/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR x)
(RULES
g(g(x)) -> g(h(g(x)))
g(h(g(x))) -> g(x)
h(h(x)) -> h(f(h(x),x))
)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 G(g(x)) -> G(h(g(x)))
-> Rules:
 g(g(x)) -> g(h(g(x)))
 g(h(g(x))) -> g(x)
 h(h(x)) -> h(f(h(x),x))
-> Usable rules:
 g(g(x)) -> g(h(g(x)))
 g(h(g(x))) -> g(x)
 h(h(x)) -> h(f(h(x),x))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[g](X) = 1
[h](X) = 0
[f](X1,X2) = 2.X1 + 2.X2
[G](X) = 2.X

Problem 1: 

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

The problem is finite.