/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 v_NonEmpty:S X:S)
(RULES
a(X:S) -> e
b(X:S) -> e
c(b(a(X:S))) -> a(a(b(b(c(c(X:S))))))
c(X:S) -> e
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 C(b(a(X:S))) -> A(a(b(b(c(c(X:S))))))
 C(b(a(X:S))) -> A(b(b(c(c(X:S)))))
 C(b(a(X:S))) -> B(b(c(c(X:S))))
 C(b(a(X:S))) -> B(c(c(X:S)))
 C(b(a(X:S))) -> C(c(X:S))
 C(b(a(X:S))) -> C(X:S)
-> Rules:
 a(X:S) -> e
 b(X:S) -> e
 c(b(a(X:S))) -> a(a(b(b(c(c(X:S))))))
 c(X:S) -> e

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 C(b(a(X:S))) -> C(c(X:S))
 C(b(a(X:S))) -> C(X:S)
-> Rules:
 a(X:S) -> e
 b(X:S) -> e
 c(b(a(X:S))) -> a(a(b(b(c(c(X:S))))))
 c(X:S) -> e
-> Usable rules:
 a(X:S) -> e
 b(X:S) -> e
 c(b(a(X:S))) -> a(a(b(b(c(c(X:S))))))
 c(X:S) -> e
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 1/2.X + 1/2
[b](X) = 2.X
[c](X) = X
[e] = 0
[C](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 C(b(a(X:S))) -> C(X:S)
-> Rules:
 a(X:S) -> e
 b(X:S) -> e
 c(b(a(X:S))) -> a(a(b(b(c(c(X:S))))))
 c(X:S) -> e
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 C(b(a(X:S))) -> C(X:S)
->->-> Rules:
 a(X:S) -> e
 b(X:S) -> e
 c(b(a(X:S))) -> a(a(b(b(c(c(X:S))))))
 c(X:S) -> e

Problem 1: 

Subterm Processor:
-> Pairs:
 C(b(a(X:S))) -> C(X:S)
-> Rules:
 a(X:S) -> e
 b(X:S) -> e
 c(b(a(X:S))) -> a(a(b(b(c(c(X:S))))))
 c(X:S) -> e
->Projection:
 pi(C) = 1

Problem 1: 

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

The problem is finite.