/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)
(RULES
f(0) -> s(0)
f(s(x:S)) -> s(s(g(x:S)))
g(0) -> 0
g(s(x:S)) -> f(x:S)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(0) -> s(0)
 f(s(x:S)) -> s(s(g(x:S)))
 g(0) -> 0
 g(s(x:S)) -> 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(s(x:S)) -> G(x:S)
 G(s(x:S)) -> F(x:S)
-> Rules:
 f(0) -> s(0)
 f(s(x:S)) -> s(s(g(x:S)))
 g(0) -> 0
 g(s(x:S)) -> f(x:S)

Problem 1: 

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

Problem 1: 

Subterm Processor:
-> Pairs:
 F(s(x:S)) -> G(x:S)
 G(s(x:S)) -> F(x:S)
-> Rules:
 f(0) -> s(0)
 f(s(x:S)) -> s(s(g(x:S)))
 g(0) -> 0
 g(s(x:S)) -> f(x:S)
->Projection:
 pi(F) = 1
 pi(G) = 1

Problem 1: 

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

The problem is finite.