G-nonadjacent-item-realtime #0
Let:
  T1 = {:index 128, :time 1980291849, :type :ok, :process 7, :f :txn, :value [[:append 3 1]]}
  T2 = {:index 192, :time 2136523493, :type :ok, :process 2, :f :txn, :value [[:append 5 2] [:append 14 3] [:r 14 [2 3]] [:r 3 [1]]]}
  T3 = {:index 664, :time 3204753544, :type :ok, :process 5, :f :txn, :value [[:append 3 7]]}
  T4 = {:index 890, :time 3592384730, :type :ok, :process 6, :f :txn, :value [[:r 34 [4 5]] [:append 8 141] [:append 3 8]]}
  T5 = {:index 896, :time 3608130840, :type :ok, :process 9, :f :txn, :value [[:append 8 142] [:r 34 [4 5]] [:append 34 12]]}
  T6 = {:index 916, :time 3656187882, :type :ok, :process 4, :f :txn, :value [[:append 34 2] [:append 34 3]]}
  T7 = {:index 918, :time 3656630958, :type :ok, :process 4, :f :txn, :value [[:append 35 8]]}
  T8 = {:index 926, :time 3667007942, :type :ok, :process 7, :f :txn, :value [[:append 35 9] [:r 35 [2 8 9]] [:append 36 1]]}
  T9 = {:index 946, :time 3680336949, :type :ok, :process 7, :f :txn, :value [[:r 35 [2 8 9]] [:append 35 11]]}
  T10 = {:index 1004, :time 3813202559, :type :ok, :process 7, :f :txn, :value [[:append 37 1] [:append 37 2]]}
  T11 = {:index 1022, :time 3842281052, :type :ok, :process 7, :f :txn, :value [[:r 39 [3 9 7]] [:append 39 13]]}
  T12 = {:index 1068, :time 3937057352, :type :ok, :process 3, :f :txn, :value [[:append 5 17] [:r 39 [3 9 7 13 12 30]]]}
  T13 = {:index 1482, :time 4712018137, :type :ok, :process 8, :f :txn, :value [[:r 5 [2 3 8 9 12 13 15 16 18 17]]]}
  T14 = {:index 1502, :time 4757798452, :type :ok, :process 8, :f :txn, :value [[:append 3 9] [:append 49 23] [:r 49 [8 14 18 23]] [:r 49 [8 14 18 23]]]}
  T15 = {:index 1518, :time 4796203051, :type :ok, :process 2, :f :txn, :value [[:r 49 [8 14 18 23]] [:r 49 [8 14 18 23]]]}
  T16 = {:index 1524, :time 4818907972, :type :ok, :process 6, :f :txn, :value [[:append 56 3] [:append 57 3]]}
  T17 = {:index 1530, :time 4850990738, :type :ok, :process 5, :f :txn, :value [[:append 55 25] [:r 42 [3 9 15 19 22 26 28 25 30 31 33 35]] [:append 56 1]]}
  T18 = {:index 1536, :time 4856738802, :type :ok, :process 4, :f :txn, :value [[:r 57 [3]] [:r 57 [3]] [:r 54 [1]] [:r 56 [3 1]]]}
  T19 = {:index 1556, :time 4883788102, :type :ok, :process 9, :f :txn, :value [[:r 3 nil]]}

Then:
  - T1 < T2, because T2 observed T1's append of 1 to key 3.
  - T2 < T3, because T2 did not observe T3's append of 7 to 3.
  - T3 < T4, because T4 appended 8 after T3 appended 7 to 3.
  - T4 < T5, because T5 appended 142 after T4 appended 141 to 8.
  - T5 < T6, because T5 did not observe T6's append of 2 to 34.
  - T6 < T7, because T6 completed at index 916, 0.000 seconds before the invocation of T7, at index 917.
  - T7 < T8, because T8 appended 9 after T7 appended 8 to 35.
  - T8 < T9, because T9 appended 11 after T8 appended 9 to 35.
  - T9 < T10, because T9 completed at index 946, 0.000 seconds before the invocation of T10, at index 947.
  - T10 < T11, because T10 completed at index 1004, 0.000 seconds before the invocation of T11, at index 1005.
  - T11 < T12, because T11 completed at index 1022, 0.002 seconds before the invocation of T12, at index 1027.
