YES

Problem:
 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))

Proof:
 Bounds Processor:
  bound: 0
  enrichment: top
  automaton:
   final states: {9,8,5,2,1}
   transitions:
    f30() -> 8*,4,5,3,2,1
    or0(8,3) -> 9*
    or0(8,9) -> 9*
    or0(9,8) -> 9*
    or0(4,8) -> 9*
    or0(8,8) -> 9*
    or0(9,3) -> 9*
    or0(4,3) -> 9*,4,5,3,2
    or0(9,9) -> 9*
    or0(4,9) -> 9*
    not0(1) -> 9*,5,2,4,3
    not0(8) -> 9*
    and0(8,3) -> 9*
    and0(3,3) -> 9*,4,2,3,5
    and0(8,9) -> 9*
    and0(3,9) -> 9*
    and0(9,8) -> 9*
    and0(8,8) -> 9*
    and0(3,8) -> 9*
    and0(9,3) -> 9*
    and0(9,9) -> 9*
    1 -> 3,5,4
    2 -> 3,5,4
    3 -> 9,5,2
    4 -> 2*
    5 -> 4*
    8 -> 9*
  problem:
   
  Qed