YES

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

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

  a_A(x1) = 2
  b_A(x1) = x1 + 4
  c_A(x1) = 1
  d_A(x1) = 3
  e_A(x1) = 0
  a#_A(x1) = 0

weights

  w0 = 1
  w(a) = 8
  w(b) = 11
  w(c) = 2
  w(d) = 5
  w(e) = 1

and precedence:

e > b > a > c > d
)