YES(?,O(n^3))
TRS:
 {
           f a() -> g h a(),
           h g x -> g h f x,
  k(x, h x, a()) -> h x,
    k(f x, y, x) -> f x
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
             f a() -> g h a(),
             h g x -> g h f x,
    k(x, h x, a()) -> h x,
      k(f x, y, x) -> f x
   }
  Matrix Interpretation:
   Interpretation class: triangular
       [X8]  [X5]  [X2]    [1 0 3][X8]   [1 0 0][X5]   [1 0 0][X2]   [2]
   [k]([X7], [X4], [X1]) = [0 1 2][X7] + [0 0 0][X4] + [0 1 1][X1] + [0]
       [X6]  [X3]  [X0]    [0 0 1][X6]   [0 0 0][X3]   [0 0 0][X0]   [2]
   
         [2]
   [a] = [0]
         [2]
   
       [X2]    [1 2 0][X2]   [0]
   [h]([X1]) = [0 1 0][X1] + [2]
       [X0]    [0 0 0][X0]   [1]
   
       [X2]    [1 0 0][X2]   [0]
   [g]([X1]) = [0 0 2][X1] + [2]
       [X0]    [0 0 0][X0]   [0]
   
       [X2]    [1 0 0][X2]   [1]
   [f]([X1]) = [0 0 2][X1] + [0]
       [X0]    [0 0 0][X0]   [2]
   
   
   Qed