Consider the TRS R consisting of the rewrite rules

1: g(f(x),y) -> f(h(x,y))
2: h(x,y) -> g(x,f(y))

There are 2 dependency pairs:

3: G(f(x),y) -> H(x,y)
4: H(x,y) -> G(x,f(y))

The approximated dependency graph contains one SCC:
{3,4}.

- Consider the SCC {3,4}.
There are no usable rules.
By taking the polynomial interpretation
[f](x) = [G](x,y) = [H](x,y) = x + 1,
rule 4
is weakly decreasing and
rule 3
is strictly decreasing.

Hence the TRS is terminating.