Lambda Calculus: alpha conversion

Question

This is an alpha conversion. Although I have completed this, I am not too sure whether this is a correct answer or not.

λx y.((λx y.x) x ((λx. x) y)) ((λx y. y)((λy. y) x) y)
=λx y.((λx1 y1. x1) x((λx2. x2) y1)) ((λx3 y2. y2)((λy3. y3) x3) y)

Is this a correct answer?

Answer 1

You've made two mistakes. The bolded variables are not in scope when you use them:

λx y.((λx1 y1. x1) x((λx2. x2) y1)) ((λx3 y2. y2)((λy3. y3) x3) y)