Consider the TRS R consisting of the rewrite rules

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

There are 2 dependency pairs:

3: F(0,1,x) -> F(s(x),x,x)
4: F(x,y,s(z)) -> F(0,1,z)

The approximated dependency graph contains one SCC:
{3,4}.

- Consider the SCC {3,4}.
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 3
is weakly decreasing and
rule 4
is strictly decreasing.

Hence the TRS is terminating.