$[10$ Points$]$ Consider the language $L=\{a^{n+1}{b}^n$:$n0\}.$

$($a$)(5$ points$)$ Describe in English the complement $\frac{?}{\text{b}\text{a}\text{r}}(L)$ of $L.$ Your description should specify the types of strings that are in $\frac{?}{\text{b}\text{a}\text{r}}(L).$ That is$,$ it is not acceptable to say $\frac{?}{\text{b}\text{a}\text{r}}(L)$ includes every string over $\{a,b\}$ that is not in $L,$ which is obviously true.

$($b$)(5$ points$)$ Give a CFG for $\frac{?}{\text{b}\text{a}\text{r}}(L).$