YES

(VAR x0 x y)
(RULES
  g(j(h(x0))) -> i(h(x0))
  g(f(x,x)) -> i(x)
  f(h(x),y) -> j(h(x))
  f(x,h(y)) -> j(x)
)

(COMMENT
Termination is shown by EKBO with interpretations on natural numbers

  f_A(x1,x2) = x1 + x2 + 1
  h_A(x1) = x1 + 29243
  j_A(x1) = x1 + 1
  g_A(x1) = x1
  i_A(x1) = 0
  f#_A(x1,x2) = x1 + x2

weights

  w0 = 2
  w(f) = 0
  w(h) = 1
  w(j) = 1
  w(g) = 1
  w(i) = 1

and precedence:

h > f > j > g > i
)