Complete supplied first-order equations under declared LPO precedence, returning...
https://detect.halowerk.com/v1/F-TD2000-DATASTRUCTURES-15/firstorder-lpo-oriented-knuth-bendix-completion-confluence-certificateOverview
Complete supplied first-order equations under declared LPO precedence, returning a termination/confluence-checkable rewrite basis when the bounded completion terminates.
Protocol
x402 (POST)
Price
$0.0030
Payment Asset
USD Coin
Payment Network
eip155:8453
Category
uncategorized
Provider
detect
Source
bazaar
Indexed
2026-11-02 17:26:09
Health
Status
unknown
Latency (p50)
—
Uptime (30d)
—
Reliability Score
—
Last Checked
Never
Last Healthy
Never
Consecutive Failures
0
x402 Payment Validation
Payment Requirements
—
Asset Verified
—
Facilitator
—
Input Schema
{
"body": {
"artifact": {
"knuthBendix": {
"claim": null,
"data": {
"arities": [
0,
0,
1,
1,
2
],
"equations": [
{
"left": {
"arguments": [
{
"arguments": [
{
"variable": 0
}
],
"symbol": 2
}
],
"symbol": 2
},
"right": {
"arguments": [
{
"variable": 0
}
],
"symbol": 2
}
}
],
"precedence": [
4,
2,
3,
1,
0
],
"queries": [
{
"arguments": [
{
"arguments": [
{
"arguments": [],
"symbol": 0
}
],
"symbol": 2
}
],
"symbol": 2
},
{
"arguments": [
{
"arguments": [
{
"variable": 0
}
],
"symbol": 3
}
],
"symbol": 2
},
{
"arguments": [
{
"arguments": [],
"symbol": 0
},
{
"arguments": [],
"symbol": 1
}
],
"symbol": 4
}
]
}
}
}
},
"bodyType": "json",
"method": "POST",
"type": "http"
}
Output Schema
{
"example": {
"billable": true,
"findings": [
{
"confidence": 1,
"evidence": [
{
"page_indices": [],
"page_url": null,
"pattern": "firstorder-lpo-oriented-knuth-bendix-completion-confluence-certificate_scoped_evidence",
"type": "artifact"
}
],
"limits": [
"Baader/Nipkow1998 Term Rewriting and All That Chapter7 exact Huet completion with Chapter4 normalization/unification, Chapter5LPO and Chapter6 variable-apart overlaps: generate and certify a complete rewrite basis from supplied universally quantified equations."
],
"module": "firstorder-lpo-oriented-knuth-bendix-completion-confluence-certificate",
"state": "observed",
"value": {
"claim_matches": false,
"computed": {
"certificate": {
"all_critical_pairs_join": true,
"all_equations_preserved": true,
"all_rules_decrease": true,
"critical_pair_count": 2,
"order": "strict_declared_LPO"
},
"equation_normal_forms": [
{
"arguments": [
{
"variable": 0
}
],
"symbol": 2
}
],
"outcome": "complete",
"query_normal_forms": [
{
"arguments": [
{
"arguments": [],
"symbol": 0
}
],
"symbol": 2
},
{
"arguments": [
{
"arguments": [
{
"variable": 0
}
],
"symbol": 3
}
],
"symbol": 2
},
{
"arguments": [
{
"arguments": [],
"symbol": 0
},
{
"arguments": [],
"symbol": 1
}
],
"symbol": 4
}
],
"rules": [
{
"left": {
"arguments": [
{
"arguments": [
{
"variable": 0
}
],
"symbol": 2
}
],
"symbol": 2
},
"right": {
"arguments": [
{
"variable": 0
}
],
"symbol": 2
}
}
]
}
},
"warnings": []
}
],
"known_count": 1,
"scope": {
"contact_values_returned": false,
"network": false,
"supplied_artifact_only": true
},
"warnings": []
},
"type": "json"
}