Consider the TRS R consisting of the rewrite rules 1: minus(minus(x)) -> x 2: minus(h(x)) -> h(minus(x)) 3: minus(f(x,y)) -> f(minus(y),minus(x)) There are 3 dependency pairs: 4: MINUS(h(x)) -> MINUS(x) 5: MINUS(f(x,y)) -> MINUS(y) 6: MINUS(f(x,y)) -> MINUS(x) The approximated dependency graph contains one SCC: {4-6}. - Consider the SCC {4-6}. There are no usable rules. By taking the polynomial interpretation [h](x) = [MINUS](x) = x + 1 and [f](x,y) = x + y + 1, the rules in {4-6} are strictly decreasing. Hence the TRS is terminating.