YES

(VAR x0 x)
(RULES
  d(d(d(c(x0)))) -> d(d(d(d(x0))))
  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))
  e(d(x)) -> d(d(d(d(e(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) = 4
  b_A(x1) = 5
  c_A(x1) = x1 + 3
  d_A(x1) = 4
  e_A(x1) = 9
  c#_A(x1) = x1
  d#_A(x1) = x1

and precedence:

e > c > b > a > d
)