Consider the TRS R consisting of the rewrite rule 1: x * (minus(y) * y) -> minus(y * y) * x There are 2 dependency pairs: 2: x *# (minus(y) * y) -> minus(y * y) *# x 3: x *# (minus(y) * y) -> y *# y The approximated dependency graph contains one SCC: {2,3}. - Consider the SCC {2,3}. By taking the polynomial interpretation [minus](x) = x + 1 and [*](x,y) = [*#](x,y) = x + y + 1, the rules in {1,2} are weakly decreasing and rule 3 is strictly decreasing. There is one new SCC. - Consider the SCC {2}. By taking the polynomial interpretation [minus](x) = 1 and [*](x,y) = [*#](x,y) = x + y + 1, the rules in {1,2} are strictly decreasing. Hence the TRS is terminating.