The proof of Lemma 2.41 says that (q, x) is a looping situation for a DPDA P

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The proof of Lemma 2.41 says that (q, x) is a looping situation for a DPDA P if when P is started in state q with x ∈ Γ on the top of the stack, it never pops anything below x and it never reads an input symbol. Show that F is decidable, where F = {〈P, q, x〉| (q, x) is a looping situation for P}.

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