Leaf-balanced binary tree

A leaf-labelled binary tree is leaf-balanced when the leaf counts of the two subtrees at every internal node differ by at most one. Splitting a finite nonempty list into pieces of sizes $\lfloor n/2\rfloor$ and $\lceil n/2\rceil$ and applying the same construction recursively preserves the original leaf order and gives this balance condition. Both pieces are nonempty for $n\ge 2$ and strictly shorter than the input; induction proves termination and balance. This leaf-count convention is different from demanding equal subtree heights.