/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1 }, it remains to prove termination of the 2-rule system { 0 0 0 0 ⟶ 0 0 0 1 , 1 0 0 1 ⟶ 0 0 1 0 } Applying sparse tiling TRFC(2) [Geser/Hofbauer/Waldmann, FSCD 2019]. After renaming modulo the bijection { (0,0) ↦ 0, (0,1) ↦ 1, (1,0) ↦ 2, (1,1) ↦ 3, (0,3) ↦ 4, (1,3) ↦ 5, (2,0) ↦ 6 }, it remains to prove termination of the 15-rule system { 0 0 0 0 0 ⟶ 0 0 0 1 2 , 0 0 0 0 1 ⟶ 0 0 0 1 3 , 0 0 0 0 4 ⟶ 0 0 0 1 5 , 2 0 0 0 0 ⟶ 2 0 0 1 2 , 2 0 0 0 1 ⟶ 2 0 0 1 3 , 2 0 0 0 4 ⟶ 2 0 0 1 5 , 6 0 0 0 0 ⟶ 6 0 0 1 2 , 6 0 0 0 1 ⟶ 6 0 0 1 3 , 6 0 0 0 4 ⟶ 6 0 0 1 5 , 1 2 0 1 2 ⟶ 0 0 1 2 0 , 1 2 0 1 3 ⟶ 0 0 1 2 1 , 1 2 0 1 5 ⟶ 0 0 1 2 4 , 3 2 0 1 2 ⟶ 2 0 1 2 0 , 3 2 0 1 3 ⟶ 2 0 1 2 1 , 3 2 0 1 5 ⟶ 2 0 1 2 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6 }, it remains to prove termination of the 14-rule system { 0 0 0 0 0 ⟶ 0 0 0 1 2 , 0 0 0 0 1 ⟶ 0 0 0 1 3 , 0 0 0 0 4 ⟶ 0 0 0 1 5 , 2 0 0 0 0 ⟶ 2 0 0 1 2 , 2 0 0 0 1 ⟶ 2 0 0 1 3 , 2 0 0 0 4 ⟶ 2 0 0 1 5 , 6 0 0 0 0 ⟶ 6 0 0 1 2 , 6 0 0 0 1 ⟶ 6 0 0 1 3 , 1 2 0 1 2 ⟶ 0 0 1 2 0 , 1 2 0 1 3 ⟶ 0 0 1 2 1 , 1 2 0 1 5 ⟶ 0 0 1 2 4 , 3 2 0 1 2 ⟶ 2 0 1 2 0 , 3 2 0 1 3 ⟶ 2 0 1 2 1 , 3 2 0 1 5 ⟶ 2 0 1 2 4 } The system was reversed. After renaming modulo the bijection { 0 ↦ 0, 2 ↦ 1, 1 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6 }, it remains to prove termination of the 14-rule system { 0 0 0 0 0 ⟶ 1 2 0 0 0 , 2 0 0 0 0 ⟶ 3 2 0 0 0 , 4 0 0 0 0 ⟶ 5 2 0 0 0 , 0 0 0 0 1 ⟶ 1 2 0 0 1 , 2 0 0 0 1 ⟶ 3 2 0 0 1 , 4 0 0 0 1 ⟶ 5 2 0 0 1 , 0 0 0 0 6 ⟶ 1 2 0 0 6 , 2 0 0 0 6 ⟶ 3 2 0 0 6 , 1 2 0 1 2 ⟶ 0 1 2 0 0 , 3 2 0 1 2 ⟶ 2 1 2 0 0 , 5 2 0 1 2 ⟶ 4 1 2 0 0 , 1 2 0 1 3 ⟶ 0 1 2 0 1 , 3 2 0 1 3 ⟶ 2 1 2 0 1 , 5 2 0 1 3 ⟶ 4 1 2 0 1 } Applying the dependency pairs