MakeWellFormed strategy when attempting to fix invalid markup messes it up even more

MakeWellFormed strategy when attempting to fix invalid markup messes it up even more. Please consider the following test script:

<?php
$config = HTMLPurifier_Config::createDefault();
$purifier = new HTMLPurifier($config);
echo $purifier->purify('<p><i><ul><li>text</li></ul></i></p>');

one would expect the output:

<p><i></i></p><ul><li>text</li></ul>

or ideally:

<p><i></i></p><ul><li><i>text</i></li></ul>

Instead we get:

<p><i></i></p><i>text</i>

Tested against HTMLPurifier 4.12.0.

By doing some digging I found that setting $formatting property to false on <i> element definition in the Presentation module helps a little - the <ul> structure is retained. The drawback of this is that the carrying <i> element no longer works.

This suggests that the tree-fixing algorithm in HTMLPurifier_Strategy_MakeWellFormed::execute() requires some tuning.

Start with the provided PHP reproduction and inspect HTMLPurifier_Strategy_MakeWellFormed::execute() around the linked location. Compare its handling of the nested p, i, ul, and li elements with the behavior of the formatting property in HTMLPurifier/HTMLModule/Presentation.php. Done means preserving the ul/li structure and producing one of the expected corrected outputs, with a regression test for the example.