YES
O(n^4)
TRS:
 {
            g(h2(x, y, h1(z, u))) -> h2(s(x), y, h1(z, u)),
                   f(x, h1(y, z)) -> h2(0(), x, h1(y, z)),
                    f(j(x, y), y) -> g(f(x, k(y))),
                      k(h1(x, y)) -> h1(s(x), y),
                          k(h(x)) -> h1(0(), x),
  h2(x, j(y, h1(z, u)), h1(z, u)) -> h2(s(x), y, h1(s(z), u)),
                    i(f(x, h(y))) -> y,
         i(h2(s(x), y, h1(x, z))) -> z
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
              g(h2(x, y, h1(z, u))) -> h2(s(x), y, h1(z, u)),
                     f(x, h1(y, z)) -> h2(0(), x, h1(y, z)),
                      f(j(x, y), y) -> g(f(x, k(y))),
                        k(h1(x, y)) -> h1(s(x), y),
                            k(h(x)) -> h1(0(), x),
    h2(x, j(y, h1(z, u)), h1(z, u)) -> h2(s(x), y, h1(s(z), u)),
                      i(f(x, h(y))) -> y,
           i(h2(s(x), y, h1(x, z))) -> z
   }
  Matrix Interpretation:
   Interpretation class: triangular
       [X3]    [1 1 1 0][X3]   [0]
       [X2]    [0 1 0 0][X2]   [1]
   [h]([X1]) = [0 0 1 0][X1] + [1]
       [X0]    [0 0 0 1][X0]   [0]
   
       [X3]    [1 0 0 0][X3]   [1]
       [X2]    [0 1 0 0][X2]   [0]
   [i]([X1]) = [0 0 1 0][X1] + [0]
       [X0]    [0 0 0 1][X0]   [0]
   
       [X3]    [1 0 0 0][X3]   [0]
       [X2]    [0 0 0 0][X2]   [0]
   [s]([X1]) = [0 0 0 0][X1] + [0]
       [X0]    [0 0 0 0][X0]   [0]
   
        [X7]  [X3]    [1 0 0 0][X7]   [1 1 0 0][X3]   [0]
        [X6]  [X2]    [0 0 0 0][X6]   [0 1 0 0][X2]   [1]
   [h1]([X5], [X1]) = [0 0 0 0][X5] + [0 0 1 0][X1] + [1]
        [X4]  [X0]    [0 0 0 0][X4]   [0 0 0 1][X0]   [0]
   
         [0]
         [0]
   [0] = [0]
         [0]
   
        [X11]  [X7]  [X3]    [1 0 0 0][X11]   [1 0 0 0][X7]   [1 0 0 0][X3]   [0]
        [X10]  [X6]  [X2]    [0 0 0 0][X10]   [0 0 0 0][X6]   [0 1 0 0][X2]   [0]
   [h2]([ X9], [X5], [X1]) = [0 0 0 0][X9] + [0 0 0 0][X5] + [0 0 1 0][X1] + [0]
        [ X8]  [X4]  [X0]    [0 0 0 1][X8]   [0 0 0 0][X4]   [0 0 0 1][X0]   [0]
   
       [X7]  [X3]    [1 0 0 0][X7]   [1 1 1 0][X3]   [1]
       [X6]  [X2]    [0 1 0 0][X6]   [0 0 1 0][X2]   [0]
   [j]([X5], [X1]) = [0 0 1 0][X5] + [0 0 1 0][X1] + [0]
       [X4]  [X0]    [0 0 0 0][X4]   [0 0 0 0][X0]   [0]
   
       [X3]    [1 0 1 0][X3]   [0]
       [X2]    [0 1 1 0][X2]   [0]
   [k]([X1]) = [0 0 1 0][X1] + [0]
       [X0]    [0 0 0 1][X0]   [0]
   
       [X7]  [X3]    [1 1 1 0][X7]   [1 1 0 0][X3]   [0]
       [X6]  [X2]    [0 0 1 0][X6]   [0 1 0 0][X2]   [0]
   [f]([X5], [X1]) = [0 0 0 0][X5] + [0 0 1 0][X1] + [0]
       [X4]  [X0]    [0 0 0 0][X4]   [0 0 0 1][X0]   [0]
   
       [X3]    [1 0 1 0][X3]   [0]
       [X2]    [0 1 0 0][X2]   [0]
   [g]([X1]) = [0 0 1 0][X1] + [0]
       [X0]    [0 0 0 1][X0]   [0]
   
   
   Qed