// Derived from an example in the Boogie distribution

// isr computes the (non-negative) integer square root of its input
method isr(n: int) returns (r : int)
  requires n >= 0;
  // r is the largest non-negative integer whose square is at most n 
  ensures 0 <= r*r && r*r <= n && n < (r+1)*(r+1);
{
  r := 0 ;
  while ((r+1) * (r+1) <= n)
    invariant r*r <= n ;
  {
    r := r+1 ;
  }
}


method Main() {
  var res ;

  call res := isr(36) ;
  assert (res == 6) ;
	
  call res := isr(35) ;
  assert res == 5 ;
}