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Well-formed formulae in prefix notation over a set of symbols and a set of binary operators are defined recursively by these rules:

(i) if x is a symbol, then x is a well-formed formula in prefix notation;

(ii) if X and Y are well-formed formulae and ∗is an operator, then ∗XY is a well-formed formula.

Show that an ordered rooted tree is uniquely determined when a list of vertices generated by a post order traversal of the tree and the number of children of each vertex are specified.

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