a(c(c(_x31)))))
c#(a(w(a(w(a(w(w(b(u(u(c(_x31))))))))))))a#(a(c(b(b(_x31)))))c#(a(w(_x21)))c#(_x21)
b#(c(x))b#(x)c#(a(w(a(w(a(a(_x61)))))))a#(a(a(c(a(c(c(_x61)))))))
b#(c(c(_x21)))b#(c(b(b(_x21))))c#(a(w(a(w(a(w(w(b(_x31)))))))))a#(b(a(a(a(a(_x31))))))
a#(b(x))b#(a(a(x)))a#(b(u(_x21)))a#(_x21)
c#(a(x))c#(x)c#(a(w(w(_x21))))a#(_x21)
a#(b(x))a#(x)c#(a(w(a(w(w(u(_x21)))))))a#(_x21)
c#(a(w(a(w(a(w(a(_x41))))))))a#(a(a(a(c(c(_x41))))))c#(a(w(a(w(a(w(w(b(u(u(v(_x31))))))))))))a#(a(_x31))
c#(a(w(a(w(a(w(w(b(u(u(_x21)))))))))))a#(b(a(a(_x21))))a#(b(b(_x21)))a#(b(a(a(_x21))))
c#(a(a(_x21)))c#(a(c(c(_x21))))b#(c(c(_x31)))c#(b(c(b(b(_x31)))))
b#(c(v(c(_x21))))c#(c(b(b(_x21))))b#(c(v(v(_x21))))c#(_x21)

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(a(w(w(b(u(b(_x41))))))))))) → a#(a(b(b(a(a(_x41)))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(a(b(b(a(b(a(a(_x71)))))))) 
a#(a(b(b(a(_x71))))) 
a#(b(a(a(b(a(a(_x41))))))) 
Thus, the rule c#(a(w(a(w(a(w(w(b(u(b(_x41))))))))))) → a#(a(b(b(a(a(_x41)))))) is replaced by the following rules:
c#(a(w(a(w(a(w(w(b(u(b(u(_x71)))))))))))) → a#(a(b(b(a(_x71)))))c#(a(w(a(w(a(w(w(b(u(b(b(_x71)))))))))))) → a#(a(b(b(a(b(a(a(_x71))))))))
c#(a(w(a(w(a(w(w(b(u(b(_x41))))))))))) → a#(b(a(a(b(a(a(_x41)))))))

Problem 18: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(w(a(w(a(w(w(b(u(_x61))))))))))a#(b(a(a(a(_x61)))))c#(a(w(a(w(a(w(w(b(b(_x61))))))))))a#(a(b(a(b(a(a(_x61)))))))
c#(a(w(a(w(a(w(w(u(_x31)))))))))a#(a(_x31))c#(a(w(a(w(w(b(_x21)))))))a#(b(a(a(_x21))))
c#(a(w(a(w(a(w(w(b(u(b(u(_x71))))))))))))a#(a(b(b(a(_x71)))))c#(a(a(_x31)))a#(c(a(c(c(_x31)))))
c#(a(w(a(a(_x51)))))a#(a(c(a(c(c(_x51))))))b#(c(v(_x21)))b#(_x21)
c#(a(w(a(w(a(w(w(b(u(b(_x41)))))))))))a#(b(a(a(b(a(a(_x41)))))))c#(a(w(a(w(a(w(w(b(u(u(c(_x31))))))))))))a#(a(c(b(b(_x31)))))
c#(a(w(_x21)))c#(_x21)b#(c(x))b#(x)
c#(a(w(a(w(a(a(_x61)))))))a#(a(a(c(a(c(c(_x61)))))))b#(c(c(_x21)))b#(c(b(b(_x21))))
c#(a(w(a(w(a(w(w(b(_x31)))))))))a#(b(a(a(a(a(_x31))))))a#(b(x))b#(a(a(x)))
a#(b(u(_x21)))a#(_x21)c#(a(x))c#(x)
c#(a(w(w(_x21))))a#(_x21)a#(b(x))a#(x)
c#(a(w(a(w(w(u(_x21)))))))a#(_x21)c#(a(w(a(w(a(w(a(_x41))))))))a#(a(a(a(c(c(_x41))))))
c#(a(w(a(w(a(w(w(b(u(u(v(_x31))))))))))))a#(a(_x31))c#(a(w(a(w(a(w(w(b(u(u(_x21)))))))))))a#(b(a(a(_x21))))
a#(b(b(_x21)))a#(b(a(a(_x21))))c#(a(a(_x21)))c#(a(c(c(_x21))))
c#(a(w(a(w(a(w(w(b(u(b(b(_x71))))))))))))a#(a(b(b(a(b(a(a(_x71))))))))b#(c(v(c(_x21))))c#(c(b(b(_x21))))
b#(c(c(_x31)))c#(b(c(b(b(_x31)))))b#(c(v(v(_x21))))c#(_x21)

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(a(w(w(b(b(_x61)))))))))) → a#(a(b(a(b(a(a(_x61))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(a(b(a(b(a(b(a(a(_x81))))))))) 
a#(a(b(a(b(a(_x81)))))) 
a#(b(a(a(a(b(a(a(_x61)))))))) 
a#(a(b(b(a(a(a(a(_x61)))))))) 
Thus, the rule c#(a(w(a(w(a(w(w(b(b(_x61)))))))))) → a#(a(b(a(b(a(a(_x61))))))) is replaced by the following rules:
c#(a(w(a(w(a(w(w(b(b(_x61)))))))))) → a#(a(b(b(a(a(a(a(_x61))))))))c#(a(w(a(w(a(w(w(b(b(u(_x81))))))))))) → a#(a(b(a(b(a(_x81))))))
c#(a(w(a(w(a(w(w(b(b(b(_x81))))))))))) → a#(a(b(a(b(a(b(a(a(_x81)))))))))c#(a(w(a(w(a(w(w(b(b(_x61)))))))))) → a#(b(a(a(a(b(a(a(_x61))))))))

Problem 19: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(w(a(w(a(w(w(b(u(_x61))))))))))a#(b(a(a(a(_x61)))))c#(a(w(a(w(a(w(w(u(_x31)))))))))a#(a(_x31))
c#(a(w(a(w(w(b(_x21)))))))a#(b(a(a(_x21))))c#(a(w(a(w(a(w(w(b(u(b(u(_x71))))))))))))a#(a(b(b(a(_x71)))))
c#(a(w(a(w(a(w(w(b(u(b(_x41)))))))))))a#(b(a(a(b(a(a(_x41)))))))b#(c(v(_x21)))b#(_x21)
c#(a(w(a(a(_x51)))))a#(a(c(a(c(c(_x51))))))c#(a(a(_x31)))a#(c(a(c(c(_x31)))))
c#(a(w(a(w(a(w(w(b(u(u(c(_x31))))))))))))a#(a(c(b(b(_x31)))))c#(a(w(_x21)))c#(_x21)
b#(c(x))b#(x)b#(c(c(_x21)))b#(c(b(b(_x21))))
c#(a(w(a(w(a(a(_x61)))))))a#(a(a(c(a(c(c(_x61)))))))c#(a(w(a(w(a(w(w(b(_x31)))))))))a#(b(a(a(a(a(_x31))))))
a#(b(x))b#(a(a(x)))c#(a(w(a(w(a(w(w(b(b(_x61))))))))))a#(a(b(b(a(a(a(a(_x61))))))))
a#(b(u(_x21)))a#(_x21)c#(a(x))c#(x)
c#(a(w(w(_x21))))a#(_x21)c#(a(w(a(w(a(w(w(b(b(u(_x81)))))))))))a#(a(b(a(b(a(_x81))))))
a#(b(x))a#(x)c#(a(w(a(w(w(u(_x21)))))))a#(_x21)
c#(a(w(a(w(a(w(a(_x41))))))))a#(a(a(a(c(c(_x41))))))c#(a(w(a(w(a(w(w(b(u(u(v(_x31))))))))))))a#(a(_x31))
a#(b(b(_x21)))a#(b(a(a(_x21))))c#(a(w(a(w(a(w(w(b(u(u(_x21)))))))))))a#(b(a(a(_x21))))
c#(a(a(_x21)))c#(a(c(c(_x21))))c#(a(w(a(w(a(w(w(b(u(b(b(_x71))))))))))))a#(a(b(b(a(b(a(a(_x71))))))))
b#(c(c(_x31)))c#(b(c(b(b(_x31)))))b#(c(v(c(_x21))))c#(c(b(b(_x21))))
c#(a(w(a(w(a(w(w(b(b(b(_x81)))))))))))a#(a(b(a(b(a(b(a(a(_x81)))))))))b#(c(v(v(_x21))))c#(_x21)
c#(a(w(a(w(a(w(w(b(b(_x61))))))))))a#(b(a(a(a(b(a(a(_x61))))))))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(a(w(w(u(_x31))))))))) → a#(a(_x31)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(b(a(a(_x21)))) 
a#(_x21) 
Thus, the rule c#(a(w(a(w(a(w(w(u(_x31))))))))) → a#(a(_x31)) is replaced by the following rules:
c#(a(w(a(w(a(w(w(u(b(_x21)))))))))) → a#(b(a(a(_x21))))c#(a(w(a(w(a(w(w(u(u(_x21)))))))))) → a#(_x21)

Problem 20: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(w(a(w(a(w(w(b(u(_x61))))))))))a#(b(a(a(a(_x61)))))c#(a(w(a(w(w(b(_x21)))))))a#(b(a(a(_x21))))
c#(a(w(a(w(a(w(w(b(u(b(u(_x71))))))))))))a#(a(b(b(a(_x71)))))c#(a(a(_x31)))a#(c(a(c(c(_x31)))))
c#(a(w(a(a(_x51)))))a#(a(c(a(c(c(_x51))))))b#(c(v(_x21)))b#(_x21)
c#(a(w(a(w(a(w(w(b(u(b(_x41)))))))))))a#(b(a(a(b(a(a(_x41)))))))c#(a(w(a(w(a(w(w(b(u(u(c(_x31))))))))))))a#(a(c(b(b(_x31)))))
c#(a(w(_x21)))c#(_x21)b#(c(x))b#(x)
c#(a(w(a(w(a(a(_x61)))))))a#(a(a(c(a(c(c(_x61)))))))b#(c(c(_x21)))b#(c(b(b(_x21))))
c#(a(w(a(w(a(w(w(u(u(_x21))))))))))a#(_x21)c#(a(w(a(w(a(w(w(b(_x31)))))))))a#(b(a(a(a(a(_x31))))))
a#(b(x))b#(a(a(x)))c#(a(w(a(w(a(w(w(u(b(_x21))))))))))a#(b(a(a(_x21))))
c#(a(w(a(w(a(w(w(b(b(_x61))))))))))a#(a(b(b(a(a(a(a(_x61))))))))a#(b(u(_x21)))a#(_x21)
c#(a(x))c#(x)c#(a(w(w(_x21))))a#(_x21)
c#(a(w(a(w(a(w(w(b(b(u(_x81)))))))))))a#(a(b(a(b(a(_x81))))))a#(b(x))a#(x)
c#(a(w(a(w(w(u(_x21)))))))a#(_x21)c#(a(w(a(w(a(w(a(_x41))))))))a#(a(a(a(c(c(_x41))))))
c#(a(w(a(w(a(w(w(b(u(u(v(_x31))))))))))))a#(a(_x31))c#(a(w(a(w(a(w(w(b(u(u(_x21)))))))))))a#(b(a(a(_x21))))
a#(b(b(_x21)))a#(b(a(a(_x21))))c#(a(a(_x21)))c#(a(c(c(_x21))))
c#(a(w(a(w(a(w(w(b(u(b(b(_x71))))))))))))a#(a(b(b(a(b(a(a(_x71))))))))c#(a(w(a(w(a(w(w(b(b(b(_x81)))))))))))a#(a(b(a(b(a(b(a(a(_x81)))))))))
b#(c(v(c(_x21))))c#(c(b(b(_x21))))b#(c(c(_x31)))c#(b(c(b(b(_x31)))))
b#(c(v(v(_x21))))c#(_x21)c#(a(w(a(w(a(w(w(b(b(_x61))))))))))a#(b(a(a(a(b(a(a(_x61))))))))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(a(w(w(b(u(b(u(_x71)))))))))))) → a#(a(b(b(a(_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
a#(a(b(b(_x51)))) 
a#(a(b(b(b(a(a(_x51))))))) 
a#(b(a(a(b(a(_x71)))))) 
Thus, the rule c#(a(w(a(w(a(w(w(b(u(b(u(_x71)))))))))))) → a#(a(b(b(a(_x71))))) is replaced by the following rules:
c#(a(w(a(w(a(w(w(b(u(b(u(_x71)))))))))))) → a#(b(a(a(b(a(_x71))))))c#(a(w(a(w(a(w(w(b(u(b(u(u(_x51))))))))))))) → a#(a(b(b(_x51))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(_x51))))))))))))) → a#(a(b(b(b(a(a(_x51)))))))

