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