= Solution
\b[There are $G=2mn+n(n-1)$ distinct <ground actions>, or $tG$ time-indexed action <variables> over $t$ transition steps.] Each of <STRIPS>'s pick and drop <action schemas> has $mn$ type-correct instantiations. A move chooses an ordered pair of distinct buckets, giving $n(n-1)$. Every physical action is a <ground action> before it receives a time index in <SATPlan>.
$$
\boxed{G=2mn+n(n-1),\qquad G_t=t\,[2mn+n(n-1)]=O\bigl(t(mn+n^2)\bigr).}
$$
These counts exclude static type checks after <action grounding> and exclude optional persistence/no-op action symbols. Using <successor-state axioms> supplies persistence without separate no-op action <variables>. If one action occurrence is allowed per layer, it is selected from the same ground-action set; a parallel encoding also begins with these physical <ground actions>, but has a different exclusion policy.
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