YES

TRS:

  active(2nd(cons1(X,cons(Y,Z)))) -> mark(Y)
  active(2nd(cons(X,X1))) -> mark(2nd(cons1(X,X1)))
  active(from(X)) -> mark(cons(X,from(s(X))))
  active(2nd(X)) -> 2nd(active(X))
  active(cons(X1,X2)) -> cons(active(X1),X2)
  active(from(X)) -> from(active(X))
  active(s(X)) -> s(active(X))
  active(cons1(X1,X2)) -> cons1(active(X1),X2)
  active(cons1(X1,X2)) -> cons1(X1,active(X2))
  2nd(mark(X)) -> mark(2nd(X))
  cons(mark(X1),X2) -> mark(cons(X1,X2))
  from(mark(X)) -> mark(from(X))
  s(mark(X)) -> mark(s(X))
  cons1(mark(X1),X2) -> mark(cons1(X1,X2))
  cons1(X1,mark(X2)) -> mark(cons1(X1,X2))
  proper(2nd(X)) -> 2nd(proper(X))
  proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
  proper(from(X)) -> from(proper(X))
  proper(s(X)) -> s(proper(X))
  proper(cons1(X1,X2)) -> cons1(proper(X1),proper(X2))
  2nd(ok(X)) -> ok(2nd(X))
  cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
  from(ok(X)) -> ok(from(X))
  s(ok(X)) -> ok(s(X))
  cons1(ok(X1),ok(X2)) -> ok(cons1(X1,X2))
  top(mark(X)) -> top(proper(X))
  top(ok(X)) -> top(active(X))

max/plus interpretations on N:

  active_A(x1) = max{24, 20 + x1}
  active#_A(x1) = max{49, 51 + x1}
  2nd_A(x1) = max{11, x1}
  2nd#_A(x1) = max{1, 60}
  cons1_A(x1,x2) = max{25, x1, x2}
  cons1#_A(x1,x2) = max{61, 2 + x1, 28 + x2}
  cons_A(x1,x2) = max{8, x1, -9 + x2}
  cons#_A(x1,x2) = max{44, 43, 58}
  mark_A(x1) = max{27, x1}
  mark#_A(x1) = max{58, 18}
  from_A(x1) = max{7, x1}
  from#_A(x1) = max{56, 58}
  s_A(x1) = max{8, x1}
  s#_A(x1) = max{50, 58}
  proper_A(x1) = max{25, 0}
  proper#_A(x1) = max{61, 59}
  ok_A(x1) = max{53, 28 + x1}
  ok#_A(x1) = max{0, 57}
  top_A(x1) = max{0, 0}
  top#_A(x1) = max{88, 62 + x1}

precedence:

  top > active > cons > cons1 = proper > ok > 2nd = from > s > mark