  In this study, we address the problem of compacting Church numerals. Church
numerals appear as a representation of the repetitive part of data in
higher-order compression. We propose a novel decomposition scheme for a natural
number using tetration, which leads to a compact representation of
$\lambda$-terms equivalent to the original Church numerals. For natural number
$n$, we prove that the size of the $\lambda$-term obtained by the proposed
method is $O(({\rm slog}_{2}n)^{\log n/ \log \log n})$. Moreover, we
quantitatively confirmed experimentally that the proposed method outperforms a
binary expression of Church numerals when $n$ is less than approximately 10000.
