Consider the TRS R consisting of the rewrite rules

1: f(0) -> cons(0)
2: f(s(0)) -> f(p(s(0)))
3: p(s(0)) -> 0

There are 2 dependency pairs:

4: F(s(0)) -> F(p(s(0)))
5: F(s(0)) -> P(s(0))

The approximated dependency graph contains one SCC:
{4}.

- Consider the SCC {4}.
The usable rules are {3}.
By taking the polynomial interpretation
[0] = [p](x) = 1
and [F](x) = [s](x) = x + 1,
rule 3
is weakly decreasing and
rule 4
is strictly decreasing.

Hence the TRS is terminating.