Tabling avoids many of the shortcomings of SLD(NF) execution and provides a more flexible and efficient execution mechanism for logic programs. In particular, tabled execution of logic programs terminates more often than execution based on SLD-resolution. One of the few works studying termination under a tabled execution mechanism is that of Decorte et al. They introduce and characterise two notions of universal termination of logic programs w.r.t. sets of queries executed under SLG-resolution, using the left-to-right selection rule; namely the notion of quasi-termination and the (stronger) notion of LG-termination. This paper extends the results of Decorte ct al in two ways: (1) we consider a mix of tabled and Prolog execution, and (2) besides a characterisation of the two notions of universal termination under such a mixed execution, we also give modular termination conditions. From both practical and efficiency considerations, it is important to allow tabled and non-tabled predicates to be freely intermixed. This motivates the first extension. Concerning the second extension, it was already noted in the literature in the context of termination under SLD-resolution (by e.g. Apt and Pedreschi), that it is important for programming in the large to have modular termination proofs, i.e. proofs that are capable of combining termination proofs of separate programs to obtain termination proofs of combined programs.
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