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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.