YES

(VAR x y w)
(RULES
  response(a(),response(a(),b())) -> b()
  c() -> response(a(),b())
  response(compose(x,y),w) -> response(x,response(y,w))
)

(COMMENT
Termination is shown by KBO with weight

  w0 = 1
  w(response) = 0
  w(compose) = 1
  w(a) = 1
  w(b) = 1
  w(c) = 3

and precedence:

  a > compose > b > c > response
)