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The study of formal languages (sets of strings or trees over an alphabet), rewriting systems and algorithms, recognition automata/algorithms, and related questions.

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How can I catalog these generalized Collatz problems?

This is a ruleset whose termination is independent from $\mathrm{PRA}$, primitive recursive arithmetic, letting $\langle x,y\rangle$ be short for $(x+y)(x+y+1)+2y$: $\langle y,\langle 0,z+1\rangle\ra …
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