Question 4
A string consists of letters $A$ and $B$. Any of these replacements is allowed: $BBA\to A$, $ABA\to B$, $A\to BBA$, $B\to ABA$. Starting with $BA\cdots A$ (one $B$ followed by $2019$ letters $A$), can one obtain $A\cdots AB$ ($2019$ letters $A$ followed by one $B$) after finitely many replacements? Explain.
