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

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