/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 x1)
(RULES
P(p(x1)) -> x1
R(r(x1)) -> x1
R(x1) -> r(x1)
p(P(x1)) -> x1
r(P(P(x1))) -> P(P(r(x1)))
r(R(x1)) -> x1
r(p(x1)) -> p(p(r(P(x1))))
r(r(x1)) -> x1
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 R#(x1) -> R(x1)
 R(P(P(x1))) -> P#(P(r(x1)))
 R(P(P(x1))) -> P#(r(x1))
 R(P(P(x1))) -> R(x1)
 R(p(x1)) -> P#(x1)
 R(p(x1)) -> P(p(r(P(x1))))
 R(p(x1)) -> P(r(P(x1)))
 R(p(x1)) -> R(P(x1))
-> Rules:
 P(p(x1)) -> x1
 R(r(x1)) -> x1
 R(x1) -> r(x1)
 p(P(x1)) -> x1
 r(P(P(x1))) -> P(P(r(x1)))
 r(R(x1)) -> x1
 r(p(x1)) -> p(p(r(P(x1))))
 r(r(x1)) -> x1

Problem 1: 

SCC Processor:
-> Pairs:
 R#(x1) -> R(x1)
 R(P(P(x1))) -> P#(P(r(x1)))
 R(P(P(x1))) -> P#(r(x1))
 R(P(P(x1))) -> R(x1)
 R(p(x1)) -> P#(x1)
 R(p(x1)) -> P(p(r(P(x1))))
 R(p(x1)) -> P(r(P(x1)))
 R(p(x1)) -> R(P(x1))
-> Rules:
 P(p(x1)) -> x1
 R(r(x1)) -> x1
 R(x1) -> r(x1)
 p(P(x1)) -> x1
 r(P(P(x1))) -> P(P(r(x1)))
 r(R(x1)) -> x1
 r(p(x1)) -> p(p(r(P(x1))))
 r(r(x1)) -> x1
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 R(P(P(x1))) -> R(x1)
 R(p(x1)) -> R(P(x1))
->->-> Rules:
 P(p(x1)) -> x1
 R(r(x1)) -> x1
 R(x1) -> r(x1)
 p(P(x1)) -> x1
 r(P(P(x1))) -> P(P(r(x1)))
 r(R(x1)) -> x1
 r(p(x1)) -> p(p(r(P(x1))))
 r(r(x1)) -> x1

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 R(P(P(x1))) -> R(x1)
 R(p(x1)) -> R(P(x1))
-> Rules:
 P(p(x1)) -> x1
 R(r(x1)) -> x1
 R(x1) -> r(x1)
 p(P(x1)) -> x1
 r(P(P(x1))) -> P(P(r(x1)))
 r(R(x1)) -> x1
 r(p(x1)) -> p(p(r(P(x1))))
 r(r(x1)) -> x1
-> Usable rules:
 P(p(x1)) -> x1
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[P](X) = 2.X + 2
[p](X) = 2.X + 2
[R](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 R(p(x1)) -> R(P(x1))
-> Rules:
 P(p(x1)) -> x1
 R(r(x1)) -> x1
 R(x1) -> r(x1)
 p(P(x1)) -> x1
 r(P(P(x1))) -> P(P(r(x1)))
 r(R(x1)) -> x1
 r(p(x1)) -> p(p(r(P(x1))))
 r(r(x1)) -> x1
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 R(p(x1)) -> R(P(x1))
->->-> Rules:
 P(p(x1)) -> x1
 R(r(x1)) -> x1
 R(x1) -> r(x1)
 p(P(x1)) -> x1
 r(P(P(x1))) -> P(P(r(x1)))
 r(R(x1)) -> x1
 r(p(x1)) -> p(p(r(P(x1))))
 r(r(x1)) -> x1

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 R(p(x1)) -> R(P(x1))
-> Rules:
 P(p(x1)) -> x1
 R(r(x1)) -> x1
 R(x1) -> r(x1)
 p(P(x1)) -> x1
 r(P(P(x1))) -> P(P(r(x1)))
 r(R(x1)) -> x1
 r(p(x1)) -> p(p(r(P(x1))))
 r(r(x1)) -> x1
-> Usable rules:
 P(p(x1)) -> x1
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[P](X) = 2.X + 1
[p](X) = 2.X + 2
[R](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 P(p(x1)) -> x1
 R(r(x1)) -> x1
 R(x1) -> r(x1)
 p(P(x1)) -> x1
 r(P(P(x1))) -> P(P(r(x1)))
 r(R(x1)) -> x1
 r(p(x1)) -> p(p(r(P(x1))))
 r(r(x1)) -> x1
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.