Pith Number

pith:5IU3BKUJ

pith:2026:5IU3BKUJEPV6XT5WJN3YT5ZBWH

not attested not anchored not stored refs pending

Termination of Innermost-Terminating Right-Linear Overlay Term Rewrite Systems

Naoki Nishida

Right-linear overlay term rewrite systems terminate if and only if they innermost terminate.

arxiv:2604.20754 v2 · 2026-04-22 · cs.LO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5IU3BKUJEPV6XT5WJN3YT5ZBWH}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

for a right-linear overlay TRS, there is no infinite minimal dependency-pair chain if and only if there is no infinite innermost minimal dependency-pair chain. This implies that a right-linear overlay TRS is terminating if and only if it is innermost terminating.

C2weakest assumption

The previously established simulation property that, for a terminating right-linear overlay TRS, any rewrite sequence ending in a normal form can be simulated by innermost reduction.

C3one line summary

Right-linear overlay TRSs terminate if and only if they are innermost terminating, because absence of infinite minimal dependency-pair chains is equivalent to absence of infinite innermost minimal dependency-pair chains.

Receipt and verification

First computed	2026-06-26T01:15:51.948191Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea29b0aa8923ebebcfb64b7789f721b1ca3751f25334a80425870860e22b0dcd

Aliases

arxiv: 2604.20754 · arxiv_version: 2604.20754v2 · doi: 10.48550/arxiv.2604.20754 · pith_short_12: 5IU3BKUJEPV6 · pith_short_16: 5IU3BKUJEPV6XT5W · pith_short_8: 5IU3BKUJ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5IU3BKUJEPV6XT5WJN3YT5ZBWH \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ea29b0aa8923ebebcfb64b7789f721b1ca3751f25334a80425870860e22b0dcd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96c131c60b789d7b09d47780d41aa0d41418e860c5d76523e72557e3ac30e17c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-04-22T16:44:24Z",
    "title_canon_sha256": "eed48e3da34e0384edbd68f2f2fbcfe5b41bd8450cbfcef2e18c42aaa10b29b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.20754",
    "kind": "arxiv",
    "version": 2
  }
}