Consider the TRS R consisting of the rewrite rule 1: x * (y + z) -> (x * y) + (x * z) There are 2 dependency pairs: 2: x *# (y + z) -> x *# y 3: x *# (y + z) -> x *# z The approximated dependency graph contains one SCC: {2,3}. - Consider the SCC {2,3}. There are no usable rules. By taking the polynomial interpretation [*#](x,y) = [+](x,y) = x + y + 1, the rules in {2,3} are strictly decreasing. Hence the TRS is terminating.