Past exam of the computer science course of the University of Oxford / 2023 / Artificial intelligence / 2 / d / Solution

For $i=1,\dots ,n$, executeand, if $i<n$, append $\mathrm{Move}(\mathrm{WEST},\mathrm{EAST})$ before the next iteration.

Each load starts with an empty boat beside an undelivered item. Each unload leaves that item west and restores the loading precondition. By mathematical induction on $i$, after iteration $i$ the first $i$ items are west and the remaining items are east. Thus the automated planning goal holds after $2n-1$ crossings and $4n-1$ actions for $n\ge 1$. For $n=0$, the empty plan already achieves the goal.