This paper improves top-down execution models of logic programs based on a twophase abstract interpretation which consists of a bottom-up analysis followed by a topdown one. The two-phase analysis provides an approximation of all (possibly nonground) success patterns of clauses relevant to a query. It is specialized by considering Sato and Tamaki’s depth k abstraction as abstract function. By the ability of the analysis to approximate possibly nonground success patterns of clauses relevant to a query, it can be statically determined whether some subgoals will fail during execution and some succeeding subgoals do not participate in success patterns of program clauses relevant to a given query. These properties are utilized to improve execution models. This approach can be easily applied to any top-down (parallel) execution models. As instances, it is shown to be applicable to linear execution model and AND/OR Process Model.