YES

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

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

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

and precedence:

a > w > b > c
)