/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR x)
(RULES
a(a(f(b,a(x)))) -> f(a(a(a(x))),b)
a(a(x)) -> f(b,a(f(a(x),b)))
f(a(x),b) -> f(b,a(x))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(a(f(b,a(x)))) -> A(a(a(x)))
 A(a(f(b,a(x)))) -> A(a(x))
 A(a(f(b,a(x)))) -> F(a(a(a(x))),b)
 A(a(x)) -> A(f(a(x),b))
 A(a(x)) -> F(a(x),b)
 A(a(x)) -> F(b,a(f(a(x),b)))
 F(a(x),b) -> F(b,a(x))
-> Rules:
 a(a(f(b,a(x)))) -> f(a(a(a(x))),b)
 a(a(x)) -> f(b,a(f(a(x),b)))
 f(a(x),b) -> f(b,a(x))

Problem 1: 

SCC Processor:
-> Pairs:
 A(a(f(b,a(x)))) -> A(a(a(x)))
 A(a(f(b,a(x)))) -> A(a(x))
 A(a(f(b,a(x)))) -> F(a(a(a(x))),b)
 A(a(x)) -> A(f(a(x),b))
 A(a(x)) -> F(a(x),b)
 A(a(x)) -> F(b,a(f(a(x),b)))
 F(a(x),b) -> F(b,a(x))
-> Rules:
 a(a(f(b,a(x)))) -> f(a(a(a(x))),b)
 a(a(x)) -> f(b,a(f(a(x),b)))
 f(a(x),b) -> f(b,a(x))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(a(f(b,a(x)))) -> A(a(a(x)))
 A(a(f(b,a(x)))) -> A(a(x))
 A(a(x)) -> A(f(a(x),b))
->->-> Rules:
 a(a(f(b,a(x)))) -> f(a(a(a(x))),b)
 a(a(x)) -> f(b,a(f(a(x),b)))
 f(a(x),b) -> f(b,a(x))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(a(f(b,a(x)))) -> A(a(a(x)))
 A(a(f(b,a(x)))) -> A(a(x))
 A(a(x)) -> A(f(a(x),b))
-> Rules:
 a(a(f(b,a(x)))) -> f(a(a(a(x))),b)
 a(a(x)) -> f(b,a(f(a(x),b)))
 f(a(x),b) -> f(b,a(x))
-> Usable rules:
 a(a(f(b,a(x)))) -> f(a(a(a(x))),b)
 a(a(x)) -> f(b,a(f(a(x),b)))
 f(a(x),b) -> f(b,a(x))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2.X + 2
[f](X1,X2) = X1 + X2
[b] = 0
[A](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 A(a(f(b,a(x)))) -> A(a(a(x)))
 A(a(x)) -> A(f(a(x),b))
-> Rules:
 a(a(f(b,a(x)))) -> f(a(a(a(x))),b)
 a(a(x)) -> f(b,a(f(a(x),b)))
 f(a(x),b) -> f(b,a(x))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(a(f(b,a(x)))) -> A(a(a(x)))
 A(a(x)) -> A(f(a(x),b))
->->-> Rules:
 a(a(f(b,a(x)))) -> f(a(a(a(x))),b)
 a(a(x)) -> f(b,a(f(a(x),b)))
 f(a(x),b) -> f(b,a(x))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(a(f(b,a(x)))) -> A(a(a(x)))
 A(a(x)) -> A(f(a(x),b))
-> Rules:
 a(a(f(b,a(x)))) -> f(a(a(a(x))),b)
 a(a(x)) -> f(b,a(f(a(x),b)))
 f(a(x),b) -> f(b,a(x))
-> Usable rules:
 a(a(f(b,a(x)))) -> f(a(a(a(x))),b)
 a(a(x)) -> f(b,a(f(a(x),b)))
 f(a(x),b) -> f(b,a(x))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2
[f](X1,X2) = 0
[b] = 2
[A](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 A(a(f(b,a(x)))) -> A(a(a(x)))
-> Rules:
 a(a(f(b,a(x)))) -> f(a(a(a(x))),b)
 a(a(x)) -> f(b,a(f(a(x),b)))
 f(a(x),b) -> f(b,a(x))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(a(f(b,a(x)))) -> A(a(a(x)))
->->-> Rules:
 a(a(f(b,a(x)))) -> f(a(a(a(x))),b)
 a(a(x)) -> f(b,a(f(a(x),b)))
 f(a(x),b) -> f(b,a(x))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(a(f(b,a(x)))) -> A(a(a(x)))
-> Rules:
 a(a(f(b,a(x)))) -> f(a(a(a(x))),b)
 a(a(x)) -> f(b,a(f(a(x),b)))
 f(a(x),b) -> f(b,a(x))
-> Usable rules:
 a(a(f(b,a(x)))) -> f(a(a(a(x))),b)
 a(a(x)) -> f(b,a(f(a(x),b)))
 f(a(x),b) -> f(b,a(x))
->Interpretation type:
 Simple mixed
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2.X.X + X + 1
[f](X1,X2) = X1 + X2
[b] = 0
[A](X) = 2.X.X + 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a(a(f(b,a(x)))) -> f(a(a(a(x))),b)
 a(a(x)) -> f(b,a(f(a(x),b)))
 f(a(x),b) -> f(b,a(x))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.