Consider the TRS R consisting of the rewrite rules 1: fst(0,Z) -> nil 2: fst(s,cons(Y)) -> cons(Y) 3: from(X) -> cons(X) 4: add(0,X) -> X 5: add(s,Y) -> s 6: len(nil) -> 0 7: len(cons(X)) -> s There are no dependency pairs. Hence the TRS is trivially terminating.