Improving Dependency Tuples for Almost-Sure Innermost Termination of Probabilistic Term Rewriting

Recently, we adapted the well-known dependency pair (DP) framework to a dependency tuple (DT) framework in order to prove almost-sure innermost termination (iAST) of probabilistic term rewriting systems. In this paper, we improve this approach into a complete criterion for iAST by considering positions of subterms. Based on this, we extend the probabilistic DT framework by new transformations. Our implementation in the tool AProVE shows that they increase its power substantially.