rewriting rules are more like function/predicate definitions in FP or LP and not like axioms. Term rewriting does have its own axioms, like ZFC does. What you'

rewriting rules are more like function/predicate definitions in FP or LP and not like axioms. Term rewriting does have its own axioms, like ZFC does. What you're saying is akin to "not all functions are interesting". Well, yes... But that's true for any model of computation.