I am a bit confused on the theory of the pumping lemma. As I know is used to decide if a language is regular or not.
This is what I have understood so far though For a regular language $L$, there exists a $p > 0$ such that for all $w ∈ L$ where $|w| ≥ p$, there exists some split $w = vxu$, for which the following holds:
$|vx| ≤ p$
$|x| > 0$
$vx^iu ∈ L$ for all $i ≥ 0$
but what is the rationale behind the requirement of $|vx| ≤ p$ what happens if we drop that requirement??