YES

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

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

  a_A(x1) = 1
  e_A(x1) = 1
  d_A(x1) = 1
  b_A(x1) = 1
  c_A(x1) = 1
  e#_A(x1) = 0
  d#_A(x1) = 0
  b#_A(x1) = x1

weights

  w0 = 1
  w(a) = 4
  w(e) = 16
  w(d) = 10
  w(b) = 1
  w(c) = 1

and precedence:

c > e > b > a > d
)