  - T12 < T13, because T13 observed T12's append of 17 to key 5.
  - T13 < T14, because T13 completed at index 1482, 0.000 seconds before the invocation of T14, at index 1483.
  - T14 < T15, because T15 observed T14's append of 23 to key 49.
  - T15 < T16, because T15 completed at index 1518, 0.020 seconds before the invocation of T16, at index 1523.
  - T16 < T17, because T17 appended 1 after T16 appended 3 to 56.
  - T17 < T18, because T18 observed T17's append of 1 to key 56.
  - T18 < T19, because T18 completed at index 1536, 0.001 seconds before the invocation of T19, at index 1539.
  - However, T19 < T1, because T19 observed the initial (nil) state of 3, which T1 created by appending 1: a contradiction!


G-nonadjacent-item-realtime #1
Let:
  T1 = {:index 4180, :time 10376061124, :type :ok, :process 0, :f :txn, :value [[:append 88 1] [:append 4 46] [:append 62 63]]}
  T2 = {:index 4296, :time 10603945232, :type :ok, :process 9, :f :txn, :value [[:r 84 [3 11 12 16 17 19 24 26 27 29 28 30 33 35 40 44 45 47 48]] [:r 4 [2 3 4 7 11 21 25 29 34 35 38 44 46]] [:append 86 75] [:append 62 73]]}
  T3 = {:index 4312, :time 10632526065, :type :ok, :process 1, :f :txn, :value [[:r 86 [1 5 2 3 15 16 18 14 34 33 62 65 75]] [:append 86 80] [:r 86 [1 5 2 3 15 16 18 14 34 33 62 65 75 80]] [:append 86 81]]}
  T4 = {:index 4316, :time 10634859239, :type :ok, :process 7, :f :txn, :value [[:append 86 83]]}
  T5 = {:index 4324, :time 10650155073, :type :ok, :process 0, :f :txn, :value [[:r 84 [3 11 12 16 17 19 24 26 27 29 28 30 33 35 40 44 45 47 48 51 52]]]}
  T6 = {:index 4338, :time 10669696763, :type :ok, :process 0, :f :txn, :value [[:r 86 nil]]}
  T7 = {:index 4346, :time 10707916106, :type :ok, :process 0, :f :txn, :value [[:r 86 [1 5 2 3 15 16 18 14 34 33 62 65 75 80 81 83 84]] [:r 86 [1 5 2 3 15 16 18 14 34 33 62 65 75 80 81 83 84]] [:append 86 93] [:append 89 10]]}
  T8 = {:index 4368, :time 10740685627, :type :ok, :process 9, :f :txn, :value [[:r 89 [10]]]}
  T9 = {:index 4372, :time 10748884046, :type :ok, :process 2, :f :txn, :value [[:append 89 16]]}
  T10 = {:index 4432, :time 10828864328, :type :ok, :process 6, :f :txn, :value [[:append 89 21]]}
  T11 = {:index 4448, :time 10857413091, :type :ok, :process 5, :f :txn, :value [[:r 89 [10 16 22 24 21]] [:r 89 [10 16 22 24 21]]]}
  T12 = {:index 4446, :time 10856679294, :type :ok, :process 6, :f :txn, :value [[:append 86 125] [:append 89 26] [:append 86 126]]}
  T13 = {:index 4496, :time 10945536286, :type :ok, :process 0, :f :txn, :value [[:r 89 [10 16 22 24 21 26]] [:append 84 64] [:r 86 [1 5 2 3 15 16 18 14 34 33 62 65 75 80 81 83 84 93 102 108 113 117 112 125 126 130 140]] [:append 89 31]]}
  T14 = {:index 4498, :time 10954141385, :type :ok, :process 9, :f :txn, :value [[:r 89 [10 16 22 24 21 26 31]] [:r 89 [10 16 22 24 21 26 31]]]}
  T15 = {:index 4504, :time 10965707291, :type :ok, :process 9, :f :txn, :value [[:r 89 [10 16 22 24 21 26 31]] [:r 86 [1 5 2 3 15 16 18 14 34 33 62 65 75 80 81 83 84 93 102 108 113 117 112 125 126 130 140 141]]]}
  T16 = {:index 4516, :time 10982699132, :type :ok, :process 7, :f :txn, :value [[:r 86 [1 5 2 3 15 16 18 14 34 33 62 65 75 80 81 83 84 93 102 108 113 117 112 125 126 130 140 141]] [:r 84 [3 11 12 16 17 19 24 26 27 29 28 30 33 35 40 44 45 47 48 51 52 56 59 63 65 64 67]]]}
  T17 = {:index 4536, :time 11011737614, :type :ok, :process 6, :f :txn, :value [[:r 89 [10 16 22 24 21 26 31 35]]]}
