/*
Author: Yihao

Download LCP.zip from: http://fm2012.verifythis.org/challenges

-----------------
Problem description:

This is a verifyThis problem in 2012.
This task asks you to get the longest common prefix of
two subStrings.

-----------------
Verification task:

Implement a the lcp function which takes an array, its length and two indices as input
and verify that it behaves as described.

command: civl verify quantifiedComp.cvl

result: 
For arrays with length less than 5, lcp function returns an integer n which is
the length of the longest common prefix between its two suffixes: The two suffixes
are the same with indexes from 0 to n-1 while they are different at index n.
*/

#include <civlc.cvh>
#include <assert.h>

$input int n=3;
$input int x;
$input int y;
$input int X1[n];

$assume (x < n && y < n && x >=0 && y>=0);

int lcp (int *arr, int n, int x, int y) {
  int l=0;

  while (x+l<n && y+l<n && arr[x+l]==arr[y+l]) {
      l++;
  }
  return l;
}

void main() {
  int result = lcp(X1, n, x, y);
  
  assert($forall (int i: 0 .. result-1) X1[x+i] == X1[y+i]);
}