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-// VSComp 2010, problem 1, compute the sum and max of the elements of an array and prove
-// that 'sum <= N * max'.
-// Rustan Leino, 18 August 2010.
-//
-// The problem statement gave the pseudo-code for the method, but did not ask to prove
-// that 'sum' or 'max' return as the sum and max, respectively, of the array.  The
-// given assumption that the array's elements are non-negative is not needed to establish
-// the requested postcondition.
-
-method M(N: int, a: array<int>) returns (sum: int, max: int)
-  requires 0 <= N && a != null && a.Length == N && (forall k :: 0 <= k && k < N ==> 0 <= a[k]);
-  ensures sum <= N * max;
-{
-  sum := 0;
-  max := 0;
-  var i := 0;
-  while (i < N)
-    invariant i <= N && sum <= i * max;
-  {
-    if (max < a[i]) {
-      max := a[i];
-    }
-    sum := sum + a[i];
-    i := i + 1;
-  }
-}
-
-method Main()
-{
-  var a := new int[10];
-  a[0] := 9;
-  a[1] := 5;
-  a[2] := 0;
-  a[3] := 2;
-  a[4] := 7;
-  a[5] := 3;
-  a[6] := 2;
-  a[7] := 1;
-  a[8] := 10;
-  a[9] := 6;
-  var s, m := M(10, a);
-  print "N = ", a.Length, "  sum = ", s, "  max = ", m, "\n";
-}