# What's wrong with my answer to this constraint satisfaction problem, which needs to be solved the AC-3 algorithm?

I was watching the video Constraint Satisfaction: the AC-3 algorithm, and I tried to solve this question:

Given the variables A, B, C and D, with domain {1, 2, 3, 4} in each of them and restrictions A> B, B = C and D ≠ A, use the AC algorithm.

But the teacher told me that my answer below is wrong!

He gave me a tip: Domain D will not be changed!

Below, I is my answer step by step. If someone can help me find the error, I appreciate it!

To solve this exercise, it is first necessary to organize the data in order to separate what is the domain, agenda and arc.

Soon after, we will analyze the first item on the agenda “A> B” with domain A, in order to eliminate unnecessary elements from the domain.

Analyze domain B with the agenda item “B <A”

Analyze domain B with the agenda item “B = C” and add the constraint “A> B”

Analyze domain D with the agenda item “D ≠ A” and add the constraint “B <A”

Analyze domain A with the agenda item “A ≠ D”

Analyze domain A with the agenda item “A> B”

Analyze domain B with the agenda item “B = C”

Analyze domain B with the agenda item “B <A”

Result

To satisfy $$D\ne A$$, for each element in the domain of $$D$$, say $$d$$, there must be at least one element in the domain of $$A$$, say $$a$$, that $$d \ne a$$.
Domain of $$D$$: $$\{ 1, 2, 3, 4 \}$$
Domain of $$A$$: $$\{ 2, 3, 4 \}$$
So, for example if $$d=2$$, there is at least one element in the domain of $$A$$ like $$a$$ such that $$d \ne\ a$$. E.g. $$1, 3$$ and $$4$$. So, $$2$$ remains in the domain of $$D$$. This is the case for other elements of $$D$$.