Consider the TRS R consisting of the rewrite rules

1: p(f(f(x))) -> q(f(g(x)))
2: p(g(g(x))) -> q(g(f(x)))
3: q(f(f(x))) -> p(f(g(x)))
4: q(g(g(x))) -> p(g(f(x)))

There are 4 dependency pairs:

5: P(f(f(x))) -> Q(f(g(x)))
6: P(g(g(x))) -> Q(g(f(x)))
7: Q(f(f(x))) -> P(f(g(x)))
8: Q(g(g(x))) -> P(g(f(x)))

The approximated dependency graph contains no SCCs
and hence the TRS is trivially terminating.