Q$2(5$ points$)$

Let $L$ be the set of $\{0,1\}$ strings

$($i$)$ Not starting with $1$

$($ii$)$ Not ending with $0$

$($iii$)$ Not containing the substring $000011.$

Argue that $L=lon((000000){11}^{**}{00000}^{**}1)L$ and deduce the generating function for $L$ with respect to length.