Consider the TRS R consisting of the rewrite rule

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

There is one dependency pair:

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

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

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

Hence the TRS is terminating.