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


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rm: cannot remove ‘/tmp/muTerm2142757034116087764.in.dec’: Operation not permitted
rm: cannot remove ‘/tmp/muTerm2142757034116087764.in.form’: Operation not permitted
YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.