Consider the following premises. w -> r. r -> s_4. r_1 -> w. r_6 -> r_1. s_4 -> r_6. Can we infer w <-> r_1 from them?
 From w -> r, r -> s_4 we can infer w -> s_4. From w -> s_4, s_4 -> r_6 we can infer w -> r_6. From w -> r_6, r_6 -> r_1 we can infer w -> r_1. Finally, from w -> r_1, r_1 -> w we can infer w <-> r_1. Therefore, the answer is yes.