Consider the TRS R consisting of the rewrite rules

1: x * (y + z) -> (x * y) + (x * z)
2: (x + y) * z -> (x * z) + (y * z)
3: x * 1 -> x
4: 1 * y -> y

There are 4 dependency pairs:

5: x *# (y + z) -> x *# y
6: x *# (y + z) -> x *# z
7: (x + y) *# z -> x *# z
8: (x + y) *# z -> y *# z

The approximated dependency graph contains one SCC:
{5-8}.

- Consider the SCC {5-8}.
There are no usable rules.
By taking the polynomial interpretation
[*#](x,y) = [+](x,y) = x + y + 1,
the rules in {5-8}
are strictly decreasing.

Hence the TRS is terminating.