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+\documentclass{article}
+\usepackage{expl3}
+\ExplSyntaxOn
+\cs_new:Npn \hakviiaiii_tarai:nnn #1#2#3 {%
+ \int_compare:nTF{#1 <= #2}
+ {#2}
+ {\hakviiaiii_tarai:nnn
+ {\hakviiaiii_tarai:nnn{\int_eval:n{#1 - 1}}{#2}{#3}}
+ {\hakviiaiii_tarai:nnn{\int_eval:n{#2 - 1}}{#3}{#1}}
+ {\hakviiaiii_tarai:nnn{\int_eval:n{#3 - 1}}{#1}{#2}}}}
+\cs_new_eq:NN \tarai \hakviiaiii_tarai:nnn
+\ExplSyntaxOff
+\begin{document}
+ $\mathrm{Tarai}(14,12,10) = \tarai{14}{12}{10}$
+\end{document} \ No newline at end of file