Consider the TRS R consisting of the rewrite rules

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

There are 2 dependency pairs:

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

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

- 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.

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

Hence the TRS is terminating.