Counting Occurrences Using Regular Expressions Let $\backslash$Sigma $=\{$a$,$ b$\}$ Write a regular expression that generates precisely those words over $\backslash$Sigma that contain at most $1$ non$-$overlapping occurrences of the $($contiguous$)$ subword aab. Examples: $-$ b a b a b contains $1$ non$-$overlapping occurrences of bab: babab or b a b a b $-$ bababab contains $2$ non$-$overlapping occurrences of bab: bababab The regular expressions have the following syntax: $-$ for union, for concatenation and for Kleene star $-\backslash$lambda or for $\backslash$lambda $,$ the language containing only the empty word $-0($zero$)$ for $,$ the empty language $-$ can often be left out Example expression: abc $*$ d$($a$+$L$+$Obc$)^*$c is short for a $$ b $$ c$^*$ d $($a$+\backslash$lambda $+$ b $$ c$)^*$ c$.$Let $=\{a,b\}.$

Write a regular expression that generates precisely those words over $$ that contain at most $1$ non$-$overlapping occurrences of the $($contiguous$)$ subword bba.

This question is for automata, example and more detials are in picture.