YES

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

(COMMENT
Termination is shown by LPO with precedence:

  a > e > v > b > d > u > c > w
)