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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.