Consider the TRS R consisting of the rewrite rule

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

There is one dependency pair:

2: F(g(x,y),f(y,y)) -> F(g(y,x),y)

The approximated dependency graph contains one SCC:
{2}.

- Consider the SCC {2}.
There are no usable rules.
By taking the polynomial interpretation
[f](x,y) = [F](x,y) = [g](x,y) = x + y + 1,
rule 2
is strictly decreasing.

Hence the TRS is terminating.