An alternative approach of Pumping Lemma to prove a language to be non regular

This paper proposes an alternative approach of Pumping Lemma to prove a language to be non regular. In general, to prove a language to be non regular, pumping lemma decomposes the string to xyz and takes xy part into consideration for the proof (|xy|<=n and |y|>0). Instead of taking the first part of the string, the second part of the string is taken (|yz|<=n and |y|>0) to prove the non regularity of the Language. This also satisfies the pigeonhole principle where the last p+1 state in the sequence will contain repetition if p is the pumping length.