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

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 A(b(a(x1))) -> A(a(b(b(a(a(x1))))))
 A(b(a(x1))) -> A(a(x1))
 A(b(a(x1))) -> A(b(b(a(a(x1)))))
-> Rules:
 a(b(a(x1))) -> a(a(b(b(a(a(x1))))))
 b(a(a(b(x1)))) -> b(a(b(x1)))
-> Usable rules:
 a(b(a(x1))) -> a(a(b(b(a(a(x1))))))
 b(a(a(b(x1)))) -> b(a(b(x1)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 0
[b](X) = 2
[A](X) = 2.X

Problem 1.2: 

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

Problem 1.2: 

Reduction Pair Processor:
-> Pairs:
 A(b(a(x1))) -> A(a(x1))
 A(b(a(x1))) -> A(b(b(a(a(x1)))))
-> Rules:
 a(b(a(x1))) -> a(a(b(b(a(a(x1))))))
 b(a(a(b(x1)))) -> b(a(b(x1)))
-> Usable rules:
 a(b(a(x1))) -> a(a(b(b(a(a(x1))))))
 b(a(a(b(x1)))) -> b(a(b(x1)))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 0
[b](X) = 2
[A](X) = 2.X

Problem 1.2: 

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

Problem 1.2: 

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

Problem 1.2: 

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

The problem is finite.