public class InsertionSort{
 
    /*@ public normal_behavior
      @  requires a != null;
      @  ensures (\forall int i; 0<=i && i<a.length-1; a[i]<=a[i+1]);
      @*/
    public static void sort(int[] a){
	/* Outer loop: Sort the ith prefix of the array */
	int i = 0;
	/*@ loop_invariant a != null && 0 <= i && i <= a.length &&
	  @            (\forall int k; 0 <= k && k < i-1; a[k] <= a[k+1]);
	  @ modifies a[*],i;
	  @ decreases a.length - i;
	  @*/
	while(i < a.length) {
	    /* Inner loop: Insert the ith element into the prefix at its
	     * position according to order.
	     */

	    int j = i;
	    /*@ loop_invariant a != null && 0 <= j && j <= i
	      @  && (\forall int k; 0 <= k && k < i && k != j-1; 
	      @      a[k] <= a[k+1])
	      @  && (j > 0 && j < i ==> a[j-1] <= a[j+1]);
	      @ modifies a[*],j;
	      @ decreases j;
	      @*/
	    while (j > 0 && a[j-1] > a[j]) {
		int help = a[j];
		a[j] = a[j-1];
		a[j-1] = help;
		j--;
	    }
	    i++;
	}
    }

    public static /*@pure@*/ boolean equalsModOrdering(int[] a, int[] b){
	if(a.length!=b.length){
	    return false;
	}
	for (int i = 0; i < a.length; i++) {
	    int counta, countb;
	    for (int j = 0; j < a.length; j++) {
		if (a[i] == a[j])
		    counta++;
		if (a[i] == b[j])
		    countb++;
	    }
	    if (counta != countb)
		return false;
	}
	return true;
    }
}