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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.