/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)
(RULES
f(a) -> g(h(a))
h(g(x:S)) -> g(h(f(x:S)))
k(f(x:S),y:S,x:S) -> f(x:S)
k(x:S,h(x:S),a) -> h(x:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 H(g(x:S)) -> F(x:S)
 H(g(x:S)) -> H(f(x:S))
-> Rules:
 f(a) -> g(h(a))
 h(g(x:S)) -> g(h(f(x:S)))
 k(f(x:S),y:S,x:S) -> f(x:S)
 k(x:S,h(x:S),a) -> h(x:S)

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 H(g(x:S)) -> H(f(x:S))
-> Rules:
 f(a) -> g(h(a))
 h(g(x:S)) -> g(h(f(x:S)))
 k(f(x:S),y:S,x:S) -> f(x:S)
 k(x:S,h(x:S),a) -> h(x:S)
-> Usable rules:
 f(a) -> g(h(a))
 h(g(x:S)) -> g(h(f(x:S)))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X) = 1/2.X
[h](X) = 1
[a] = 2
[g](X) = 1/2.X + 1/2
[H](X) = 2.X

Problem 1: 

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

The problem is finite.