YES

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

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

  a_A(x1) = 1
  b_A(x1) = 1
  c_A(x1) = 2
  d_A(x1) = 1
  e_A(x1) = 2
  c#_A(x1) = x1

and precedence:

c > a > b > e > d
)