Given the same input, i$.$e$.,$ a sequence of characters starting with $$ and

ending with #$,$ and any combination of $0$s and $1$s in$-$between, specify a

set of rewrite rules that determine whether the string contains an even

number of $0$s$.$

Here is some sample $$output$$:

$0011$# should be rewritten as $0011->$ A

$10001$# should be rewritten as $10001->$ B

$110110$# should be rewritten as $110110->$ A

$0001100$# should be rewritten as $0001100->$ B

$($b$)$ Is there at most only a single rewrite rule that can be applied at any

point in time during the rewrite process $($using your own rewriting

rules$)?$ Explain.

$($c$)$ Show the steps of your rewrite system for the input strings $0101$#

and $1000$#$.$