Problem 21: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(_x71))))))))))))))))))))a#(b(a(a(b(c(b(_x71)))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x81)))))))))))))))))))a#(b(a(a(b(c(b(c(_x81))))))))
c#(a(w(a(w(a(w(w(b(b(_x61))))))))))a#(b(a(a(b(a(a(a(a(_x61)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x91)))))))))))))))))))a#(b(a(a(c(b(b(b(c(_x91)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(a(b(c(b(b(c(b(b(b(_x101))))))))))c#(a(w(_x21)))c#(_x21)
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(v(_x61)))))))))))))))))))))a#(a(b(b(c(_x61)))))c#(a(w(a(w(a(w(w(u(u(_x21))))))))))a#(_x21)
c#(a(w(a(w(a(w(w(b(_x31)))))))))a#(b(a(a(a(a(_x31))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x101))))))))))))))))))a#(a(b(b(c(b(c(b(c(b(b(_x101)))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(_x81)))))))))))))))))a#(b(a(a(b(c(b(c(b(b(_x81))))))))))c#(a(w(a(w(w(u(_x21)))))))a#(_x21)
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(_x71)))))))))))))))a#(a(c(c(b(c(b(b(_x71))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(_x71))))))))))))))))))))a#(a(b(c(b(b(b(_x71)))))))
c#(a(w(a(w(a(w(w(b(b(u(_x91)))))))))))a#(a(b(b(a(a(a(_x91)))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(_x81)))))))))))))))))a#(a(b(c(b(b(b(c(b(b(_x81))))))))))
c#(a(w(a(w(a(w(w(b(u(u(c(c(v(_x81))))))))))))))a#(a(c(b(c(b(_x81))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x91)))))))))))))))))))a#(a(b(c(b(b(b(c(c(b(b(_x91)))))))))))
c#(a(w(a(w(a(a(w(a(_x71)))))))))a#(a(a(a(c(c(a(c(c(_x71)))))))))b#(c(v(c(_x21))))c#(c(b(b(_x21))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(_x81))))))))))))))))))))a#(a(b(c(b(b(b(_x81)))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x71)))))))))))))))))))a#(a(b(c(b(b(c(b(b(_x71)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(a(_x81))))))))))))))))))))a#(a(b(c(b(b(b(a(c(c(_x81))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(_x51))))))))))))))))a#(a(b(b(_x51))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(_x111))))))))))))))))))))a#(a(b(b(c(b(c(c(b(_x111)))))))))c#(a(w(a(w(a(a(w(_x81))))))))a#(a(a(c(a(c(_x81))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(b(a(a(b(c(b(c(b(_x101)))))))))c#(a(w(a(w(a(a(a(_x91))))))))a#(a(a(a(c(c(c(a(c(c(_x91))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(c(_x61)))))))))))))))))))))a#(a(b(b(c(c(b(b(_x61))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(_x81))))))))))))))a#(b(a(a(b(b(a(_x81)))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(_x51))))))))))))))))a#(a(b(c(b(b(b(b(_x51))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x81)))))))))))))))))))a#(a(b(c(b(b(b(c(c(b(b(_x81)))))))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(v(c(_x51))))))))))))))))a#(a(c(c(c(b(b(_x51)))))))b#(c(c(_x21)))b#(c(b(b(_x21))))
c#(a(w(a(w(a(w(w(b(u(b(u(u(v(_x41))))))))))))))a#(a(b(_x41)))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(v(v(_x51))))))))))))))))a#(a(c(c(_x51))))
c#(a(w(a(w(a(w(w(b(u(u(c(c(c(_x81))))))))))))))a#(a(c(b(c(b(c(b(b(_x81)))))))))c#(a(w(a(a(a(_x71))))))a#(a(c(a(c(a(c(c(_x71))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(_x51))))))))))))))))a#(b(a(a(b(c(b(b(_x51))))))))c#(a(w(w(_x21))))a#(_x21)
c#(a(x))c#(x)c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x81)))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(_x81)))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x81)))))))))))))))))))a#(a(b(b(c(c(b(b(c(b(b(_x81)))))))))))a#(b(x))a#(x)
c#(a(w(a(w(a(a(a(_x81))))))))a#(a(a(c(a(c(a(c(c(_x81)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(v(_x81)))))))))))))))))a#(a(b(b(c(b(_x81))))))
c#(a(w(a(w(a(w(w(b(b(b(_x91)))))))))))a#(a(b(b(a(a(a(b(a(a(_x91))))))))))c#(a(a(a(_x61))))a#(c(a(c(a(c(c(_x61)))))))
c#(a(w(a(a(_x51)))))a#(a(a(c(c(c(c(_x51)))))))c#(a(w(a(w(a(w(w(b(u(u(c(c(_x61)))))))))))))a#(a(c(c(b(b(b(b(_x61))))))))
c#(a(w(a(a(w(_x71))))))a#(a(a(c(c(c(_x71))))))c#(a(w(a(w(a(w(w(b(u(u(_x21)))))))))))a#(b(a(a(_x21))))
c#(a(w(a(w(a(w(w(b(u(b(b(_x71))))))))))))a#(a(b(b(a(b(a(a(_x71))))))))c#(a(w(a(w(a(w(w(b(u(b(u(_x71))))))))))))a#(b(a(a(b(a(_x71))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(v(a(a(_x61))))))))))))))))a#(a(a(c(a(c(c(_x61)))))))c#(a(w(a(w(a(a(w(w(_x71)))))))))a#(a(a(a(c(c(_x71))))))
c#(a(w(a(a(w(a(a(_x81))))))))a#(a(c(a(a(c(a(c(c(_x81)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(_x51)))))))))))))a#(b(a(a(b(b(a(a(_x51))))))))
b#(c(c(_x31)))c#(b(c(b(b(_x31)))))c#(a(w(a(w(a(w(w(b(u(b(u(u(c(_x41))))))))))))))a#(a(b(c(b(b(_x41))))))
c#(a(w(a(w(a(w(w(b(b(_x61))))))))))a#(b(a(a(a(b(a(a(_x61))))))))c#(a(w(a(w(a(w(w(b(u(_x61))))))))))a#(b(a(a(a(_x61)))))
b#(c(v(_x21)))b#(_x21)b#(c(x))b#(x)
c#(a(w(a(w(a(w(w(b(u(b(u(u(_x51)))))))))))))a#(b(a(a(b(_x51)))))a#(b(u(_x21)))a#(_x21)
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(_x81)))))))))))))))))a#(a(b(b(c(c(b(b(b(b(_x81))))))))))c#(a(w(a(a(w(a(_x51)))))))a#(a(a(c(a(c(c(c(c(_x51)))))))))
c#(a(w(a(w(a(w(a(_x41))))))))a#(a(a(a(c(c(_x41))))))c#(a(a(_x31)))a#(a(c(c(c(c(_x31))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(a(c(b(b(b(b(b(c(b(_x101))))))))))c#(a(w(a(w(a(w(w(b(u(u(v(_x31))))))))))))a#(a(_x31))
a#(b(b(_x21)))a#(b(a(a(_x21))))c#(a(a(_x21)))c#(a(c(c(_x21))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x61)))))))))))))))))))a#(a(b(b(c(c(b(b(_x61))))))))a#(b(u(_x31)))b#(a(_x31))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(_x61)))))))))))))))a#(b(a(a(b(b(_x61))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x91)))))))))))))))))))a#(a(c(b(b(b(b(b(c(_x91)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(b(_x61)))))))))))))))a#(a(b(b(b(b(a(a(_x61))))))))c#(a(w(a(w(w(b(_x21)))))))a#(b(a(a(_x21))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(v(w(_x31)))))))))))))))a#(a(_x31))c#(a(a(w(w(_x41)))))a#(c(a(_x41)))
c#(a(w(a(w(a(w(w(b(u(b(_x41)))))))))))a#(b(a(a(b(a(a(_x41)))))))c#(a(w(a(a(w(w(_x51)))))))a#(a(c(a(_x51))))
c#(a(w(a(w(a(w(w(u(b(_x21))))))))))a#(b(a(a(_x21))))c#(a(a(w(a(_x41)))))a#(c(a(a(c(c(_x41))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x81)))))))))))))))))))a#(a(b(c(b(b(b(c(_x81))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(a(_x71))))))))))))))))))))a#(a(b(b(c(b(a(c(c(_x71)))))))))
c#(a(a(w(_x61))))a#(a(c(c(c(_x61)))))c#(a(w(a(w(a(w(w(b(u(u(c(v(v(a(w(_x61))))))))))))))))a#(a(a(c(_x61))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(b(_x81))))))))))))))a#(a(b(b(b(a(b(a(a(_x81)))))))))c#(a(w(a(w(a(w(w(b(b(u(_x81)))))))))))a#(a(b(a(b(a(_x81))))))
c#(a(w(a(a(w(a(w(_x81))))))))a#(a(c(a(a(c(_x81))))))c#(a(w(a(a(w(a(a(_x91))))))))a#(a(a(c(c(a(c(a(c(c(_x91))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(a(b(b(c(c(b(b(b(_x101)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(b(a(a(c(b(b(b(c(b(_x101))))))))))
a#(b(b(_x31)))b#(a(b(a(a(_x31)))))c#(a(w(a(a(w(a(w(_x91))))))))a#(a(a(c(c(a(c(_x91)))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(c(_x111))))))))))))))))))))a#(a(b(b(c(b(c(c(b(c(b(b(_x111))))))))))))c#(a(w(a(w(a(w(w(b(b(b(_x81)))))))))))a#(a(b(a(b(a(b(a(a(_x81)))))))))
b#(c(v(v(_x21))))c#(_x21)

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101)))))))))))))))))) → a#(a(b(c(b(b(c(b(b(b(_x101)))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(a(c(b(b(b(b(c(b(b(b(_x101))))))))))) 
a#(a(b(c(b(c(b(b(b(b(b(_x101))))))))))) 
a#(a(b(c(b(b(c(b(b(c(b(b(_x111)))))))))))) 
a#(a(b(c(b(b(c(b(b(_x111))))))))) 
a#(b(a(a(c(b(b(c(b(b(b(_x101))))))))))) 
Thus, the rule c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101)))))))))))))))))) → a#(a(b(c(b(b(c(b(b(b(_x101)))))))))) is replaced by the following rules:
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101)))))))))))))))))) → a#(b(a(a(c(b(b(c(b(b(b(_x101)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111))))))))))))))))))) → a#(a(b(c(b(b(c(b(b(c(b(b(_x111))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101)))))))))))))))))) → a#(a(c(b(b(b(b(c(b(b(b(_x101)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101)))))))))))))))))) → a#(a(b(c(b(c(b(b(b(b(b(_x101)))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x111))))))))))))))))))) → a#(a(b(c(b(b(c(b(b(_x111)))))))))

