Improved Modular Termination Proofs Using Dependency Pairs

The dependency pair approach is one of the most powerful techniques for automated (innermost) termination proofs of term rewrite systems (TRSs). For any TRS, it generates inequality constraints that have to be satisfied by well-founded orders. However, proving innermost termination is considerably easier than termination, since the constraints for innermost termination are a subset of those for termination. We show that surprisingly, the dependency pair approach for termination can be improved by only generating the same constraints as for innermost termination. In other words, proving full termination becomes virtually as easy as proving innermost termination. Our results are based on splitting the termination proof into several modular independent subproofs. We implemented our contributions in the automated termination prover AProVE and evaluated them on large collections of examples. These experiments show that our improvements increase the power and efficiency of automated termination proving substantially.