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