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

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 G(f(x:S,y:S),z:S) -> G(y:S,z:S)
 G(h(x:S,y:S),z:S) -> G(x:S,f(y:S,z:S))
 G(x:S,h(y:S,z:S)) -> G(x:S,y:S)
-> Rules:
 g(f(x:S,y:S),z:S) -> f(x:S,g(y:S,z:S))
 g(h(x:S,y:S),z:S) -> g(x:S,f(y:S,z:S))
 g(x:S,h(y:S,z:S)) -> h(g(x:S,y:S),z:S)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.