Soundness of Unravelings for Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity

Unravelings are transformations from conditional term rewriting systems(CTRSs) into unconditional term rewriting systems (TRSs) over extended signatures.They are complete, but in general, not sound w.r.t. reduction. Here, soundness w.r.t. reduction for a CTRS means that for every term over the original signature of the CTRS,if the corresponding unraveled TRS reduces the term to a term over the original signa-ture, then so does the original CTRS. In this paper, we show that an optimized variant of Ohlebusch’s unraveling for deterministic CTRSs is sound w.r.t. reduction if the correspond-ing unraveled TRSs are left-linear, or both right-linear and non-erasing. Then, we showthat soundness of the variant implies soundness of Ohlebusch’s unraveling, and show that soundness of Marchiori’s unravelings for join and normal CTRSs also implies soundness ofOhlebusch’s unraveling. Finally, we show that soundness of a transformation proposed byŞerbănuţă and Roşu for deterministic CTRSs implies soundness of Ohlebusch’s unraveling.