YES

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

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

  b_A(x1) = x1 + 1
  d_A(x1) = x1 + 1
  a_A(x1) = x1 + 1
  e_A(x1) = x1 + 1
  c_A(x1) = x1 + 1
  c#_A(x1) = 0

weights

  w0 = 1
  w(b) = 1
  w(d) = 1
  w(a) = 1
  w(e) = 1
  w(c) = 1

and precedence:

d > c > e > b > a
)