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


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR X)
(RULES
activate(n__f(X)) -> f(X)
activate(X) -> X
f(0) -> cons(0,n__f(s(0)))
f(s(0)) -> f(p(s(0)))
f(X) -> n__f(X)
p(s(0)) -> 0
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVATE(n__f(X)) -> F(X)
 F(s(0)) -> F(p(s(0)))
 F(s(0)) -> P(s(0))
-> Rules:
 activate(n__f(X)) -> f(X)
 activate(X) -> X
 f(0) -> cons(0,n__f(s(0)))
 f(s(0)) -> f(p(s(0)))
 f(X) -> n__f(X)
 p(s(0)) -> 0

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__f(X)) -> F(X)
 F(s(0)) -> F(p(s(0)))
 F(s(0)) -> P(s(0))
-> Rules:
 activate(n__f(X)) -> f(X)
 activate(X) -> X
 f(0) -> cons(0,n__f(s(0)))
 f(s(0)) -> f(p(s(0)))
 f(X) -> n__f(X)
 p(s(0)) -> 0
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(s(0)) -> F(p(s(0)))
->->-> Rules:
 activate(n__f(X)) -> f(X)
 activate(X) -> X
 f(0) -> cons(0,n__f(s(0)))
 f(s(0)) -> f(p(s(0)))
 f(X) -> n__f(X)
 p(s(0)) -> 0

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(s(0)) -> F(p(s(0)))
-> Rules:
 activate(n__f(X)) -> f(X)
 activate(X) -> X
 f(0) -> cons(0,n__f(s(0)))
 f(s(0)) -> f(p(s(0)))
 f(X) -> n__f(X)
 p(s(0)) -> 0
-> Usable rules:
 p(s(0)) -> 0
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[p](X) = 2
[0] = 2
[s](X) = 2.X + 2
[F](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 activate(n__f(X)) -> f(X)
 activate(X) -> X
 f(0) -> cons(0,n__f(s(0)))
 f(s(0)) -> f(p(s(0)))
 f(X) -> n__f(X)
 p(s(0)) -> 0
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.