Consider a project that consists of three consecutive activities of equal length as shown in the network diagram. The project manager would like to complete the project as quickly as possible and realizes that the diagram's logic is misleading

Instead of waiting until activity A is completed before activity B can begin, he can actually begin activity B once activity A has begun. The same reasoning holds for the relationship between activity B and activity C. The project manager decides to divide each activity in half, a technique known as "laddering". The second diagram shows the new network logic. In this diagram, activity A is divided into activity A1 and A2 where A1 must be finished before A2 can begin and before B1 can begin. The manager still isn't satisfied with the completion time of the project. Derive an expression or draw a diagram that demonstrates the fastest possible completion time of the project.

The original length of the project is A+B+C. When laddering is performed the first time, the project length becomes A1+B1+C1+C2; this is because A2 can be performed concurrently with B1 and B2 can be performed concurrently with C1. Alternatively, you can choose to focus on the completion of activity A and indicate that the new project length is A1 + A2 + B2 + C2 (or even A1 + B1 B2 + C2).
If the activities are divided again, the project length will be A1 + B1 + C1 + C2 + C3 + C4; because A2, A3, A4, B2, B3, and B4 can be performed concurrently with other activities.
In general, the project can be viewed as the length of C plus the waiting time while completing the length of subdivided activities A and B. As the number of iterations of laddering these activities becomes large, the length of sub-activity A1 and B1 becomes small, effectively reducing project length to the length of activity C.
Expressed mathematically where P is the project length:

Without laddering P = A + B + C
1st ladder P = + + C
2nd ladder P = + + C
Subsequent P = = C

A Gantt chart showing two halvings of the activities is shown below. The three activities were 4 days long before laddering and are now are effectively twelve activities that are each one day in length.