wellfounded relation
wellfounded relation A particular kind of partial ordering, used in termination proofs (see program correctness proof). A wellfounded relation on a set S consists of a partial ordering R ⊆ S × S
such that there does not exist any infinite sequence x_{1}, x_{2}, x_{3},… of members of S for which each pair 〈x_{i},x_{i}_{+1}〉 belongs to R. As an example, if S consists of the natural numbers, then the “greater than” relation, containing all pairs 〈m,n〉 such that m>n, is wellfounded, since there are no infinite descending sequences of natural numbers. On the other hand “greater than or equal to”, and “less than” are not wellfounded. On the set of integers, none of these relations are wellfounded. As another example, if S is the set of all finite sets of natural numbers, then “proper superset of” is wellfounded.
In the application to terminate proofs it is shown that, whenever a certain point in the program is visited during execution, the current value of some quantity lies within S and also that, if x is the value of that quantity at one such visit, and x′ its value at a later visit, the pair 〈x,x′〉 belongs to R. It then follows that that point in the program cannot be visited infinitely often. By considering enough such points it can be concluded that any execution must have finite length.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"wellfounded relation." A Dictionary of Computing. . Encyclopedia.com. 14 Aug. 2018 <http://www.encyclopedia.com>.
"wellfounded relation." A Dictionary of Computing. . Encyclopedia.com. (August 14, 2018). http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/wellfoundedrelation
"wellfounded relation." A Dictionary of Computing. . Retrieved August 14, 2018 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/wellfoundedrelation
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.