transformation. Here, ↑ marks so-called defined symbols. After renaming modulo the bijection { (0,↑) ↦ 0, (0,↓) ↦ 1, (1,↑) ↦ 2, (2,↓) ↦ 3, (2,↑) ↦ 4, (3,↑) ↦ 5, (4,↑) ↦ 6, (5,↑) ↦ 7, (1,↓) ↦ 8, (6,↓) ↦ 9, (3,↓) ↦ 10, (4,↓) ↦ 11, (5,↓) ↦ 12 }, it remains to prove termination of the 60-rule system { 0 1 1 1 1 ⟶ 2 3 1 1 1 , 0 1 1 1 1 ⟶ 4 1 1 1 , 4 1 1 1 1 ⟶ 5 3 1 1 1 , 4 1 1 1 1 ⟶ 4 1 1 1 , 6 1 1 1 1 ⟶ 7 3 1 1 1 , 6 1 1 1 1 ⟶ 4 1 1 1 , 0 1 1 1 8 ⟶ 2 3 1 1 8 , 0 1 1 1 8 ⟶ 4 1 1 8 , 4 1 1 1 8 ⟶ 5 3 1 1 8 , 4 1 1 1 8 ⟶ 4 1 1 8 , 6 1 1 1 8 ⟶ 7 3 1 1 8 , 6 1 1 1 8 ⟶ 4 1 1 8 , 0 1 1 1 9 ⟶ 2 3 1 1 9 , 0 1 1 1 9 ⟶ 4 1 1 9 , 4 1 1 1 9 ⟶ 5 3 1 1 9 , 4 1 1 1 9 ⟶ 4 1 1 9 , 2 3 1 8 3 ⟶ 0 8 3 1 1 , 2 3 1 8 3 ⟶ 2 3 1 1 , 2 3 1 8 3 ⟶ 4 1 1 , 2 3 1 8 3 ⟶ 0 1 , 2 3 1 8 3 ⟶ 0 , 5 3 1 8 3 ⟶ 4 8 3 1 1 , 5 3 1 8 3 ⟶ 2 3 1 1 , 5 3 1 8 3 ⟶ 4 1 1 , 5 3 1 8 3 ⟶ 0 1 , 5 3 1 8 3 ⟶ 0 , 7 3 1 8 3 ⟶ 6 8 3 1 1 , 7 3 1 8 3 ⟶ 2 3 1 1 , 7 3 1 8 3 ⟶ 4 1 1 , 7 3 1 8 3 ⟶ 0 1 , 7 3 1 8 3 ⟶ 0 , 2 3 1 8 10 ⟶ 0 8 3 1 8 , 2 3 1 8 10 ⟶ 2 3 1 8 , 2 3 1 8 10 ⟶ 4 1 8 , 2 3 1 8 10 ⟶ 0 8 , 2 3 1 8 10 ⟶ 2 , 5 3 1 8 10 ⟶ 4 8 3 1 8 , 5 3 1 8 10 ⟶ 2 3 1 8 , 5 3 1 8 10 ⟶ 4 1 8 , 5 3 1 8 10 ⟶ 0 8 , 5 3 1 8 10 ⟶ 2 , 7 3 1 8 10 ⟶ 6 8 3 1 8 , 7 3 1 8 10 ⟶ 2 3 1 8 , 7 3 1 8 10 ⟶ 4 1 8 , 7 3 1 8 10 ⟶ 0 8 , 7 3 1 8 10 ⟶ 2 , 1 1 1 1 1 →= 8 3 1 1 1 , 3 1 1 1 1 →= 10 3 1 1 1 , 11 1 1 1 1 →= 12 3 1 1 1 , 1 1 1 1 8 →= 8 3 1 1 8 , 3 1 1 1 8 →= 10 3 1 1 8 , 11 1 1 1 8 →= 12 3 1 1 8 , 1 1 1 1 9 →= 8 3 1 1 9 , 3 1 1 1 9 →= 10 3 1 1 9 , 8 3 1 8 3 →= 1 8 3 1 1 , 10 3 1 8 3 →= 3 8 3 1 1 , 12 3 1 8 3 →= 11 8 3 1 1 , 8 3 1 8 10 →= 1 8 3 1 8 , 10 3 1 8 10 →= 3 8 3 1 8 , 12 3 1 8 10 →= 11 8 3 1 8 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 }, it remains to prove termination of the 28-rule system { 0 