Consider the TRS R consisting of the rewrite rules

1: f(a,x) -> g(a,x)
2: g(a,x) -> f(b,x)
3: f(a,x) -> f(b,x)

There are 3 dependency pairs:

4: F(a,x) -> G(a,x)
5: G(a,x) -> F(b,x)
6: F(a,x) -> F(b,x)

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