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The blocks world is a classical planning model of movable blocks arranged in stacks on an unlimited table. Each block has one support, each block supports at most one other block, and the support relation has no directed cycle. A clear block can move onto another clear block or onto the table. In a direct-transfer STRIPS representation, an action includes the entire pickup-and-placement operation; a separate holding or empty-hand planning fluent is unnecessary unless the action model explicitly splits those operations.

The table has unlimited capacity, so its availability must not be deleted when a block is placed there. Planning state invariants connect the predicate describing a clear block to the absence of any block directly above it. Goal interaction in planning makes this small model useful for testing automated planning methods.

A restricted goal-by-goal planning procedure chooses one subgoal, constructs a subplan for it without preparation motivated by other pending subgoals, then moves on while treating the earlier goal as protected. Destructive goal interaction in planning can defeat either ordering. Merely requiring the final plan to be a concatenation of subplans is a weaker condition: a subplan may already contain preparatory work useful to a later goal. A claimed impossibility must specify the stronger restriction rather than infer it from concatenation alone.

The Sussman anomaly is a blocks world example in which independently constructing the obvious subplans for two stacking goals gives destructive goal interaction in planning. Clearing a block in advance allows a short joint plan, while prematurely achieving either isolated goal can block the other. It demonstrates the inadequacy of restricted goal-by-goal planning, rather than a prohibition on every possible ordering of final goal achievements. Preparatory actions can make such an ordering succeed. For a concrete instance, start with $C$ on $A$ and $A,B$ on the table, and require $A$ on $B$ and $B$ on $C$. Moving $C$ to the table, then $B$ onto $C$, then $A$ onto $B$ succeeds. The first move is preparation that an isolated shortest subplan for the second stacking goal would omit.