Consider the TRS R consisting of the rewrite rule 1: and(not(not(x)),y,not(z)) -> and(y,band(x,z),x) There is one dependency pair: 2: AND(not(not(x)),y,not(z)) -> AND(y,band(x,z),x) The approximated dependency graph contains one SCC: {2}. - Consider the SCC {2}. There are no usable rules. By taking the polynomial interpretation [not](x) = x + 1, [AND](x,y,z) = x + y + z + 1 and [band](x,y) = y + 1, rule 2 is strictly decreasing. Hence the TRS is terminating.