/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 x y)
(RULES
f(x,f(a,y)) -> f(a,f(f(a,h(f(a,x))),y))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(x,f(a,y)) -> F(f(a,h(f(a,x))),y)
 F(x,f(a,y)) -> F(a,f(f(a,h(f(a,x))),y))
 F(x,f(a,y)) -> F(a,h(f(a,x)))
 F(x,f(a,y)) -> F(a,x)
-> Rules:
 f(x,f(a,y)) -> f(a,f(f(a,h(f(a,x))),y))

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(x,f(a,y)) -> F(a,f(f(a,h(f(a,x))),y))
-> Rules:
 f(x,f(a,y)) -> f(a,f(f(a,h(f(a,x))),y))
-> Usable rules:
 f(x,f(a,y)) -> f(a,f(f(a,h(f(a,x))),y))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X1,X2) = 1/2.X1 + 2.X2
[a] = 2
[h](X) = 0
[F](X1,X2) = X2

Problem 1: 

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

The problem is finite.