Problem 22: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(_x111))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(_x111))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(b(a(a(c(c(b(b(b(b(b(b(c(b(b(_x111)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x91)))))))))))))))))))a#(b(a(a(c(b(b(b(c(_x91)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x131)))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(b(c(b(b(_x131)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(_x81)))))))))))))))))a#(b(a(a(b(c(b(c(b(b(_x81))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(b(c(b(b(b(b(_x151)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(u(_x121)))))))))))))a#(b(a(a(b(b(a(a(a(a(a(_x121)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(b(_x161))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(_x71))))))))))))))))))a#(a(c(b(b(b(c(b(b(_x71)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(c(_x61)))))))))))))))))))))a#(a(b(b(c(c(b(b(_x61))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(_x81))))))))))))))a#(b(a(a(b(b(a(_x81)))))))c#(a(w(a(w(a(w(w(b(b(u(b(u(u(_x81))))))))))))))a#(a(b(b(a(a(b(_x81)))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(_x141))))))))))))))))))))a#(a(b(c(b(c(b(b(b(b(c(b(_x141))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x81)))))))))))))))))))a#(a(b(c(b(b(b(c(c(b(b(_x81)))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(b(b(b(c(b(_x161))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x141))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(b(c(b(c(b(b(_x141))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x101))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(b(b(_x101))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(v(c(_x51))))))))))))))))a#(a(c(c(c(b(b(_x51)))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(c(v(c(_x111))))))))))))))))))))a#(a(c(c(c(b(b(b(c(c(c(b(b(_x111)))))))))))))b#(c(c(_x21)))b#(c(b(b(_x21))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(c(b(b(b(b(b(b(_x151))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(b(b(c(b(_x161))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(v(_x91)))))))))))))))))))))a#(b(a(a(b(c(b(c(c(_x91)))))))))c#(a(w(a(w(a(w(w(b(b(u(_x91)))))))))))a#(b(a(a(b(a(a(a(_x91))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(v(_x121)))))))))))))))))))a#(a(b(b(c(b(c(b(c(b(_x121))))))))))c#(a(w(w(_x21))))a#(_x21)
a#(b(x))a#(x)c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(c(v(_x131)))))))))))))))))))a#(a(c(c(c(b(b(c(b(b(c(b(_x131))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(v(_x81)))))))))))))))))a#(a(b(b(c(b(_x81))))))c#(a(a(a(_x61))))a#(c(a(c(a(c(c(_x61)))))))
c#(a(w(a(w(a(w(w(b(b(b(_x91)))))))))))a#(a(b(b(a(a(a(b(a(a(_x91))))))))))c#(a(w(a(a(_x51)))))a#(a(a(c(c(c(c(_x51)))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(v(_x141))))))))))))))))))))a#(a(b(b(c(b(c(b(c(b(c(b(_x141))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x181)))))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(c(b(b(b(c(b(_x181))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(_x161)))))))))))))))))))))a#(a(b(b(c(b(c(b(c(b(c(b(c(b(c(b(b(_x161)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(c(_x61)))))))))))))a#(a(c(c(b(b(b(b(_x61))))))))
c#(a(w(a(a(w(_x71))))))a#(a(a(c(c(c(_x71))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x121)))))))))))))))))))a#(a(b(c(b(b(b(c(c(b(b(c(b(b(b(b(_x121))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(b(_x71))))))))))))a#(a(b(b(a(b(a(a(_x71))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x191)))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(b(c(b(b(b(b(b(_x191))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(v(a(a(_x61))))))))))))))))a#(a(a(c(a(c(c(_x61)))))))c#(a(w(a(w(a(w(w(b(u(b(u(_x71))))))))))))a#(b(a(a(b(a(_x71))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(a(c(b(b(b(b(c(b(b(b(_x101)))))))))))c#(a(w(a(a(w(a(a(_x81))))))))a#(a(c(a(a(c(a(c(c(_x81)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(_x71))))))))))))))))))))a#(b(a(a(c(b(b(b(_x71))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(_x51)))))))))))))a#(b(a(a(b(b(a(a(_x51))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(u(c(_x41))))))))))))))a#(a(b(c(b(b(_x41))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x141))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(b(c(b(c(b(b(_x141))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x151))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(b(c(_x151))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x181)))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(b(_x181))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(_x61))))))))))a#(b(a(a(a(_x61)))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(_x111))))))))))))))))))))a#(a(b(c(b(b(b(c(c(b(_x111))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x141))))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(b(c(b(c(b(b(_x141))))))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(v(_x91))))))))))))))))a#(a(c(c(c(b(b(b(_x91))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(c(b(b(c(b(b(b(b(_x151)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(a(b(c(b(b(c(b(b(b(c(c(b(b(c(b(b(b(b(_x151)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(c(_x151))))))))))))))))))))a#(b(a(a(c(c(b(b(b(b(b(b(c(b(c(b(b(_x151)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(a(b(b(c(b(c(b(c(b(c(c(b(b(b(_x161)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(_x81)))))))))))))))))a#(a(c(b(b(b(b(b(c(b(b(_x81)))))))))))c#(a(w(a(w(a(w(w(b(b(u(b(b(_x101)))))))))))))a#(a(b(b(a(a(b(a(b(a(a(_x101)))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(v(_x81)))))))))))))))))))))a#(a(b(c(b(b(_x81))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(_x201)))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(b(c(b(b(b(b(b(c(b(b(_x201)))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(_x71))))))))))))))))))a#(b(a(a(c(b(c(b(b(_x71)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(b(a(a(c(b(b(c(b(b(c(b(b(_x111)))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x191)))))))))))))))))))))a#(a(b(b(c(c(b(b(c(b(b(c(b(b(c(b(b(b(_x191))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x121)))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(b(b(b(b(_x121)))))))))))))))
b#(c(x))b#(x)c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(c(_x81)))))))))))))))))))))a#(a(b(c(b(b(c(b(b(_x81)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(_x71))))))))))))))))))))a#(a(c(b(b(b(b(b(_x71))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(b(c(b(c(b(_x161)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(_x181)))))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(c(b(b(b(c(b(c(b(b(_x181)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(_x81)))))))))))))))))a#(a(b(b(c(c(b(b(b(b(_x81))))))))))
c#(a(w(a(a(w(a(_x51)))))))a#(a(a(c(a(c(c(c(c(_x51)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(_x161))))))))))))))))))))a#(a(b(c(c(b(b(b(b(b(c(b(b(b(_x161))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(u(b(_x101))))))))))))))a#(a(b(b(b(a(a(a(a(b(a(a(_x101))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x141))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(b(c(b(b(_x141))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(c(c(_x131)))))))))))))))))))a#(a(c(c(c(b(b(b(c(c(b(c(b(b(_x131))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(c(_x151))))))))))))))))))))a#(a(c(b(b(c(b(b(b(b(b(b(c(c(b(b(b(b(_x151))))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(u(_x101)))))))))))))a#(a(b(b(a(b(a(a(a(_x101)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(a(c(b(b(b(b(b(c(b(_x101))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x111))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(b(b(_x111))))))))))))c#(a(w(a(w(a(w(w(b(u(u(v(_x31))))))))))))a#(a(_x31))
a#(b(b(_x21)))a#(b(a(a(_x21))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x61)))))))))))))))))))a#(a(b(b(c(c(b(b(_x61))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x171)))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(b(c(b(_x171)))))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(c(c(_x141))))))))))))))))))a#(a(c(c(c(b(b(c(b(b(b(c(b(c(b(b(_x141))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(_x141))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(b(c(b(c(c(b(b(_x141))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(b(a(a(c(b(b(c(b(b(b(_x101)))))))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(v(w(_x91)))))))))))))))))))a#(a(c(c(c(b(b(b(_x91))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(a(b(b(c(c(b(b(c(b(b(c(b(b(c(b(b(b(b(_x151)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(c(_x151))))))))))))))))))))a#(b(a(a(c(c(b(b(b(b(b(b(c(c(b(b(b(b(_x151))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x91)))))))))))))))))))a#(a(c(b(b(b(b(b(c(_x91)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(a(b(c(b(b(b(c(c(b(b(c(b(b(c(b(b(b(b(_x151)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x101))))))))))))))))))a#(a(b(c(b(b(c(b(b(b(c(b(b(_x101)))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x111))))))))))))))))))a#(a(b(c(b(b(b(c(b(_x111)))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(c(_x111)))))))))))))))))a#(a(c(c(c(b(b(b(c(c(b(b(b(b(_x111))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x101))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(b(b(_x101))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(c(c(v(_x161)))))))))))))))))))a#(a(c(c(b(c(c(b(b(b(c(b(c(b(_x161))))))))))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(v(_x81))))))))))))))))))a#(a(c(c(c(b(b(c(b(b(_x81))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(b(_x61)))))))))))))))a#(a(b(b(b(b(a(a(_x61))))))))
c#(a(w(a(w(w(b(_x21)))))))a#(b(a(a(_x21))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(c(v(_x141))))))))))))))))))a#(a(c(c(b(c(b(c(c(b(b(b(_x141))))))))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(v(w(_x31)))))))))))))))a#(a(_x31))c#(a(a(w(w(_x41)))))a#(c(a(_x41)))
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c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(v(w(_x81))))))))))))))))))))))a#(a(b(b(c(b(c(_x81)))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(_x91))))))))))))))))a#(a(c(c(c(b(b(b(c(b(b(_x91)))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(a(c(b(b(b(b(c(b(b(c(b(b(_x111)))))))))))))b#(c(c(_x31)))c#(b(c(b(b(_x31)))))
c#(a(w(a(w(a(w(w(b(b(_x61))))))))))a#(b(a(a(a(b(a(a(_x61))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x101))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(b(b(_x101))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(b(b(b(c(b(b(_x151)))))))))))))))))c#(a(w(a(w(a(w(w(b(b(u(b(b(_x111)))))))))))))a#(a(b(b(a(b(a(a(a(b(a(a(_x111))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(a(b(b(c(c(b(b(c(b(b(c(b(c(b(b(b(b(b(b(_x151))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(b(b(c(b(b(_x151)))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(_x71))))))))))))a#(b(a(a(b(a(b(a(a(a(a(_x71)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x131)))))))))))))))))))a#(a(b(c(b(b(c(b(b(b(c(b(c(b(b(_x131)))))))))))))))
b#(c(v(_x21)))b#(_x21)c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(c(c(_x141))))))))))))))))))a#(a(c(c(b(c(c(b(b(c(b(b(b(c(b(b(_x141))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x101))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(b(b(_x101)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(u(_x51)))))))))))))a#(b(a(a(b(_x51)))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(b(a(a(c(b(c(b(b(b(b(c(b(b(_x111))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(v(_x61)))))))))))))))))))))a#(b(a(a(b(c(_x61))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(c(_x111)))))))))))))))))a#(a(c(c(c(b(b(b(c(b(c(b(b(_x111)))))))))))))a#(b(u(_x21)))a#(_x21)
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(c(_x151))))))))))))))))))))a#(a(c(b(b(c(b(b(b(b(b(b(c(b(c(b(b(_x151)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x121)))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(b(c(b(b(_x121))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(c(_x161))))))))))))))))))))a#(a(b(c(c(b(b(b(b(b(c(b(b(b(c(b(b(_x161)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(c(v(_x141))))))))))))))))))a#(a(c(c(b(c(c(b(b(b(c(b(_x141))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(_x41)))))))))))))))))a#(b(a(a(c(b(b(_x41)))))))c#(a(w(a(w(a(w(w(b(b(u(b(_x71))))))))))))a#(b(a(a(b(a(a(b(a(a(_x71))))))))))
c#(a(w(a(w(a(w(a(_x41))))))))a#(a(a(a(c(c(_x41))))))c#(a(a(_x31)))a#(a(c(c(c(c(_x31))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(_x71))))))))))))))))))a#(a(b(c(c(b(b(b(b(_x71)))))))))c#(a(a(_x21)))c#(a(c(c(_x21))))
a#(b(u(_x31)))b#(a(_x31))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x121)))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(b(c(b(b(_x121))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(_x171)))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(b(c(b(c(b(b(_x171))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(_x61)))))))))))))))a#(b(a(a(b(b(_x61))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(v(a(_x91)))))))))))))))))))a#(a(c(c(c(b(b(b(a(c(c(_x91)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(a(b(c(b(b(c(b(b(b(c(c(b(c(b(b(b(b(b(b(_x151))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(b(_x121)))))))))))))a#(a(b(b(b(a(a(a(a(a(b(a(a(_x121)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x191)))))))))))))))))))))a#(a(b(c(b(b(c(b(b(b(c(c(b(b(c(b(b(b(_x191))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(v(w(_x51))))))))))))))))))))))a#(a(b(b(_x51))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(c(_x91))))))))))))))))))a#(a(c(c(b(c(b(c(c(b(b(_x91)))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(v(_x41)))))))))))))))))))))a#(a(b(c(b(b(_x41))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(_x71)))))))))))))))a#(a(c(c(c(b(b(b(b(_x71)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x101))))))))))))))))))a#(a(b(b(c(c(b(b(c(b(b(b(b(_x101)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(v(_x91)))))))))))))))))))))a#(a(b(b(c(c(b(b(c(_x91)))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(u(_x111)))))))))))))a#(a(b(b(a(b(a(a(a(_x111)))))))))c#(a(w(a(w(a(w(w(b(b(u(u(_x71))))))))))))a#(a(b(b(a(a(_x71))))))
c#(a(w(a(w(a(w(w(b(u(b(_x41)))))))))))a#(b(a(a(b(a(a(_x41)))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(c(b(b(b(c(b(_x161))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(c(c(c(_x161)))))))))))))))))))a#(a(c(c(b(c(c(b(b(b(c(b(c(b(c(b(b(_x161)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x121)))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(b(c(b(b(_x121))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(a(b(c(b(c(b(b(b(c(b(b(b(b(_x111))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(c(c(_x181)))))))))))))))))))))a#(a(b(c(c(b(b(b(b(b(b(c(c(b(b(b(c(b(b(_x181)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(c(c(_x141))))))))))))))))))a#(a(c(c(b(c(b(c(c(b(b(b(c(b(b(_x141)))))))))))))))c#(a(a(w(a(_x41)))))a#(c(a(a(c(c(_x41))))))
c#(a(w(a(w(a(w(w(u(b(_x21))))))))))a#(b(a(a(_x21))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(b(c(b(c(b(b(_x151))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(v(c(_x71)))))))))))))))))a#(a(c(c(b(c(c(b(b(_x71)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(a(b(c(c(b(b(b(b(c(b(b(b(b(b(b(_x111))))))))))))))))
c#(a(a(w(_x61))))a#(a(c(c(c(_x61)))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(b(b(b(c(b(_x161))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(_x81)))))))))))a#(a(b(a(b(a(_x81))))))c#(a(w(a(a(w(a(w(_x81))))))))a#(a(c(a(a(c(_x81))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(b(b(c(b(b(b(b(_x151))))))))))))))))))c#(a(w(a(a(w(a(a(_x91))))))))a#(a(a(c(c(a(c(a(c(c(_x91))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x201)))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(b(c(b(b(b(b(b(_x201))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(a(b(b(c(c(b(b(b(_x101)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(a(c(b(b(c(b(b(b(b(b(c(b(b(b(b(_x111))))))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(c(_x111)))))))))))))))))a#(a(c(c(c(b(b(c(b(b(b(c(b(b(_x111))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(v(_x131)))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(b(_x131)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(b(a(a(c(c(b(b(b(b(b(c(b(b(b(b(_x111))))))))))))))))
c#(a(w(a(a(w(a(w(_x91))))))))a#(a(a(c(c(a(c(_x91)))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(v(a(_x51))))))))))))))))))))))a#(a(b(b(a(c(c(_x51)))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(c(_x101))))))))))))))))))a#(a(c(c(c(b(b(c(b(b(c(b(b(_x101)))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(v(_x91))))))))))))))))))a#(a(c(c(b(c(b(c(_x91))))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(c(v(_x131))))))))))))))))))a#(a(c(c(b(c(b(c(b(c(b(_x131)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(a(c(b(b(c(b(b(b(b(b(b(c(b(b(_x111)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x111)))))))))))))))))))a#(a(b(c(b(b(c(b(b(_x111)))))))))b#(c(v(v(_x21))))c#(_x21)

