Issue with regular expression gym simplication

[arunaabh95]

These 2 expressions are same but give different output in the Regular Expression Gym

Input : b+ab*a+(b+$+ab*a)(b+ab*a)*(b+$+ab*a)
Gives: (b+ab*a)*

but Input b+ab*a+(b+ab*a)(b+ab*a)*(b+ab*a)
does not simplify at all.

I believe output 1 is the correct answer but I wanted to double-check this

[vvulpes0]

The given expressions do not represent the same languages. They have different behaviour on the empty string. The second is equivalent not to (b+ab*a)* but to (b+ab*a)(b+ab*a)*