Consider the TRS R consisting of the rewrite rules

1: g(x,y) -> x
2: g(x,y) -> y
3: f(0,1,x) -> f(s(x),x,x)
4: f(x,y,s(z)) -> s(f(0,1,z))

There are 2 dependency pairs:

5: F(0,1,x) -> F(s(x),x,x)
6: F(x,y,s(z)) -> F(0,1,z)

The approximated dependency graph contains one SCC:
{5,6}.

- Consider the SCC {5,6}.
There are no usable rules.
By taking the polynomial interpretation
[0] = [1] = 1,
[s](x) = x + 1
and [F](x,y,z) = z + 1,
rule 5
is weakly decreasing and
rule 6
is strictly decreasing.

Hence the TRS is terminating.