YES

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

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

  a_A(x1) = 8
  d_A(x1) = 9
  c_A(x1) = 8
  b_A(x1) = 8

and precedence:

d > a > b > c
)