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

Innermost 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
Rewriting 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

Strategy:

innermost

On this DP problem, a Rewriting 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
Rw
→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

Strategy:

innermost

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