YES

TRS:

  not(not(x)) -> x
  not(or(x,y)) -> and(not(not(not(x))),not(not(not(y))))
  not(and(x,y)) -> or(not(not(not(x))),not(not(not(y))))

max/plus interpretations on N:

  not_A(x1) = max{3, x1}
  not#_A(x1) = max{1, -4 + x1}
  or_A(x1,x2) = max{12, 9 + x1, 8 + x2}
  or#_A(x1,x2) = max{8, -5 + x1, 2}
  and_A(x1,x2) = max{12, 9 + x1, 8 + x2}
  and#_A(x1,x2) = max{0, 1, x2}

precedence:

  and > not > or