Language of words whose run lengths are all distinct
The definition of your language is not completely clear, but whatever it is, if you consider
$$ L \cap 1^* 0^* = \{ 1^a 0^b \mid a \neq b \} $$
then you immediately see that $L$ is not regular.

If you have to prove it using the pumping lemma, then simply take a proof that works for the above language; it will work for $L$ as well.