Consider the TRS R consisting of the rewrite rules

1: p(s(x)) -> x
2: fac(0) -> s(0)
3: fac(s(x)) -> times(s(x),fac(p(s(x))))

There are 2 dependency pairs:

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

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

- Consider the SCC {4}.
The usable rules are {1}.
By taking the polynomial interpretation
[FAC](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.