This illustates the crucial lemmat

If the preferance function is, [7, 10, 6, 2, 4, 6, 5, 1, 8],

    then the final parking arrangement is, [8, 4, 0, 5, 7, 3, 1, 6, 9, 2],

    whose empty is, 3

Moving, 1,  units clockwise we get, [8, 1, 7, 3, 5, 7, 6, 2, 9],

    with final parking arrangement is, [2, 8, 4, 0, 5, 7, 3, 1, 6, 9],

    whose empty is, 4

Moving, 2,  units clockwise we get, [9, 2, 8, 4, 6, 8, 7, 3, 10],

    with final parking arrangement is, [9, 2, 8, 4, 0, 5, 7, 3, 1, 6],

    whose empty is, 5

Moving, 3,  units clockwise we get, [10, 3, 9, 5, 7, 9, 8, 4, 1],

    with final parking arrangement is, [6, 9, 2, 8, 4, 0, 5, 7, 3, 1],

    whose empty is, 6

Moving, 4,  units clockwise we get, [1, 4, 10, 6, 8, 10, 9, 5, 2],

    with final parking arrangement is, [1, 6, 9, 2, 8, 4, 0, 5, 7, 3],

    whose empty is, 7

Moving, 5,  units clockwise we get, [2, 5, 1, 7, 9, 1, 10, 6, 3],

    with final parking arrangement is, [3, 1, 6, 9, 2, 8, 4, 0, 5, 7],

    whose empty is, 8

Moving, 6,  units clockwise we get, [3, 6, 2, 8, 10, 2, 1, 7, 4],

    with final parking arrangement is, [7, 3, 1, 6, 9, 2, 8, 4, 0, 5],

    whose empty is, 9

Moving, 7,  units clockwise we get, [4, 7, 3, 9, 1, 3, 2, 8, 5],

    with final parking arrangement is, [5, 7, 3, 1, 6, 9, 2, 8, 4, 0],

    whose empty is, 10

Moving, 8,  units clockwise we get, [5, 8, 4, 10, 2, 4, 3, 9, 6],

    with final parking arrangement is, [0, 5, 7, 3, 1, 6, 9, 2, 8, 4],

    whose empty is, 1

Moving, 9,  units clockwise we get, [6, 9, 5, 1, 3, 5, 4, 10, 7],

    with final parking arrangement is, [4, 0, 5, 7, 3, 1, 6, 9, 2, 8],

    whose empty is, 2