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161))))))))))))))))))))) → a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(b(_x161)))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(a(b(c(b(b(b(c(b(c(c(b(b(c(b(b(b(_x161))))))))))))))))) 
a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(_x171))))))))))))))) 
a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(c(b(b(_x171)))))))))))))))))) 
a#(a(b(b(c(b(c(c(b(b(c(b(b(c(b(b(b(_x161))))))))))))))))) 
a#(b(a(a(b(c(b(c(b(c(c(b(b(c(b(b(b(_x161))))))))))))))))) 
a#(a(b(b(c(b(c(b(c(c(b(c(b(b(b(b(b(_x161))))))))))))))))) 
a#(a(b(b(c(c(b(b(b(c(c(b(b(c(b(b(b(_x161))))))))))))))))) 
Thus, the rule c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161))))))))))))))))))))) → a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(b(_x161)))))))))))))))) is replaced by the following rules:
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161))))))))))))))))))))) → a#(a(b(b(c(b(c(b(c(c(b(c(b(b(b(b(b(_x161)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161))))))))))))))))))))) → a#(a(b(b(c(c(b(b(b(c(c(b(b(c(b(b(b(_x161)))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161))))))))))))))))))))) → a#(a(b(c(b(b(b(c(b(c(c(b(b(c(b(b(b(_x161)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x171)))))))))))))))))))))) → a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(_x171)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(_x171)))))))))))))))))))))) → a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(c(b(b(_x171))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161))))))))))))))))))))) → a#(a(b(b(c(b(c(c(b(b(c(b(b(c(b(b(b(_x161)))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161))))))))))))))))))))) → a#(b(a(a(b(c(b(c(b(c(c(b(b(c(b(b(b(_x161)))))))))))))))))

Problem 23: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(_x111))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(_x111))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(b(a(a(c(c(b(b(b(b(b(b(c(b(b(_x111)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(b(c(b(b(b(_x161)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x101))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(b(b(_x101)))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x131)))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(b(c(b(b(_x131)))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(_x81)))))))))))))))))a#(b(a(a(b(c(b(c(b(b(_x81))))))))))
c#(a(a(a(w(_x81)))))a#(c(a(a(c(c(c(_x81)))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(b(c(b(b(b(b(_x151)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(u(u(_x81))))))))))))))a#(b(a(a(b(a(a(b(_x81))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(_x81))))))))))))))a#(b(a(a(b(b(a(_x81)))))))
b#(c(c(_x21)))b#(c(b(b(_x21))))c#(a(w(w(_x21))))a#(_x21)
a#(b(x))a#(x)c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x181)))))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(c(b(b(b(c(b(_x181))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(v(_x141))))))))))))))))))))))))a#(a(c(c(b(b(b(b(b(c(c(b(_x141))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x191)))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(b(c(b(b(b(b(b(_x191))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(_x71))))))))))))a#(b(a(a(b(a(_x71))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(c(_x111))))))))))))))))))))))a#(a(c(b(b(c(c(b(b(b(c(b(b(_x111)))))))))))))
c#(a(w(a(a(w(a(a(_x81))))))))a#(a(c(a(a(c(a(c(c(_x81)))))))))c#(a(a(a(a(_x81)))))a#(c(a(c(a(c(a(c(c(_x81)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x151))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(b(c(_x151))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(_x101)))))))))))))))))))))))a#(a(c(c(b(b(b(b(c(b(b(c(b(b(_x101))))))))))))))
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c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(v(_x121)))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(b(_x121)))))))))))c#(a(w(a(w(a(w(w(b(b(u(_x81)))))))))))a#(a(b(a(b(a(_x81))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(_x101)))))))))))))))))))))))a#(a(c(c(b(b(b(b(b(c(_x101))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(v(c(v(_x91)))))))))))))))))))a#(a(b(b(c(c(b(_x91)))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(a(b(b(c(c(b(b(b(_x101)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(b(a(a(c(c(b(b(b(b(b(c(b(b(b(b(_x111))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x181))))))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(c(b(c(b(b(b(b(_x181))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(c(v(v(_x111))))))))))))))))))))))))))a#(a(c(b(c(b(b(c(b(c(_x111))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(_x101)))))))))))))))))))))a#(a(c(b(c(b(b(b(c(b(b(_x101)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(v(a(_x51))))))))))))))))))))))a#(a(b(b(a(c(c(_x51)))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(c(_x111))))))))))))))))))))))))a#(a(c(c(b(b(b(c(b(b(b(c(b(b(_x111))))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(c(_x101))))))))))))))))))a#(a(c(c(c(b(b(c(b(b(c(b(b(_x101)))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(a(c(b(b(c(b(b(b(b(b(b(c(b(b(_x111)))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x111)))))))))))))))))))a#(a(b(c(b(b(c(b(b(_x111)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(_x141))))))))))))))))))))a#(b(a(a(c(b(c(b(b(b(b(c(b(_x141)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(v(c(c(_x91)))))))))))))))))))a#(a(b(b(c(c(b(c(b(b(_x91))))))))))
b#(c(v(v(_x21))))c#(_x21)

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(a(a(w(_x81))))) → a#(c(a(a(c(c(c(_x81))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(a(c(c(a(c(c(c(_x81)))))))) 
a#(c(a(a(c(c(_x71)))))) 
a#(c(a(a(c(c(a(c(c(_x71))))))))) 
Thus, the rule c#(a(a(a(w(_x81))))) → a#(c(a(a(c(c(c(_x81))))))) is replaced by the following rules:
c#(a(a(a(w(a(_x71)))))) → a#(c(a(a(c(c(a(c(c(_x71)))))))))c#(a(a(a(w(w(_x71)))))) → a#(c(a(a(c(c(_x71))))))
c#(a(a(a(w(_x81))))) → a#(a(c(c(a(c(c(c(_x81))))))))

