Comparing cubic time complexity algorithm with a fourth-power complexity

   I thought of comparing n³ and n⁴ running times to feel what it means to have a slow algorithm.

Let us suppose we have an algorithm with cubic runtime complexity:

 int n = 2500;
 int[] arr = new int[n];
 System.out.println("Start");
 long st = System.currentTimeMillis();
 for (int i = 0; < n; i++) {
   for (int j = 0; j < n; j++) {
     for (int k = 0; k < n; k++) {
       arr[k]++;
    }
   } 
 }
 System.out.printf("%dms\nDone!", System.currentTimeMillis() - st);

For n = 2500, it completed in 1.827 seconds on a modern i5 CPU :

 Start  
 1827ms  
 Done!  

Now, an algorithm of power 4 time complexity,

 int n = 2500;
 int[] arr = new int[n];
 System.out.println("Start");
 long st = System.currentTimeMillis();
 for (int i = 0; i < n; i++) { 
   for (int j = 0; j < n; j++) {
     for (int k = 0; k < n; k++) {
       for (int l = 0; l < n; l++) {
         arr[l]++;
      }  
     }  
   }  
 }  
 System.out.printf("%dms\nDone!", System.currentTimeMillis() - st);

With just one additional loop, for the same n=2500, it took:

Well, it didn't complete... I waited 15 minutes, yet no answer!!
EDIT: It completed after 47 minutes!

 Start  
 2863936ms  
 Done! 

Why is this comparison important to me?
  This comparison became interesting to me because I have implemented a Tree Edit Distance algorithm which has a fourth-power time complexity of the input size (number of nodes in the trees). I used this algorithm on HTML DOM trees which have around 1000 to 2500 HTML elements.

Summary 
 Thus, an algorithm with power 4 is not an acceptable solution for tree edit distance for web pages with more than 1000 HTML elements.
I am seeking a better algorithm.