/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
a(p(x1)) -> p(a(A(x1)))
a(A(x1)) -> A(a(x1))
p(A(A(x1))) -> a(p(x1))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(p(x1)) -> A(A(x1))
 A(p(x1)) -> P(a(A(x1)))
 A(A(x1)) -> A(x1)
 P(A(A(x1))) -> A(p(x1))
 P(A(A(x1))) -> P(x1)
-> Rules:
 a(p(x1)) -> p(a(A(x1)))
 a(A(x1)) -> A(a(x1))
 p(A(A(x1))) -> a(p(x1))

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(p(x1)) -> P(a(A(x1)))
 P(A(A(x1))) -> A(p(x1))
 P(A(A(x1))) -> P(x1)
-> Rules:
 a(p(x1)) -> p(a(A(x1)))
 a(A(x1)) -> A(a(x1))
 p(A(A(x1))) -> a(p(x1))
-> Usable rules:
 a(p(x1)) -> p(a(A(x1)))
 a(A(x1)) -> A(a(x1))
 p(A(A(x1))) -> a(p(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = X + 2
[p](X) = 1/2.X
[A](X) = X + 2
[A](X) = X + 2
[P](X) = 1/2.X

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(p(x1)) -> P(a(A(x1)))
 P(A(A(x1))) -> A(p(x1))
-> Rules:
 a(p(x1)) -> p(a(A(x1)))
 a(A(x1)) -> A(a(x1))
 p(A(A(x1))) -> a(p(x1))
-> Usable rules:
 a(p(x1)) -> p(a(A(x1)))
 a(A(x1)) -> A(a(x1))
 p(A(A(x1))) -> a(p(x1))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[a](X) = X + 1/4
[p](X) = 1/4.X + 1/4
[A](X) = X + 2/3
[A](X) = 2.X + 3/2
[P](X) = 1/2.X + 4/3

Problem 1: 

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

The problem is finite.