Problem 24: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(_x111))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(_x111))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(b(a(a(c(c(b(b(b(b(b(b(c(b(b(_x111)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(_x181)))))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(b(c(b(b(c(b(_x181)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(b(c(b(b(b(_x161)))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x101))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(b(b(_x101)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x131)))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(b(c(b(b(_x131)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(_x81)))))))))))))))))a#(b(a(a(b(c(b(c(b(b(_x81))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221))))))))))))))))))))))a#(b(a(a(c(b(b(c(b(c(b(b(b(b(c(b(c(b(b(b(b(_x221)))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(b(c(b(b(b(b(_x151)))))))))))))))))))c#(a(w(a(w(a(w(w(b(b(u(b(u(u(_x81))))))))))))))a#(b(a(a(b(a(a(b(_x81))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(_x81))))))))))))))a#(b(a(a(b(b(a(_x81)))))))b#(c(c(_x21)))b#(c(b(b(_x21))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221))))))))))))))))))))))a#(a(b(c(b(b(c(c(b(b(b(b(b(b(c(b(c(b(b(b(b(_x221)))))))))))))))))))))c#(a(w(w(_x21))))a#(_x21)
a#(b(x))a#(x)c#(a(w(a(w(a(w(w(b(u(b(u(_x71))))))))))))a#(b(a(a(b(a(_x71))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(_x151))))))))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(c(b(b(c(b(c(b(b(_x151)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(c(_x101)))))))))))))))))))))a#(b(a(a(c(b(b(b(c(c(c(b(b(_x101)))))))))))))
c#(a(w(a(w(a(w(w(b(u(_x61))))))))))a#(b(a(a(a(_x61)))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(c(b(b(c(b(b(b(b(_x151)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(_x81)))))))))))))))))a#(a(c(b(b(b(b(b(c(b(b(_x81)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(v(_x101)))))))))))))))))))))a#(a(c(b(c(b(b(b(_x101))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(c(_x131))))))))))))))))))))))a#(a(c(b(c(b(b(c(b(b(b(c(b(b(_x131))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221))))))))))))))))))))))a#(a(b(c(b(c(b(b(b(c(b(b(b(b(c(b(c(b(b(b(b(_x221)))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(b(_x101)))))))))))))a#(a(b(b(a(a(b(a(b(a(a(_x101)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(b(a(a(c(b(b(c(b(b(c(b(b(_x111)))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(_x71))))))))))))))))))a#(b(a(a(c(b(c(b(b(_x71)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x121)))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(b(b(b(b(_x121)))))))))))))))
c#(a(a(a(a(a(_x101))))))a#(c(a(c(a(c(a(c(a(c(c(_x101)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(c(_x81)))))))))))))))))))))a#(a(b(c(b(b(c(b(b(_x81)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x181))))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(c(b(b(b(b(_x181)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(_x71))))))))))))))))))))a#(a(c(b(b(b(b(b(_x71))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x181)))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(b(b(c(b(_x181)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(b(c(b(c(b(_x161)))))))))))))))
c#(a(a(a(a(w(_x131))))))a#(c(a(a(c(a(c(c(c(c(c(_x131)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x191)))))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(c(b(c(b(b(b(b(b(_x191)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(_x81)))))))))))))))))a#(a(b(b(c(c(b(b(b(b(_x81))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(_x171))))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(c(b(b(b(b(c(_x171)))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(u(b(_x101))))))))))))))a#(a(b(b(b(a(a(a(a(b(a(a(_x101))))))))))))c#(a(w(a(a(w(a(_x51)))))))a#(a(a(c(a(c(c(c(c(_x51)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(v(_x91)))))))))))))))))))))a#(a(c(b(c(b(b(b(_x91))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x191)))))))))))))))))))))a#(a(b(c(b(b(c(b(c(b(b(b(c(b(b(b(c(b(b(b(b(b(_x191))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(c(c(_x131)))))))))))))))))))a#(a(c(c(c(b(b(b(c(c(b(c(b(b(_x131))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(_x101)))))))))))))))))))))))a#(a(c(c(b(b(b(c(b(b(b(b(c(b(b(_x101)))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(u(_x101)))))))))))))a#(a(b(b(a(b(a(a(a(_x101)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x181)))))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(c(b(b(c(b(b(b(_x181)))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x181))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(b(c(b(b(b(b(_x181)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(_x191)))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(c(b(b(b(b(b(c(b(b(_x191))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(b(c(c(b(b(c(b(c(b(b(b(c(b(b(_x181)))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(a(c(b(b(b(b(b(c(b(_x101))))))))))
c#(a(w(a(w(a(w(w(b(u(u(v(_x31))))))))))))a#(a(_x31))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(v(v(_x121)))))))))))))))))))))))))a#(a(c(c(b(b(b(b(b(c(c(_x121)))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(_x201))))))))))))))))))))))a#(a(b(c(b(c(b(b(b(b(b(c(c(b(c(b(b(b(b(c(b(b(_x201))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(v(w(_x91)))))))))))))))))))a#(a(c(c(c(b(b(b(_x91))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(_x231))))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(b(b(c(b(c(b(b(b(c(b(_x231)))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(_x151))))))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(b(c(b(c(b(b(_x151))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(c(_x151))))))))))))))))))))a#(b(a(a(c(c(b(b(b(b(b(b(c(c(b(b(b(b(_x151))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(c(_x131))))))))))))))))))))))))a#(a(c(b(c(b(b(b(c(c(b(c(b(b(_x131))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(c(c(_x131)))))))))))))))))))))))))a#(a(c(b(c(b(b(c(b(c(b(c(b(b(_x131))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x91)))))))))))))))))))a#(a(c(b(b(b(b(b(c(_x91)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x101))))))))))))))))))a#(a(b(c(b(b(c(b(b(b(c(b(b(_x101)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(c(_x171))))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(c(c(b(b(_x171)))))))))))))))))))
c#(a(a(a(w(w(a(w(_x91))))))))a#(c(a(a(c(a(c(_x91)))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x111))))))))))))))))))a#(a(b(c(b(b(b(c(b(_x111)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(_x111)))))))))))))))))))))))a#(a(c(b(c(b(c(b(b(b(b(c(b(b(_x111))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(c(b(c(b(b(_x181))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(c(v(_x171)))))))))))))))))))))))))a#(a(c(c(b(b(b(b(c(b(b(c(b(c(b(_x171)))))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(v(_x81))))))))))))))))))a#(a(c(c(c(b(b(c(b(b(_x81))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(_x151))))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(b(b(c(b(c(b(b(_x151))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(_x181)))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(c(b(c(b(b(b(_x181))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(b(_x61)))))))))))))))a#(a(b(b(b(b(a(a(_x61))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(b(c(b(b(b(c(c(b(b(b(c(c(b(b(c(b(c(b(b(_x181)))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(_x111)))))))))))))))))))))a#(a(c(c(b(b(b(b(b(c(b(b(_x111))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(w(_x141)))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(b(_x141)))))))))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(c(v(_x141))))))))))))))))))a#(a(c(c(b(c(b(c(c(b(b(b(_x141))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(v(c(_x71))))))))))))))))))))))a#(a(c(b(b(c(c(b(b(_x71)))))))))
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c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(v(_x141))))))))))))))))))))))))a#(a(c(c(b(b(b(b(c(b(c(b(b(b(_x141))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(_x111)))))))))))))))))))))))a#(a(c(c(b(b(b(b(c(b(c(b(b(b(b(_x111)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(v(_x121)))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(b(_x121)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(b(c(b(b(c(b(b(b(c(c(b(b(c(b(c(b(b(b(c(b(b(_x181)))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(_x81)))))))))))a#(a(b(a(b(a(_x81))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221))))))))))))))))))))))a#(a(c(b(b(b(b(c(b(c(b(b(b(b(c(b(c(b(b(b(b(_x221)))))))))))))))))))))
c#(a(a(a(a(_x81)))))a#(a(c(c(a(c(c(a(c(c(c(c(_x81))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(_x101)))))))))))))))))))))))a#(a(c(c(b(b(b(b(b(c(_x101))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(v(c(v(_x91)))))))))))))))))))a#(a(b(b(c(c(b(_x91)))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(a(b(b(c(c(b(b(b(_x101)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(v(_x141))))))))))))))))))))))))a#(a(c(c(b(b(b(c(b(b(b(b(c(b(_x141))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(b(a(a(c(c(b(b(b(b(b(c(b(b(b(b(_x111))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x181))))))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(c(b(c(b(b(b(b(_x181))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(c(v(v(_x111))))))))))))))))))))))))))a#(a(c(b(c(b(b(c(b(c(_x111))))))))))
c#(a(a(a(w(w(w(_x81)))))))a#(a(c(c(a(c(_x81))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(_x101)))))))))))))))))))))a#(a(c(b(c(b(b(b(c(b(b(_x101)))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(v(a(_x51))))))))))))))))))))))a#(a(b(b(a(c(c(_x51)))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(c(_x111))))))))))))))))))))))))a#(a(c(c(b(b(b(c(b(b(b(c(b(b(_x111))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(_x101)))))))))))))))))))))))a#(a(c(c(b(b(b(b(c(b(c(b(b(b(b(_x101)))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(v(c(_x131)))))))))))))))))))))))))a#(a(c(c(b(b(b(b(c(b(b(c(c(b(b(_x131)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(c(_x101))))))))))))))))))a#(a(c(c(c(b(b(c(b(b(c(b(b(_x101)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(_x151))))))))))))))))))))))))a#(a(b(b(c(c(b(b(c(b(b(c(b(b(c(b(c(b(b(_x151)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(a(c(b(b(c(b(b(b(b(b(b(c(b(b(_x111)))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x111)))))))))))))))))))a#(a(b(c(b(b(c(b(b(_x111)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(_x141))))))))))))))))))))a#(b(a(a(c(b(c(b(b(b(b(c(b(_x141)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(v(c(c(_x91)))))))))))))))))))a#(a(b(b(c(c(b(c(b(b(_x91))))))))))
b#(c(v(v(_x21))))c#(_x21)c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(b(c(b(b(b(c(c(b(b(c(b(b(c(b(c(b(b(b(c(b(b(_x181)))))))))))))))))))))))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221)))))))))))))))))))))) → a#(a(b(c(b(b(c(c(b(b(b(b(b(b(c(b(c(b(b(b(b(_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
a#(a(b(c(b(b(c(c(b(b(b(b(b(b(c(b(c(b(b(b(_x231)))))))))))))))))))) 
a#(a(b(c(b(c(b(b(c(b(b(b(b(b(b(c(b(c(b(b(b(b(_x221)))))))))))))))))))))) 
a#(a(b(c(b(b(c(c(b(b(b(b(b(b(c(b(c(b(b(b(c(b(b(_x231))))))))))))))))))))))) 
a#(a(b(c(b(b(c(c(b(b(b(b(b(c(b(b(b(c(b(b(b(b(_x221)))))))))))))))))))))) 
a#(a(b(c(b(b(c(c(b(b(b(b(b(b(c(c(b(b(b(b(b(b(_x221)))))))))))))))))))))) 
a#(a(c(b(b(b(b(c(c(b(b(b(b(b(b(c(b(c(b(b(b(b(_x221)))))))))))))))))))))) 
a#(b(a(a(c(b(b(c(c(b(b(b(b(b(b(c(b(c(b(b(b(b(_x221)))))))))))))))))))))) 
Thus, the rule c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221)))))))))))))))))))))) → a#(a(b(c(b(b(c(c(b(b(b(b(b(b(c(b(c(b(b(b(b(_x221))))))))))))))))))))) is replaced by the following rules:
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221)))))))))))))))))))))) → a#(a(b(c(b(b(c(c(b(b(b(b(b(c(b(b(b(c(b(b(b(b(_x221))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(c(_x231))))))))))))))))))))))) → a#(a(b(c(b(b(c(c(b(b(b(b(b(b(c(b(c(b(b(b(c(b(b(_x231)))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221)))))))))))))))))))))) → a#(a(b(c(b(c(b(b(c(b(b(b(b(b(b(c(b(c(b(b(b(b(_x221))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(v(_x231))))))))))))))))))))))) → a#(a(b(c(b(b(c(c(b(b(b(b(b(b(c(b(c(b(b(b(_x231))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221)))))))))))))))))))))) → a#(a(c(b(b(b(b(c(c(b(b(b(b(b(b(c(b(c(b(b(b(b(_x221))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221)))))))))))))))))))))) → a#(a(b(c(b(b(c(c(b(b(b(b(b(b(c(c(b(b(b(b(b(b(_x221))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221)))))))))))))))))))))) → a#(b(a(a(c(b(b(c(c(b(b(b(b(b(b(c(b(c(b(b(b(b(_x221))))))))))))))))))))))

