YES

TRS:

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

max/plus interpretations on N:

  not_A(x1) = max{12, -2 + x1}
  not#_A(x1) = max{4, -2}
  and_A(x1,x2) = max{7, 11, 12}
  and#_A(x1,x2) = max{0, 1, 3}
  or_A(x1,x2) = max{10, 9, 11}
  or#_A(x1,x2) = max{2, -1, 3}

precedence:

  not > and > or