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


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YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

Problem 1.2: 

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

Problem 1.2: 

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

Problem 1.2: 

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

The problem is finite.