Consider the TRS R consisting of the rewrite rules 1: 2nd(cons(X,n__cons(Y,Z))) -> activate(Y) 2: from(X) -> cons(X,n__from(s(X))) 3: cons(X1,X2) -> n__cons(X1,X2) 4: from(X) -> n__from(X) 5: activate(n__cons(X1,X2)) -> cons(X1,X2) 6: activate(n__from(X)) -> from(X) 7: activate(X) -> X There are 4 dependency pairs: 8: 2nd#(cons(X,n__cons(Y,Z))) -> ACTIVATE(Y) 9: FROM(X) -> CONS(X,n__from(s(X))) 10: ACTIVATE(n__cons(X1,X2)) -> CONS(X1,X2) 11: ACTIVATE(n__from(X)) -> FROM(X) The approximated dependency graph contains no SCCs and hence the TRS is trivially terminating.