A locking algorithm is based on transaction ID and works in the following way. Assume transactions are all assigned an integer as an ID $($e$.$g$.,$ transaction $1,2,3...).$ A lock can be obtained by a transaction if either no other transaction is holding it$,$ or if the transaction that is holding it has a lower ID number. In the latter case, if the transaction with the higher ID tries to obtain the lock it causes the transaction with the lower ID to unlock it$,$ and the transaction with the higher ID obtains it$.$

Try to run the strict two$-$phase locking protocol with this lock. Does it guarantee serializability? If not, provide an example of a schedule that is not serializable using this locking mechanism.