YES

TRS:

  f(j(x,y),y) -> g(f(x,k(y)))
  f(x,h1(y,z)) -> h2(0(),x,h1(y,z))
  g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u))
  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
  k(h(x)) -> h1(0(),x)
  k(h1(x,y)) -> h1(s(x),y)

max/plus interpretations on N:

  f_A(x1,x2) = max{1, 29 + x1, -43 + x2}
  f#_A(x1,x2) = max{69, 69 + x1, 71}
  j_A(x1,x2) = max{0, 31 + x1, -24 + x2}
  j#_A(x1,x2) = max{1, -1, -1 + x2}
  g_A(x1) = max{30, 31 + x1}
  g#_A(x1) = max{46, 43 + x1}
  k_A(x1) = max{0, x1}
  k#_A(x1) = max{82, 39 + x1}
  h1_A(x1,x2) = max{44, 47 + x1, 83 + x2}
  h1#_A(x1,x2) = max{70, 81, 2 + x2}
  h2_A(x1,x2,x3) = max{5, 30, 29 + x2, -84 + x3}
  h2#_A(x1,x2,x3) = max{71, 71, 49 + x2, 69}
  0_A = 1
  0#_A = 0
  s_A(x1) = max{1, x1}
  s#_A(x1) = max{47, 71}
  i_A(x1) = max{0, 1 + x1}
  i#_A(x1) = max{0, x1}
  h_A(x1) = max{43, 83 + x1}
  h#_A(x1) = max{1, -1}

precedence:

  j > g > f = i = h > k = h2 > h1 > 0 = s