{"paper":{"title":"Termination of Triangular Polynomial Loops","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Florian Frohn, J\\\"urgen Giesl, Marcel Hark","submitted_at":"2019-10-25T09:18:15Z","abstract_excerpt":"We consider the problem of proving termination for triangular weakly non-linear loops (twn-loops) over some ring $\\mathcal{S}$ like $\\mathbb{Z}$, $\\mathbb{Q}$, or $\\mathbb{R}$. The guard of such a loop is an arbitrary quantifier-free Boolean formula over (possibly non-linear) polynomial inequations, and the body is a single assignment of the form $(x_1, \\ldots, x_d) \\longleftarrow (c_1 \\cdot x_1 + p_1, \\ldots, c_d \\cdot x_d + p_d)$ where each $x_i$ is a variable, $c_i \\in \\mathcal{S}$, and each $p_i$ is a (possibly non-linear) polynomial over $\\mathcal{S}$ and the variables $x_{i+1},\\ldots,x_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.11588","kind":"arxiv","version":7},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.11588/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}