YES TRS: fst(0(),Z) -> nil() fst(s(X),cons(Y,Z)) -> cons(Y,n__fst(activate(X),activate(Z))) from(X) -> cons(X,n__from(s(X))) add(0(),X) -> X add(s(X),Y) -> s(n__add(activate(X),Y)) len(nil()) -> 0() len(cons(X,Z)) -> s(n__len(activate(Z))) fst(X1,X2) -> n__fst(X1,X2) from(X) -> n__from(X) add(X1,X2) -> n__add(X1,X2) len(X) -> n__len(X) activate(n__fst(X1,X2)) -> fst(X1,X2) activate(n__from(X)) -> from(X) activate(n__add(X1,X2)) -> add(X1,X2) activate(n__len(X)) -> len(X) activate(X) -> X max/plus interpretations on N: fst_A(x1,x2) = max{33, 20 + x1, 23 + x2} fst#_A(x1,x2) = max{33, 20 + x1, 23 + x2} 0_A = 1 0#_A = 1 nil_A = 0 nil#_A = 0 s_A(x1) = max{5, 4 + x1} s#_A(x1) = max{5, 4 + x1} cons_A(x1,x2) = max{28, 27 + x1, 4 + x2} cons#_A(x1,x2) = max{28, 27 + x1, 4 + x2} n__fst_A(x1,x2) = max{19, 6 + x1, 9 + x2} n__fst#_A(x1,x2) = max{19, 6 + x1, 9 + x2} activate_A(x1) = max{26, 14 + x1} activate#_A(x1) = max{26, 14 + x1} from_A(x1) = max{25, 28 + x1} from#_A(x1) = max{25, 28 + x1} n__from_A(x1) = max{24, 19 + x1} n__from#_A(x1) = max{24, 19 + x1} add_A(x1,x2) = max{44, 23 + x1, 34 + x2} add#_A(x1,x2) = max{44, 23 + x1, 34 + x2} n__add_A(x1,x2) = max{29, 9 + x1, 30 + x2} n__add#_A(x1,x2) = max{29, 9 + x1, 30 + x2} len_A(x1) = max{43, 32 + x1} len#_A(x1) = max{43, 32 + x1} n__len_A(x1) = max{29, 18 + x1} n__len#_A(x1) = max{29, 18 + x1} precedence: 0 > nil > fst = activate = n__from = len > n__fst = from = add > cons = n__add > s = n__len