/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)
(RULES
f(x,x) -> f(g(x),x)
g(x) -> s(x)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(x,x) -> f(g(x),x)
 g(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(x,x) -> F(g(x),x)
 F(x,x) -> G(x)
-> Rules:
 f(x,x) -> f(g(x),x)
 g(x) -> s(x)

Problem 1: 

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

Problem 1: 

Narrowing Processor:
-> Pairs:
 F(x,x) -> F(g(x),x)
-> Rules:
 f(x,x) -> f(g(x),x)
 g(x) -> s(x)
->Narrowed Pairs:
->->Original Pair:
 F(x,x) -> F(g(x),x)
->-> Narrowed pairs:
 F(x,x) -> F(s(x),x)

Problem 1: 

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

The problem is finite.