YES TRS: active(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) max/plus interpretations on N: active_A(x1) = max{3, x1} active#_A(x1) = max{57, 38 + x1} 2nd_A(x1) = max{24, 18 + x1} 2nd#_A(x1) = max{0, 44 + x1} cons_A(x1,x2) = max{7, 23 + x1, -21 + x2} cons#_A(x1,x2) = max{23, 47 + x1, 45} mark_A(x1) = max{4, 5 + x1} mark#_A(x1) = max{1, 45 + x1} from_A(x1) = max{0, 31 + x1} from#_A(x1) = max{44, 46} s_A(x1) = max{1, 13 + x1} s#_A(x1) = max{3, 0} precedence: cons > mark > 2nd = s > active > from