YES
O(n^4)
TRS:
 {
          h(g(x)) -> g(h(f(x))),
           f(a()) -> g(h(a())),
  k(x, h(x), a()) -> h(x),
    k(f(x), y, x) -> f(x)
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
            h(g(x)) -> g(h(f(x))),
             f(a()) -> g(h(a())),
    k(x, h(x), a()) -> h(x),
      k(f(x), y, x) -> f(x)
   }
  Matrix Interpretation:
   Interpretation class: triangular
       [X11]  [X7]  [X3]    [1 1 0 0][X11]   [1 1 0 0][X7]   [1 0 0 0][X3]   [1]
       [X10]  [X6]  [X2]    [0 1 0 0][X10]   [0 1 0 0][X6]   [0 0 1 0][X2]   [0]
   [k]([ X9], [X5], [X1]) = [0 0 0 0][X9] + [0 0 0 0][X5] + [0 0 0 1][X1] + [0]
       [ X8]  [X4]  [X0]    [0 0 0 0][X8]   [0 0 0 0][X4]   [0 0 0 0][X0]   [1]
   
       [X3]    [1 0 1 0][X3]   [0]
       [X2]    [0 0 1 0][X2]   [0]
   [f]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 0][X0]   [0]
   
         [0]
         [0]
   [a] = [1]
         [0]
   
       [X3]    [1 1 0 0][X3]   [0]
       [X2]    [0 0 0 0][X2]   [1]
   [h]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 0][X0]   [0]
   
       [X3]    [1 0 1 0][X3]   [0]
       [X2]    [0 0 1 0][X2]   [1]
   [g]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 0][X0]   [0]
   
   
   Qed