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On Proving Confluence of Conditional Term Rewriting Systems via the Computationally Equivalent Transformation ∗

This paper improves the existing criterion for proving confluence of a normal conditional term rewriting system (CTRS) via the Şerbănuţă-Roşu transformation, a computationally equivalent transformation of CTRSs into unconditional term rewriting systems (TRS), showing that a weakly left-linear normal CTRS is confluent if the transformed TRS is confluent. Then, we discuss usefulness of the optimization of the Şerbănuţă-Roşu transformation, which has informally been proposed in the literature.