Problem 25: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(_x181)))))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(b(c(b(b(c(b(_x181)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(b(c(b(b(b(_x161)))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x101))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(b(b(_x101)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x131)))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(b(c(b(b(_x131)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221))))))))))))))))))))))a#(b(a(a(c(b(b(c(b(c(b(b(b(b(c(b(c(b(b(b(b(_x221)))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(b(c(b(b(b(b(_x151)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(u(u(_x81))))))))))))))a#(b(a(a(b(a(a(b(_x81))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(_x81))))))))))))))a#(b(a(a(b(b(a(_x81)))))))
b#(c(c(_x21)))b#(c(b(b(_x21))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(_x261))))))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(b(b(c(c(b(b(b(b(b(c(c(b(c(b(b(_x261))))))))))))))))))))))))))
a#(b(x))a#(x)c#(a(w(a(w(a(w(w(b(u(b(u(_x71))))))))))))a#(b(a(a(b(a(_x71))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(_x221)))))))))))))))))))))))))a#(a(b(c(b(b(b(c(c(b(c(b(b(b(b(c(b(c(b(b(b(c(c(b(b(_x221)))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(_x71))))))))))))))))))a#(b(a(a(c(b(c(b(b(_x71)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(b(a(a(c(b(b(c(b(b(c(b(b(_x111)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x181))))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(c(b(b(b(b(_x181)))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x191)))))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(c(b(c(b(b(b(b(b(_x191)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(_x151))))))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(b(c(b(c(b(b(_x151))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(c(c(_x111))))))))))))))))))))))a#(a(c(b(b(b(b(c(c(b(b(b(b(_x111)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(v(v(_x211))))))))))))))))))))))))a#(a(b(c(b(c(b(b(b(c(b(b(b(b(c(b(c(b(b(_x211)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(c(_x131))))))))))))))))))))))))a#(a(c(b(c(b(b(b(c(c(b(c(b(b(_x131))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(c(c(_x131)))))))))))))))))))))))))a#(a(c(b(c(b(b(c(b(c(b(c(b(b(_x131))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x101))))))))))))))))))a#(a(b(c(b(b(c(b(b(b(c(b(b(_x101)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(c(_x171))))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(c(c(b(b(_x171)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(c(v(_x171)))))))))))))))))))))))))a#(a(c(c(b(b(b(b(c(b(b(c(b(c(b(_x171)))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(_x151))))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(b(b(c(b(c(b(b(_x151))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(_x111)))))))))))))))))))))a#(a(c(c(b(b(b(b(b(c(b(b(_x111))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(b(c(b(b(b(c(c(b(b(b(c(c(b(b(c(b(c(b(b(_x181)))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(w(_x141)))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(b(_x141)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(v(c(_x71))))))))))))))))))))))a#(a(c(b(b(c(c(b(b(_x71)))))))))
c#(a(w(a(w(a(w(w(b(u(u(v(b(_x21)))))))))))))a#(b(a(a(_x21))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(_x191)))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(b(b(c(b(b(b(c(b(b(_x191))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(v(_x231)))))))))))))))))))))))a#(a(c(b(b(b(c(b(b(b(c(b(b(b(b(c(b(c(b(b(b(_x231)))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(v(_x111)))))))))))))))))))))a#(a(c(c(b(b(b(b(b(_x111)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221))))))))))))))))))))))a#(a(b(c(b(b(c(c(b(b(b(b(b(b(c(c(b(b(b(b(b(b(_x221))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(c(v(v(_x91)))))))))))))))))))))))a#(a(b(c(b(c(b(b(_x91))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(c(_x91)))))))))))))))))))a#(a(b(c(b(c(b(c(b(b(_x91))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x81)))))))))))))))))))a#(a(b(c(b(b(b(c(_x81))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(_x111)))))))))))))))))))))))a#(a(c(c(b(b(b(c(b(b(b(b(c(b(b(_x111)))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(_x91)))))))))))))))))))))a#(a(c(c(b(b(b(b(b(c(b(b(_x91))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x181)))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(c(b(b(b(b(b(_x181)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(a(_x161)))))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(a(c(c(_x161))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(_x201))))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(c(b(b(b(b(b(b(c(b(b(_x201)))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(c(b(b(b(b(c(b(b(b(c(c(b(b(c(b(c(b(b(c(b(b(b(b(_x181)))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(_x91))))))))))))))))a#(a(c(c(b(c(c(b(b(b(b(_x91)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(b(a(a(c(b(b(b(c(b(_x101))))))))))
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c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(_x81)))))))))))))))))a#(a(b(c(b(b(c(b(b(b(b(_x81)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(_x111))))))))))))))))))))a#(a(b(b(c(c(b(b(c(b(_x111))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x141))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(b(c(b(c(_x141)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x121)))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(b(b(b(_x121)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(v(v(w(v(_x51))))))))))))))))))))))))a#(a(c(b(_x51))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x141))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(b(c(b(c(b(b(_x141))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(_x171))))))))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(c(b(b(c(b(b(c(_x171)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(_x221)))))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(c(b(b(c(b(b(c(b(c(b(b(b(c(c(b(b(_x221)))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(c(_x211)))))))))))))))))))))))a#(a(b(c(b(b(c(b(c(b(b(b(b(c(c(b(b(b(b(b(c(b(b(_x211)))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(_x231))))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(b(c(b(b(b(c(b(b(b(c(b(_x231))))))))))))))))))))))
c#(a(a(a(a(a(a(_x121)))))))a#(c(a(c(a(c(a(c(a(c(a(c(c(_x121)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(_x191)))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(c(b(b(b(b(c(b(b(b(b(_x191)))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(_x61))))))))))a#(b(a(a(a(b(a(a(_x61))))))))c#(a(w(a(w(a(w(w(b(b(u(b(u(u(c(_x71)))))))))))))))a#(a(b(b(a(a(c(b(b(_x71)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(v(_x191)))))))))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(c(b(b(c(b(c(b(_x191))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(c(_x101)))))))))))))))))))a#(a(c(b(b(b(c(b(c(b(b(_x101)))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(_x211))))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(b(c(c(b(b(c(b(c(b(_x211)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(c(_x61)))))))))))))))))))))a#(a(b(c(b(b(c(b(b(_x61)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(_x191)))))))))))))))))))))a#(a(c(b(b(b(b(b(c(b(c(c(b(c(b(b(b(b(b(c(b(b(_x191))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(c(_x221))))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(b(b(c(b(b(c(b(c(b(c(b(b(_x221)))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(c(_x191)))))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(c(b(b(b(b(b(c(b(b(_x191))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(_x171))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(c(b(b(_x171))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(_x121))))))))))))))))))))))a#(a(c(c(b(b(b(b(b(c(b(_x121)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(b(a(a(c(b(b(b(c(b(c(b(c(c(b(b(c(b(c(b(b(_x181)))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(b(b(b(_x151)))))))))))))))a#(a(b(b(a(b(a(a(b(a(a(a(b(a(b(a(a(_x151)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x181))))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(c(b(b(b(b(b(b(_x181))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x121))))))))))))))))))a#(a(c(b(b(b(b(b(c(b(_x121))))))))))c#(a(a(a(a(a(_x111))))))a#(c(a(a(c(c(c(a(c(a(c(c(_x111))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(c(v(_x131)))))))))))))))))))))))))a#(a(c(b(c(b(c(b(b(b(c(b(_x131))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(b(b(c(b(c(b(b(c(b(b(b(b(_x181)))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(b(b(b(_x151)))))))))))))))a#(a(b(b(a(a(b(b(a(a(a(b(b(a(a(a(a(_x151)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(c(v(v(_x121))))))))))))))))))))))))))a#(a(c(c(b(b(b(b(c(b(c(_x121)))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(u(b(_x101))))))))))))))a#(a(b(b(b(a(a(a(b(a(a(a(a(_x101)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(v(_x181)))))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(c(b(c(b(_x181))))))))))))))))
c#(a(a(a(a(w(a(_x111)))))))a#(c(a(a(c(a(c(c(c(c(a(c(c(_x111)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(c(_x121))))))))))))))))))))))a#(a(c(b(c(b(b(b(c(b(c(b(b(_x121)))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(c(c(_x131)))))))))))))))))))))))a#(a(c(b(b(c(b(c(b(c(b(c(b(b(_x131))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(_x41)))))))))))))))))a#(b(a(a(c(b(b(_x41)))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(c(_x81)))))))))))))))))))))a#(a(b(c(c(b(b(b(b(b(b(_x81)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221))))))))))))))))))))))a#(b(a(a(c(b(b(c(c(b(b(b(b(b(b(c(b(c(b(b(b(b(_x221))))))))))))))))))))))
c#(a(a(_x21)))c#(a(c(c(_x21))))a#(b(u(_x31)))b#(a(_x31))
c#(a(w(a(w(a(w(w(b(b(u(b(b(b(b(b(_x181))))))))))))))))a#(a(b(b(a(a(b(b(a(a(b(a(a(a(b(b(a(a(a(a(_x181))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(_x171)))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(b(c(b(c(b(b(_x171))))))))))))))))))
c#(a(a(a(a(w(a(w(_x161))))))))a#(a(c(c(a(a(c(c(c(c(c(c(a(c(_x161))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(_x71))))))))))))))))))a#(a(c(b(b(c(b(b(b(b(_x71))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(c(b(b(b(b(c(b(b(b(c(c(b(c(b(b(b(c(b(b(b(c(b(b(_x181)))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(c(v(_x131))))))))))))))))))))))a#(a(b(c(b(b(b(c(c(c(b(_x131)))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x181)))))))))))))))))))))a#(a(b(b(c(b(c(c(b(c(b(b(b(b(c(b(b(b(_x181))))))))))))))))))c#(a(w(a(w(a(w(w(b(b(u(u(_x71))))))))))))a#(a(b(b(a(a(_x71))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(c(_x111))))))))))))))))))))))a#(a(c(c(b(b(b(b(c(b(b(b(c(b(b(_x111)))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(c(b(b(b(c(b(_x161))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(c(c(_x141)))))))))))))))))))))))))a#(a(c(c(b(b(b(b(c(c(b(b(b(c(b(b(_x141))))))))))))))))c#(a(a(a(a(a(_x101))))))a#(c(a(a(c(c(c(a(c(a(c(c(_x101))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(u(b(u(_x131)))))))))))))))a#(a(b(b(b(a(a(a(a(b(a(_x131)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(c(c(_x181)))))))))))))))))))))a#(a(b(c(c(b(b(b(b(b(b(c(c(b(b(b(c(b(b(_x181)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(v(_x91)))))))))))))))))))))a#(a(c(c(b(b(b(b(b(_x91)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x171))))))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(c(b(b(c(b(b(_x171))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(b(c(b(c(b(b(_x151))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(_x151))))))))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(c(b(b(c(b(c(b(b(_x151))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(b(c(b(b(c(b(b(b(c(c(b(b(c(b(c(b(b(b(c(b(b(_x181)))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(v(_x121)))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(b(_x121)))))))))))
c#(a(a(a(a(_x81)))))a#(a(c(c(a(c(c(a(c(c(c(c(_x81))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221))))))))))))))))))))))a#(a(c(b(b(b(b(c(b(c(b(b(b(b(c(b(c(b(b(b(b(_x221)))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(_x101)))))))))))))))))))))))a#(a(c(c(b(b(b(b(b(c(_x101))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(v(_x221)))))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(b(b(c(b(c(b(b(b(c(_x221))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(a(b(b(c(c(b(b(b(_x101)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(v(_x141))))))))))))))))))))))))a#(a(c(c(b(b(b(c(b(b(b(b(c(b(_x141))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(b(a(a(c(c(b(b(b(b(b(c(b(b(b(b(_x111))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(_x151))))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(b(c(b(c(c(b(b(_x151)))))))))))))))))
c#(a(a(a(w(w(w(_x81)))))))a#(a(c(c(a(c(_x81))))))c#(a(w(a(w(a(w(w(b(b(u(b(b(_x101)))))))))))))a#(b(a(a(b(a(a(b(a(b(a(a(_x101))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(_x101)))))))))))))))))))))a#(a(c(b(c(b(b(b(c(b(b(_x101)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(v(a(_x51))))))))))))))))))))))a#(a(b(b(a(c(c(_x51)))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(c(_x111))))))))))))))))))))))))a#(a(c(c(b(b(b(c(b(b(b(c(b(b(_x111))))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(c(_x101))))))))))))))))))a#(a(c(c(c(b(b(c(b(b(c(b(b(_x101)))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(v(c(_x131)))))))))))))))))))))))))a#(a(c(c(b(b(b(b(c(b(b(c(c(b(b(_x131)))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(_x151))))))))))))))))))))))))a#(a(b(b(c(c(b(b(c(b(b(c(b(b(c(b(c(b(b(_x151)))))))))))))))))))
c#(a(a(a(a(a(_x101))))))a#(c(a(c(a(a(c(c(c(a(c(c(_x101))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(v(c(c(_x91)))))))))))))))))))a#(a(b(b(c(c(b(c(b(b(_x91))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x111)))))))))))))))))))a#(a(b(c(b(b(c(b(b(_x111)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(a(c(b(b(c(b(b(b(b(b(b(c(b(b(_x111)))))))))))))))
b#(c(v(v(_x21))))c#(_x21)c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(b(c(b(b(b(c(c(b(b(c(b(b(c(b(c(b(b(b(c(b(b(_x181)))))))))))))))))))))))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(_x261)))))))))))))))))))))))))) → a#(a(b(c(b(b(b(c(b(c(c(b(b(c(c(b(b(b(b(b(c(c(b(c(b(b(_x261)))))))))))))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(a(b(c(b(b(b(c(b(c(c(b(b(c(c(b(b(b(b(c(b(b(c(b(c(b(b(_x261))))))))))))))))))))))))))) 
a#(b(a(a(c(b(b(b(c(b(c(c(b(b(c(c(b(b(b(b(b(c(c(b(c(b(b(_x261))))))))))))))))))))))))))) 
a#(a(b(c(b(b(b(c(b(c(c(b(c(b(b(c(b(b(b(b(b(c(c(b(c(b(b(_x261))))))))))))))))))))))))))) 
a#(a(b(c(b(b(b(c(c(b(b(c(b(b(c(c(b(b(b(b(b(c(c(b(c(b(b(_x261))))))))))))))))))))))))))) 
a#(a(b(c(b(b(b(c(b(c(c(b(b(c(c(b(b(b(b(b(c(c(b(c(b(_x281))))))))))))))))))))))))) 
a#(a(b(c(b(b(b(c(b(c(c(b(b(c(c(b(b(b(b(b(c(c(b(c(b(c(b(b(_x281)))))))))))))))))))))))))))) 
a#(a(b(c(b(b(b(c(b(c(c(b(b(c(c(b(b(b(b(b(c(c(c(b(b(b(b(_x261))))))))))))))))))))))))))) 
a#(a(c(b(b(b(b(b(c(b(c(c(b(b(c(c(b(b(b(b(b(c(c(b(c(b(b(_x261))))))))))))))))))))))))))) 
a#(a(b(c(b(b(c(b(b(b(c(c(b(b(c(c(b(b(b(b(b(c(c(b(c(b(b(_x261))))))))))))))))))))))))))) 
Thus, the rule c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(_x261)))))))))))))))))))))))))) → a#(a(b(c(b(b(b(c(b(c(c(b(b(c(c(b(b(b(b(b(c(c(b(c(b(b(_x261)))))))))))))))))))))))))) is replaced by the following rules:
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(_x261)))))))))))))))))))))))))) → a#(a(b(c(b(b(b(c(b(c(c(b(b(c(c(b(b(b(b(b(c(c(c(b(b(b(b(_x261)))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(_x261)))))))))))))))))))))))))) → a#(a(b(c(b(b(b(c(b(c(c(b(c(b(b(c(b(b(b(b(b(c(c(b(c(b(b(_x261)))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(v(_x281))))))))))))))))))))))))))) → a#(a(b(c(b(b(b(c(b(c(c(b(b(c(c(b(b(b(b(b(c(c(b(c(b(_x281)))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(_x261)))))))))))))))))))))))))) → a#(b(a(a(c(b(b(b(c(b(c(c(b(b(c(c(b(b(b(b(b(c(c(b(c(b(b(_x261)))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(_x261)))))))))))))))))))))))))) → a#(a(b(c(b(b(b(c(b(c(c(b(b(c(c(b(b(b(b(c(b(b(c(b(c(b(b(_x261)))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(_x261)))))))))))))))))))))))))) → a#(a(b(c(b(b(b(c(c(b(b(c(b(b(c(c(b(b(b(b(b(c(c(b(c(b(b(_x261)))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(_x261)))))))))))))))))))))))))) → a#(a(b(c(b(b(c(b(b(b(c(c(b(b(c(c(b(b(b(b(b(c(c(b(c(b(b(_x261)))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(_x281))))))))))))))))))))))))))) → a#(a(b(c(b(b(b(c(b(c(c(b(b(c(c(b(b(b(b(b(c(c(b(c(b(c(b(b(_x281))))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(_x261)))))))))))))))))))))))))) → a#(a(c(b(b(b(b(b(c(b(c(c(b(b(c(c(b(b(b(b(b(c(c(b(c(b(b(_x261)))))))))))))))))))))))))))

