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A semi-untethered jailbreak is similar to an untethered jailbreak, but it gives the ability to start the device on its own. On each boot, the device startup sequence is unmodified and it boots into its original, non-jailbroken configuration. However, rather than having to run a tool from a computer to jailbreak, like a tethered or semi-tethered cases, the user is able to re-jailbreak their device with the help of an app (usually sideloaded using Cydia Impactor) running on their device. In the case of the iOS 9.2-9.3.3 jailbreak, a Safari-based exploit was available, thereby meaning a website could be used to rejailbreak.
Some semi-untethered jailbreaks can be completed entirely on the device using a sideloaded app (which still requires a computer). Others require a computer to be used first, and then an app or website can be used to rejailbreak after each reboot.
Semi-Untethered jailbreaks have become the norm, as the last known code signing bypass - which is required for execution on boot - has been exploited by Pangu with iOS 9.0-9.1 and the shared cache malformation bug.