Kripke Quotient Structure

Question

I am trying to solve the following exercise:

However, my solution seems to be wrong.

I also tried solving it with the Tool:

Which, if I am correct, should be the same as my solution. I just removed the deadend states since they get merged with S0 / S1 / S2 respectively:

Where am I wrong?

Answer 1

This is my solution:

vars a,c,d;
init 1;
labels 0:a,c;1:a,c,d;2:a,c,d;
transitions 0->0;0->1;1->0;1->2;2->0;

This was your solution:
vars a,c,d;
init 1;
labels 0:a,c; 1:a,c,d; 2:a,c,d;
transitions 0->0; 0->1; 1->0: 1->2; 2->0;

You can see that your third transition wasn't ended by a semicolon but by a colon.