/assets/jquery-1.7.1.min.js is not relative but absolute*, the / takes it to the root even with a base tag.
If you remove that /, it should make it relative off the current path, which, when a base tag is present would be http://localhost/framework/.
Note: You will also need to add a trailing / to the end of the href, to indicate that it’s a folder.
Full working example:
<!doctype html>
<html>
<head>
<base href="https://stackoverflow.com/test/" />
<script src="assets/test.js"></script>
<body>
hi
</body>
</html>
* Actually depending on who you ask, it’s still relative since it is relative off the current domain. But I prefer to call this absolute since it’s signifying the path is from the root, based on the current domain. Although, I guess technically that makes it relative in the grand scheme of things, and absolute only in terms of the current domain. Whatever.