YES TRS: a__2nd(cons(X,cons(Y,Z))) -> mark(Y) a__from(X) -> cons(mark(X),from(s(X))) mark(2nd(X)) -> a__2nd(mark(X)) mark(from(X)) -> a__from(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__2nd(X) -> 2nd(X) a__from(X) -> from(X) max/plus interpretations on N: a__2nd_A(x1) = max{4, x1} a__2nd#_A(x1) = max{6, 6} cons_A(x1,x2) = max{2, 9 + x1, -3 + x2} cons#_A(x1,x2) = max{2, 7, -2 + x2} mark_A(x1) = max{3, 3 + x1} mark#_A(x1) = max{1, 6 + x1} a__from_A(x1) = max{4, 12 + x1} a__from#_A(x1) = max{16, 12 + x1} from_A(x1) = max{0, 12 + x1} from#_A(x1) = max{13, 15} s_A(x1) = max{1, 2 + x1} s#_A(x1) = max{0, -1} 2nd_A(x1) = max{1, x1} 2nd#_A(x1) = max{5, 6} precedence: a__2nd = from > a__from = 2nd > cons > mark > s