/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 x1)
(RULES
a(a(a(x1))) -> b(a(a(b(x1))))
b(a(x1)) -> a(b(x1))
b(b(b(b(x1)))) -> a(x1)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A(a(a(x1))) -> A(a(b(x1)))
 A(a(a(x1))) -> A(b(x1))
 A(a(a(x1))) -> B(a(a(b(x1))))
 A(a(a(x1))) -> B(x1)
 B(a(x1)) -> A(b(x1))
 B(a(x1)) -> B(x1)
 B(b(b(b(x1)))) -> A(x1)
-> Rules:
 a(a(a(x1))) -> b(a(a(b(x1))))
 b(a(x1)) -> a(b(x1))
 b(b(b(b(x1)))) -> a(x1)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.