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Find a grammar equivalent to $S\rightarrow aAB, A\rightarrow bBb, B\rightarrow A|\lambda$ that satisfies the conditions of Theorem 5.2.

Theorem 5.2
Suppose that $G = (V, T, S, P)$ is a context-free grammar that does not have any rules of the form $A → λ,$ or $A → B,$ where $A, B ∈ V.$ Then the exhaustive search parsing method can be made into an algorithm which, for any $w ∈ Σ^*,$ either produces a parsing of $w$ or tells us that no parsing is possible.

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