MIT Press, November 1999. The only assumption about the selection rule is that derivations are input-consuming, that is, in each derivation step, the input arguments of the selected atom do not become instantiated. This assumption is a natural abstraction of previous work on programs with delay declarations. The method for showing that a predicate is in that class is based on level mappings, closely following the traditional approach for LD-derivations. Programs are assumed to be well and nicely moded, which are two widely used concepts for verification.
Many predicates terminate under such weak assumptions.
Knowing these predicates is useful even for programs where not all predicates have this property.