Let L be regular, and it is accepted by an n-state FA.

Choose . Does it work?

Alternatively, choose from L.
( )

By pumping lemma, such that , and .

Case 1: , for .
Then, choose
.

Case 2: .
Then z has been broken up as
Choose i=3

( what about i=0,1 or 2?)

Hence, .
e.g. k=1, .
(For i=0, k=1, .
(For i=2, k=1, .

Case 3: , . Choose i=3.

Case 4: , . Choose i=2.

Thus, for all possibilities of v and u, .
Therefore, l is not regular.