Consider the TRS R consisting of the rewrite rules

1: f(c(s(x),y)) -> f(c(x,s(y)))
2: g(c(x,s(y))) -> g(c(s(x),y))

There are 2 dependency pairs:

3: F(c(s(x),y)) -> F(c(x,s(y)))
4: G(c(x,s(y))) -> G(c(s(x),y))

The approximated dependency graph contains 2 SCCs:
{3}
and {4}.

- Consider the SCC {3}.
There are no usable rules.
By taking the polynomial interpretation
[c](x,y) = [F](x) = [s](x) = x + 1,
rule 3
is strictly decreasing.

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

Hence the TRS is terminating.