Consider the TRS R consisting of the rewrite rules

1: f(empty,l) -> l
2: f(cons(x,k),l) -> g(k,l,cons(x,k))
3: g(a,b,c) -> f(a,cons(b,c))

There are 2 dependency pairs:

4: F(cons(x,k),l) -> G(k,l,cons(x,k))
5: G(a,b,c) -> F(a,cons(b,c))

The approximated dependency graph contains one SCC:
{4,5}.

- Consider the SCC {4,5}.
There are no usable rules.
By taking the polynomial interpretation
[F](x,y) = [G](x,y,z) = x + 1
and [cons](x,y) = x + y + 1,
rule 5
is weakly decreasing and
rule 4
is strictly decreasing.

Hence the TRS is terminating.