We have computed the following equivalence relation:

B1 = {(S0,S0);(S1,S1);(S2,S2);(S3,S3);(S4,S4);(S5,S5);
(S0,S3);(S1,S4);(S2,S5);
(S3,S0);(S4,S1);(S5,S2)}

That equivalence relation partitions the set of states into the following classes:

{S0;S3}
{S1;S4}
{S2;S5}

The quotient structure is a state transition system on these classes, and instead of using the above classes, we pick a representative of each class (which is the state with least index). The transitions between classes are added whenever the classes contain states which were connected by a transition.

The self-loop on S1 of the quotient structure is actually a self-loop from the class {S1;S4} to itself. Why is it there? Since we had a transition from S4 to S4 which is contained in the class of S1. Recall that the transitions of {S1;S4} (which is actually the state S1 in the quotient structure) are the transitions of S1 and also of S4.