/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR x)
(RULES
fac(s(x)) -> *(fac(p(s(x))),s(x))
p(s(0)) -> 0
p(s(s(x))) -> s(p(s(x)))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 fac(s(x)) -> *(fac(p(s(x))),s(x))
 p(s(0)) -> 0
 p(s(s(x))) -> s(p(s(x)))
-> 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)) -> FAC(p(s(x)))
 FAC(s(x)) -> P(s(x))
 P(s(s(x))) -> P(s(x))
-> Rules:
 fac(s(x)) -> *(fac(p(s(x))),s(x))
 p(s(0)) -> 0
 p(s(s(x))) -> s(p(s(x)))

Problem 1: 

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


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 P(s(s(x))) -> P(s(x))
-> Rules:
 fac(s(x)) -> *(fac(p(s(x))),s(x))
 p(s(0)) -> 0
 p(s(s(x))) -> s(p(s(x)))
->Projection:
 pi(P) = 1

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

Reduction Pairs Processor:
-> Pairs:
 FAC(s(x)) -> FAC(p(s(x)))
-> Rules:
 fac(s(x)) -> *(fac(p(s(x))),s(x))
 p(s(0)) -> 0
 p(s(s(x))) -> s(p(s(x)))
-> Usable rules:
 p(s(0)) -> 0
 p(s(s(x))) -> s(p(s(x)))
->Interpretation type:
 Simple mixed
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[p](X) = 1/2.X
[0] = 0
[s](X) = 2.X.X + X + 1
[FAC](X) = 2.X

Problem 1.2: 

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

The problem is finite.