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