Current norm-based automatic termination analysis techniques for logic programs can be split up into different components: inference of mode or type information, derivation of models, generation of well-founded orders, and verification of the termination conditions themselves. Although providing high-precision results, these techniques suffer from an efficiency point of view, as several of these analyses are often performed through abstract interpretation. We present a new termination analysis which integrates the various components and produces a set of constraints that, when solvable, identifies successful termination proofs. The proposed method is both efficient and precise. The use of constraint sets enables the propagation of information over all different phases while the need for multiple analyses is considerably reduced.

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We provide a theoretical basis for studying the termination of tabled logic programs executed under SLG-resolution using a leftto-right computation rule. To this end, we study the classes of quasiterminating and LG-terminating programs (for a set of atomic goals S). These are tabled logic programs where execution of each call from S leads to only a nite number of di erent (i.e., non-variant) calls, and a nite number of di erent calls and computed answer substitutions for them, respectively. We then relate these two classes through a program transformation, and present a characterisation of quasi-termination by means of the notion of quasi-acceptability of tabled programs. The latter provides us with a practical method of proving termination and the method is illustrated on non-trivial examples of tabled logic programs.

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