“…In this work, we focus on the so called deterministic conditional rewrite systems (DCTRSs), which are typical functional programs with local declarations [23]. When the rewrite systems are automatically generated (e.g., by program inversion [2,14,15,17,22,27,26,28] or partial evaluation [1,7,8,35]), they often have a poor syntactic structure that might hide some properties. For instance, the rewriting systems generated by program inversion sometimes have overlapping left-hand sides despite the fact that they actually have the unique normal form property w.r.t.…”