// only when it's smaller than the limiting value.
		// Two conditions must happen listed below to accept ind
		// as an induction variable.

		// First condition: loop entry has a single predecessor, which
		// is the header block.  This implies that b.Succs[0] is
		// reached iff ind < limit.
		if len(b.Succs[0].b.Preds) != 1 {
			// b.Succs[1] must exit the loop.
			continue
		}

						phis = append(phis, v)
					}
					continue
				}
				for _, a := range v.Args {
					if s.values[a.ID].needSlot {
						live.add(a.ID)
					}
				}
			}

			// for each predecessor of b, expand its list of live-at-end values
			// invariant: s contains the values live at the start of b (excluding phi inputs)
			for i, e := range b.Preds {
				p := e.b
				t.clear()
				t.addAll(s.live[p.ID])

			// cannot determine the real line number.
			if f.begin > expand {
				f.begin -= expand
			} else if f.begin > 1 {
				f.begin = 1
			}
		} else {
			// Find gap from predecessor and divide between predecessor and f.
			halfGap := (f.begin - funcs[i-1].end) / 2
			if halfGap > expand {
				halfGap = expand
			}
			funcs[i-1].end += halfGap
			f.begin -= halfGap
		}
		funcs[i] = f
	}

				}
				if m.Op == ssa.OpPhi {
					break
				}
			}
			// Find the two predecessor blocks (write barrier on and write barrier off)
			if len(m.Args) != 2 {
				lv.f.Fatalf("phi before write barrier end mark has %d args, want 2", len(m.Args))
			}
			c := b.Preds[0].Block()
			d := b.Preds[1].Block()

			// Find their common predecessor block (the one that branches based on wb on/off).

// Creates a pass that propagates TPU devices to users.
std::unique_ptr<OperationPass<func::FuncOp>> CreateTPUDevicePropagationPass();

// Create a pass that colocates each `Split` with its predecessor.
std::unique_ptr<OperationPass<func::FuncOp>> CreateTPUColocateSplitsPass();

// Creates a pass that replicates the tf._TPUCompileMlir op on each host that

	{name: "FMA", argLength: 3}, // compute (a*b)+c without intermediate rounding

	// Data movement. Max argument length for Phi is indefinite.
	{name: "Phi", argLength: -1, zeroWidth: true}, // select an argument based on which predecessor block we came from
	{name: "Copy", argLength: 1},                  // output = arg0
	// Convert converts between pointers and integers.
	// We have a special op for this so as to not confuse GC

    assume().that(graphIsMutable()).isTrue();

    addNode(N2);
    Set<Integer> predecessors = graph.predecessors(N2);
    UnsupportedOperationException e =
        assertThrows(UnsupportedOperationException.class, () -> predecessors.add(N1));
    putEdge(N1, N2);
    assertThat(graph.predecessors(N2)).containsExactlyElementsIn(predecessors);
  }

  @Override
  @Test
  public void successors_checkReturnedSetMutability() {

  public void predecessors_checkReturnedSetMutability() {
    addNode(N2);
    Set<Integer> predecessors = network.predecessors(N2);
    UnsupportedOperationException e =
        assertThrows(UnsupportedOperationException.class, () -> predecessors.add(N1));
    addEdge(N1, N2, E12);
    assertThat(network.predecessors(N2)).containsExactlyElementsIn(predecessors);
  }

  @Override
  @Test

                        Object key = getPluginKey().apply(plugin);

                        master.put(key, plugin);
                    }
                }

                Map<Object, List<Plugin>> predecessors = new LinkedHashMap<>();
                List<Plugin> pending = new ArrayList<>();
                for (Plugin element : tgt) {
                    Object key = getPluginKey().apply(element);

    }

    @Override
    Graph<N> delegate() {
      return graph;
    }

    @Override
    public Set<N> predecessors(N node) {
      return delegate().successors(node); // transpose
    }

    @Override
    public Set<N> successors(N node) {
      return delegate().predecessors(node); // transpose
    }

    @Override
    public Set<EndpointPair<N>> incidentEdges(N node) {