YES

(VAR x0 x)
(RULES
  v(a(w(x0))) -> b(c(w(x0)))
  d(w(x)) -> c(w(x))
  e(a(w(x))) -> b(c(w(x)))
  u(x) -> c(w(x))
  v(b(x)) -> b(d(x))
  e(b(x)) -> b(c(x))
  a(d(x)) -> v(a(x))
  a(c(x)) -> e(a(x))
)

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

  a_A(x1) = x1 + 1
  c_A(x1) = x1 + 3
  e_A(x1) = 3
  d_A(x1) = x1 + 3
  v_A(x1) = x1 + 3
  b_A(x1) = 3
  u_A(x1) = 4
  w_A(x1) = 1
  a#_A(x1) = x1
  e#_A(x1) = x1
  v#_A(x1) = x1
  b#_A(x1) = x1

weights

  w0 = 1
  w(a) = 3
  w(c) = 1
  w(e) = 1
  w(d) = 2
  w(v) = 2
  w(b) = 1
  w(u) = 4
  w(w) = 1

and precedence:

w > a > e > v > b > d > u > c
)