YES
O(n^4)
TRS:
 {
     a__f(X) -> g(h(f(X))),
     a__f(X) -> f(X),
  mark(g(X)) -> g(X),
  mark(h(X)) -> h(mark(X)),
  mark(f(X)) -> a__f(mark(X))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
       a__f(X) -> g(h(f(X))),
       a__f(X) -> f(X),
    mark(g(X)) -> g(X),
    mark(h(X)) -> h(mark(X)),
    mark(f(X)) -> a__f(mark(X))
   }
  Matrix Interpretation:
   Interpretation class: triangular
          [X3]    [1 1 1 0][X3]   [0]
          [X2]    [0 1 1 1][X2]   [0]
   [mark]([X1]) = [0 0 1 0][X1] + [0]
          [X0]    [0 0 0 1][X0]   [0]
   
          [X3]    [1 0 0 0][X3]   [1]
          [X2]    [0 1 0 0][X2]   [1]
   [a__f]([X1]) = [0 0 1 1][X1] + [1]
          [X0]    [0 0 0 0][X0]   [0]
   
       [X3]    [1 0 0 0][X3]   [0]
       [X2]    [0 1 0 0][X2]   [1]
   [f]([X1]) = [0 0 1 1][X1] + [1]
       [X0]    [0 0 0 0][X0]   [0]
   
       [X3]    [1 0 0 0][X3]   [0]
       [X2]    [0 1 0 0][X2]   [0]
   [h]([X1]) = [0 0 1 1][X1] + [1]
       [X0]    [0 0 0 0][X0]   [1]
   
       [X3]    [1 0 0 0][X3]   [0]
       [X2]    [0 0 0 0][X2]   [1]
   [g]([X1]) = [0 0 0 0][X1] + [1]
       [X0]    [0 0 0 0][X0]   [0]
   
   
   Qed