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