{"id":156127,"date":"2000-04-01T00:00:00","date_gmt":"2000-04-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/farmers-theorem-revisited\/"},"modified":"2018-10-16T20:21:35","modified_gmt":"2018-10-17T03:21:35","slug":"farmers-theorem-revisited","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/farmers-theorem-revisited\/","title":{"rendered":"Farmer&#8217;s Theorem revisited"},"content":{"rendered":"<div class=\"asset-content\">\n<p>The main result is that there is an integer n, such that second-order unification is undecidable in all non-monadic second-order term languages with at least n first-order variables, and even if the arguments of all second-order variables are ground terms of size bounded by n and the total number of variable occurrences is at most n.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The main result is that there is an integer n, such that second-order unification is undecidable in all non-monadic second-order term languages with at least n first-order variables, and even if the arguments of all second-order variables are ground terms of size bounded by n and the total number of variable occurrences is at most 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