I have a logical question that I can't quite crack.
Given two Automatas accepting the same language L, does one have to refine the other? 

meaning, does `R_a1` equivalence relations have to refine `R_a2` equivalence relations? (or vice versa)

I am leaning toward the answer yes because if we have a regular language L which is accepted by an automaton A, we can show that the relation R_A refines the relation R_L, meaning Ra⊑Rl.
which means both Ra1⊑Rl and Ra2⊑Rl. 

We are currently studying the Myhill-Nerode Theorem so I'm guessing it has to do something with it.
I've tried combining few theorems together but came out empty.