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