YES
O(n^5)
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
       [X14]  [X9]  [X4]    [1 0 0 0 1][X14]   [1 0 0 0 0][X9]   [1 1 0 0 0][X4]   [1]
       [X13]  [X8]  [X3]    [0 0 0 0 0][X13]   [0 0 0 0 0][X8]   [0 0 0 1 0][X3]   [0]
   [k]([X12], [X7], [X2]) = [0 0 0 1 0][X12] + [0 0 1 0 0][X7] + [0 0 0 0 0][X2] + [0]
       [X11]  [X6]  [X1]    [0 0 0 1 0][X11]   [0 0 0 0 0][X6]   [0 0 0 0 0][X1]   [0]
       [X10]  [X5]  [X0]    [0 0 0 0 0][X10]   [0 0 0 0 0][X5]   [0 0 0 0 0][X0]   [1]
   
       [X4]    [1 0 0 1 0][X4]   [0]
       [X3]    [0 0 0 0 0][X3]   [0]
   [f]([X2]) = [0 0 0 0 1][X2] + [0]
       [X1]    [0 0 0 1 1][X1]   [0]
       [X0]    [0 0 0 0 0][X0]   [1]
   
         [0]
         [0]
   [a] = [0]
         [1]
         [1]
   
       [X4]    [1 0 1 0 0][X4]   [0]
       [X3]    [0 0 0 0 0][X3]   [0]
   [h]([X2]) = [0 0 0 0 0][X2] + [1]
       [X1]    [0 0 0 0 0][X1]   [0]
       [X0]    [0 0 0 0 0][X0]   [0]
   
       [X4]    [1 0 0 1 0][X4]   [0]
       [X3]    [0 0 0 0 0][X3]   [0]
   [g]([X2]) = [0 0 0 0 1][X2] + [1]
       [X1]    [0 0 0 0 0][X1]   [0]
       [X0]    [0 0 0 0 0][X0]   [0]
   
   
   Qed