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 ELPO with interpretations on natural numbers

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

and precedence:

e > d > b > c > a
)