Consider the TRS R consisting of the rewrite rules

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

There are 3 dependency pairs:

4: F(g(x)) -> F(f(x))
5: F(g(x)) -> F(x)
6: F'(s(x),y,y) -> F'(y,x,s(x))

The approximated dependency graph contains 2 SCCs:
{4,5}
and {6}.

- Consider the SCC {4,5}.
The usable rules are {1,2}.
By taking the polynomial interpretation
[h](x) = 1,
[f](x) = x
and [F](x) = [g](x) = x + 1,
the rules in {1,2}
are weakly decreasing and
the rules in {4,5}
are strictly decreasing.

- Consider the SCC {6}.
There are no usable rules.
By taking the polynomial interpretation
[s](x) = x + 1
and [F'](x,y,z) = x + y + 1,
rule 6
is strictly decreasing.

Hence the TRS is terminating.