Consider the following SQL Query:

SELECT c$.$name, a$.$atype, b$.$b$\_$address

FROM customer AS c$,$ customer$\_$account AS ca$,$ account AS a$,$ bank$\_$branch AS b

WHERE c$.$ssn $=$ ca$.$cssn AND ca$.$ano $=$ a$.$anum AND a$.$bno $=$ b$.$bnum

AND a$.$atype$=$'student' AND b$.$b$\_$address$=$ 'Armidale';

a$)$ Construct an initial $($i$.$e$.$ Canonical$)$ query$-$tree representation of this query.

b$)$ Show how your canonical query$-$tree from part a$)$ can be optimised using The Heuristic Algebraic Optimisation Algorithm. Make sure that you show your query tree after applying each step of the algorithm.