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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Subterm Processor:
-> Pairs:
 F(g(x:S),a) -> F(x:S,g(a))
 F(g(x:S),g(y:S)) -> H(g(y:S),x:S,g(y:S))
 H(g(x:S),y:S,z:S) -> F(y:S,h(x:S,y:S,z:S))
 H(g(x:S),y:S,z:S) -> H(x:S,y:S,z:S)
-> Rules:
 f(a,g(y:S)) -> g(g(y:S))
 f(g(x:S),a) -> f(x:S,g(a))
 f(g(x:S),g(y:S)) -> h(g(y:S),x:S,g(y:S))
 h(a,y:S,z:S) -> z:S
 h(g(x:S),y:S,z:S) -> f(y:S,h(x:S,y:S,z:S))
->Projection:
 pi(F) = 1
 pi(H) = 2

Problem 1: 

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

Problem 1: 

Subterm Processor:
-> Pairs:
 H(g(x:S),y:S,z:S) -> H(x:S,y:S,z:S)
-> Rules:
 f(a,g(y:S)) -> g(g(y:S))
 f(g(x:S),a) -> f(x:S,g(a))
 f(g(x:S),g(y:S)) -> h(g(y:S),x:S,g(y:S))
 h(a,y:S,z:S) -> z:S
 h(g(x:S),y:S,z:S) -> f(y:S,h(x:S,y:S,z:S))
->Projection:
 pi(H) = 1

Problem 1: 

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

The problem is finite.