/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 v_NonEmpty:S X:S)
(RULES
0 -> n__0
activate(n__0) -> 0
activate(n__f(X:S)) -> f(activate(X:S))
activate(n__s(X:S)) -> s(activate(X:S))
activate(X:S) -> X:S
f(0) -> cons(0,n__f(n__s(n__0)))
f(s(0)) -> f(p(s(0)))
f(X:S) -> n__f(X:S)
p(s(X:S)) -> X:S
s(X:S) -> n__s(X:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVATE(n__0) -> 0#
 ACTIVATE(n__f(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__f(X:S)) -> F(activate(X:S))
 ACTIVATE(n__s(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__s(X:S)) -> S(activate(X:S))
 F(s(0)) -> F(p(s(0)))
 F(s(0)) -> P(s(0))
-> Rules:
 0 -> n__0
 activate(n__0) -> 0
 activate(n__f(X:S)) -> f(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 f(0) -> cons(0,n__f(n__s(n__0)))
 f(s(0)) -> f(p(s(0)))
 f(X:S) -> n__f(X:S)
 p(s(X:S)) -> X:S
 s(X:S) -> n__s(X:S)

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__0) -> 0#
 ACTIVATE(n__f(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__f(X:S)) -> F(activate(X:S))
 ACTIVATE(n__s(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__s(X:S)) -> S(activate(X:S))
 F(s(0)) -> F(p(s(0)))
 F(s(0)) -> P(s(0))
-> Rules:
 0 -> n__0
 activate(n__0) -> 0
 activate(n__f(X:S)) -> f(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 f(0) -> cons(0,n__f(n__s(n__0)))
 f(s(0)) -> f(p(s(0)))
 f(X:S) -> n__f(X:S)
 p(s(X:S)) -> X:S
 s(X:S) -> n__s(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(s(0)) -> F(p(s(0)))
->->-> Rules:
 0 -> n__0
 activate(n__0) -> 0
 activate(n__f(X:S)) -> f(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 f(0) -> cons(0,n__f(n__s(n__0)))
 f(s(0)) -> f(p(s(0)))
 f(X:S) -> n__f(X:S)
 p(s(X:S)) -> X:S
 s(X:S) -> n__s(X:S)
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__f(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__s(X:S)) -> ACTIVATE(X:S)
->->-> Rules:
 0 -> n__0
 activate(n__0) -> 0
 activate(n__f(X:S)) -> f(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 f(0) -> cons(0,n__f(n__s(n__0)))
 f(s(0)) -> f(p(s(0)))
 f(X:S) -> n__f(X:S)
 p(s(X:S)) -> X:S
 s(X:S) -> n__s(X:S)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 F(s(0)) -> F(p(s(0)))
-> Rules:
 0 -> n__0
 activate(n__0) -> 0
 activate(n__f(X:S)) -> f(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 f(0) -> cons(0,n__f(n__s(n__0)))
 f(s(0)) -> f(p(s(0)))
 f(X:S) -> n__f(X:S)
 p(s(X:S)) -> X:S
 s(X:S) -> n__s(X:S)
-> Usable rules:
 0 -> n__0
 p(s(X:S)) -> X:S
 s(X:S) -> n__s(X:S)
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[0] = 0
[p](X) = 1/2.X + 1/2
[s](X) = 2.X + 2
[n__0] = 0
[n__s](X) = 2.X
[F](X) = 2.X

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 0 -> n__0
 activate(n__0) -> 0
 activate(n__f(X:S)) -> f(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 f(0) -> cons(0,n__f(n__s(n__0)))
 f(s(0)) -> f(p(s(0)))
 f(X:S) -> n__f(X:S)
 p(s(X:S)) -> X:S
 s(X:S) -> n__s(X:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 ACTIVATE(n__f(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__s(X:S)) -> ACTIVATE(X:S)
-> Rules:
 0 -> n__0
 activate(n__0) -> 0
 activate(n__f(X:S)) -> f(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 f(0) -> cons(0,n__f(n__s(n__0)))
 f(s(0)) -> f(p(s(0)))
 f(X:S) -> n__f(X:S)
 p(s(X:S)) -> X:S
 s(X:S) -> n__s(X:S)
->Projection:
 pi(ACTIVATE) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 0 -> n__0
 activate(n__0) -> 0
 activate(n__f(X:S)) -> f(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 f(0) -> cons(0,n__f(n__s(n__0)))
 f(s(0)) -> f(p(s(0)))
 f(X:S) -> n__f(X:S)
 p(s(X:S)) -> X:S
 s(X:S) -> n__s(X:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.