Consider the TRS R consisting of the rewrite rules

1: f(f(x)) -> f(c(f(x)))
2: f(f(x)) -> f(d(f(x)))
3: g(c(x)) -> x
4: g(d(x)) -> x
5: g(c(0)) -> g(d(1))
6: g(c(1)) -> g(d(0))

There are 4 dependency pairs:

7: F(f(x)) -> F(c(f(x)))
8: F(f(x)) -> F(d(f(x)))
9: G(c(0)) -> G(d(1))
10: G(c(1)) -> G(d(0))

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