YES(?,O(n^3))
TRS:
 {
    f mark X -> f X,
  f active X -> f X,
    g mark X -> g X,
  g active X -> g X,
    h mark X -> h X,
  h active X -> h X,
    mark f X -> active f mark X,
    mark g X -> active g X,
    mark h X -> active h mark X,
  active f X -> mark g h f X
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
      f mark X -> f X,
    f active X -> f X,
      g mark X -> g X,
    g active X -> g X,
      h mark X -> h X,
    h active X -> h X,
      mark f X -> active f mark X,
      mark g X -> active g X,
      mark h X -> active h mark X,
    active f X -> mark g h f X
   }
  Matrix Interpretation:
   Interpretation class: triangular
            [X2]    [1 0 3][X2]   [2]
   [active]([X1]) = [0 1 0][X1] + [0]
            [X0]    [0 0 1][X0]   [0]
   
          [X2]    [1 3 3][X2]   [1]
   [mark]([X1]) = [0 1 0][X1] + [0]
          [X0]    [0 0 1][X0]   [0]
   
       [X2]    [1 0 0][X2]   [0]
   [h]([X1]) = [0 1 2][X1] + [2]
       [X0]    [0 0 0][X0]   [0]
   
       [X2]    [1 0 0][X2]   [0]
   [g]([X1]) = [0 0 0][X1] + [3]
       [X0]    [0 0 0][X0]   [0]
   
       [X2]    [1 0 0][X2]   [0]
   [f]([X1]) = [0 1 3][X1] + [3]
       [X0]    [0 0 0][X0]   [3]
   
   
   Qed