Consider the TRS R consisting of the rewrite rules 1: rev(a) -> a 2: rev(b) -> b 3: rev(x ++ y) -> rev(y) ++ rev(x) 4: rev(x ++ x) -> rev(x) There are 3 dependency pairs: 5: REV(x ++ y) -> REV(y) 6: REV(x ++ y) -> REV(x) 7: REV(x ++ x) -> REV(x) The approximated dependency graph contains one SCC: {5-7}. - Consider the SCC {5-7}. There are no usable rules. By taking the polynomial interpretation [REV](x) = x + 1 and [++](x,y) = x + y + 1, the rules in {5-7} are strictly decreasing. Hence the TRS is terminating.