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)

linear polynomial interpretations on N:

  f_A(x1,x2) = x1 + x2 + 2
  f#_A(x1,x2) = x1 + x2 + 2
  j_A(x1,x2) = x1 + x2 + 5
  j#_A(x1,x2) = x1 + x2 + 5
  g_A(x1) = x1 + 1
  g#_A(x1) = x1 + 1
  k_A(x1) = x1 + 1
  k#_A(x1) = x1 + 1
  h1_A(x1,x2) = x1 + x2 + 1
  h1#_A(x1,x2) = x1 + x2 + 1
  h2_A(x1,x2,x3) = x1 + x2 + x3 + 1
  h2#_A(x1,x2,x3) = x1 + x2 + x3 + 1
  0_A = 0
  0#_A = 0
  s_A(x1) = x1
  s#_A(x1) = x1
  i_A(x1) = x1
  i#_A(x1) = x1
  h_A(x1) = x1 + 2
  h#_A(x1) = x1 + 2

precedence:

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