/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 v_NonEmpty:S x:S y:S)
(RULES
f(+(x:S,s(0))) -> +(s(s(0)),f(x:S))
f(+(x:S,y:S)) -> *(f(x:S),f(y:S))
f(0) -> s(0)
f(s(0)) -> *(s(s(0)),f(0))
f(s(0)) -> s(s(0))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(+(x:S,s(0))) -> F(x:S)
 F(+(x:S,y:S)) -> F(x:S)
 F(+(x:S,y:S)) -> F(y:S)
 F(s(0)) -> F(0)
-> Rules:
 f(+(x:S,s(0))) -> +(s(s(0)),f(x:S))
 f(+(x:S,y:S)) -> *(f(x:S),f(y:S))
 f(0) -> s(0)
 f(s(0)) -> *(s(s(0)),f(0))
 f(s(0)) -> s(s(0))

Problem 1: 

SCC Processor:
-> Pairs:
 F(+(x:S,s(0))) -> F(x:S)
 F(+(x:S,y:S)) -> F(x:S)
 F(+(x:S,y:S)) -> F(y:S)
 F(s(0)) -> F(0)
-> Rules:
 f(+(x:S,s(0))) -> +(s(s(0)),f(x:S))
 f(+(x:S,y:S)) -> *(f(x:S),f(y:S))
 f(0) -> s(0)
 f(s(0)) -> *(s(s(0)),f(0))
 f(s(0)) -> s(s(0))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(+(x:S,s(0))) -> F(x:S)
 F(+(x:S,y:S)) -> F(x:S)
 F(+(x:S,y:S)) -> F(y:S)
->->-> Rules:
 f(+(x:S,s(0))) -> +(s(s(0)),f(x:S))
 f(+(x:S,y:S)) -> *(f(x:S),f(y:S))
 f(0) -> s(0)
 f(s(0)) -> *(s(s(0)),f(0))
 f(s(0)) -> s(s(0))

Problem 1: 

Subterm Processor:
-> Pairs:
 F(+(x:S,s(0))) -> F(x:S)
 F(+(x:S,y:S)) -> F(x:S)
 F(+(x:S,y:S)) -> F(y:S)
-> Rules:
 f(+(x:S,s(0))) -> +(s(s(0)),f(x:S))
 f(+(x:S,y:S)) -> *(f(x:S),f(y:S))
 f(0) -> s(0)
 f(s(0)) -> *(s(s(0)),f(0))
 f(s(0)) -> s(s(0))
->Projection:
 pi(F) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(+(x:S,s(0))) -> +(s(s(0)),f(x:S))
 f(+(x:S,y:S)) -> *(f(x:S),f(y:S))
 f(0) -> s(0)
 f(s(0)) -> *(s(s(0)),f(0))
 f(s(0)) -> s(s(0))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.