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We present new methods of automating the construction of index pairs,essential ingredients of discrete Conley index theory. These new algorithms arefurther steps in the direction of automating computer-assisted proofs ofsemi-conjugacies from a map on a manifold to a subshift of finite type. Weapply these new algorithms to the standard map at different values of theperturbative parameter {\epsilon} and obtain rigorous lower bounds for itstopological entropy for {\epsilon} in [.7, 2].

Efficient automation of index pairs in computational Conley index theory