http://termination-portal.org/mediawiki/index.php?action=history&feed=atom&title=TRS_Conditional
TRS Conditional - Revision history
2026-06-23T23:39:21Z
Revision history for this page on the wiki
MediaWiki 1.34.2
http://termination-portal.org/mediawiki/index.php?title=TRS_Conditional&diff=2202&oldid=prev
JCKassing: Small fixes
2026-06-09T12:18:56Z
<p>Small fixes</p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 12:18, 9 June 2026</td>
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<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The TRS Conditional category is concerned with the question "Will every possible sequence of conditional <del class="diffchange diffchange-inline">rewrites </del>steps terminate?"</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The TRS Conditional category is concerned with the question "Will every possible sequence of conditional <ins class="diffchange diffchange-inline">rewrite </ins>steps terminate?"</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>where a conditional rewrite step may depend on the reachability between two independent terms, e.g., can 'leq(<i>t</i>,<i>s</i>)' be evaluated to 'true'?</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>where a conditional rewrite step may depend on the reachability between two independent terms, e.g., can 'leq(<i>t</i>,<i>s</i>)' be evaluated to 'true'?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><b>Possible Outputs</b>: </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><b>Possible Outputs</b>: </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* "<b>YES</b>" followed by a termination proof, e.g., a ranking function proving termination of R.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* "<b>YES</b>" followed by a termination proof, e.g., a ranking function proving termination of R.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* "<b>NO</b>" followed by a nontermination proof, e.g., a loop that indicates an infinite rewrite of R.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* "<b>NO</b>" followed by a nontermination proof, e.g., a loop that indicates an infinite rewrite <ins class="diffchange diffchange-inline">sequence </ins>of R.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* "<b>MAYBE</b>" (indicating that the solver cannot prove termination of R).</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* "<b>MAYBE</b>" (indicating that the solver cannot prove termination of R).</div></td></tr>
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JCKassing
http://termination-portal.org/mediawiki/index.php?title=TRS_Conditional&diff=2173&oldid=prev
JCKassing: Added TRS Conditional Page
2026-03-18T11:37:59Z
<p>Added TRS Conditional Page</p>
<p><b>New page</b></p><div>The TRS Conditional category is concerned with the question "Will every possible sequence of conditional rewrites steps terminate?"<br />
where a conditional rewrite step may depend on the reachability between two independent terms, e.g., can 'leq(<i>t</i>,<i>s</i>)' be evaluated to 'true'?<br />
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== Syntax & Semantic ==<br />
<br />
Formally, a conditional term rewrite system is a set R = {l<sub>1</sub> &rarr; r<sub>1</sub> | c<sub>1</sub>,...,l<sub>n</sub> &rarr; r<sub>n</sub> | c<sub>n</sub>} of finitely many conditional rewrite rules.<br />
A conditional rewrite rule is a rewrite rule l &rarr; r with an additional condition, a reachability constraint, that has to be satisfied to use the rewrite rule.<br />
There are multiple different ways one can interpret these conditions, e.g., oriented, joined, and convertible.<br />
<br />
== Problem ==<br />
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<b>Input</b>: A conditional term rewrite system R.<br />
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<b>Question</b>: Does R terminate?<br />
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<b>Possible Outputs</b>: <br />
* "<b>YES</b>" followed by a termination proof, e.g., a ranking function proving termination of R.<br />
* "<b>NO</b>" followed by a nontermination proof, e.g., a loop that indicates an infinite rewrite of R.<br />
* "<b>MAYBE</b>" (indicating that the solver cannot prove termination of R).<br />
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== References ==<br />
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[[Category:Categories]]</div>
JCKassing