Problem 26: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(_x181)))))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(b(c(b(b(c(b(_x181)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(b(c(b(b(b(_x161)))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x101))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(b(b(_x101)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x131)))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(b(c(b(b(_x131)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221))))))))))))))))))))))a#(b(a(a(c(b(b(c(b(c(b(b(b(b(c(b(c(b(b(b(b(_x221)))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(c(c(_x201)))))))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(b(c(b(b(c(c(c(b(b(b(b(_x201)))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(b(c(b(b(b(b(_x151)))))))))))))))))))c#(a(w(a(w(a(w(w(b(b(u(b(u(u(_x81))))))))))))))a#(b(a(a(b(a(a(b(_x81))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(c(v(v(_x91)))))))))))))))))))))))a#(b(a(a(c(b(c(b(b(_x91)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x81)))))))))))))))))))a#(b(a(a(c(b(b(b(c(_x81)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(_x81))))))))))))))a#(b(a(a(b(b(a(_x81)))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(c(v(v(a(_x241)))))))))))))))))))))))))a#(b(a(a(c(b(b(c(b(b(b(c(c(b(b(c(b(b(c(b(b(b(a(c(c(_x241)))))))))))))))))))))))))
b#(c(c(_x21)))b#(c(b(b(_x21))))a#(b(x))a#(x)
c#(a(w(a(w(a(w(w(b(u(b(u(_x71))))))))))))a#(b(a(a(b(a(_x71))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(b(a(a(c(b(b(c(b(b(c(b(b(_x111)))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(_x71))))))))))))))))))a#(b(a(a(c(b(c(b(b(_x71)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x181))))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(c(b(b(b(b(_x181)))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x191)))))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(c(b(c(b(b(b(b(b(_x191)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(_x151))))))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(b(c(b(c(b(b(_x151))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(_x191)))))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(c(b(b(c(b(b(b(c(b(b(_x191)))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(v(_x211))))))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(c(b(b(c(b(b(b(c(b(_x211))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(u(v(b(_x21)))))))))))))a#(b(a(a(_x21))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x181)))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(c(b(b(b(b(b(_x181)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(a(_x161)))))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(a(c(c(_x161))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(_x201))))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(c(b(b(b(b(b(b(c(b(b(_x201)))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(c(b(b(b(b(c(b(b(b(c(c(b(b(c(b(c(b(b(c(b(b(b(b(_x181)))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(_x91))))))))))))))))a#(a(c(c(b(c(c(b(b(b(b(_x91)))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(b(a(a(c(b(b(b(c(b(_x101))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(b(c(b(c(c(b(b(c(b(c(b(b(_x181)))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(c(v(_x171)))))))))))))))))))))))))a#(a(c(c(b(b(b(c(b(b(b(b(c(b(c(b(_x171))))))))))))))))c#(a(w(a(w(a(w(w(b(b(u(b(b(b(b(b(_x171))))))))))))))))a#(a(b(b(a(a(b(b(a(a(a(b(a(b(a(b(a(a(_x171))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(v(v(c(_x221)))))))))))))))))))))))))a#(a(b(c(c(b(b(b(b(b(c(b(b(b(b(c(b(c(b(c(b(b(_x221))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(_x221)))))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(b(c(b(b(b(c(b(b(b(c(c(b(b(_x221))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x141))))))))))))))))))))a#(a(b(b(c(b(c(b(c(b(c(c(b(b(b(b(_x141))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221))))))))))))))))))))))a#(a(b(c(c(b(b(b(b(b(c(b(b(b(b(c(b(c(b(b(b(b(_x221))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(c(_x91)))))))))))))))))))a#(a(c(b(b(c(b(b(b(c(b(b(_x91))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(c(v(_x251)))))))))))))))))))))))a#(a(b(b(c(c(b(b(c(b(c(b(b(b(c(b(b(b(b(c(b(b(b(c(b(_x251)))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(c(v(v(_x231))))))))))))))))))))))))a#(a(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(b(c(_x231)))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(a(c(b(b(b(b(b(c(b(c(c(b(b(b(c(b(_x161)))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(v(_x171)))))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(b(c(b(b(b(_x171))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(c(_x211))))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(b(c(b(b(b(b(b(c(b(c(b(b(_x211)))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(b(_x81)))))))))))a#(a(b(a(b(a(b(a(a(_x81)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(v(_x91)))))))))))))))))))))a#(a(b(c(b(b(b(c(c(_x91)))))))))
c#(a(a(a(a(w(w(_x121)))))))a#(c(a(a(a(c(c(c(c(c(c(_x121)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(c(v(v(w(c(_x231))))))))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(b(c(b(b(b(b(c(b(b(c(b(b(_x231)))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x121)))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(b(b(b(_x121))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x111))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(b(b(_x111))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(c(c(_x111))))))))))))))))))))a#(a(b(c(b(c(b(c(c(b(b(b(b(_x111)))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(b(c(b(c(b(_x161)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(c(v(v(w(_x221)))))))))))))))))))))))))a#(a(b(c(b(b(c(b(b(b(c(c(b(b(c(b(b(c(b(b(b(_x221)))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(_x271))))))))))))))))))))))))))a#(a(b(c(b(b(b(c(c(b(c(b(b(b(b(c(b(c(b(b(b(c(c(b(c(b(b(_x271)))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x191)))))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(c(b(b(c(b(b(b(_x191))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(_x131))))))))))))))))))))a#(a(b(c(b(b(c(b(b(c(b(_x131)))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x181)))))))))))))))))))))a#(a(b(c(b(b(b(c(c(b(b(c(b(b(b(c(b(_x181)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(c(c(c(_x231))))))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(c(c(b(c(b(c(b(b(_x231)))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(c(c(_x111))))))))))))))))))))a#(a(b(c(b(c(c(b(b(b(c(b(b(_x111)))))))))))))c#(a(w(_x21)))c#(_x21)
c#(a(w(a(w(a(w(w(b(b(u(b(u(_x101)))))))))))))a#(b(a(a(b(a(a(b(a(_x101)))))))))c#(a(w(a(w(a(w(w(u(u(_x21))))))))))a#(_x21)
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(_x231)))))))))))))))))))))))a#(a(b(c(b(b(c(b(b(b(c(c(b(c(b(b(b(b(c(b(_x231))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(c(_x141))))))))))))))))))))))))a#(a(c(c(b(b(b(b(b(c(c(b(c(b(b(_x141)))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(c(v(v(a(_x241)))))))))))))))))))))))))a#(a(c(b(b(b(b(c(b(b(b(c(c(b(b(c(b(b(c(b(b(b(a(c(c(_x241)))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(_x181)))))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(_x181)))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(c(c(_x141)))))))))))))))))))))))))a#(a(c(c(b(b(b(c(b(b(b(c(b(c(b(b(_x141))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(_x221)))))))))))))))))))))))))a#(a(b(c(b(b(c(b(b(b(c(c(b(b(c(c(b(b(b(b(b(c(c(b(b(_x221)))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(c(_x111))))))))))))))))))))))a#(a(c(b(c(b(b(b(c(b(c(b(b(_x111)))))))))))))c#(a(a(a(a(w(a(_x121)))))))a#(c(a(a(a(c(c(c(c(c(c(a(c(c(_x121))))))))))))))
c#(a(w(a(w(a(w(w(b(b(b(_x91)))))))))))a#(b(a(a(b(a(a(a(b(a(a(_x91)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(v(c(_x111))))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(c(b(b(_x111)))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(c(v(_x141)))))))))))))))))))))))a#(a(c(b(b(c(c(b(b(b(c(b(_x141))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(c(c(_x141))))))))))))))))))a#(a(c(c(b(c(c(b(b(b(c(c(b(b(b(b(_x141))))))))))))))))
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c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(v(_x221)))))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(b(b(c(b(c(b(b(b(c(_x221))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(a(b(b(c(c(b(b(b(_x101)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(v(_x141))))))))))))))))))))))))a#(a(c(c(b(b(b(c(b(b(b(b(c(b(_x141))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(c(_x91)))))))))))))))))))a#(a(c(b(b(b(c(c(b(b(b(b(_x91))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(b(a(a(c(c(b(b(b(b(b(c(b(b(b(b(_x111))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(_x151))))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(b(c(b(c(c(b(b(_x151)))))))))))))))))
c#(a(a(a(w(w(w(_x81)))))))a#(a(c(c(a(c(_x81))))))c#(a(w(a(w(a(w(w(b(b(u(b(b(_x101)))))))))))))a#(b(a(a(b(a(a(b(a(b(a(a(_x101))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(_x101)))))))))))))))))))))a#(a(c(b(c(b(b(b(c(b(b(_x101)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(v(a(_x51))))))))))))))))))))))a#(a(b(b(a(c(c(_x51)))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(c(_x111))))))))))))))))))))))))a#(a(c(c(b(b(b(c(b(b(b(c(b(b(_x111))))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(c(_x101))))))))))))))))))a#(a(c(c(c(b(b(c(b(b(c(b(b(_x101)))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(v(c(_x131)))))))))))))))))))))))))a#(a(c(c(b(b(b(b(c(b(b(c(c(b(b(_x131)))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(_x151))))))))))))))))))))))))a#(a(b(b(c(c(b(b(c(b(b(c(b(b(c(b(c(b(b(_x151)))))))))))))))))))
c#(a(a(a(a(a(_x101))))))a#(c(a(c(a(a(c(c(c(a(c(c(_x101))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(v(c(c(_x91)))))))))))))))))))a#(a(b(b(c(c(b(c(b(b(_x91))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x111)))))))))))))))))))a#(a(b(c(b(b(c(b(b(_x111)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(a(c(b(b(c(b(b(b(b(b(b(c(b(b(_x111)))))))))))))))
b#(c(v(v(_x21))))c#(_x21)c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(b(c(b(b(b(c(c(b(b(c(b(b(c(b(c(b(b(b(c(b(b(_x181)))))))))))))))))))))))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(a(_x161))))))))))))))))))))))))) → a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(a(c(c(_x161)))))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
a#(a(b(b(c(b(c(c(b(b(c(b(b(c(b(b(a(c(c(_x161))))))))))))))))))) 
a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(a(c(a(c(c(_x191)))))))))))))))))))) 
a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(a(c(_x191))))))))))))))))) 
a#(a(b(c(b(b(b(c(b(c(c(b(b(c(b(b(a(c(c(_x161))))))))))))))))))) 
a#(a(b(b(c(c(b(b(b(c(c(b(b(c(b(b(a(c(c(_x161))))))))))))))))))) 
a#(b(a(a(b(c(b(c(b(c(c(b(b(c(b(b(a(c(c(_x161))))))))))))))))))) 
a#(a(b(b(c(b(c(b(c(c(b(c(b(b(b(b(a(c(c(_x161))))))))))))))))))) 
Thus, the rule c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(a(_x161))))))))))))))))))))))))) → a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(a(c(c(_x161)))))))))))))))))) is replaced by the following rules:
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(a(a(_x191)))))))))))))))))))))))))) → a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(a(c(a(c(c(_x191))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(a(_x161))))))))))))))))))))))))) → a#(b(a(a(b(c(b(c(b(c(c(b(b(c(b(b(a(c(c(_x161)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(a(_x161))))))))))))))))))))))))) → a#(a(b(c(b(b(b(c(b(c(c(b(b(c(b(b(a(c(c(_x161)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(a(_x161))))))))))))))))))))))))) → a#(a(b(b(c(b(c(b(c(c(b(c(b(b(b(b(a(c(c(_x161)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(a(_x161))))))))))))))))))))))))) → a#(a(b(b(c(c(b(b(b(c(c(b(b(c(b(b(a(c(c(_x161)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(a(_x161))))))))))))))))))))))))) → a#(a(b(b(c(b(c(c(b(b(c(b(b(c(b(b(a(c(c(_x161)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(a(w(_x191)))))))))))))))))))))))))) → a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(a(c(_x191)))))))))))))))))

