Show Language is not context free without pumping lemma Can we show that following language is not context free using Push down automata approach?

L = {a^i b^i a^i : i&gt;=1} 


For every a we will Push 'A' onto stack, for every b we will pop 'A' out of stack so at the end we will have a's onto stack and the input word would be empty as string would be something like aabbaa

Does it seem correct?
Your approach doesn't work. We don't know how a putative push-down automaton for the language works. What you show is that a particular PDA doesn't work, but perhaps another one does.