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Originator: Yoshihito Toyama
Date: April 1991
Summary: Is the extension of Combinatory Logic by Boolean constants confluent?
Consider the following extension of Combinatory Logic with constants T (true), F (false), C (conditional):

Is this (nonterminating) “semiequational” (or “natural”, as such are called in [DO90]) conditional rewrite system confluent? Note that if we take the above system plus the rule x ↔^{*} y ⇒ Czxy → y, the resulting conditional rewrite system is confluent (cf. [Klo92][de 90]).
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