/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 x3)
(RULES
p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(a(a(b(x1))),p(a(a(x0)),x3))
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(a(a(x0)),x3)
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
-> Rules:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))

Problem 1: 

SCC Processor:
-> Pairs:
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(a(a(b(x1))),p(a(a(x0)),x3))
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(a(a(x0)),x3)
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
-> Rules:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(a(a(b(x1))),p(a(a(x0)),x3))
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(a(a(x0)),x3)
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
->->-> Rules:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(a(a(b(x1))),p(a(a(x0)),x3))
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(a(a(x0)),x3)
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
-> Rules:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
-> Usable rules:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[p](X1,X2) = X1 + X2 + 2
[a](X) = 2.X
[b](X) = 0
[P](X1,X2) = 2.X1 + 2.X2

Problem 1: 

SCC Processor:
-> Pairs:
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(a(a(x0)),x3)
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
-> Rules:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(a(a(x0)),x3)
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
->->-> Rules:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(a(a(x0)),x3)
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
-> Rules:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
-> Usable rules:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[p](X1,X2) = 2.X2 + 2
[a](X) = 2
[b](X) = X
[P](X1,X2) = 2.X2

Problem 1: 

SCC Processor:
-> Pairs:
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
-> Rules:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
->->-> Rules:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 P(a(a(x0)),p(x1,p(a(x2),x3))) -> P(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
-> Rules:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
-> Usable rules:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[p](X1,X2) = 3/4.X1 + 2/3.X2
[a](X) = 3.X + 4
[b](X) = 0
[P](X1,X2) = 3/2.X1 + X2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 p(a(a(x0)),p(x1,p(a(x2),x3))) -> p(x2,p(a(a(b(x1))),p(a(a(x0)),x3)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.