YES

(VAR x0 x)
(RULES
  d(a(a(x0))) -> a(d(a(x0)))
  b(a(x0)) -> a(c(x0))
  c(a(x0)) -> a(c(x0))
  c(d(a(x))) -> a(x)
  d(a(c(x))) -> a(x)
  e(x) -> d(a(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 + 2
  c_A(x1) = x1 + 1

weights

  w0 = 1
  w(b) = 1
  w(d) = 1
  w(a) = 1
  w(e) = 3
  w(c) = 1

and precedence:

c > b > d > a > e
)