$($a$)$ State the definition of an $s-$grammar.

$($b$)$ Find an $s-$grammar for $L(aa{a}^{*}b+b).$

$($c$)$ Find an $s-$grammar for $L=\{a^n{b}^{n+1}$:$n1\}.$

Hint: drawing a nfa or a derivation tree may be helpful.