by Ciro Santilli (@cirosantilli, 36)
To get an intuition for it, see the sample computation at: en.wikipedia.org/w/index.php?title=Ackermann_function&oldid=1170238965#TRS,_based_on_2-ary_function where in this context. From this, we immediately get the intuition that these functions are recursive somehow.

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Ackermann function by Wikipedia Bot 0 1970-01-01
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