Consider the TRS R consisting of the rewrite rules

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

There are 2 dependency pairs:

3: H(f(x),y) -> G(x,y)
4: G(x,y) -> H(x,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) = x + 1
and [G](x,y) = [H](x,y) = x + y + 1,
rule 4
is weakly decreasing and
rule 3
is strictly decreasing.

Hence the TRS is terminating.