# Drawing a PDA for a language

I am initiating myself into TOC and using sort of random resources from the web. I was looking at this problem from a Berkeley problem set: Construct a PDA to accept $$L = {a^ib^j|i \neq j , 2i \neq j}$$ And I don't understand the given solution here.(Problem 4) http://www.cs.berkeley.edu/~isabelle/cs302/ps3-solutions.pdf

When can we say this machine accepts a string? From my understanding, it seems to accept ab,aabb,aaabbb etc as well when it shouldn't.

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If you follow the behaviour of the automaton in the answer, you will find that for words $a^ib^i$ or $a^ib^{2i}$, if you arrive in a final state, the stack will not be empty, so the word is not accepted.