The paper repackages the known failure of direct measures on a step-duplicating rewrite rule as 'operational inexpressibility' and claims dependency-pair confessional proofs mirror Gödel's incompleteness move, but the equivalence claims are definitional.
The orientation boundary for step-duplicating recursors: Mechanized im- possibility, escape, and certification
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Operational Inexpressibility at the Step-Duplicating Primitive Recursor Orientation Boundary
The paper repackages the known failure of direct measures on a step-duplicating rewrite rule as 'operational inexpressibility' and claims dependency-pair confessional proofs mirror Gödel's incompleteness move, but the equivalence claims are definitional.