Is there an algorithm to decide if a symlink loops?

Unix systems usually just error out if they are confronted with a path that contains a symlink loop or just too many symlinks, because they have a limit to the number of symlinks they will traverse in one path lookup. But is there a way to actually decide if a given path resolves to something or contains a loop, even if it contains more links than a unix is willing to follow? Or is this a formally undecidable problem? And if it can be decided, can it be decided in a reasonable amount of time/memory (e.g. without having to visit all files on a filesystem)? Some examples: a/b/c/d where a/b is a symlink to ../e and e is a symlink to f and f is a symlink to a/b a/b/c/d where a/b/c is a symlink to ../c a/b/c/d where a/b/c is a symlink to ../c/d a/b/c/d where a/b/c is a symlink to /a/b/e where a/b/e is a symlink to /a/b/f where a/b/f is a symlink to /a/b/g **Edit**: To clarify, I am not asking about finding loops in the file system, I am asking about a decision algorithm that decides of a given path whether it resolves to a definite file/directory or whether it does not resolve at all. For example in the following system, there is a loop, but the given path still resolves fine: / -- a -- b where b is a symlink to /a This directory tree clearly has a cycle, but the path a/b/b/b/b/b still resolves fine to /a.