/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S)
(RULES
f(x:S,f(a,y:S)) -> f(a,f(f(f(a,x:S),h(a)),y:S))
)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(x:S,f(a,y:S)) -> F(a,f(f(f(a,x:S),h(a)),y:S))
-> Rules:
 f(x:S,f(a,y:S)) -> f(a,f(f(f(a,x:S),h(a)),y:S))
-> Usable rules:
 f(x:S,f(a,y:S)) -> f(a,f(f(f(a,x:S),h(a)),y:S))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[f](X1,X2) = 1/3.X1 + 3/2.X2
[a] = 4
[h](X) = 1/2
[F](X1,X2) = 1/4.X1 + 4/3.X2

Problem 1: 

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

The problem is finite.