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Abstract

The Lexicographic Path Order (LPO) and the Knuth-Bendix Ordering (KBO) are two prominent term orders that are utilised in automated theorem provers. The LPO features some properties that allow it to be used in the context of hierarchic signature extensions and in the presence of term definitions, where special ordering criteria are desired for the defined terms. The KBO, on the other hand, can be computed more efficiently than the LPO and it correlates better with the size of terms, but the KBO cannot be used in the afore-mentioned situations, in which a single term should supersede infinitely many smaller terms of arbitrary sizes. In this diploma thesis, we present two extensions of the KBO that overcome these limitations. The first extension order is suitable for hierarchic signature extensions and its main characteristic is that it uses pairs of positive real numbers as symbol weights, whereas the second extension can handle the required ordering of term definitions through the usage of ordinal numbers as symbol weights.