  The notion of normal forms is ubiquitous in various equivalent
transformations. Confluence (CR), one of the central properties of term
rewriting systems (TRSs), concerns uniqueness of normal forms. Yet another such
property, which is weaker than confluence, is the property of unique normal
forms w.r.t. conversion (UNC). Famous examples having UNC but not CR include
the TRSs consisting of S,K,I-rules for the combinatory logic supplemented with
various pairing rules (de Vrijer, 1999). Recently, automated confluence proof
of TRSs has caught attentions leading to investigations of automatable methods
for (dis)proving CR of TRSs; some powerful confluence tools have been developed
as well. In contrast, there have been little efforts on (dis)proving UNC
automatically yet. Indeed, there are few tools that are capable of (dis)proving
UNC; furthermore, only few UNC criteria have been elaborated in these tools. In
this paper, we address automated methods to prove or disprove UNC of given
TRSs. We report automation of some criteria known so far, and also present some
new criteria and methods for proving or disproving UNC. Presented methods are
implemented over the confluence prover ACP (Aoto et al., 2009) and an
experimental evaluation is reported.
