YES
O(n^4)
TRS:
 {
        or(x, x) -> x,
       and(x, x) -> x,
   not(or(x, y)) -> and(not(x), not(y)),
  not(and(x, y)) -> or(not(x), not(y)),
     not(not(x)) -> x
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
          or(x, x) -> x,
         and(x, x) -> x,
     not(or(x, y)) -> and(not(x), not(y)),
    not(and(x, y)) -> or(not(x), not(y)),
       not(not(x)) -> x
   }
  Matrix Interpretation:
   Interpretation class: triangular
         [X3]    [1 1 1 1][X3]   [0]
         [X2]    [0 1 1 1][X2]   [0]
   [not]([X1]) = [0 0 1 1][X1] + [1]
         [X0]    [0 0 0 1][X0]   [0]
   
         [X7]  [X3]    [1 0 0 1][X7]   [1 0 1 0][X3]   [1]
         [X6]  [X2]    [0 1 1 0][X6]   [0 1 1 1][X2]   [1]
   [and]([X5], [X1]) = [0 0 1 1][X5] + [0 0 1 1][X1] + [1]
         [X4]  [X0]    [0 0 0 1][X4]   [0 0 0 1][X0]   [1]
   
        [X7]  [X3]    [1 0 0 0][X7]   [1 0 0 1][X3]   [1]
        [X6]  [X2]    [0 1 1 0][X6]   [0 1 1 1][X2]   [1]
   [or]([X5], [X1]) = [0 0 1 1][X5] + [0 0 1 1][X1] + [1]
        [X4]  [X0]    [0 0 0 1][X4]   [0 0 0 1][X0]   [1]
   
   
   Qed