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This paper introduces an innovative algorithm for automatic instruction-set extension, which gives a pseudo-optimal solution within polynomial time to the size of a graph. The algorithm uses top-down dynamic programming strategy with the branch-and-bound algorithm in order to exploit overlapping of subproblems. Correctness of the algorithm is formally proved, and time complexity is analyzed from it. Also, it is verified that the algorithm gives an optimal solution for some type of merit functions, and has very small possibility of obtaining non-optimal solution in general. Furthermore, several experimental results are presented as evidence of the fact that the proposed algorithm has notable performance improvement.