1 1 1 1 ⟶ 2 3 1 1 1 , 4 1 1 1 1 ⟶ 5 3 1 1 1 , 6 1 1 1 1 ⟶ 7 3 1 1 1 , 0 1 1 1 8 ⟶ 2 3 1 1 8 , 4 1 1 1 8 ⟶ 5 3 1 1 8 , 6 1 1 1 8 ⟶ 7 3 1 1 8 , 0 1 1 1 9 ⟶ 2 3 1 1 9 , 4 1 1 1 9 ⟶ 5 3 1 1 9 , 2 3 1 8 3 ⟶ 0 8 3 1 1 , 5 3 1 8 3 ⟶ 4 8 3 1 1 , 7 3 1 8 3 ⟶ 6 8 3 1 1 , 2 3 1 8 10 ⟶ 0 8 3 1 8 , 5 3 1 8 10 ⟶ 4 8 3 1 8 , 7 3 1 8 10 ⟶ 6 8 3 1 8 , 1 1 1 1 1 →= 8 3 1 1 1 , 3 1 1 1 1 →= 10 3 1 1 1 , 11 1 1 1 1 →= 12 3 1 1 1 , 1 1 1 1 8 →= 8 3 1 1 8 , 3 1 1 1 8 →= 10 3 1 1 8 , 11 1 1 1 8 →= 12 3 1 1 8 , 1 1 1 1 9 →= 8 3 1 1 9 , 3 1 1 1 9 →= 10 3 1 1 9 , 8 3 1 8 3 →= 1 8 3 1 1 , 10 3 1 8 3 →= 3 8 3 1 1 , 12 3 1 8 3 →= 11 8 3 1 1 , 8 3 1 8 10 →= 1 8 3 1 8 , 10 3 1 8 10 →= 3 8 3 1 8 , 12 3 1 8 10 →= 11 8 3 1 8 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12 }, it remains to prove termination of the 27-rule system { 0 1 1 1 1 ⟶ 2 3 1 1 1 , 4 1 1 1 1 ⟶ 5 3 1 1 1 , 6 1 1 1 1 ⟶ 7 3 1 1 1 , 0 1 1 1 8 ⟶ 2 3 1 1 8 , 4 1 1 1 8 ⟶ 5 3 1 1 8 , 6 1 1 1 8 ⟶ 7 3 1 1 8 , 4 1 1 1 9 ⟶ 5 3 1 1 9 , 2 3 1 8 3 ⟶ 0 8 3 1 1 , 5 3 1 8 3 ⟶ 4 8 3 1 1 , 7 3 1 8 3 ⟶ 6 8 3 1 1 , 2 3 1 8 10 ⟶ 0 8 3 1 8 , 5 3 1 8 10 ⟶ 4 8 3 1 8 , 7 3 1 8 10 ⟶ 6 8 3 1 8 , 1 1 1 1 1 →= 8 3 1 1 1 , 3 1 1 1 1 →= 10 3 1 1 1 , 11 1 1 1 1 →= 12 3 1 1 1 , 1 1 1 1 8 →= 8 3 1 1 8 , 3 1 1 1 8 →= 10 3 1 1 8 , 11 1 1 1 8 →= 12 3 1 1 8 , 1 1 1 1 9 →= 8 3 1 1 9 , 3 1 1 1 9 →= 10 3 1 1 9 , 8 3 1 8 3 →= 1 8 3 1 1 , 10 3 1 8 3 →= 3 8 3 1 1 , 12 3 1 8 3 →= 11 8 3 1 1 , 8 3 1 8 10 →= 1 8 3 1 8 , 10 3 1 8 10 →= 3 8 3 1 8 , 12 3 1 8 10 →= 11 8 3 1 8 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 9 ↦ 12 }, it remains to prove termination of the 26-rule system { 0 1 1 1 1 ⟶ 2 3 1 1 1 , 4 1 1 1 1 ⟶ 5 3 1 1 1 , 6 1 1 1 1 ⟶ 7 3 1 1 1 , 0 1 1 1 8 ⟶ 2 3 1 1 8 , 4 1 1 1 8 ⟶ 5 3 1 1 8 , 6 1 1 1 8 ⟶ 7 3 1 1 8 , 2 