YES

(VAR x)
(RULES
  w(a(c(x))) -> a(c(x))
  a(b(x)) -> w(a(x))
)

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

  w_A(x1) = x1 + 1
  a_A(x1) = x1 + 1
  b_A(x1) = x1 + 1
  c_A(x1) = x1 + 1
  a#_A(x1) = x1

weights

  w0 = 1
  w(w) = 1
  w(a) = 1
  w(b) = 2
  w(c) = 1

and precedence:

c > b > a > w
)