Demonstrate Arc consistency:

To demonstrate the worth of performing an arc-consistency check before starting a serarch for a solution, we'll use an example from Barbara Smith's tutorial. Suppose that we have four tasks to complete, A, B, C and D, and we're trying to schedule them. They are subject to the constraints that: 

-  Task A lasts 3 hours and precedes tasks B and C 

-  Task B lasts 2 hours and precedes task D 

-  Task C lasts 4 hours and precedes task D 

-  Task D lasts 2 hours 

We will model this problem with a variable for each of the task start times, namely startA, startB, startC and startD. We'll also have a variable for the overall start time: start, and a variable for the overall finishing time: finish. We will say that the domain for variable  start  is {0}, but the domains for all the other variables is {0,1,...,11}, because the summation of the duration of the tasks is 3 + 2 + 4 + 2 = 11. We can now translate our English specification of the constraints into our formal model.