A technique for automatically proving termination of constructor systems

A technique is described to prove termination of constructor systems (CSs) automatically. The technique consists of three major steps. First, determine the dependency pairs of a constructor system. Second, nd an equational theory in which the constructor system is contained, and third, prove that no in nite chain w.r.t. the equational theory of these dependency pairs exists. The rst step is easy and can be performed completely automatically. Here we rst concentrate on the last step. We assume the equational theory given in the form of a complete TRS and present several general criteria on the syntax of the dependency pairs to prove that no in nite chain can exist with respect to the given equational theory. For these criteria no semantic uni cation is needed and they can be performed completely automatically. Second we demonstrate a technique to nd a complete TRS automatically in case the CS that has to be proved terminating is of a special form. We combine all techniques to show how a CS introduced by R. Kennaway of almost 400 lines can be proved terminating completely automatically.