YES(?,O(n^2))

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:
 Matrix Interpretation Processor:
  dimension: 2
  interpretation:
               [1 3]     [2]
   [not](x0) = [0 1]x0 + [0],
   
                        [1 1]     [2]
   [and](x0, x1) = x0 + [0 1]x1 + [2],
   
                       [1 1]     [2]
   [or](x0, x1) = x0 + [0 1]x1 + [2]
  orientation:
             [2 1]    [2]         
   or(x,x) = [0 2]x + [2] >= x = x
   
              [2 1]    [2]         
   and(x,x) = [0 2]x + [2] >= x = x
   
                 [1 6]    [4]         
   not(not(x)) = [0 1]x + [0] >= x = x
   
                   [1 3]    [1 4]    [10]    [1 3]    [1 4]    [6]                    
   not(and(x,y)) = [0 1]x + [0 1]y + [2 ] >= [0 1]x + [0 1]y + [2] = or(not(x),not(y))
   
                  [1 3]    [1 4]    [10]    [1 3]    [1 4]    [6]                     
   not(or(x,y)) = [0 1]x + [0 1]y + [2 ] >= [0 1]x + [0 1]y + [2] = and(not(x),not(y))
  problem:
   
  Qed