/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 x1)
(RULES
f(f(g(x1))) -> g(f(x1))
g(f(c(x1))) -> g(f(f(c(x1))))
g(g(x1)) -> g(f(g(x1)))
g(c(x1)) -> g(f(c(x1)))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(f(g(x1))) -> F(x1)
 F(f(g(x1))) -> G(f(x1))
 G(g(x1)) -> F(g(x1))
 G(g(x1)) -> G(f(g(x1)))
 G(c(x1)) -> G(f(c(x1)))
-> Rules:
 f(f(g(x1))) -> g(f(x1))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 g(c(x1)) -> g(f(c(x1)))

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(g(x1))) -> F(x1)
 F(f(g(x1))) -> G(f(x1))
 G(g(x1)) -> F(g(x1))
 G(g(x1)) -> G(f(g(x1)))
 G(c(x1)) -> G(f(c(x1)))
-> Rules:
 f(f(g(x1))) -> g(f(x1))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 g(c(x1)) -> g(f(c(x1)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(f(g(x1))) -> F(x1)
 F(f(g(x1))) -> G(f(x1))
 G(g(x1)) -> F(g(x1))
 G(g(x1)) -> G(f(g(x1)))
->->-> Rules:
 f(f(g(x1))) -> g(f(x1))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 g(c(x1)) -> g(f(c(x1)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(f(g(x1))) -> F(x1)
 F(f(g(x1))) -> G(f(x1))
 G(g(x1)) -> F(g(x1))
 G(g(x1)) -> G(f(g(x1)))
-> Rules:
 f(f(g(x1))) -> g(f(x1))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 g(c(x1)) -> g(f(c(x1)))
-> Usable rules:
 f(f(g(x1))) -> g(f(x1))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 g(c(x1)) -> g(f(c(x1)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X) = X
[g](X) = 2.X + 1
[c](X) = 2.X
[F](X) = X + 1
[G](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(g(x1))) -> G(f(x1))
 G(g(x1)) -> F(g(x1))
 G(g(x1)) -> G(f(g(x1)))
-> Rules:
 f(f(g(x1))) -> g(f(x1))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 g(c(x1)) -> g(f(c(x1)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(f(g(x1))) -> G(f(x1))
 G(g(x1)) -> F(g(x1))
 G(g(x1)) -> G(f(g(x1)))
->->-> Rules:
 f(f(g(x1))) -> g(f(x1))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 g(c(x1)) -> g(f(c(x1)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(f(g(x1))) -> G(f(x1))
 G(g(x1)) -> F(g(x1))
 G(g(x1)) -> G(f(g(x1)))
-> Rules:
 f(f(g(x1))) -> g(f(x1))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 g(c(x1)) -> g(f(c(x1)))
-> Usable rules:
 f(f(g(x1))) -> g(f(x1))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 g(c(x1)) -> g(f(c(x1)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X) = X
[g](X) = 2.X + 1
[c](X) = 0
[F](X) = X + 1
[G](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 G(g(x1)) -> F(g(x1))
 G(g(x1)) -> G(f(g(x1)))
-> Rules:
 f(f(g(x1))) -> g(f(x1))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 g(c(x1)) -> g(f(c(x1)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G(g(x1)) -> G(f(g(x1)))
->->-> Rules:
 f(f(g(x1))) -> g(f(x1))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 g(c(x1)) -> g(f(c(x1)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 G(g(x1)) -> G(f(g(x1)))
-> Rules:
 f(f(g(x1))) -> g(f(x1))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 g(c(x1)) -> g(f(c(x1)))
-> Usable rules:
 f(f(g(x1))) -> g(f(x1))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 g(c(x1)) -> g(f(c(x1)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[f](X) = [0 1;1 0].X
[g](X) = [1 1;0 0].X + [1;0]
[c](X) = [1 1;1 1].X + [1;1]
[G](X) = [1 0;1 1].X

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(f(g(x1))) -> g(f(x1))
 g(f(c(x1))) -> g(f(f(c(x1))))
 g(g(x1)) -> g(f(g(x1)))
 g(c(x1)) -> g(f(c(x1)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.