Consider the TRS R consisting of the rewrite rules

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

There is one dependency pair:

4: F(s(x),y,y) -> F(y,x,s(x))

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

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

Hence the TRS is terminating.