/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
f(0(x1)) -> 0(x1)
f(s(x1)) -> s(s(f(p(s(x1)))))
p(s(x1)) -> x1
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(0(x1)) -> 0(x1)
 f(s(x1)) -> s(s(f(p(s(x1)))))
 p(s(x1)) -> x1
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(s(x1)) -> F(p(s(x1)))
 F(s(x1)) -> P(s(x1))
-> Rules:
 f(0(x1)) -> 0(x1)
 f(s(x1)) -> s(s(f(p(s(x1)))))
 p(s(x1)) -> x1

Problem 1: 

SCC Processor:
-> Pairs:
 F(s(x1)) -> F(p(s(x1)))
 F(s(x1)) -> P(s(x1))
-> Rules:
 f(0(x1)) -> 0(x1)
 f(s(x1)) -> s(s(f(p(s(x1)))))
 p(s(x1)) -> x1
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(s(x1)) -> F(p(s(x1)))
->->-> Rules:
 f(0(x1)) -> 0(x1)
 f(s(x1)) -> s(s(f(p(s(x1)))))
 p(s(x1)) -> x1

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(s(x1)) -> F(p(s(x1)))
-> Rules:
 f(0(x1)) -> 0(x1)
 f(s(x1)) -> s(s(f(p(s(x1)))))
 p(s(x1)) -> x1
-> Usable rules:
 p(s(x1)) -> x1
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[p](X) = 1/2.X
[s](X) = 2.X + 1/2
[F](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(0(x1)) -> 0(x1)
 f(s(x1)) -> s(s(f(p(s(x1)))))
 p(s(x1)) -> x1
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.