/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
-(0,y) -> 0
-(x,0) -> x
-(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0)
p(0) -> 0
p(s(x)) -> x
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 -#(x,s(y)) -> -#(x,p(s(y)))
 -#(x,s(y)) -> P(s(y))
-> Rules:
 -(0,y) -> 0
 -(x,0) -> x
 -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0)
 p(0) -> 0
 p(s(x)) -> x

Problem 1: 

SCC Processor:
-> Pairs:
 -#(x,s(y)) -> -#(x,p(s(y)))
 -#(x,s(y)) -> P(s(y))
-> Rules:
 -(0,y) -> 0
 -(x,0) -> x
 -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0)
 p(0) -> 0
 p(s(x)) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 -#(x,s(y)) -> -#(x,p(s(y)))
->->-> Rules:
 -(0,y) -> 0
 -(x,0) -> x
 -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0)
 p(0) -> 0
 p(s(x)) -> x

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 -#(x,s(y)) -> -#(x,p(s(y)))
-> Rules:
 -(0,y) -> 0
 -(x,0) -> x
 -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0)
 p(0) -> 0
 p(s(x)) -> x
-> Usable rules:
 p(0) -> 0
 p(s(x)) -> x
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[p](X) = 1/2.X + 1/2
[0] = 1/2
[s](X) = 2.X + 2
[-#](X1,X2) = 2.X2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 -(0,y) -> 0
 -(x,0) -> x
 -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0)
 p(0) -> 0
 p(s(x)) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.