// searches should terminate quickly (this makes BFS preferable to DFS).
// If higher performance is needed, the paths can be cached during the first
// traversal in function `CheckControlDependenciesForFunc`.
void EmitDependencyWarningsForPath(IslandOp source_op, IslandOp target_op,
                                   int path_idx) {
  std::vector<IslandOp> path;