State Elimination?

Computer Science Level 2

Which of the following regular expression best describes the above finite automata?

Note: ${ a }^{ \star }$ means $0$ or more number of $a$ 's $,$ ${ a }^{ + }=a{ a }^{ \star }$ and $A+B$ implies either $A$ or $B$ . $S1$ is the start state and $S4$ is the final state.

{a}^{+}{(b{a}^{\star})}^{+}c{[d\{a{a}^{+}{(b{a}^{+})}^{\star}c+b\}]}^{\star}

{a}^{+}{(b{a}^{+})}^{\star}c{[da{a}^{\star}{(b{a}^{+})}^{\star}c + db] }^{ \star }

{a}^{+}{(b{a}^{\star})}^{+}c{[da{a}^{+}{(b{a}^{+})}^{\star}c + db] }^{ \star }

{a}^{+}{(b{a}^{+})}^{\star}c{[da{a}^{+}{(b{a}^{+})}^{\star}c +db]}^{\star}

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State Elimination?

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