Consider the TRS R consisting of the rewrite rules

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

There are 3 dependency pairs:

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

The approximated dependency graph contains 2 SCCs:
{5}
and {4}.

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

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

Hence the TRS is terminating.