Proof the following graph is loop less

Question

Suppose we have a K-regular graph G. Let k = a+b+1. We want to partition vertices of G into 2 parts A and B such that every vertex in A has maximum number of a neighbor s in A and every vertex in B has maximum number of b neighbors in B.
To do that follow this algorithm: first we put all vertices in A. Then at each step if there was a vertex that didn't fit the condition, we move it into the other part. Make another graph G2 where any vertex represents a state in algorithm and each edge represents that there is a way between two states. Proof that G2 is loop less so the algorithm works.