/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 v_NonEmpty:S x1:S)
(RULES
a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
a(b(b(b(x1:S)))) -> b(b(b(a(x1:S))))
b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
)

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

Problem 1.1: 

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

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

Problem 1.2: 

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

Problem 1.2: 

Subterm Processor:
-> Pairs:
 A(b(b(b(x1:S)))) -> A(x1:S)
-> Rules:
 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
 a(b(b(b(x1:S)))) -> b(b(b(a(x1:S))))
 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
->Projection:
 pi(A) = 1

Problem 1.2: 

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

The problem is finite.