How to show that the two-phase locking protocol ensures conflict serializability?

The two-phase locking (2PL) protocol ensures conflict serializability by preventing cycles in the serialization graph, which is pivotal for avoiding deadlocks. In the first phase, transactions acquire locks without releasing any, ensuring that once a lock is obtained, the transaction can only proceed forward, not backward. During the second phase, transactions release locks but do not acquire any new ones, preserving the order of operations. This locking mechanism guarantees that the execution of transactions can be serialized in a way that reflects the order of conflicting operations, thereby ensuring conflict serializability.