YES
O(n^2)
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
       [X1]    [1 1][X1]   [0]
   [h]([X0]) = [0 1][X0] + [1]
   
       [X1]    [1 1][X1]   [1]
   [i]([X0]) = [0 1][X0] + [1]
   
       [X1]    [1 0][X1]   [0]
   [s]([X0]) = [0 0][X0] + [0]
   
        [X3]  [X1]    [1 0][X3]   [1 0][X1]   [0]
   [h1]([X2], [X0]) = [0 0][X2] + [0 1][X0] + [1]
   
         [0]
   [0] = [0]
   
        [X5]  [X3]  [X1]    [1 0][X5]   [1 1][X3]   [1 0][X1]   [0]
   [h2]([X4], [X2], [X0]) = [0 0][X4] + [0 0][X2] + [0 1][X0] + [0]
   
       [X3]  [X1]    [1 1][X3]   [1 1][X1]   [1]
   [j]([X2], [X0]) = [0 1][X2] + [0 1][X0] + [1]
   
       [X1]    [1 1][X1]   [0]
   [k]([X0]) = [0 1][X0] + [0]
   
       [X3]  [X1]    [1 1][X3]   [1 0][X1]   [1]
   [f]([X2], [X0]) = [0 1][X2] + [0 1][X0] + [0]
   
       [X1]    [1 1][X1]   [0]
   [g]([X0]) = [0 1][X0] + [0]
   
   
   Qed