3 1 8 3 ⟶ 0 8 3 1 1 , 5 3 1 8 3 ⟶ 4 8 3 1 1 , 7 3 1 8 3 ⟶ 6 8 3 1 1 , 2 3 1 8 9 ⟶ 0 8 3 1 8 , 5 3 1 8 9 ⟶ 4 8 3 1 8 , 7 3 1 8 9 ⟶ 6 8 3 1 8 , 1 1 1 1 1 →= 8 3 1 1 1 , 3 1 1 1 1 →= 9 3 1 1 1 , 10 1 1 1 1 →= 11 3 1 1 1 , 1 1 1 1 8 →= 8 3 1 1 8 , 3 1 1 1 8 →= 9 3 1 1 8 , 10 1 1 1 8 →= 11 3 1 1 8 , 1 1 1 1 12 →= 8 3 1 1 12 , 3 1 1 1 12 →= 9 3 1 1 12 , 8 3 1 8 3 →= 1 8 3 1 1 , 9 3 1 8 3 →= 3 8 3 1 1 , 11 3 1 8 3 →= 10 8 3 1 1 , 8 3 1 8 9 →= 1 8 3 1 8 , 9 3 1 8 9 →= 3 8 3 1 8 , 11 3 1 8 9 →= 10 8 3 1 8 } Applying sparse tiling TROC(2) [Geser/Hofbauer/Waldmann, FSCD 2019]. After renaming modulo the bijection { (13,0) ↦ 0, (0,1) ↦ 1, (1,1) ↦ 2, (13,2) ↦ 3, (2,3) ↦ 4, (3,1) ↦ 5, (1,8) ↦ 6, (1,12) ↦ 7, (1,14) ↦ 8, (13,4) ↦ 9, (4,1) ↦ 10, (13,5) ↦ 11, (5,3) ↦ 12, (13,6) ↦ 13, (6,1) ↦ 14, (13,7) ↦ 15, (7,3) ↦ 16, (8,3) ↦ 17, (8,9) ↦ 18, (8,14) ↦ 19, (0,8) ↦ 20, (3,8) ↦ 21, (4,8) ↦ 22, (6,8) ↦ 23, (9,3) ↦ 24, (9,9) ↦ 25, (10,1) ↦ 26, (10,8) ↦ 27, (13,1) ↦ 28, (13,8) ↦ 29, (2,9) ↦ 30, (5,9) ↦ 31, (7,9) ↦ 32, (11,3) ↦ 33, (11,9) ↦ 34, (13,3) ↦ 35, (13,9) ↦ 36, (13,10) ↦ 37, (13,11) ↦ 38, (12,14) ↦ 39 }, it remains to prove termination of the 212-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 0 1 2 2 2 7 ⟶ 3 4 5 2 2 7 , 0 1 2 2 2 8 ⟶ 3 4 5 2 2 8 , 9 10 2 2 2 2 ⟶ 11 12 5 2 2 2 , 9 10 2 2 2 6 ⟶ 11 12 5 2 2 6 , 9 10 2 2 2 7 ⟶ 11 12 5 2 2 7 , 9 10 2 2 2 8 ⟶ 11 12 5 2 2 8 , 13 14 2 2 2 2 ⟶ 15 16 5 2 2 2 , 13 14 2 2 2 6 ⟶ 15 16 5 2 2 6 , 13 14 2 2 2 7 ⟶ 15 16 5 2 2 7 , 13 14 2 2 2 8 ⟶ 15 16 5 2 2 8 , 0 1 2 2 6 17 ⟶ 3 4 5 2 6 17 , 0 1 2 2 6 18 ⟶ 3 4 5 2 6 18 , 0 1 2 2 6 19 ⟶ 3 4 5 2 6 19 , 9 10 2 2 6 17 ⟶ 11 12 5 2 6 17 , 9 10 2 2 6 18 ⟶ 11 12 5 2 6 18 , 9 10 2 2 6 19 ⟶ 11 12 5 2 6 19 , 13 14 2 2 6 17 ⟶ 15 16 5 2 6 17 , 13 14 2 2 6 18 ⟶ 15 16 5 2 