In this old exam-task I don't understand all the steps to convert the DFA below to a Regular Expression. The $q_2$ state is eliminated first. The provided solution to eliminate $q_2$ is:
If we first eliminate $q_2$ we obtain an intermediate automata with $3$ states $(q_0$,$q_1,q_3)$ such that:
- We go from $q_0$ to $q_1$ with RE $a+ba$
- We go from $q_0$ to $q_3$ with RE $bb$
- We go from $q_1$ to $q_1$ with RE $ba$
- We go from $q_1$ to $q_3$ with RE $a+bb$
I don't understand nr2. $q_3$ can also be reached using RE $aa$. Why is this left out?