Editing Collatz conjecture (section)

===As a tag system===
For the Collatz function in the shortcut form

<math> f(n) = \begin{cases} \frac{n}{2} &\text{if } n \equiv 0 \\ \frac{3n+1}{2} & \text{if } n \equiv 1. \end{cases} \pmod{2}</math>

Hailstone sequences can be computed by the [[Tag system#Example: Computation of Collatz sequences|2-tag system]] with production rules

:{{math|''a'' → ''bc''}}, {{math|''b'' → ''a''}}, {{math|''c'' → ''aaa''}}.

In this system, the positive integer {{mvar|n}} is represented by a string of {{mvar|n}} copies of {{mvar|a}}, and iteration of the tag operation halts on any word of length less than&nbsp;2. (Adapted from De Mol.)

The Collatz conjecture equivalently states that this tag system, with an arbitrary finite string of {{mvar|a}} as the initial word, eventually halts (see ''[[Tag system#Example: Computation of Collatz sequences|Tag system]]'' for a worked example).