Domino Cross

A Double six domino set is placed in the shape of a cross, as shown below. However, the sides of the dominoes have been removed and the spots have been replaced by numbers. Can you draw the sides in the diagram so that it becomes clear exactly how the dominoes are positioned? 

      5  3  3  3  2

      6  5  0  6  6

2  0  5  4  1  3  4  4  5

3  6  6  1  5  1  0  6  5

3  5  6  1  1  2  2  4  2

1  1  3  2  5  4  4  3  4

      0  6  0  1  2

      4  0  0  0  2
Feel free to also send a short description of the logic used to reach your solution.

Source: Submitted by reader Joe Celko. This problem first appeared in the Fifth World Puzzle Championship held in Utrecht (The Netherlands) on 1996 October 15 thru October 20 as a puzzle called DOMINO HUNT (10 points)

A solution was received from Alexander Doskey: 
    +-+---+-+-+
    |5|3 3|3|2|
    | +-+-+ | |
    |6|5|0|6|6|
+-+-+-+ | +-+-+-+-+
|2|0 5|4|1|3|4 4|5|
| +---+-+-+ +-+-+ |
|3|6 6|1 5|1|0|6|5|
+-+-+-+-+-+-+ | +-+
|3 5|6 1|1 2|2|4|2|
+---+-+-+-+-+-+-+ |
|1 1|3|2 5|4|4 3|4|
+---+ +---+ +-+-+-+
    |0|6 0|1|2|
    +-+-+-+-+ |
    |4 0|0 0|2|
    +---+---+-+

I started by looking for pairs of numbers that only existed once in the
whole puzzle.  For example, 5-5 can only be found in one place.  Using
this technique, I found:
-->  5-5, 2-5, 2-6, 2-3
In some cases there were more than one occurrence, but they were reduced
to one occurrence when other pairs were blocked off.  For example once
5-5 is found, there is only one 2-5 left.
At this point I could find no other forced pieces, so I had to look into
options.  I noticed that 3-3 occurred in only 2 spots, both of which
included the middle 3 of the top row.  I then looked to see if this lead
to any limitations, and found that since that middle 3 could not be used
to form a 0-3, there was only one 0-3 left (in the lower right).
-->  0-3
>From here, there were structural limitations:
0-4 below 0-3 was forced because of the 4 in the corner and so on:
-->  0-4, 0-6, 0-0, 2-2, 1-4
At this point there was only one 0-2 left:
-->  0-2
Which forced more structural limitations:
-->  3-4, 2-4, 4-6, 4-4
I then found a few more forced pieces:
-->  0-1, 0-5, 4-5
Which then created more structural limits:
-->  5-6, 3-3, 3-6, 1-3, 1-2, 1-5, 1-6, 6-6
And this left only two pieces left:
-->  3-5, 1-1
Since all moves were forced, there can be only this one solution to this
particular arrangement.
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