Term Rewriting System R:
[]
f(0) -> cons(0, f(s(0)))
f(s(0)) -> f(p(s(0)))
p(s(0)) -> 0

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

F(0) -> F(s(0))
F(s(0)) -> F(p(s(0)))
F(s(0)) -> P(s(0))

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Narrowing Transformation


Dependency Pairs:

F(s(0)) -> F(p(s(0)))
F(0) -> F(s(0))


Rules:


f(0) -> cons(0, f(s(0)))
f(s(0)) -> f(p(s(0)))
p(s(0)) -> 0





On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

F(s(0)) -> F(p(s(0)))
one new Dependency Pair is created:

F(s(0)) -> F(0)

The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Nar
           →DP Problem 2
             ↳Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

F(s(0)) -> F(0)
F(0) -> F(s(0))


Rules:


f(0) -> cons(0, f(s(0)))
f(s(0)) -> f(p(s(0)))
p(s(0)) -> 0




Termination of R could not be shown.
Duration:
0:00 minutes