Consider the TRS R consisting of the rewrite rules

1: f(g(x)) -> g(g(f(x)))
2: f(g(x)) -> g(g(g(x)))

There is one dependency pair:

3: F(g(x)) -> F(x)

The approximated dependency graph contains one SCC:
{3}.

- Consider the SCC {3}.
There are no usable rules.
By taking the polynomial interpretation
[F](x) = [g](x) = x + 1,
rule 3
is strictly decreasing.

Hence the TRS is terminating.