YES
O(n^4)
TRS:
 {
    mark(g(X)) -> active(g(X)),
    mark(h(X)) -> active(h(mark(X))),
    mark(f(X)) -> active(f(mark(X))),
    g(mark(X)) -> g(X),
  g(active(X)) -> g(X),
    h(mark(X)) -> h(X),
  h(active(X)) -> h(X),
    f(mark(X)) -> f(X),
  f(active(X)) -> f(X),
  active(f(X)) -> mark(g(h(f(X))))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
      mark(g(X)) -> active(g(X)),
      mark(h(X)) -> active(h(mark(X))),
      mark(f(X)) -> active(f(mark(X))),
      g(mark(X)) -> g(X),
    g(active(X)) -> g(X),
      h(mark(X)) -> h(X),
    h(active(X)) -> h(X),
      f(mark(X)) -> f(X),
    f(active(X)) -> f(X),
    active(f(X)) -> mark(g(h(f(X))))
   }
  Matrix Interpretation:
   Interpretation class: triangular
            [X3]    [1 2 0 0][X3]   [1]
            [X2]    [0 0 0 0][X2]   [0]
   [active]([X1]) = [0 0 0 0][X1] + [0]
            [X0]    [0 0 0 1][X0]   [0]
   
       [X3]    [1 0 0 0][X3]   [3]
       [X2]    [0 0 0 0][X2]   [2]
   [f]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 1][X0]   [3]
   
       [X3]    [1 0 0 0][X3]   [0]
       [X2]    [0 0 0 0][X2]   [0]
   [h]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 1][X0]   [1]
   
       [X3]    [1 0 0 0][X3]   [0]
       [X2]    [0 0 0 0][X2]   [0]
   [g]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 0][X0]   [1]
   
          [X3]    [1 0 0 2][X3]   [1]
          [X2]    [0 0 0 0][X2]   [0]
   [mark]([X1]) = [0 0 0 0][X1] + [0]
          [X0]    [0 0 0 1][X0]   [0]
   
   
   Qed