[Jtsummers]

No, it can operate on a data structure as well. There's string rewriting which does operate on text (but this can be stored in a structure amenable to applying rewrite rules versus brute force copying it or something silly). For term rewriting, there are plenty of efficient ways to store and operate on the information besides just textually.

[alxmng]

Hmm maybe I misunderstand. All the rules must be applied to fixpoint or elimination, for every input right? And the larger the program (rule set) the worse the performance since more rules must be evaluated at each “tick” of the program, unless you play tricks with ordering rules.

[Jtsummers]

Yes, that's often the objective. If they're properly written they will terminate, but not all sets of rules may terminate. It's possible for rules to cause divergence or cycles.

  A -> A B (1)

  A -> B   (2)
  B -> A

(1) never terminates, always adding a new B on application but not removing the A. (2) doesn't grow, but never terminates since each term is replaced with the other.