YES

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

(COMMENT
Termination is shown by KBO with weight

  w0 = 1
  w(a) = 11
  w(d) = 8
  w(c) = 1
  w(b) = 14

and precedence:

  c > b > a > d
)