SOP Boolean expression of state variable and output of a Moore FSM

Question

Disclaimer: I'm studying for an exam, but I don't have to hand in anything.

I have the state transition diagram of the FSM and its states encoding: I want to find the Sum-Of-Products Boolean expression of S¹₀ , S¹₁ and ouput y.

I've drawn tables for each next state, based on all current states (S₀ and S₁) and inputs (A and B): After this, I don't have very clear how to proceed with drawing the output and state table truth / k-map to get the final Boolean expression.