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