/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR x1)
(RULES
a(a(x1)) -> a(b(b(b(x1))))
a(b(b(c(x1)))) -> a(a(a(b(x1))))
b(a(x1)) -> b(b(c(x1)))
)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Narrowing Processor:
-> Pairs:
 A(a(x1)) -> A(b(b(b(x1))))
 A(b(b(c(x1)))) -> A(a(a(b(x1))))
 A(b(b(c(x1)))) -> A(a(b(x1)))
 A(b(b(c(x1)))) -> A(b(x1))
-> Rules:
 a(a(x1)) -> a(b(b(b(x1))))
 a(b(b(c(x1)))) -> a(a(a(b(x1))))
 b(a(x1)) -> b(b(c(x1)))
->Narrowed Pairs:
->->Original Pair:
 A(a(x1)) -> A(b(b(b(x1))))
->-> Narrowed pairs:
 A(a(a(x1))) -> A(b(b(b(b(c(x1))))))

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.