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