Even when there is an objective ordering of the children of every node, you still have four traversal options: {preorder, postorder} × {BF, DF}.
Note: For children lacking an objective ordering, you might apply generic rules to define a traversal order, but you’d end up with as many depth-first traversals as there are possible orders—essentially a crude heuristic. If you want the evaluation order to be dynamic at each step (e.g., using RL), the complexity grows geometrically worse. That’s been my experience tinkering with a custom AST DSL for ARC-AGI.