YES

TRS:

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

max/plus interpretations on N:

  or_A(x1,x2) = max{0, x1, x2}
  or#_A(x1,x2) = max{0, x1, x2}
  and_A(x1,x2) = max{0, x1, x2}
  and#_A(x1,x2) = max{0, x1, x2}
  not_A(x1) = max{0, x1}
  not#_A(x1) = max{0, x1}

precedence:

  not > or > and