Ranking functions are a tool successfully used in termination analysis, complexity analysis, and program parallelization. Among the different types of ranking functions and approaches to finding them, this talk will concentrate on functions that are found by linear programming techniques. The setting is that of a loop that has been pre-abstracted so that it is described by linear constraints over a finite set of numeric variables. I will review results (more or less recent) regarding the search for ranking functions which are either linear or lexicographic-linear
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