Read regular Expression from NFA Good evening everyone!
Can someone help me with the following task?
So we have this NFA:

I was supposed to create a regular expression out of it. Now the solution says: $a^{+}b^{+}(c|ca^{*}b^{+})^{*}$
Unfortunately I don't understand how this is possible. If I look at the NFA, then we can accept a word that only includes one a without any b's. But the regular expression in the solution does not make that possible.  Or am I missing something?
I also converted the NFA to a DFA however that didn't help much.
Thanks!
The direct edge (a) from initial state 1 to final state 3 is not included in the RE.