6 18 , 13 14 2 2 6 19 ⟶ 15 16 5 2 6 19 , 3 4 5 6 17 5 ⟶ 0 20 17 5 2 2 , 3 4 5 6 17 21 ⟶ 0 20 17 5 2 6 , 11 12 5 6 17 5 ⟶ 9 22 17 5 2 2 , 11 12 5 6 17 21 ⟶ 9 22 17 5 2 6 , 15 16 5 6 17 5 ⟶ 13 23 17 5 2 2 , 15 16 5 6 17 21 ⟶ 13 23 17 5 2 6 , 3 4 5 6 18 24 ⟶ 0 20 17 5 6 17 , 3 4 5 6 18 25 ⟶ 0 20 17 5 6 18 , 11 12 5 6 18 24 ⟶ 9 22 17 5 6 17 , 11 12 5 6 18 25 ⟶ 9 22 17 5 6 18 , 15 16 5 6 18 24 ⟶ 13 23 17 5 6 17 , 15 16 5 6 18 25 ⟶ 13 23 17 5 6 18 , 1 2 2 2 2 2 →= 20 17 5 2 2 2 , 1 2 2 2 2 6 →= 20 17 5 2 2 6 , 1 2 2 2 2 7 →= 20 17 5 2 2 7 , 1 2 2 2 2 8 →= 20 17 5 2 2 8 , 2 2 2 2 2 2 →= 6 17 5 2 2 2 , 2 2 2 2 2 6 →= 6 17 5 2 2 6 , 2 2 2 2 2 7 →= 6 17 5 2 2 7 , 2 2 2 2 2 8 →= 6 17 5 2 2 8 , 5 2 2 2 2 2 →= 21 17 5 2 2 2 , 5 2 2 2 2 6 →= 21 17 5 2 2 6 , 5 2 2 2 2 7 →= 21 17 5 2 2 7 , 5 2 2 2 2 8 →= 21 17 5 2 2 8 , 10 2 2 2 2 2 →= 22 17 5 2 2 2 , 10 2 2 2 2 6 →= 22 17 5 2 2 6 , 10 2 2 2 2 7 →= 22 17 5 2 2 7 , 10 2 2 2 2 8 →= 22 17 5 2 2 8 , 14 2 2 2 2 2 →= 23 17 5 2 2 2 , 14 2 2 2 2 6 →= 23 17 5 2 2 6 , 14 2 2 2 2 7 →= 23 17 5 2 2 7 , 14 2 2 2 2 8 →= 23 17 5 2 2 8 , 26 2 2 2 2 2 →= 27 17 5 2 2 2 , 26 2 2 2 2 6 →= 27 17 5 2 2 6 , 26 2 2 2 2 7 →= 27 17 5 2 2 7 , 26 2 2 2 2 8 →= 27 17 5 2 2 8 , 28 2 2 2 2 2 →= 29 17 5 2 2 2 , 28 2 2 2 2 6 →= 29 17 5 2 2 6 , 28 2 2 2 2 7 →= 29 17 5 2 2 7 , 28 2 2 2 2 8 →= 29 17 5 2 2 8 , 4 5 2 2 2 2 →= 30 24 5 2 2 2 , 4 5 2 2 2 6 →= 30 24 5 2 2 6 , 4 5 2 2 2 7 →= 30 24 5 2 2 7 , 4 5 2 2 2 8 →= 30 24 5 2 2 8 , 12 5 2 2 2 2 →= 31 24 5 2 2 2 , 12 5 2 2 2 6 →= 31 24 5 2 2 6 , 12 5 2 2 2 7 →= 31 24 5 2 2 7 , 12 5 2 2 2 8 →= 31 24 5 2 2 8 , 16 5 2 2 2 2 →= 32 24 5 2 2 2 , 16 5 2 2 2 6 →= 32 24 5 2 2 6 , 16 5 2 2 2 7 →= 32 24 5 2 2 7 , 16 5 2 2 2 8 →= 32 24 5 2 2 8 , 17 5 2 2 2 2 →= 18 24 5 2 2 2 , 17 5 2 2 2 6 →= 18 24 