It's a Semi-Thue system[0], a particular form of term rewriting system that is almost 30 years older than tag systems; introduced over a hundred years ago to formalise word problems in finitely presented semigroups (that's where the semi-part of the name comes from).
That's cool, so I'm drunk and on my phone, but it seems like tag systems are then a sort of subset of thue systems? specifically an only concatenative subset, which makes me feel like some one should definitely add a reference to the tag systems page.
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[ 3.2 ms ] story [ 11.8 ms ] thread[0] https://en.wikipedia.org/wiki/Semi-Thue_system
There's a list of alternative implementations if you feel like playing with it.
PS: IMHO, this is a better link than the free.fr link from OP. Link to this page instead, either from esolangs wiki or on HN here?