// proper subgraphs.
class LiveOuts {
 public:
  LiveOuts() = default;

  explicit LiveOuts(OperandRange range)
      : liveouts_(range.begin(), range.end()), prev_liveouts_(liveouts_) {}

  // Delete the current op from liveouts and moves on to the parent ops.
  void update(Operation& op) {
    for (Value result_value : op.getResults()) {
      liveouts_.remove(result_value);
    }

  return_builder.create<tf_device::ReturnOp>(return_builder.getUnknownLoc(),
                                             live_outs);

  llvm::SmallVector<Type, 4> live_out_types;
  live_out_types.reserve(live_outs.size());
  for (Value v : live_outs) {
    live_out_types.emplace_back(v.getType());
  }

  tf_device::LaunchOp launch_op = builder->create<tf_device::LaunchOp>(
      builder->getUnknownLoc(), builder->getStringAttr(c.target),

				}
			}

			if !be.liveout.Eq(newliveout) {
				change = true
				be.liveout.Copy(newliveout)
			}

			// A variable is live on input to this block
			// if it is used by this block, or live on output from this block and
			// not set by the code in this block.
			//
			// in[b] = uevar[b] \cup (out[b] \setminus varkill[b])
			newlivein.AndNot(be.liveout, be.varkill)
			be.livein.Or(newlivein, be.uevar)