YES

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

(COMMENT
Termination is shown by KBO with weight

  w0 = 1
  w(a) = 15
  w(e) = 1
  w(d) = 76
  w(b) = 89
  w(c) = 12

and precedence:

  b > c > d > e > a
)