```json
{
  "criteria": {
    "c1": "not_met",
    "c2": "not_met",
    "c3": "not_met",
    "c4": "not_met",
    "c5": "not_met"
  },
  "note": "The response only provides brief assertions rather than actual inductive proofs, lacks base cases and well-founded measure details for termination, and uses sets instead of multisets for the permutation proofs."
}
```