Consider the TRS R consisting of the rewrite rules

1: f(a) -> b
2: f(c) -> d
3: f(g(x,y)) -> g(f(x),f(y))
4: f(h(x,y)) -> g(h(y,f(x)),h(x,f(y)))
5: g(x,x) -> h(e,x)

There are 6 dependency pairs:

6: F(g(x,y)) -> G(f(x),f(y))
7: F(g(x,y)) -> F(x)
8: F(g(x,y)) -> F(y)
9: F(h(x,y)) -> G(h(y,f(x)),h(x,f(y)))
10: F(h(x,y)) -> F(x)
11: F(h(x,y)) -> F(y)

The approximated dependency graph contains one SCC:
{7,8,10,11}.

- Consider the SCC {7,8,10,11}.
There are no usable rules.
By taking the polynomial interpretation
[F](x) = x + 1
and [g](x,y) = [h](x,y) = x + y + 1,
the rules in {7,8,10,11}
are strictly decreasing.

Hence the TRS is terminating.