Consider the TRS R consisting of the rewrite rules 1: rev(ls) -> r1(ls,empty) 2: r1(empty,a) -> a 3: r1(cons(x,k),a) -> r1(k,cons(x,a)) There are 2 dependency pairs: 4: REV(ls) -> R1(ls,empty) 5: R1(cons(x,k),a) -> R1(k,cons(x,a)) The approximated dependency graph contains one SCC: {5}. - Consider the SCC {5}. There are no usable rules. By taking the polynomial interpretation [R1](x,y) = x + 1 and [cons](x,y) = x + y + 1, rule 5 is strictly decreasing. Hence the TRS is terminating.