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What is regex for the DFA:

I am coming up with following two:

1. b*a(a+b)* and

2. b*a(b+ab*a)*+b*ab*a(ab*a+b)*

Both seems to be correct to me. 

For X1, we have regex b*a(b+ab*a)
For X2, we have regex b*ab*a(ab*a+b)*
(Try navigating automata with those regex. )
Regex 2 is a union of these two.

Main question: I want to  know if I can simplify regex 2 to regex 1 by regex identities, but not by any other approach say by dfa minimization. Is it possible? 

 

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