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Rendering engines are the programme parts in a browser responsible for displaying the content.
While it should be best practice to associate different browser rendering behaviour to their rendering engines, the user agent actually does not give the proper information for this.
E.g.IE9’s Compatibility View will map to IE7 Standards Mode, and IE9’s UA string when in Compatibility View will be:
Mozilla/4.0 (compatible; MSIE 7.0; Windows NT 6.0; Trident/5.0)
For style sheet programmers it means that the expected rendering behaviour must be anticipated from the browser's version, not from the rendering engine's version.