  T18 = {:index 4550, :time 11038144639, :type :ok, :process 5, :f :txn, :value [[:append 86 155] [:append 84 71] [:append 86 156] [:append 5 83]]}
  T19 = {:index 4562, :time 11074513074, :type :ok, :process 6, :f :txn, :value [[:append 84 72] [:append 86 168] [:append 86 169]]}
  T20 = {:index 4592, :time 11155674836, :type :ok, :process 4, :f :txn, :value [[:append 86 176] [:append 86 177] [:r 86 [1 5 2 3 15 16 18 14 34 33 62 65 75 80 81 83 84 93 102 108 113 117 112 125 126 130 140 141 149 155 156 154 168 169 175 176 177]] [:r 86 [1 5 2 3 15 16 18 14 34 33 62 65 75 80 81 83 84 93 102 108 113 117 112 125 126 130 140 141 149 155 156 154 168 169 175 176 177]]]}
  T21 = {:index 4600, :time 11181561675, :type :ok, :process 0, :f :txn, :value [[:r 86 [1 5 2 3 15 16 18 14 34 33 62 65 75 80 81 83 84 93 102 108 113 117 112 125 126 130 140 141 149 155 156 154 168 169 175 176 177 184]] [:append 86 187] [:append 89 47]]}
  T22 = {:index 4626, :time 11228965716, :type :ok, :process 9, :f :txn, :value [[:append 89 53] [:append 89 54] [:r 1 [5 6]] [:append 86 198]]}
  T23 = {:index 4666, :time 11321696308, :type :ok, :process 3, :f :txn, :value [[:r 89 [10 16 22 24 21 26 31 35 37 39 36 43 47 53 54]] [:r 84 [3 11 12 16 17 19 24 26 27 29 28 30 33 35 40 44 45 47 48 51 52 56 59 63 65 64 67 70 71 72 76 77]]]}
  T24 = {:index 4682, :time 11354568938, :type :ok, :process 9, :f :txn, :value [[:r 86 nil]]}
  T25 = {:index 4730, :time 11474063799, :type :ok, :process 5, :f :txn, :value [[:r 86 [1 5 2 3 15 16 18 14 34 33 62 65 75 80 81 83 84 93 102 108 113 117 112 125 126 130 140 141 149 155 156 154 168 169 175 176 177 184 187 189 192 193 198 191 204 200 209 207]] [:r 84 [3 11 12 16 17 19 24 26 27 29 28 30 33 35 40 44 45 47 48 51 52 56 59 63 65 64 67 70 71 72 76 77 85]] [:r 84 [3 11 12 16 17 19 24 26 27 29 28 30 33 35 40 44 45 47 48 51 52 56 59 63 65 64 67 70 71 72 76 77 85]]]}
  T26 = {:index 4762, :time 11529962087, :type :ok, :process 3, :f :txn, :value [[:append 86 234] [:append 86 235]]}
  T27 = {:index 4782, :time 11555569273, :type :ok, :process 4, :f :txn, :value [[:r 89 [10 16 22 24 21 26 31 35 37 39 36 43 47 53 54 60 56 59 67 70 75 76]]]}
  T28 = {:index 4786, :time 11562864223, :type :ok, :process 7, :f :txn, :value [[:append 86 247] [:append 86 248]]}
  T29 = {:index 4796, :time 11573455590, :type :ok, :process 8, :f :txn, :value [[:r 84 [3 11 12 16 17 19 24 26 27 29 28 30 33 35 40 44 45 47 48 51 52 56 59 63 65 64 67 70 71 72 76 77 85 89 93]]]}
  T30 = {:index 4802, :time 11587459262, :type :ok, :process 7, :f :txn, :value [[:r 86 nil]]}
  T31 = {:index 4060, :time 10108618820, :type :ok, :process 6, :f :txn, :value [[:r 85 [2]] [:append 86 1]]}
  T32 = {:index 4116, :time 10223232769, :type :ok, :process 6, :f :txn, :value [[:append 86 2] [:r 86 [1 5 2]] [:append 86 3]]}
  T33 = {:index 4118, :time 10226053509, :type :ok, :process 8, :f :txn, :value [[:append 87 3] [:append 86 15] [:append 86 16]]}
  T34 = {:index 4138, :time 10258441889, :type :ok, :process 6, :f :txn, :value [[:append 87 6]]}
  T35 = {:index 4150, :time 10314268175, :type :ok, :process 9, :f :txn, :value [[:r 86 [1 5 2 3 15 16 18 14]] [:r 87 [2 3 6]]]}
  T36 = {:index 4158, :time 10333622255, :type :ok, :process 3, :f :txn, :value [[:append 86 34]]}

Then:
  - T1 < T2, because T2 observed T1's append of 46 to key 4.
