YES

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

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

  a_A(x1) = 3
  d_A(x1) = 4
  c_A(x1) = 2
  b_A(x1) = 1
  d#_A(x1) = x1
  c#_A(x1) = x1

weights

  w0 = 1
  w(a) = 7
  w(d) = 9
  w(c) = 5
  w(b) = 6

and precedence:

d > a > b > c
)