Problem $2(25$ points$)$: In the following schedule for transactions, w$\_($i$)($A$)$ and r$\_($i$)($A$)$ correspond to read

and write operations by transaction i on item A and RL$\_($A$)^($i$)$ and WL$\_($A$)^($i$)$ refer to read and write locking

operations on item A by transaction i$.$

RL$\_($x$)^(1)$r$\_(1)($x$)$RL$\_($Z$)^(2)$r$\_(2)($Z$)$RL$\_($x$)^(3)$r$\_(3)($x$)$RL$\_($Z$)^(1)$r$\_(1)($Z$)$RL$\_($Y$)^(2)$r$\_(2)($Y$)$WL$\_($Z$)^(2)$w$\_(2)($Z$)$WL$\_($x$)^(1)$w$\_(1)($x$)$WL$\_($Y$)^(3)$w$\_(3)($Y$)$WL$\_($Y$)^(2)$w$\_(2)($Y$)$

$($a$)$ Insert unlock operations into the above schedule so that locks are released as soon as possible

while maintaining two$-$phase locking $(2$ PL $)$ protocol. Which version of $2$ PL $($basic$,$ conservative,

rigorous$)$ does this schedule correspond to$?$ Show the corresponding wait$-$for graph and explain if

this schedule produces deadlocks or not. $(14$ points$)($b$)$ When and what transactions, if any, will

be aborted if wait$-$die and wound$-$wait protocols were used on this schedule? $(6$ points$)($c$)$ For this

part, ignore the locking operations in the schedule. When and what transactions, will be aborted by

Basic Timestamp Ordering $($TO$)?$ What will be the difference in execution between Basic TO and

Thomas's Write Rule? $(5$ points$)$