Convert DFA to Regular Expression 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?



:



:
The conversion in each step forms REs that describe


The previous direct edge from one state to another and
the path(s) that use(s) only the removed state as an intermediate state.


In your example, the path for $aa$ goes through $q_1$, which is not removed in this step. Thus it is not added to the RE.