Consider the TRS R consisting of the rewrite rules

1: f(x,empty) -> x
2: f(empty,cons(a,k)) -> f(cons(a,k),k)
3: f(cons(a,k),y) -> f(y,k)

There are 2 dependency pairs:

4: F(empty,cons(a,k)) -> F(cons(a,k),k)
5: F(cons(a,k),y) -> F(y,k)

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

- Consider the SCC {4,5}.
There are no usable rules.
By taking the polynomial interpretation
[empty] = 1,
[F](x,y) = 2x + 3y + 1
and [cons](x,y) = x + 3y + 1,
the rules in {4,5}
are strictly decreasing.

Hence the TRS is terminating.