I was studying the given finite automaton. Using $R_{ij}^{(k)}$ method, I found out that the Regular Expression that this automaton accepts is $R^*(U^{+}TR^*S)^*$$R^*S(U+TR^*S)^*$. But my book says, the regular expression for the accepted strings can be described in various ways. One is $(R^+SU^*T)^*SU^*$$(R+SU^*T)^*SU^*$.
How do I show that these two regular expressions are equivalent?
This is the method I am referring as $R^{(k)}_{ij}$ method.
