/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)
(RULES
f(s(x),y) -> f(x,s(s(x)))
f(x,s(s(y))) -> f(y,x)
)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.