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{10, 4 + x1, 8 + x2}
  or#_A(x1,x2) = max{0, 2, -6}
  and_A(x1,x2) = max{3, 4 + x1, 8 + x2}
  and#_A(x1,x2) = max{4, 4, 4}
  not_A(x1) = max{2, 2 + x1}
  not#_A(x1) = max{1, -5 + x1}

precedence:

  and > not > or