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))

linear polynomial interpretations on N:

  or_A(x1,x2) = x1 + x2 + 1
  or#_A(x1,x2) = x1 + x2 + 1
  and_A(x1,x2) = x1 + x2 + 1
  and#_A(x1,x2) = x1 + x2 + 1
  not_A(x1) = x1
  not#_A(x1) = x1

precedence:

  not > or = and