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