Consider the TRS R consisting of the rewrite rule

1: f(g(x)) -> f(a(g(g(f(x))),g(f(x))))

There are 2 dependency pairs:

2: F(g(x)) -> F(a(g(g(f(x))),g(f(x))))
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.