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 ELPO with interpretations on natural numbers

  response_A(x1,x2) = 1
  compose_A(x1,x2) = x1 + 1
  a_A = 0
  b_A = 1
  c_A = 1
  a#_A = 0
  b#_A = 0
  c#_A = 0

and precedence:

compose > c > b > a > response
)