On Some Implementation Aspects of VMTL

VMTL (Vienna Modular Termination Laboratory [12]) is a program designed to (semi-) automatically prove termination of various classes of term rewriting systems (TRSs). In particular, conditional and context-sensitive TRSs (CTRSs and CSRSs) are supported. Based on the well-known dependency pair framework of [1, 7, 4], VMTL is extensible by new dependency pair processors and transformations (from (C)TRSs/CSRSs to (C)TRSs/CSRSs). An important design goal of VMTL is to make extension as easy as possible. Moreover, VMTL provides implementations of several standard and new dependency pair processors as well as of transformations (from CTRSs to CSRSs). In this work we briefly discuss some implementation details of the DP processors of VMTL, focussing in particular on the non-standard ones. The processors currently available in VMTL are a dependency graph processor, used for decomposition of dependency pair problems (based on [1, Section 4.1]), a subterm-criterion processor, based on [9], a reduction pair processor using recursive path orderings with status implemented using an external SAT solver, based on [13], a reduction pair processor using polynomial orderings with coefficients from N and constants from Z, based on [6], narrowing and instantiation processors based on [7, 11] and a size change principle processor, based on [14]. The inclusion of the (compared to the other ones) more “exotic” size-change principle processor is a tribute to the commitment of VMTL to specialize to a certain extent on the termination analysis of conditional TRSs. The size-change principle processor is able to trace (the size of) argument terms over several function calls not necessarily comparing arguments at the same positions. This may be advantageous in the setting of TRSs obtained by transforming CTRSs, since there argument terms of auxiliary function symbols change positions frequently. In the following we discuss some of these processors and their particular implementation in some detail. We assume familiarity with the basic notions and notations of term rewriting, context-sensitive rewriting and the dependency pair framework (cf. e.g. [5, 10, 7]).