YES

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

(COMMENT
Termination is shown by LPO with precedence:

  a > c > b > d > e
)