Consider the TRS R consisting of the rewrite rules

1: sum(0) -> 0
2: sum(s(x)) -> sqr(s(x)) + sum(x)
3: sqr(x) -> x * x
4: sum(s(x)) -> (s(x) * s(x)) + sum(x)

There are 2 dependency pairs:

5: SUM(s(x)) -> SQR(s(x))
6: SUM(s(x)) -> SUM(x)

The approximated dependency graph contains one SCC:
{6}.

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

Hence the TRS is terminating.