Consider the TRS R consisting of the rewrite rules

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

There is one dependency pair:

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

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

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

Hence the TRS is terminating.