YES

Problem 1: 

(VAR v_NonEmpty:S)
(RULES
f(0) -> cons(0)
f(s(0)) -> f(p(s(0)))
p(s(0)) -> 0
) 
(STRATEGY INNERMOST)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.