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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.