Termination test for logic programs

We give a condition for termination of logic programs (when evaluated top-down). The condition is couched in terms of datalog (i.e., function-free) programs with (possibly) infinite EDB relations that satisfy some partial order constraints among argument sizes. However, this condition can also show (in many cases) the termination of logic programs with function symbols. It is also shown that in the framework discussed in the paper (i.e., datalog programs with constraints on the EDB relations), the condition is not just sufficient, but also necessary for the lack of infinite branches in a top-down evaluation tree. The condition can be tested in exponential time in the size of the program (the time does not depend on the size of the EDB).