YES(?,O(n^2))
TRS:
 {
      implies(x, or(y, z)) -> or(y, implies(x, z)),
         implies(not x, y) -> or(x, y),
  implies(not x, or(y, z)) -> implies(y, or(x, z))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
        implies(x, or(y, z)) -> or(y, implies(x, z)),
           implies(not x, y) -> or(x, y),
    implies(not x, or(y, z)) -> implies(y, or(x, z))
   }
  Matrix Interpretation:
   Interpretation class: triangular
         [X1]    [1 1][X1]   [3]
   [not]([X0]) = [0 0][X0] + [2]
   
             [X3]  [X1]    [1 1][X3]   [1 2][X1]   [0]
   [implies]([X2], [X0]) = [0 0][X2] + [0 1][X0] + [3]
   
        [X3]  [X1]    [1 1][X3]   [1 0][X1]   [0]
   [or]([X2], [X0]) = [0 0][X2] + [0 1][X0] + [2]
   
   
   Qed