Turing Machine M over input alphabet $=\{$a$,$ b$\}$:

$0\_\_$ L $1$

$0**$ R $0$

$1$ b $\_$ L $2$

$2$ a $\_$ L $3$

$1\_\_*$ halt$\_$accept

$3\_\_$ R $0$

$3**$ L $3$

$1.$ State five strings that are in L$($M$),$ and five that are not. The strings should be over $.$

$2.$ Provide a low level description in Morphett notation of a $(1-$tape deterministic$)$ Turing Machine for the language that has time complexity at most $5$n $+5.$