Directory traversal check with Lisp

I want to write code to check directory traversal. In other words, replace ".." with other values if strings includes "..". For example, the string "/aaa/../index.html" should be replaced with "/index.html".
And I want to write this code as a recursive function. Here is a base.

(defun replace-double-dott (x r)
  (if (null x)
      r
    (let ((n (first x))
	  (o (rest x)))
      (if (equal n "..")
	  (setf r (tail-remove r))
	(setf r (append r (list n))))
      (replace-double-dott o r))))

Here is a result.

? (replace-double-dott (split "/aaa/bbb/../../index.html" "/") nil)
("index.html")
? (replace-double-dott (split "/aaa/bbb/../../../index.html" "/") nil)
("index.html")
? (replace-double-dott (split "/aaa/../bbb/../ccc/index.html" "/") nil)
("ccc" "index.html")
?