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