assertEquals(a, navigableMap.ceilingEntry(a.getKey()));
    assertEquals(a.getKey(), navigableMap.ceilingKey(a.getKey()));
    assertEquals(c, navigableMap.ceilingEntry(b.getKey()));
    assertEquals(c.getKey(), navigableMap.ceilingKey(b.getKey()));
    assertEquals(c, navigableMap.ceilingEntry(c.getKey()));
    assertEquals(c.getKey(), navigableMap.ceilingKey(c.getKey()));
  }

  @CollectionSize.Require(SEVERAL)
  public void testHigher() {

    assertEquals(a, navigableMap.ceilingEntry(a.getKey()));
    assertEquals(a.getKey(), navigableMap.ceilingKey(a.getKey()));
    assertEquals(c, navigableMap.ceilingEntry(b.getKey()));
    assertEquals(c.getKey(), navigableMap.ceilingKey(b.getKey()));
    assertEquals(c, navigableMap.ceilingEntry(c.getKey()));
    assertEquals(c.getKey(), navigableMap.ceilingKey(c.getKey()));
  }

  @CollectionSize.Require(SEVERAL)
  public void testHigher() {

    }
  }

  @Override
  public @Nullable Entry<K, V> ceilingEntry(K key) {
    return delegate.ceilingEntry(checkValid(key));
  }

  @Override
  public @Nullable K ceilingKey(K key) {
    return delegate.ceilingKey(checkValid(key));
  }

  @Override
  public void clear() {
    delegate.clear();
  }

  @Override
  public Comparator<? super K> comparator() {

    }
  }

  @Override
  public @Nullable Entry<K, V> ceilingEntry(K key) {
    return delegate.ceilingEntry(checkValid(key));
  }

  @Override
  public @Nullable K ceilingKey(K key) {
    return delegate.ceilingKey(checkValid(key));
  }

  @Override
  public void clear() {
    delegate.clear();
  }

  @Override
  public Comparator<? super K> comparator() {

      if (lowerEntry != null
          && lowerEntry.getValue().getUpperBound().compareTo(subRange.lowerBound) > 0) {
        lowerBound = subRange.lowerBound;
      } else {
        lowerBound = entriesByLowerBound.ceilingKey(subRange.lowerBound);
        if (lowerBound == null || lowerBound.compareTo(subRange.upperBound) >= 0) {
          throw new NoSuchElementException();
        }
      }

      Cut<K> upperBound;

      return transformEntry(fromMap().ceilingEntry(key));
    }

    @Override
    @CheckForNull
    public K ceilingKey(@ParametricNullness K key) {
      return fromMap().ceilingKey(key);
    }

    @Override
    public NavigableSet<K> descendingKeySet() {
      return fromMap().descendingKeySet();
    }

    @Override

        return nullableSynchronizedEntry(delegate().ceilingEntry(key), mutex);
      }
    }

    @Override
    @CheckForNull
    public K ceilingKey(K key) {
      synchronized (mutex) {
        return delegate().ceilingKey(key);
      }
    }

    @CheckForNull transient NavigableSet<K> descendingKeySet;

    @Override
    public NavigableSet<K> descendingKeySet() {

    assertEquals("three", map.higherKey("one"));
    assertEquals("three", map.higherKey("r"));
    assertEquals("three", map.ceilingKey("r"));
    assertEquals("one", map.ceilingKey("one"));
    assertEquals(mapEntry("three", 5), map.higherEntry("one"));
    assertEquals(mapEntry("one", 3), map.ceilingEntry("one"));
    assertEquals("one", map.lowerKey("three"));

    assertEquals("three", map.higherKey("one"));
    assertEquals("three", map.higherKey("r"));
    assertEquals("three", map.ceilingKey("r"));
    assertEquals("one", map.ceilingKey("one"));
    assertEquals(mapEntry("three", 5), map.higherEntry("one"));
    assertEquals(mapEntry("one", 3), map.ceilingEntry("one"));
    assertEquals("one", map.lowerKey("three"));

  }

  @Override
  @CheckForNull
  public Entry<K, V> ceilingEntry(K key) {
    return tailMap(key, true).firstEntry();
  }

  @Override
  @CheckForNull
  public K ceilingKey(K key) {
    return keyOrNull(ceilingEntry(key));
  }

  @Override
  @CheckForNull
  public Entry<K, V> higherEntry(K key) {
    return tailMap(key, false).firstEntry();
  }