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,
        mark f X -> active f mark X,
        mark g X -> active g X,
        mark a() -> active a(),
  active f f a() -> mark f g f a()
 }
 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,
          mark f X -> active f mark X,
          mark g X -> active g X,
          mark a() -> active a(),
    active f f a() -> mark f g f a()
   }
  Matrix Interpretation:
   Interpretation class: triangular
            [X1]    [1 0][X1]   [1]
   [active]([X0]) = [0 1][X0] + [0]
   
         [0]
   [a] = [1]
   
          [X1]    [1 1][X1]   [1]
   [mark]([X0]) = [0 1][X0] + [0]
   
       [X1]    [1 0][X1]   [0]
   [g]([X0]) = [0 0][X0] + [1]
   
       [X1]    [1 2][X1]   [0]
   [f]([X0]) = [0 1][X0] + [2]
   
   
   Qed