How to convert this DFA with multiple final states to a regular expression? (State elimination method)
When I eliminate say $q_1$, ..., now since $q_1$ has 2 outgoing transitions, '$a$' to $q_2$ and $\epsilon$ to $f$, what would be that regular expression?


Here are the transitions among the neighbors of $q_1$, which are $q_0, q_2$ and $f$ when $q_1$ is eliminated.


$\delta(q_0, ab)=q_0$
$\delta(q_0, aa)=q_2$
$\delta(q_0, a)=f$
$\delta(q_2, a+bb)=q_0$
$\delta(q_2, ba)=q_2$
$\delta(q_2, \epsilon+b)=f$



  $a(ba)^* + a(ba)^*a(ba)^*(aa(ba)^*a(ba)^*)^* + b(ab)^* + b(ab)^*b(ab)^*(bb(ab)^*b(ab)^*)*$


I am afraid the above is not correct since it does not include $abbaa$ nor $abbab$