/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 x y z)
(RULES
f(f(y,z),f(x,f(a,x))) -> f(f(f(a,z),f(x,a)),f(a,y))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(f(y,z),f(x,f(a,x))) -> F(f(f(a,z),f(x,a)),f(a,y))
-> Rules:
 f(f(y,z),f(x,f(a,x))) -> f(f(f(a,z),f(x,a)),f(a,y))

Problem 1: 

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

Problem 1: 

Instantiation Processor:
-> Pairs:
 F(f(y,z),f(x,f(a,x))) -> F(f(f(a,z),f(x,a)),f(a,y))
-> Rules:
 f(f(y,z),f(x,f(a,x))) -> f(f(f(a,z),f(x,a)),f(a,y))
->Instantiated Pairs:
->->Original Pair:
 F(f(y,z),f(x,f(a,x))) -> F(f(f(a,z),f(x,a)),f(a,y))
->-> Instantiated pairs:
 F(f(f(a,x3),f(x4,a)),f(a,f(a,a))) -> F(f(f(a,f(x4,a)),f(a,a)),f(a,f(a,x3)))

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(f(a,x3),f(x4,a)),f(a,f(a,a))) -> F(f(f(a,f(x4,a)),f(a,a)),f(a,f(a,x3)))
-> Rules:
 f(f(y,z),f(x,f(a,x))) -> f(f(f(a,z),f(x,a)),f(a,y))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(f(f(a,x3),f(x4,a)),f(a,f(a,a))) -> F(f(f(a,f(x4,a)),f(a,a)),f(a,f(a,x3)))
->->-> Rules:
 f(f(y,z),f(x,f(a,x))) -> f(f(f(a,z),f(x,a)),f(a,y))

Problem 1: 

Instantiation Processor:
-> Pairs:
 F(f(f(a,x3),f(x4,a)),f(a,f(a,a))) -> F(f(f(a,f(x4,a)),f(a,a)),f(a,f(a,x3)))
-> Rules:
 f(f(y,z),f(x,f(a,x))) -> f(f(f(a,z),f(x,a)),f(a,y))
->Instantiated Pairs:
->->Original Pair:
 F(f(f(a,x3),f(x4,a)),f(a,f(a,a))) -> F(f(f(a,f(x4,a)),f(a,a)),f(a,f(a,x3)))
->-> Instantiated pairs:
 F(f(f(a,f(x5,a)),f(a,a)),f(a,f(a,a))) -> F(f(f(a,f(a,a)),f(a,a)),f(a,f(a,f(x5,a))))

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(f(a,f(x5,a)),f(a,a)),f(a,f(a,a))) -> F(f(f(a,f(a,a)),f(a,a)),f(a,f(a,f(x5,a))))
-> Rules:
 f(f(y,z),f(x,f(a,x))) -> f(f(f(a,z),f(x,a)),f(a,y))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.