Consider the TRS R consisting of the rewrite rules

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

There are 2 dependency pairs:

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

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

- Consider the SCC {4}.
The usable rules are {3}.
By taking the polynomial interpretation
[F](x) = x,
[s](x) = x + 1
and [p](x) = x - 1,
we obtain a quasi-model of the usable rule.
Furthermore, dependency pair 4
is strictly decreasing.

Hence the TRS is terminating.