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