Changes

Proof:

Proof:

*A variant is normalized if and only if it is parsimonious and left aligned.  

:A variant is normalized if and only if it is parsimonious and left aligned. <br>

*A variant is normalized if and only if it is left parsimonious and right parsimonious and left aligned. (break up parsimonious definition)

:&rArr; A variant is normalized if and only if it is left parsimonious and right parsimonious and left aligned. (break up parsimonious definition) <br>

*A variant is normalized if and only if it is has no superfluous nucleotides on the left side and right parsimonious and left aligned.  (definition of left parsimony)

:&rArr; A variant is normalized if and only if it is has no superfluous nucleotides on the left side and right parsimonious and left aligned.  (definition of left parsimony) <br>

*A variant is normalized if and only if it is has no superfluous nucleotides on the left side and each allele do not end with the same type of nucleotide. (lemma 1)

:&rArr; A variant is normalized if and only if it is has no superfluous nucleotides on the left side and each allele do not end with the same type of nucleotide. (lemma 1) <br>

= Algorithm for Normalization =

= Algorithm for Normalization =