Just as @Peter B said, adding a / to the href of <base> and removing the starting / of <link> and <script> should be the best practice.

<link href="css/rendering.css" rel="stylesheet">
<script type="text/javascript" src="script/task.js"></script>
<base href="http://example.com/myservice/public/" >

If it is still not working after that, you need to check your Access-Control-Allow-Origin settings of your server.

Additionally, you've mentioned the easiest option. Then you should simply try launching Edge with command line --allow-file-access-from-files. Remember to close all Microsoft Edge instances first from task manager.