Consider the following premises. r -> w_1. w_1 -> r_1. r_1 -> r. Can we infer r <-> r_1 from them?
 From r -> w_1, w_1 -> r_1 we can infer r -> r_1. Finally, from r -> r_1, r_1 -> r we can infer r <-> r_1. Therefore, the answer is yes.