5 2 2 6 , 17 5 2 2 2 7 →= 18 24 5 2 2 7 , 17 5 2 2 2 8 →= 18 24 5 2 2 8 , 24 5 2 2 2 2 →= 25 24 5 2 2 2 , 24 5 2 2 2 6 →= 25 24 5 2 2 6 , 24 5 2 2 2 7 →= 25 24 5 2 2 7 , 24 5 2 2 2 8 →= 25 24 5 2 2 8 , 33 5 2 2 2 2 →= 34 24 5 2 2 2 , 33 5 2 2 2 6 →= 34 24 5 2 2 6 , 33 5 2 2 2 7 →= 34 24 5 2 2 7 , 33 5 2 2 2 8 →= 34 24 5 2 2 8 , 35 5 2 2 2 2 →= 36 24 5 2 2 2 , 35 5 2 2 2 6 →= 36 24 5 2 2 6 , 35 5 2 2 2 7 →= 36 24 5 2 2 7 , 35 5 2 2 2 8 →= 36 24 5 2 2 8 , 37 26 2 2 2 2 →= 38 33 5 2 2 2 , 37 26 2 2 2 6 →= 38 33 5 2 2 6 , 37 26 2 2 2 7 →= 38 33 5 2 2 7 , 37 26 2 2 2 8 →= 38 33 5 2 2 8 , 1 2 2 2 6 17 →= 20 17 5 2 6 17 , 1 2 2 2 6 18 →= 20 17 5 2 6 18 , 1 2 2 2 6 19 →= 20 17 5 2 6 19 , 2 2 2 2 6 17 →= 6 17 5 2 6 17 , 2 2 2 2 6 18 →= 6 17 5 2 6 18 , 2 2 2 2 6 19 →= 6 17 5 2 6 19 , 5 2 2 2 6 17 →= 21 17 5 2 6 17 , 5 2 2 2 6 18 →= 21 17 5 2 6 18 , 5 2 2 2 6 19 →= 21 17 5 2 6 19 , 10 2 2 2 6 17 →= 22 17 5 2 6 17 , 10 2 2 2 6 18 →= 22 17 5 2 6 18 , 10 2 2 2 6 19 →= 22 17 5 2 6 19 , 14 2 2 2 6 17 →= 23 17 5 2 6 17 , 14 2 2 2 6 18 →= 23 17 5 2 6 18 , 14 2 2 2 6 19 →= 23 17 5 2 6 19 , 26 2 2 2 6 17 →= 27 17 5 2 6 17 , 26 2 2 2 6 18 →= 27 17 5 2 6 18 , 26 2 2 2 6 19 →= 27 17 5 2 6 19 , 28 2 2 2 6 17 →= 29 17 5 2 6 17 , 28 2 2 2 6 18 →= 29 17 5 2 6 18 , 28 2 2 2 6 19 →= 29 17 5 2 6 19 , 4 5 2 2 6 17 →= 30 24 5 2 6 17 , 4 5 2 2 6 18 →= 30 24 5 2 6 18 , 4 5 2 2 6 19 →= 30 24 5 2 6 19 , 12 5 2 2 6 17 →= 31 24 5 2 6 17 , 12 5 2 2 6 18 →= 31 24 5 2 6 18 , 12 5 2 2 6 19 →= 31 24 5 2 6 19 , 16 5 2 2 6 17 →= 32 24 5 2 6 17 , 16 5 2 2 6 18 →= 32 24 5 2 6 18 , 16 5 2 2 6 19 →= 32 24 5 2 6 19 , 17 5 2 2 6 17 →= 18 24 5 2 6 17 , 17 5 2 2 6 18 →= 18 24 5 2 6 18 , 17 5 2 2 6 19 →= 18 24 5 2 6 19 , 24 5 2 2 6 17 →= 25 24 5 2 6 17 , 24 5 2 2 6 18 →= 25 24 5 2 6 