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


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YES

Problem 1: 

(VAR x0 x1 x2)
(RULES
p(a(x0),p(a(b(x1)),x2)) -> p(a(b(a(x2))),p(a(a(x1)),x2))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 P(a(x0),p(a(b(x1)),x2)) -> P(a(a(x1)),x2)
 P(a(x0),p(a(b(x1)),x2)) -> P(a(b(a(x2))),p(a(a(x1)),x2))
-> Rules:
 p(a(x0),p(a(b(x1)),x2)) -> p(a(b(a(x2))),p(a(a(x1)),x2))

Problem 1: 

SCC Processor:
-> Pairs:
 P(a(x0),p(a(b(x1)),x2)) -> P(a(a(x1)),x2)
 P(a(x0),p(a(b(x1)),x2)) -> P(a(b(a(x2))),p(a(a(x1)),x2))
-> Rules:
 p(a(x0),p(a(b(x1)),x2)) -> p(a(b(a(x2))),p(a(a(x1)),x2))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 P(a(x0),p(a(b(x1)),x2)) -> P(a(a(x1)),x2)
 P(a(x0),p(a(b(x1)),x2)) -> P(a(b(a(x2))),p(a(a(x1)),x2))
->->-> Rules:
 p(a(x0),p(a(b(x1)),x2)) -> p(a(b(a(x2))),p(a(a(x1)),x2))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 P(a(x0),p(a(b(x1)),x2)) -> P(a(a(x1)),x2)
 P(a(x0),p(a(b(x1)),x2)) -> P(a(b(a(x2))),p(a(a(x1)),x2))
-> Rules:
 p(a(x0),p(a(b(x1)),x2)) -> p(a(b(a(x2))),p(a(a(x1)),x2))
-> Usable rules:
 p(a(x0),p(a(b(x1)),x2)) -> p(a(b(a(x2))),p(a(a(x1)),x2))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[p](X1,X2) = 2.X1 + 2.X2 + 1
[a](X) = 2
[b](X) = 2
[P](X1,X2) = X1 + 2.X2

Problem 1: 

SCC Processor:
-> Pairs:
 P(a(x0),p(a(b(x1)),x2)) -> P(a(b(a(x2))),p(a(a(x1)),x2))
-> Rules:
 p(a(x0),p(a(b(x1)),x2)) -> p(a(b(a(x2))),p(a(a(x1)),x2))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 P(a(x0),p(a(b(x1)),x2)) -> P(a(b(a(x2))),p(a(a(x1)),x2))
->->-> Rules:
 p(a(x0),p(a(b(x1)),x2)) -> p(a(b(a(x2))),p(a(a(x1)),x2))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 P(a(x0),p(a(b(x1)),x2)) -> P(a(b(a(x2))),p(a(a(x1)),x2))
-> Rules:
 p(a(x0),p(a(b(x1)),x2)) -> p(a(b(a(x2))),p(a(a(x1)),x2))
-> Usable rules:
 p(a(x0),p(a(b(x1)),x2)) -> p(a(b(a(x2))),p(a(a(x1)),x2))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[p](X1,X2) = [0 1;0 0].X1 + [1 1;1 0].X2
[a](X) = [0 0;1 0].X
[b](X) = [1 0;1 0].X + [1;0]
[P](X1,X2) = [1 0;1 0].X1 + [1 0;0 0].X2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 p(a(x0),p(a(b(x1)),x2)) -> p(a(b(a(x2))),p(a(a(x1)),x2))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.