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Use backward deletion of achieved goal requirements; this decides precondition-free ground STRIPS planning in polynomial time. Let $I$ be the initial set of true facts, $G$ the positive conjunctive goal set and $\mathcal{A}$ the ground actions. Assume the usual disjoint add and delete lists; if both lists contain a fact, first normalize the net effect according to the action semantics.

Maintain residual goal set $R=G$ and an initially empty list $L$. While $R⊈I$, look for an action $a$ satisfyingIf no such action exists, reject. Otherwise record $a$ in $L$ and replace $R$ by $R\setminus \mathrm{Add}(a)$. When $R\subseteq I$, return the actions in reverse order of recording. All actions are applicable because their precondition sets are empty.

For soundness, the selected action can be put last in a plan for the current residual goals: it supplies the removed goals and deletes none of the goals still being required. Reversing all recorded selections makes the final state satisfy the original $G$.

For completeness, suppose $R$ is not already satisfied initially but a plan achieves it. Consider the last action in that plan that changes any fact of $R$. Its effective changes cannot delete any member of $R$, because no later action repairs it; it must add at least one member. Thus a candidate exists. Moreover any candidate chosen by the algorithm is safe: removing some requirements gives a subset of $R$, so a plan for $R$, if one exists, also establishes the smaller goal set. Appending the chosen last action then restores the removed requirements without harming the rest. Mathematical induction therefore preserves solvability during all choices.

Each successful iteration removes at least one residual goal, so there are at most $|G|$ iterations and the returned plan has at most $|G|$ actions. Scanning all actions and their effect lists per iteration is polynomial in the input size, for example $O(|G||\mathcal{A}||P|)$ with simple fact-set representations over $P$. Merely taking the union of all add effects would be unsound, since actions can delete each other's achievements. This algorithm is the last-achiever algorithm for precondition-free planning.

Automated planning with ground actions that are always applicable because their precondition sets are empty. Delete effects are still permitted, so taking the union of all add effects does not decide reachability. With a positive conjunctive goal, the last-achiever algorithm for precondition-free planning gives a polynomial-time algorithm.