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        break;
      case 2:
        /* Check red-black property (1) */
        if( !pNode->isBlack &&
            ( (pNode->pLeft && !pNode->pLeft->isBlack) ||
              (pNode->pRight && !pNode->pRight->isBlack) )
          ){
          char buf[128];
          sprintf(buf, "Red node with red child at %p\n", pNode);
          *msg = append_val(*msg, buf);
          *msg = append_node(*msg, tree->pHead, 0);
          *msg = append_val(*msg, "\n");
        }

        /* Check red-black property (2) */
        { 
          int leftHeight = 0;
          int rightHeight = 0;
          if( pNode->pLeft ){
            leftHeight += pNode->pLeft->nBlackHeight;
            leftHeight += (pNode->pLeft->isBlack?1:0);
          }
          if( pNode->pRight ){
            rightHeight += pNode->pRight->nBlackHeight;
            rightHeight += (pNode->pRight->isBlack?1:0);
          }
          if( leftHeight != rightHeight ){
            char buf[128];
            sprintf(buf, "Different black-heights at %p\n", pNode);
            *msg = append_val(*msg, buf);
            *msg = append_node(*msg, tree->pHead, 0);
            *msg = append_val(*msg, "\n");
          }
          pNode->nBlackHeight = leftHeight;
        }

        if( pNode->pParent ){
          if( pNode == pNode->pParent->pLeft ) prev_step = 1;
          else prev_step = 2;
        }
        pNode = pNode->pParent;
        break;
      default: assert(0);
    }
  }
} 

/*
 * Node pX has just been inserted into pTree (by code in sqliteRbtreeInsert()).
 * It is possible that pX is a red node with a red parent, which is a violation
 * of the red-black tree properties. This function performs rotations and 
 * color changes to rebalance the tree
 */
static void do_insert_balancing(BtRbTree *pTree, BtRbNode *pX)
{
  /* In the first iteration of this loop, pX points to the red node just
   * inserted in the tree. If the parent of pX exists (pX is not the root
   * node) and is red, then the properties of the red-black tree are
   * violated.
   *
   * At the start of any subsequent iterations, pX points to a red node
   * with a red parent. In all other respects the tree is a legal red-black
   * binary tree. */
  while( pX != pTree->pHead && !pX->pParent->isBlack ){
    BtRbNode *pUncle;
    BtRbNode *pGrandparent;

    /* Grandparent of pX must exist and must be black. */
    pGrandparent = pX->pParent->pParent;
    assert( pGrandparent );
    assert( pGrandparent->isBlack );

    /* Uncle of pX may or may not exist. */
    if( pX->pParent == pGrandparent->pLeft ) 
      pUncle = pGrandparent->pRight;
    else 
      pUncle = pGrandparent->pLeft;

    /* If the uncle of pX exists and is red, we do the following:
     *       |                 |
     *      G(b)              G(r)
     *      /  \              /  \        
     *   U(r)   P(r)       U(b)  P(b)
     *            \                \
     *           X(r)              X(r)
     *
     *     BEFORE             AFTER
     * pX is then set to G. If the parent of G is red, then the while loop
     * will run again.  */
    if( pUncle && !pUncle->isBlack ){
      pGrandparent->isBlack = 0;
      pUncle->isBlack = 1;
      pX->pParent->isBlack = 1;
      pX = pGrandparent;
    }else{

      if( pX->pParent == pGrandparent->pLeft ){
        if( pX == pX->pParent->pRight ){
          /* If pX is a right-child, do the following transform, essentially
           * to change pX into a left-child: 
           *       |                  | 
           *      G(b)               G(b)
           *      /  \               /  \        
           *   P(r)   U(b)        X(r)  U(b)
           *      \                /
           *     X(r)            P(r) <-- new X
           *
           *     BEFORE             AFTER
           */
          pX = pX->pParent;
          leftRotate(pTree, pX);
        }

        /* Do the following transform, which balances the tree :) 
         *       |                  | 
         *      G(b)               P(b)
         *      /  \               /  \        
         *   P(r)   U(b)        X(r)  G(r)
         *    /                         \
         *  X(r)                        U(b)
         *