I have some doubt in your PDA. Lets us say i have aaabbb.Equal a and b.
I push 9 a's into the stack. Now i have 3 b coming. How will we match this?We can do only 1 time pop for one b.We cannot pop 1a,2a,3a like this. ?
I have two approaches in mind :-
1. we can push a 1time or 2 time or 3 time in non deterministic ways an just match with b when it comes?(like @VS said)
2. we can push a in to stack and now when b comes,i can skip two b and match with 3rd(b=3a) or i can skip one b and match with a(b=2a) or i can match b directly(a=b).At evey b i have 3 choices.
Please check this and see if i am correct