Consider the TRS R consisting of the rewrite rules

1: a -> g(c)
2: g(a) -> b
3: f(g(X),b) -> f(a,X)

There are 3 dependency pairs:

4: A -> G(c)
5: F(g(X),b) -> F(a,X)
6: F(g(X),b) -> A

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

- Consider the SCC {5}.
The usable rules are {1,2}.
By taking the polynomial interpretation
[c] = 0,
[a] = [b] = 1,
[g](x) = x + 1
and [F](x,y) = x + y + 1,
rule 1
is weakly decreasing and
the rules in {2,5}
are strictly decreasing.

Hence the TRS is terminating.