YES

(VAR z x0)
(RULES
  w(e(f(j(z)))) -> w(e(z))
  h(x0) -> w(e(f(x0)))
  u(z) -> x(w(d(y(z))))
  a(z) -> i(y(z))
  y(b(z)) -> g(z)
  j(f(z)) -> z
  e(f(c(z))) -> i(y(b(c(z))))
  o(z) -> x(w(d(g(c(z)))))
  x(w(i(z))) -> x(w(d(z)))
  e(g(c(z))) -> d(g(c(z)))
  x(w(e(g(z)))) -> x(w(e(f(z))))
)

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

  x_A(x1) = 0
  w_A(x1) = x1 + 1
  e_A(x1) = 6
  f_A(x1) = x1 + 1
  g_A(x1) = x1 + 2
  c_A(x1) = 1
  d_A(x1) = x1 + 1
  i_A(x1) = x1 + 2
  u_A(x1) = 0
  b_A(x1) = x1 + 1
  o_A(x1) = x1 + 1
  a_A(x1) = x1 + 3
  j_A(x1) = x1 + 1
  h_A(x1) = 8
  y_A(x1) = x1 + 1
  x#_A(x1) = x1
  w#_A(x1) = x1
  e#_A(x1) = x1

weights

  w0 = 1
  w(x) = 1
  w(w) = 1
  w(e) = 4
  w(f) = 2
  w(g) = 2
  w(c) = 1
  w(d) = 1
  w(i) = 2
  w(u) = 4
  w(b) = 1
  w(o) = 10
  w(a) = 4
  w(j) = 1
  w(h) = 7
  w(y) = 1

and precedence:

f > b > o > u > x > h > w > i > y > g > a > e > j > d > c
)