/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)
(RULES
f(g(x:S)) -> f(a(g(g(f(x:S))),g(f(x:S))))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(g(x:S)) -> f(a(g(g(f(x:S))),g(f(x:S))))
-> 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:S)) -> F(a(g(g(f(x:S))),g(f(x:S))))
 F(g(x:S)) -> F(x:S)
-> Rules:
 f(g(x:S)) -> f(a(g(g(f(x:S))),g(f(x:S))))

Problem 1: 

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

Problem 1: 

Subterm Processor:
-> Pairs:
 F(g(x:S)) -> F(x:S)
-> Rules:
 f(g(x:S)) -> f(a(g(g(f(x:S))),g(f(x:S))))
->Projection:
 pi(F) = 1

Problem 1: 

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

The problem is finite.