Answer Happy

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Following the construction of Theorem 7.2 (Theorem 7.2:
If L = L for some ndpa M, then L is a context-free
language.), convert the following npda to an equivalent
grammar.
Show the initial results prior to
simplification, and then the final results after
simplification. You don't have to show each individual step of
simplification.
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states: {q0,q1,q2,q3}
input alphabet: {a,b}
stack alphabet: {A,Z}
initial state: q0
stack start symbol: Z
final states: {q3}
transitions:
δ(q2,λ,Z) = {(q3,λ)}
δ(q0,λ,Z) = {(q1,AZ)}
δ(q2,a,Z) = {(q1,AZ)}
δ(q1,b,A) = {(q2,λ)}
Please explain in detail how to do this question. Please
don't copy from existing answers, no existing answer correctly
explains how to do this question.