YES

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

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

  a_A(x1) = 1
  d_A(x1) = 3
  c_A(x1) = 1
  b_A(x1) = 2

weights

  w0 = 1
  w(a) = 5
  w(d) = 14
  w(c) = 7
  w(b) = 15

and precedence:

d > a > c > b
)