/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 y)
(RULES
f(f(x)) -> f(g(f(x),x))
f(f(x)) -> f(h(f(x),f(x)))
g(x,y) -> y
h(x,x) -> g(x,0)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(f(x)) -> F(g(f(x),x))
 F(f(x)) -> F(h(f(x),f(x)))
 F(f(x)) -> G(f(x),x)
 F(f(x)) -> H(f(x),f(x))
 H(x,x) -> G(x,0)
-> Rules:
 f(f(x)) -> f(g(f(x),x))
 f(f(x)) -> f(h(f(x),f(x)))
 g(x,y) -> y
 h(x,x) -> g(x,0)

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(x)) -> F(g(f(x),x))
 F(f(x)) -> F(h(f(x),f(x)))
 F(f(x)) -> G(f(x),x)
 F(f(x)) -> H(f(x),f(x))
 H(x,x) -> G(x,0)
-> Rules:
 f(f(x)) -> f(g(f(x),x))
 f(f(x)) -> f(h(f(x),f(x)))
 g(x,y) -> y
 h(x,x) -> g(x,0)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(f(x)) -> F(g(f(x),x))
 F(f(x)) -> F(h(f(x),f(x)))
->->-> Rules:
 f(f(x)) -> f(g(f(x),x))
 f(f(x)) -> f(h(f(x),f(x)))
 g(x,y) -> y
 h(x,x) -> g(x,0)

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(x)) -> F(h(f(x),f(x)))
-> Rules:
 f(f(x)) -> f(g(f(x),x))
 f(f(x)) -> f(h(f(x),f(x)))
 g(x,y) -> y
 h(x,x) -> g(x,0)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(f(x)) -> F(h(f(x),f(x)))
->->-> Rules:
 f(f(x)) -> f(g(f(x),x))
 f(f(x)) -> f(h(f(x),f(x)))
 g(x,y) -> y
 h(x,x) -> g(x,0)

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(f(x)) -> f(g(f(x),x))
 f(f(x)) -> f(h(f(x),f(x)))
 g(x,y) -> y
 h(x,x) -> g(x,0)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.