  - T2 < T3, because T3 appended 80 after T2 appended 75 to 86.
  - T3 < T4, because T4 appended 83 after T3 appended 81 to 86.
  - T4 < T5, because T4 completed at index 4316, 0.013 seconds before the invocation of T5, at index 4323.
  - T5 < T6, because T5 completed at index 4324, 0.018 seconds before the invocation of T6, at index 4337.
  - T6 < T7, because T6 completed at index 4338, 0.000 seconds before the invocation of T7, at index 4339.
  - T7 < T8, because T8 observed T7's append of 10 to key 89.
  - T8 < T9, because T8 did not observe T9's append of 16 to 89.
  - T9 < T10, because T9 completed at index 4372, 0.004 seconds before the invocation of T10, at index 4379.
  - T10 < T11, because T11 observed T10's append of 21 to key 89.
  - T11 < T12, because T11 did not observe T12's append of 26 to 89.
  - T12 < T13, because T13 appended 31 after T12 appended 26 to 89.
  - T13 < T14, because T14 observed T13's append of 31 to key 89.
  - T14 < T15, because T14 completed at index 4498, 0.000 seconds before the invocation of T15, at index 4499.
  - T15 < T16, because T15 completed at index 4504, 0.005 seconds before the invocation of T16, at index 4511.
  - T16 < T17, because T16 completed at index 4516, 0.016 seconds before the invocation of T17, at index 4525.
  - T17 < T18, because T17 completed at index 4536, 0.004 seconds before the invocation of T18, at index 4543.
  - T18 < T19, because T19 appended 72 after T18 appended 71 to 84.
  - T19 < T20, because T19 completed at index 4562, 0.014 seconds before the invocation of T20, at index 4575.
  - T20 < T21, because T20 completed at index 4592, 0.016 seconds before the invocation of T21, at index 4597.
  - T21 < T22, because T22 appended 53 after T21 appended 47 to 89.
  - T22 < T23, because T23 observed T22's append of 54 to key 89.
  - T23 < T24, because T23 completed at index 4666, 0.012 seconds before the invocation of T24, at index 4669.
  - T24 < T25, because T24 completed at index 4682, 0.020 seconds before the invocation of T25, at index 4697.
  - T25 < T26, because T25 did not observe T26's append of 234 to 86.
  - T26 < T27, because T26 completed at index 4762, 0.007 seconds before the invocation of T27, at index 4771.
  - T27 < T28, because T27 completed at index 4782, 0.000 seconds before the invocation of T28, at index 4785.
  - T28 < T29, because T28 completed at index 4786, 0.007 seconds before the invocation of T29, at index 4793.
  - T29 < T30, because T29 completed at index 4796, 0.011 seconds before the invocation of T30, at index 4799.
  - T30 < T31, because T30 observed the initial (nil) state of 86, which T31 created by appending 1.
  - T31 < T32, because T31 completed at index 4060, 0.000 seconds before the invocation of T32, at index 4061.
  - T32 < T33, because T33 appended 15 after T32 appended 3 to 86.
  - T33 < T34, because T34 appended 6 after T33 appended 3 to 87.
  - T34 < T35, because T35 observed T34's append of 6 to key 87.
  - T35 < T36, because T35 did not observe T36's append of 34 to 86.
  - However, T36 < T1, because T36 completed at index 4158, 0.011 seconds before the invocation of T1, at index 4163: a contradiction!