/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 y:S)
(RULES
f(g(x:S,y:S)) -> g(f(x:S),f(y:S))
f(a) -> b
f(c) -> d
f(h(x:S,y:S)) -> g(h(y:S,f(x:S)),h(x:S,f(y:S)))
g(x:S,x:S) -> h(e,x:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(g(x:S,y:S)) -> F(x:S)
 F(g(x:S,y:S)) -> F(y:S)
 F(g(x:S,y:S)) -> G(f(x:S),f(y:S))
 F(h(x:S,y:S)) -> F(x:S)
 F(h(x:S,y:S)) -> F(y:S)
 F(h(x:S,y:S)) -> G(h(y:S,f(x:S)),h(x:S,f(y:S)))
-> Rules:
 f(g(x:S,y:S)) -> g(f(x:S),f(y:S))
 f(a) -> b
 f(c) -> d
 f(h(x:S,y:S)) -> g(h(y:S,f(x:S)),h(x:S,f(y:S)))
 g(x:S,x:S) -> h(e,x:S)

Problem 1: 

SCC Processor:
-> Pairs:
 F(g(x:S,y:S)) -> F(x:S)
 F(g(x:S,y:S)) -> F(y:S)
 F(g(x:S,y:S)) -> G(f(x:S),f(y:S))
 F(h(x:S,y:S)) -> F(x:S)
 F(h(x:S,y:S)) -> F(y:S)
 F(h(x:S,y:S)) -> G(h(y:S,f(x:S)),h(x:S,f(y:S)))
-> Rules:
 f(g(x:S,y:S)) -> g(f(x:S),f(y:S))
 f(a) -> b
 f(c) -> d
 f(h(x:S,y:S)) -> g(h(y:S,f(x:S)),h(x:S,f(y:S)))
 g(x:S,x:S) -> h(e,x:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(g(x:S,y:S)) -> F(x:S)
 F(g(x:S,y:S)) -> F(y:S)
 F(h(x:S,y:S)) -> F(x:S)
 F(h(x:S,y:S)) -> F(y:S)
->->-> Rules:
 f(g(x:S,y:S)) -> g(f(x:S),f(y:S))
 f(a) -> b
 f(c) -> d
 f(h(x:S,y:S)) -> g(h(y:S,f(x:S)),h(x:S,f(y:S)))
 g(x:S,x:S) -> h(e,x:S)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(g(x:S,y:S)) -> F(x:S)
 F(g(x:S,y:S)) -> F(y:S)
 F(h(x:S,y:S)) -> F(x:S)
 F(h(x:S,y:S)) -> F(y:S)
-> Rules:
 f(g(x:S,y:S)) -> g(f(x:S),f(y:S))
 f(a) -> b
 f(c) -> d
 f(h(x:S,y:S)) -> g(h(y:S,f(x:S)),h(x:S,f(y:S)))
 g(x:S,x:S) -> h(e,x:S)
->Projection:
 pi(F) = 1

Problem 1: 

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

The problem is finite.