Consider the TRS R consisting of the rewrite rules

1: f(a,b) -> f(a,c)
2: f(c,d) -> f(b,d)

There are 2 dependency pairs:

3: F(a,b) -> F(a,c)
4: F(c,d) -> F(b,d)

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