/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
fac(0) -> s(0)
fac(s(x:S)) -> times(s(x:S),fac(p(s(x:S))))
p(s(x:S)) -> x:S
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 fac(0) -> s(0)
 fac(s(x:S)) -> times(s(x:S),fac(p(s(x:S))))
 p(s(x:S)) -> x:S
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 FAC(s(x:S)) -> FAC(p(s(x:S)))
 FAC(s(x:S)) -> P(s(x:S))
-> Rules:
 fac(0) -> s(0)
 fac(s(x:S)) -> times(s(x:S),fac(p(s(x:S))))
 p(s(x:S)) -> x:S

Problem 1: 

SCC Processor:
-> Pairs:
 FAC(s(x:S)) -> FAC(p(s(x:S)))
 FAC(s(x:S)) -> P(s(x:S))
-> Rules:
 fac(0) -> s(0)
 fac(s(x:S)) -> times(s(x:S),fac(p(s(x:S))))
 p(s(x:S)) -> x:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 FAC(s(x:S)) -> FAC(p(s(x:S)))
->->-> Rules:
 fac(0) -> s(0)
 fac(s(x:S)) -> times(s(x:S),fac(p(s(x:S))))
 p(s(x:S)) -> x:S

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 FAC(s(x:S)) -> FAC(p(s(x:S)))
-> Rules:
 fac(0) -> s(0)
 fac(s(x:S)) -> times(s(x:S),fac(p(s(x:S))))
 p(s(x:S)) -> x:S
-> Usable rules:
 p(s(x:S)) -> x:S
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[fac](X) = 0
[p](X) = 1/2.X
[0] = 0
[fSNonEmpty] = 0
[s](X) = 2.X + 1/2
[times](X1,X2) = 0
[FAC](X) = 2.X
[P](X) = 0

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 fac(0) -> s(0)
 fac(s(x:S)) -> times(s(x:S),fac(p(s(x:S))))
 p(s(x:S)) -> x:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.