Consider the TRS R consisting of the rewrite rules

1: x + 0 -> x
2: x + s(y) -> s(x + y)
3: 0 + s(y) -> s(y)
4: s(0 + y) -> s(y)

There are 3 dependency pairs:

5: x +# s(y) -> S(x + y)
6: x +# s(y) -> x +# y
7: S(0 + y) -> S(y)

The approximated dependency graph contains 2 SCCs:
{7}
and {6}.

- Consider the SCC {7}.
There are no usable rules.
By taking the polynomial interpretation
[0] = 1,
[S](x) = x + 1
and [+](x,y) = x + y + 1,
rule 7
is strictly decreasing.

- Consider the SCC {6}.
There are no usable rules.
By taking the polynomial interpretation
[s](x) = x + 1
and [+#](x,y) = x + y + 1,
rule 6
is strictly decreasing.

Hence the TRS is terminating.