/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


NO

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
f(s(0),g(x:S)) -> f(x:S,g(x:S))
g(s(x:S)) -> g(x:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(s(0),g(x:S)) -> F(x:S,g(x:S))
 G(s(x:S)) -> G(x:S)
-> Rules:
 f(s(0),g(x:S)) -> f(x:S,g(x:S))
 g(s(x:S)) -> g(x:S)

Problem 1: 

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

Problem 1: 

Forward Instantiation Processor:
-> Pairs:
 F(s(0),g(x:S)) -> F(x:S,g(x:S))
-> Rules:
 f(s(0),g(x:S)) -> f(x:S,g(x:S))
 g(s(x:S)) -> g(x:S)
->Instantiated Pairs:
->->Original Pair:
 F(s(0),g(x:S)) -> F(x:S,g(x:S))
->-> Instantiated pairs:
 F(s(0),g(s(0))) -> F(s(0),g(s(0)))

Problem 1: 

Infinite Processor:
-> Pairs:
 F(s(0),g(s(0))) -> F(s(0),g(s(0)))
-> Rules:
 f(s(0),g(x:S)) -> f(x:S,g(x:S))
 g(s(x:S)) -> g(x:S)
-> Pairs in cycle:
 F(s(0),g(s(0))) -> F(s(0),g(s(0)))

The problem is infinite.