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


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YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
a(a(f(b,a(x:S)))) -> f(a(a(a(x:S))),b)
a(a(x:S)) -> f(b,a(f(a(x:S),b)))
f(a(x:S),b) -> f(b,a(x:S))
)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(a(f(b,a(x:S)))) -> A(a(a(x:S)))
 A(a(f(b,a(x:S)))) -> A(a(x:S))
 A(a(x:S)) -> A(f(a(x:S),b))
-> Rules:
 a(a(f(b,a(x:S)))) -> f(a(a(a(x:S))),b)
 a(a(x:S)) -> f(b,a(f(a(x:S),b)))
 f(a(x:S),b) -> f(b,a(x:S))
-> Usable rules:
 a(a(f(b,a(x:S)))) -> f(a(a(a(x:S))),b)
 a(a(x:S)) -> f(b,a(f(a(x:S),b)))
 f(a(x:S),b) -> f(b,a(x:S))
->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:S)))) -> A(a(a(x:S)))
 A(a(x:S)) -> A(f(a(x:S),b))
-> Rules:
 a(a(f(b,a(x:S)))) -> f(a(a(a(x:S))),b)
 a(a(x:S)) -> f(b,a(f(a(x:S),b)))
 f(a(x:S),b) -> f(b,a(x:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A(a(f(b,a(x:S)))) -> A(a(a(x:S)))
 A(a(x:S)) -> A(f(a(x:S),b))
->->-> Rules:
 a(a(f(b,a(x:S)))) -> f(a(a(a(x:S))),b)
 a(a(x:S)) -> f(b,a(f(a(x:S),b)))
 f(a(x:S),b) -> f(b,a(x:S))

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.