c This is a test input for the MAX-CSP solver

c What is the maximum number of constraints that can be satisfied?
c give a proof of your claim.

p 9 8

5  : 1 2 3					0
7  :                4 5 6			0
9  :                               7 8 9	0
11 : 1              4              7		0
11 :   2              5              8		0
9  :     3              6              9		0
7  : 1                5                9		0
5  :     3            5            7		0

Let's call this instance F.

We set N = "all 0" which satisfies all constraints.

{} | F | N -> by Finale
{} | F | N

Our system would also allow:
{} | F | N -> by UP // because 5 forces 3 to false
{!3} | F | N -> by UP // because 7 forces 4 to false
{!3 !4}| F | N -> by UP // because 9 forces 7 to false
{!3 !4 !7} | F | N -> by Finale
{!3 !4 !7} |  F | N 

sometimes the transition system allows multiple correct executions.