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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(c(x1)) -> B(b(c(d(x1))))
 A(x1) -> B(b(b(x1)))
 A(x1) -> B(b(x1))
 A(x1) -> B(x1)
 B(d(b(x1))) -> A(d(x1))
-> Rules:
 a(d(x1)) -> d(b(x1))
 a(c(x1)) -> b(b(c(d(x1))))
 a(x1) -> b(b(b(x1)))
 a(x1) -> x1
 b(d(b(x1))) -> a(d(x1))
 b(c(x1)) -> c(d(d(x1)))
 d(x1) -> x1
-> Usable rules:
 a(d(x1)) -> d(b(x1))
 a(c(x1)) -> b(b(c(d(x1))))
 a(x1) -> b(b(b(x1)))
 a(x1) -> x1
 b(d(b(x1))) -> a(d(x1))
 b(c(x1)) -> c(d(d(x1)))
 d(x1) -> x1
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[a](X) = X + 4
[b](X) = X + 1
[d](X) = 3.X + 1/3
[c](X) = 4
[A](X) = 2.X + 4
[B](X) = 2.X

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(x1) -> B(b(b(x1)))
 A(x1) -> B(b(x1))
 A(x1) -> B(x1)
 B(d(b(x1))) -> A(d(x1))
-> Rules:
 a(d(x1)) -> d(b(x1))
 a(c(x1)) -> b(b(c(d(x1))))
 a(x1) -> b(b(b(x1)))
 a(x1) -> x1
 b(d(b(x1))) -> a(d(x1))
 b(c(x1)) -> c(d(d(x1)))
 d(x1) -> x1
-> Usable rules:
 a(d(x1)) -> d(b(x1))
 a(c(x1)) -> b(b(c(d(x1))))
 a(x1) -> b(b(b(x1)))
 a(x1) -> x1
 b(d(b(x1))) -> a(d(x1))
 b(c(x1)) -> c(d(d(x1)))
 d(x1) -> x1
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[a](X) = X + 4
[b](X) = X + 1
[d](X) = 4.X + 1
[c](X) = 4
[A](X) = 1/2.X + 2
[B](X) = 1/2.X + 2/3

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(x1) -> B(b(x1))
 A(x1) -> B(x1)
 B(d(b(x1))) -> A(d(x1))
-> Rules:
 a(d(x1)) -> d(b(x1))
 a(c(x1)) -> b(b(c(d(x1))))
 a(x1) -> b(b(b(x1)))
 a(x1) -> x1
 b(d(b(x1))) -> a(d(x1))
 b(c(x1)) -> c(d(d(x1)))
 d(x1) -> x1
-> Usable rules:
 a(d(x1)) -> d(b(x1))
 a(c(x1)) -> b(b(c(d(x1))))
 a(x1) -> b(b(b(x1)))
 a(x1) -> x1
 b(d(b(x1))) -> a(d(x1))
 b(c(x1)) -> c(d(d(x1)))
 d(x1) -> x1
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[a](X) = X + 4
[b](X) = X + 1
[d](X) = 3.X + 1/3
[c](X) = 1/2
[A](X) = 1/4.X + 2/3
[B](X) = 1/4.X + 1/4

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.