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


--------------------------------------------------------------------------------


YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.