YES

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

(COMMENT
Termination is shown by LPO with precedence:

  d > b > c > a
)