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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.