Consider the TRS R consisting of the rewrite rules 1: zeros -> cons(0,n__zeros) 2: tail(cons(X,XS)) -> activate(XS) 3: zeros -> n__zeros 4: activate(n__zeros) -> zeros 5: activate(X) -> X There are 2 dependency pairs: 6: TAIL(cons(X,XS)) -> ACTIVATE(XS) 7: ACTIVATE(n__zeros) -> ZEROS The approximated dependency graph contains no SCCs and hence the TRS is trivially terminating.