// class can be used to remove cycles before running inference and replace them
// after. Correct usage requires exactly one call to Remove(), followed by any
// number of calls to RemovedEdges() and at most one call to Replace(). The call
// to Replace() is optional if the graph will be discarded without being
// executed, e.g., if it is being used purely for a shape inference pass.
class BackEdgeHelper {
 public:

        }
      }
    }
  }
  for (const BackEdge& be : back_edges_) {
    graph_->RemoveEdge(be.edge);
  }
  return absl::OkStatus();
}

const std::vector<BackEdgeHelper::BackEdge>& BackEdgeHelper::RemovedEdges()
    const {
  return back_edges_;
}

Status BackEdgeHelper::Replace() {
  if (graph_ == nullptr) {
    return errors::Internal("BackEdgeHelper Replace called before Remove.");
  }
  if (replaced_) {

  // the shape inference is complete.
  BackEdgeHelper back_edge;
  TF_RETURN_IF_ERROR(back_edge.Remove(graph));
  TF_RETURN_IF_ERROR(PropagateShapes(graph, arg_shapes,
                                     back_edge.RemovedEdges(), &shape_refiner));
  TF_RETURN_IF_ERROR(back_edge.Replace());

  // Currently information does not flow "backward" from consumers to producers

  TF_RETURN_IF_ERROR(back_edge_helper_.Remove(graph_.get()));
  VLOG(1) << "Found " << (back_edge_helper_.RemovedEdges().size())
          << " backedges.";

  // Creates a map for quickly identifying whether a node output is a backedge.
  for (const auto& edge : back_edge_helper_.RemovedEdges()) {
    if (back_edge_node_output_.find(edge.src) != back_edge_node_output_.end() &&