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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.