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Question

what will be the resulting lang?

I am thinking it as regular although it may clearly seem to be CFL using closure properties, but inclusion of aⁿ in the union already take into consideration all strings derived from the CFL part i.e. aⁿbⁿ 

Hence we can short-circuit that part?

P.S: Answer given is NOT REGULAR

Comments

yes we can also write the resultant language as a*b* but since we know that every regular language is cfl 

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We can not write a*b*.

Answer 1

above language is CFL because we can make PDA for it easily.if it's regular then dfa will formed but i think there is no way to make a dfa for it due to presence of $a^{n}b^{n}.$

Answer 2

We can write like 

a*+b*+a^nb^n  .

And there are comparision between a and b so we need one stack . And given language is CFL