YES(?,O(n^2))
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,
      mark c X -> active c X,
      mark d X -> active d X,
      c mark X -> c X,
    c active X -> c X,
  active f f X -> mark c f g f X,
    active h X -> mark c d X,
    active c X -> mark d X,
      d mark X -> d X,
    d active X -> d 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,
        mark c X -> active c X,
        mark d X -> active d X,
        c mark X -> c X,
      c active X -> c X,
    active f f X -> mark c f g f X,
      active h X -> mark c d X,
      active c X -> mark d X,
        d mark X -> d X,
      d active X -> d X
   }
  Matrix Interpretation:
   Interpretation class: triangular
       [X1]    [1 0][X1]   [0]
   [d]([X0]) = [0 0][X0] + [0]
   
            [X1]    [1 0][X1]   [4]
   [active]([X0]) = [0 1][X0] + [0]
   
       [X1]    [1 0][X1]   [3]
   [c]([X0]) = [0 0][X0] + [0]
   
          [X1]    [1 4][X1]   [6]
   [mark]([X0]) = [0 1][X0] + [0]
   
       [X1]    [1 0][X1]   [6]
   [h]([X0]) = [0 1][X0] + [2]
   
       [X1]    [1 0][X1]   [0]
   [g]([X0]) = [0 0][X0] + [0]
   
       [X1]    [1 7][X1]   [2]
   [f]([X0]) = [0 1][X0] + [2]
   
   
   Qed