/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 y)
(RULES
f(g(x)) -> g(f(f(x)))
f(h(x)) -> h(g(x))
f'(s(x),y,y) -> f'(y,x,s(x))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(g(x)) -> g(f(f(x)))
 f(h(x)) -> h(g(x))
 f'(s(x),y,y) -> f'(y,x,s(x))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(g(x)) -> F(f(x))
 F(g(x)) -> F(x)
 F'(s(x),y,y) -> F'(y,x,s(x))
-> Rules:
 f(g(x)) -> g(f(f(x)))
 f(h(x)) -> h(g(x))
 f'(s(x),y,y) -> f'(y,x,s(x))

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Subterm Processor:
-> Pairs:
 F(g(x)) -> F(x)
-> Rules:
 f(g(x)) -> g(f(f(x)))
 f(h(x)) -> h(g(x))
 f'(s(x),y,y) -> f'(y,x,s(x))
->Projection:
 pi(F) = 1

Problem 1: 

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

The problem is finite.