YES
O(n^5)
TRS:
 {f(g(f(a()), h(a(), f(a())))) -> f(h(g(f(a()), a()), g(f(a()), f(a()))))}
 DUP: We consider a non-duplicating system.
  Trs:
   {f(g(f(a()), h(a(), f(a())))) -> f(h(g(f(a()), a()), g(f(a()), f(a()))))}
  Matrix Interpretation:
   Interpretation class: triangular
         [0]
         [0]
   [a] = [0]
         [0]
         [0]
   
       [X9]  [X4]    [1 0 0 0 0][X9]   [1 0 0 0 0][X4]   [0]
       [X8]  [X3]    [0 0 0 0 0][X8]   [0 0 0 0 0][X3]   [0]
   [g]([X7], [X2]) = [0 0 0 0 0][X7] + [0 0 0 0 0][X2] + [0]
       [X6]  [X1]    [0 0 0 0 0][X6]   [0 0 0 0 0][X1]   [0]
       [X5]  [X0]    [0 0 0 0 1][X5]   [0 0 0 0 0][X0]   [0]
   
       [X9]  [X4]    [1 0 0 0 0][X9]   [1 0 0 0 0][X4]   [0]
       [X8]  [X3]    [0 0 0 0 0][X8]   [0 0 0 0 0][X3]   [0]
   [h]([X7], [X2]) = [0 0 0 0 0][X7] + [0 0 0 0 0][X2] + [0]
       [X6]  [X1]    [0 0 0 0 0][X6]   [0 0 0 0 0][X1]   [0]
       [X5]  [X0]    [0 0 0 0 0][X5]   [0 0 0 0 0][X0]   [0]
   
       [X4]    [1 0 0 0 1][X4]   [0]
       [X3]    [0 0 0 0 0][X3]   [0]
   [f]([X2]) = [0 0 0 0 0][X2] + [0]
       [X1]    [0 0 0 0 0][X1]   [0]
       [X0]    [0 0 0 0 0][X0]   [1]
   
   
   Qed