On the asymptotic number of BCK(2)-terms

We investigate the asymptotic number of a particular class of closed lambda-terms. This class is a generalization of a class of terms related to the axiom system BCK which is well known in combinatory logic. We determine the asymptotic number of terms, when their size tends to infinity, up to a constant multiplicative factor and discover a surprising asymptotic behaviour involving an exponential with fractional powers in the exponent.

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