YES

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

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

  a_A(x1) = 7
  c_A(x1) = x1 + 6
  e_A(x1) = 7
  d_A(x1) = x1 + 5
  v_A(x1) = x1 + 4
  b_A(x1) = x1 + 1
  u_A(x1) = x1 + 6
  w_A(x1) = x1 + 1
  v#_A(x1) = 0

weights

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

and precedence:

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