| Initial | Final |
| (not-inflated wheel2) | (inflated wheel2) |
| (in wheel2 boot) | (on wheel2 the-hub) |
| (on wheel1 the-hub) | (in wheel1 boot) |
| Mid-point | Put W1 in boot | Inflate W2, Put W2 on Hub | |||||||||||||||||||
| A |
|
|
| Mid-point | Inflate W2 | Put W2 on Hub, Put W1 in Boot | ||||||||||||||||||
| B |
|
|
| Mid-point | Put W2 on Hub | Inflate W2, Put W1 in boot | |||||||||||||||||||||
| C |
|
|
| Mid-point | Inflate W2, put on hub | Put W1 in boot | |||||||||||||||||||
| D |
|
|
| Mid-point | W2 inflated, W1 in boot | W2 on hub | |||||||||||||||||||
| E |
|
|
| Mid-point | W2 on Hub, W1 in Boot | W2 Inflated | |||||||||||||||||||||
| F |
|
|
| Case | First Half Length | Second Half Length | Reduction Factor | A | 8 | 11 | 1.4EE09 | B | 3 | 16 | 2.7EE03 | C | 9 | 12 | 1.0EE08 | D | 11 | 8 | 1.4EE09 | E | 11 | 8 | 1.4EE09 | F | 10 | 11 | 1.3EE09 |
From this it is clear that even in the worst case, Case B with only a search space reduction of 2744, we could easily explore all these possible sub-plans still do less computation than the single plan.