YES
O(n^5)
TRS:
 {f(h(x)) -> f(i(x)),
   i(a()) -> b(),
   h(a()) -> b(),
  g(i(x)) -> g(h(x))}
 DUP: We consider a non-duplicating system.
  Trs:
   {f(h(x)) -> f(i(x)),
     i(a()) -> b(),
     h(a()) -> b(),
    g(i(x)) -> g(h(x))}
  Matrix Interpretation:
   Interpretation class: triangular
         [0]
         [0]
   [a] = [0]
         [0]
         [1]
   
         [0]
         [0]
   [b] = [0]
         [0]
         [0]
   
       [X4]    [1 0 0 0 0][X4]   [0]
       [X3]    [0 0 0 0 0][X3]   [0]
   [g]([X2]) = [0 0 0 0 0][X2] + [0]
       [X1]    [0 0 0 0 0][X1]   [0]
       [X0]    [0 0 0 0 0][X0]   [0]
   
       [X4]    [1 0 0 0 1][X4]   [0]
       [X3]    [0 0 0 0 0][X3]   [1]
   [h]([X2]) = [0 0 0 1 0][X2] + [0]
       [X1]    [0 0 0 0 0][X1]   [1]
       [X0]    [0 0 0 0 0][X0]   [0]
   
       [X4]    [1 0 0 0 1][X4]   [1]
       [X3]    [0 0 0 0 0][X3]   [0]
   [i]([X2]) = [0 0 0 0 0][X2] + [0]
       [X1]    [0 0 0 0 0][X1]   [0]
       [X0]    [0 0 0 0 0][X0]   [0]
   
       [X4]    [1 1 0 1 0][X4]   [0]
       [X3]    [0 0 0 0 0][X3]   [0]
   [f]([X2]) = [0 0 1 0 0][X2] + [0]
       [X1]    [0 0 0 0 0][X1]   [0]
       [X0]    [0 0 0 0 0][X0]   [0]
   
   
   Qed