Convert Nondeterministic Finite Automata to Regular Expression

Question

I am having a really tough time on this conversion problem. I have read, re-read and watched videos but I am pretty sure the answer I am coming up with is not correct.here is the diagram of the NFA

I have a feeling I am missing some steps. This is the expression I end up with:

(ab*(aUb)a*)Ua*

I've shared my steps in this image. (https://i.stack.imgur.com/e9xVZ.jpg)

Answer 1

I think this paper gives a very clear explanation of how to convert an NFA to a regexp.

Step by step, you create an NFA whose edges are labeled with regexps rather than tokens, and you rip out states until you've got just a single edge going from the input state to the output state.

1. Create a new unique initial state with an edge labelled ε going to the original initial state(s).
2. Create a new unique final state with an edge labelled ε going from all final states to this new final state.
3. One by one, delete internal states: Pick a state q. Look at the states that have an edge into q, in1, in2, in3... Look at the states that have an edge coming out of q, out1, out2, out3. Let the state q have a self loop of Rq (may be empty). For each pair ini, and outj, replace ini -> q -> outj with Rini(Rq*)Routj. Repeat.

https://courses.engr.illinois.edu/cs374/fa2017/extra_notes/01_nfa_to_reg.pdf has an good example.