Problem 27: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(_x181)))))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(b(c(b(b(c(b(_x181)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(_x311))))))))))))))))))))))))))a#(b(a(a(c(b(b(b(c(b(c(c(c(b(b(b(c(b(b(b(b(b(c(b(b(b(b(c(c(b(b(b(b(_x311)))))))))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(b(c(b(b(b(_x161)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(_x101))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(b(b(_x101)))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x131)))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(b(c(b(b(_x131)))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221))))))))))))))))))))))a#(b(a(a(c(b(b(c(b(c(b(b(b(b(c(b(c(b(b(b(b(_x221)))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(c(c(_x201)))))))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(b(c(b(b(c(c(c(b(b(b(b(_x201)))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(b(c(b(b(b(b(_x151)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(u(u(_x81))))))))))))))a#(b(a(a(b(a(a(b(_x81))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(c(v(v(_x91)))))))))))))))))))))))a#(b(a(a(c(b(c(b(b(_x91)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x81)))))))))))))))))))a#(b(a(a(c(b(b(b(c(_x81)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(_x81))))))))))))))a#(b(a(a(b(b(a(_x81)))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(c(_x421)))))))))))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(c(b(b(_x421)))))))))))))))))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(c(v(v(a(_x241)))))))))))))))))))))))))a#(b(a(a(c(b(b(c(b(b(b(c(c(b(b(c(b(b(c(b(b(b(a(c(c(_x241)))))))))))))))))))))))))
b#(c(c(_x21)))b#(c(b(b(_x21))))a#(b(x))a#(x)
c#(a(w(a(w(a(w(w(b(u(b(u(_x71))))))))))))a#(b(a(a(b(a(_x71))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(_x441))))))))))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(c(b(b(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(b(_x441))))))))))))))))))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(_x441))))))))))))))))))))))))))))))a#(a(c(b(b(b(b(c(b(c(b(b(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(b(_x441)))))))))))))))))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(b(a(a(c(b(b(c(b(b(c(b(b(_x111)))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(_x71))))))))))))))))))a#(b(a(a(c(b(c(b(b(_x71)))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(v(_x421)))))))))))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(_x421))))))))))))))))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x181))))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(c(b(b(b(b(_x181)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x191)))))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(c(b(c(b(b(b(b(b(_x191)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(_x421)))))))))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(c(b(b(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(b(b(_x421)))))))))))))))))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(_x151))))))))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(c(b(b(c(b(c(b(b(_x151))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(_x221)))))))))))))))))))))))))a#(b(a(a(c(b(b(b(c(b(c(c(b(c(b(b(b(c(b(b(c(b(b(c(b(b(_x221))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(_x191)))))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(c(b(b(c(b(b(b(c(b(b(_x191)))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(_x311))))))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(c(b(b(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(b(_x311)))))))))))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(v(_x211))))))))))))))))))))))a#(b(a(a(b(c(c(b(b(b(c(c(b(b(c(b(b(b(c(b(_x211))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(u(v(b(_x21)))))))))))))a#(b(a(a(_x21))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x181)))))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(c(b(b(b(b(b(_x181)))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(b(a(a(c(b(b(b(c(b(_x101))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x141))))))))))))))))))))a#(a(b(b(c(b(c(b(c(b(c(c(b(b(b(b(_x141))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221))))))))))))))))))))))a#(a(b(c(c(b(b(b(b(b(c(b(b(b(b(c(b(c(b(b(b(b(_x221))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(c(_x91)))))))))))))))))))a#(a(c(b(b(c(b(b(b(c(b(b(_x91))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(c(v(_x251)))))))))))))))))))))))a#(a(b(b(c(c(b(b(c(b(c(b(b(b(c(b(b(b(b(c(b(b(b(c(b(_x251)))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(c(v(v(_x231))))))))))))))))))))))))a#(a(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(c(b(b(b(c(_x231)))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(a(c(b(b(b(b(b(c(b(c(c(b(b(b(c(b(_x161)))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(v(_x171)))))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(b(c(b(b(b(_x171))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(c(_x211))))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(b(c(b(b(b(b(b(c(b(c(b(b(_x211)))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(b(b(_x81)))))))))))a#(a(b(a(b(a(b(a(a(_x81)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(v(v(_x91)))))))))))))))))))))a#(a(b(c(b(b(b(c(c(_x91)))))))))c#(a(a(a(a(w(w(_x121)))))))a#(c(a(a(a(c(c(c(c(c(c(_x121)))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(c(c(v(v(w(c(_x231))))))))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(c(b(c(b(b(b(b(c(b(b(c(b(b(_x231)))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(_x121)))))))))))))))))))a#(b(a(a(b(c(b(c(c(b(b(c(b(b(b(b(_x121))))))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(b(b(b(b(_x171))))))))))))))))a#(a(b(b(a(a(b(b(a(a(b(a(a(a(b(a(b(a(a(_x171)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(v(_x331)))))))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(c(b(b(b(c(b(b(b(b(b(c(b(b(b(b(c(b(c(b(_x331))))))))))))))))))))))))))))))
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c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(c(v(v(c(_x81))))))))))))))))))))))))a#(a(b(c(b(c(b(c(b(b(_x81))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(_x161)))))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(c(b(b(b(c(b(_x161))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(c(c(_x141)))))))))))))))))))))))))a#(a(c(c(b(b(b(b(c(c(b(b(b(c(b(b(_x141))))))))))))))))c#(a(a(a(a(a(_x101))))))a#(c(a(a(c(c(c(a(c(a(c(c(_x101))))))))))))
c#(a(w(a(w(a(w(w(b(b(u(b(u(b(u(_x131)))))))))))))))a#(a(b(b(b(a(a(a(a(b(a(_x131)))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(_x401))))))))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(c(b(c(b(c(b(b(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(b(_x401))))))))))))))))))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(c(c(_x181)))))))))))))))))))))a#(a(b(c(c(b(b(b(b(b(b(c(c(b(b(b(c(b(b(_x181)))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(c(b(b(b(b(c(b(b(c(b(b(c(b(b(c(b(c(c(b(b(b(b(b(b(b(b(_x181))))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(v(_x311))))))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(b(c(c(c(b(b(b(c(b(b(b(b(b(c(b(b(b(b(c(b(_x311)))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(v(_x91)))))))))))))))))))))a#(a(c(c(b(b(b(b(b(_x91)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x171))))))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(c(b(b(c(b(b(_x171))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(_x151))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(b(c(b(c(b(b(_x151))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(_x151))))))))))))))))))))))))a#(a(b(b(c(b(c(c(b(b(c(b(b(c(b(c(b(b(_x151))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(c(_x441))))))))))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(b(c(b(b(_x441))))))))))))))))))))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(_x221)))))))))))))))))))))))))a#(a(b(c(b(b(c(b(b(b(c(c(b(c(b(b(b(c(b(b(c(b(b(c(b(b(_x221))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(b(c(b(b(c(b(b(b(c(c(b(b(c(b(c(b(b(b(c(b(b(_x181)))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(v(_x121)))))))))))))))))))a#(b(a(a(b(c(b(c(b(c(b(_x121)))))))))))c#(a(a(a(a(_x81)))))a#(a(c(c(a(c(c(a(c(c(c(c(_x81))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(_x221))))))))))))))))))))))a#(a(c(b(b(b(b(c(b(c(b(b(b(b(c(b(c(b(b(b(b(_x221)))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(_x101)))))))))))))))))))))))a#(a(c(c(b(b(b(b(b(c(_x101))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(v(_x221)))))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(b(b(c(b(c(b(b(b(c(_x221))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(_x101))))))))))))))))))a#(a(b(b(c(c(b(b(b(_x101)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(v(c(c(_x321))))))))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(c(b(b(b(c(b(b(b(b(b(c(b(b(b(b(c(c(b(c(b(b(_x321))))))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(v(_x141))))))))))))))))))))))))a#(a(c(c(b(b(b(c(b(b(b(b(c(b(_x141))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(_x441))))))))))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(c(b(c(b(b(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(b(_x441))))))))))))))))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(c(_x91)))))))))))))))))))a#(a(c(b(b(b(c(c(b(b(b(b(_x91))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(_x381)))))))))))))))))))))))))))a#(a(c(b(b(b(b(c(b(b(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(b(_x381)))))))))))))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(b(a(a(c(c(b(b(b(b(b(c(b(b(b(b(_x111))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(v(_x311))))))))))))))))))))))))))a#(a(b(c(b(b(b(c(b(c(c(c(b(b(b(c(b(b(b(b(c(b(b(b(b(b(b(c(b(_x311)))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(v(v(v(c(v(_x241))))))))))))))))))))))))))a#(a(b(c(c(b(b(b(b(b(c(b(b(b(b(c(b(c(b(c(b(_x241)))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(_x151))))))))))))))))))))))a#(a(b(b(c(c(b(b(b(c(b(c(b(c(c(b(b(_x151)))))))))))))))))c#(a(a(a(w(w(w(_x81)))))))a#(a(c(c(a(c(_x81))))))
c#(a(w(a(w(a(w(w(b(b(u(b(b(_x101)))))))))))))a#(b(a(a(b(a(a(b(a(b(a(a(_x101))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(_x101)))))))))))))))))))))a#(a(c(b(c(b(b(b(c(b(b(_x101)))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(w(v(a(_x51))))))))))))))))))))))a#(a(b(b(a(c(c(_x51)))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(v(c(_x111))))))))))))))))))))))))a#(a(c(c(b(b(b(c(b(b(b(c(b(b(_x111))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(c(_x461))))))))))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(c(b(b(b(b(b(b(b(b(c(c(b(b(b(c(c(b(b(c(b(b(b(c(b(b(_x461)))))))))))))))))))))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(u(c(v(c(c(c(v(c(_x101))))))))))))))))))a#(a(c(c(c(b(b(c(b(b(c(b(b(_x101)))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(v(c(c(v(v(c(v(c(v(c(_x131)))))))))))))))))))))))))a#(a(c(c(b(b(b(b(c(b(b(c(c(b(b(_x131)))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(_x151))))))))))))))))))))))))a#(a(b(b(c(c(b(b(c(b(b(c(b(b(c(b(c(b(b(_x151)))))))))))))))))))
c#(a(a(a(a(a(_x101))))))a#(c(a(c(a(a(c(c(c(a(c(c(_x101))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(_x421)))))))))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(c(b(b(c(b(b(b(c(c(b(b(b(c(b(b(_x421))))))))))))))))))))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(_x421)))))))))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(c(b(b(c(b(b(b(c(b(c(b(c(b(b(_x421)))))))))))))))))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(_x311))))))))))))))))))))))))))a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(b(c(b(b(b(c(b(b(c(b(b(b(b(_x311))))))))))))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(v(c(c(_x91)))))))))))))))))))a#(a(b(b(c(c(b(c(b(b(_x91))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(v(_x111)))))))))))))))))))a#(a(b(c(b(b(c(b(b(_x111)))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(v(c(_x111)))))))))))))))))))a#(a(c(b(b(c(b(b(b(b(b(b(c(b(b(_x111)))))))))))))))b#(c(v(v(_x21))))c#(_x21)
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(_x181)))))))))))))))))))))))a#(a(b(c(b(b(b(c(c(b(b(c(b(b(c(b(c(b(b(b(c(b(b(_x181)))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(v(v(a(w(a(a(_x201))))))))))))))))))))))))))))a#(a(b(b(c(b(c(b(c(c(b(b(c(b(b(a(a(c(a(c(c(_x201)))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(_x311))))))))))))))))))))))))))a#(b(a(a(c(b(b(b(c(b(c(c(c(b(b(b(c(b(b(b(b(b(c(b(b(b(c(b(b(c(b(b(b(b(_x311))))))))))))))))))))))))))))))))))

Rewrite Rules

a(b(x))b(a(a(x)))b(c(x))c(b(b(x)))
c(a(x))a(c(c(x)))u(a(x))x
v(b(x))xw(c(x))x
a(u(x))xb(v(x))x
c(w(x))x

Original Signature

Termination of terms over the following signature is verified: w, v, u, b, c, a

Strategy


The right-hand side of the rule c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(c(_x421))))))))))))))))))))))))))))))) → a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(c(b(b(_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
a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(b(_x421)))))))))))))))))))))))))))))))))))))))))))) 
a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(c(b(b(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(c(b(b(_x421)))))))))))))))))))))))))))))))))))))))))))) 
a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(c(b(b(b(c(b(c(c(b(b(_x421)))))))))))))))))))))))))))))))))))))))))))) 
a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(c(b(c(b(b(_x451))))))))))))))))))))))))))))))))))))))))))))) 
a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(c(b(b(b(c(c(b(b(_x421)))))))))))))))))))))))))))))))))))))))))))) 
a#(a(c(b(b(b(b(c(b(b(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(c(b(b(_x421)))))))))))))))))))))))))))))))))))))))))))) 
a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(_x421)))))))))))))))))))))))))))))))))))))))))))) 
a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(c(b(_x451)))))))))))))))))))))))))))))))))))))))))) 
a#(a(c(b(b(b(b(b(c(c(b(c(b(b(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(c(b(b(_x421)))))))))))))))))))))))))))))))))))))))))))) 
a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(c(b(b(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(c(b(b(_x421)))))))))))))))))))))))))))))))))))))))))))) 
Thus, the rule c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(c(_x421))))))))))))))))))))))))))))))) → a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(c(b(b(_x421))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(c(_x421))))))))))))))))))))))))))))))) → a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(c(b(b(b(c(c(b(b(_x421))))))))))))))))))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(c(_x421))))))))))))))))))))))))))))))) → a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(c(b(b(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(c(b(b(_x421))))))))))))))))))))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(c(_x421))))))))))))))))))))))))))))))) → a#(a(c(b(b(b(b(b(c(c(b(c(b(b(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(c(b(b(_x421))))))))))))))))))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(c(_x421))))))))))))))))))))))))))))))) → a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(c(b(b(c(b(b(b(c(b(c(b(c(c(b(b(_x421))))))))))))))))))))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(c(_x421))))))))))))))))))))))))))))))) → a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(c(b(b(b(c(b(c(c(b(b(_x421))))))))))))))))))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(c(_x421))))))))))))))))))))))))))))))) → a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(c(b(b(c(b(b(_x421))))))))))))))))))))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(c(c(_x451)))))))))))))))))))))))))))))))) → a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(c(b(c(b(b(_x451)))))))))))))))))))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(c(v(_x451)))))))))))))))))))))))))))))))) → a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(c(b(_x451))))))))))))))))))))))))))))))))))))))))))
c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(c(_x421))))))))))))))))))))))))))))))) → a#(a(c(b(b(b(b(b(c(c(b(b(c(c(b(b(c(b(b(b(b(b(c(b(b(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(c(b(b(_x421))))))))))))))))))))))))))))))))))))))))))))c#(a(w(a(w(a(w(w(b(u(b(u(b(u(u(c(c(c(c(c(v(c(c(v(c(c(c(c(c(v(c(_x421))))))))))))))))))))))))))))))) → a#(a(c(b(b(b(b(c(b(b(c(b(b(c(c(b(b(c(b(b(b(b(b(b(c(b(b(b(b(b(b(c(c(b(b(b(c(b(c(b(c(c(b(b(_x421))))))))))))))))))))))))))))))))))))))))))))