18 , 24 5 2 2 6 19 →= 25 24 5 2 6 19 , 33 5 2 2 6 17 →= 34 24 5 2 6 17 , 33 5 2 2 6 18 →= 34 24 5 2 6 18 , 33 5 2 2 6 19 →= 34 24 5 2 6 19 , 35 5 2 2 6 17 →= 36 24 5 2 6 17 , 35 5 2 2 6 18 →= 36 24 5 2 6 18 , 35 5 2 2 6 19 →= 36 24 5 2 6 19 , 37 26 2 2 6 17 →= 38 33 5 2 6 17 , 37 26 2 2 6 18 →= 38 33 5 2 6 18 , 37 26 2 2 6 19 →= 38 33 5 2 6 19 , 1 2 2 2 7 39 →= 20 17 5 2 7 39 , 2 2 2 2 7 39 →= 6 17 5 2 7 39 , 5 2 2 2 7 39 →= 21 17 5 2 7 39 , 10 2 2 2 7 39 →= 22 17 5 2 7 39 , 14 2 2 2 7 39 →= 23 17 5 2 7 39 , 26 2 2 2 7 39 →= 27 17 5 2 7 39 , 28 2 2 2 7 39 →= 29 17 5 2 7 39 , 4 5 2 2 7 39 →= 30 24 5 2 7 39 , 12 5 2 2 7 39 →= 31 24 5 2 7 39 , 16 5 2 2 7 39 →= 32 24 5 2 7 39 , 17 5 2 2 7 39 →= 18 24 5 2 7 39 , 24 5 2 2 7 39 →= 25 24 5 2 7 39 , 33 5 2 2 7 39 →= 34 24 5 2 7 39 , 35 5 2 2 7 39 →= 36 24 5 2 7 39 , 20 17 5 6 17 5 →= 1 6 17 5 2 2 , 20 17 5 6 17 21 →= 1 6 17 5 2 6 , 6 17 5 6 17 5 →= 2 6 17 5 2 2 , 6 17 5 6 17 21 →= 2 6 17 5 2 6 , 21 17 5 6 17 5 →= 5 6 17 5 2 2 , 21 17 5 6 17 21 →= 5 6 17 5 2 6 , 22 17 5 6 17 5 →= 10 6 17 5 2 2 , 22 17 5 6 17 21 →= 10 6 17 5 2 6 , 23 17 5 6 17 5 →= 14 6 17 5 2 2 , 23 17 5 6 17 21 →= 14 6 17 5 2 6 , 27 17 5 6 17 5 →= 26 6 17 5 2 2 , 27 17 5 6 17 21 →= 26 6 17 5 2 6 , 29 17 5 6 17 5 →= 28 6 17 5 2 2 , 29 17 5 6 17 21 →= 28 6 17 5 2 6 , 30 24 5 6 17 5 →= 4 21 17 5 2 2 , 30 24 5 6 17 21 →= 4 21 17 5 2 6 , 31 24 5 6 17 5 →= 12 21 17 5 2 2 , 31 24 5 6 17 21 →= 12 21 17 5 2 6 , 32 24 5 6 17 5 →= 16 21 17 5 2 2 , 32 24 5 6 17 21 →= 16 21 17 5 2 6 , 18 24 5 6 17 5 →= 17 21 17 5 2 2 , 18 24 5 6 17 21 →= 17 21 17 5 2 6 , 25 24 5 6 17 5 →= 24 21 17 5 2 2 , 25 24 5 6 17 21 →= 24 21 17 5 2 6 , 34 24 5 6 17 5 →= 33 21 17 5 2 2 , 34 24 5 6 17 21 →= 33 21 17 5 2 6 , 36 24 5 6 17 5 →= 35 21 17 5 2 2 , 36 24 5 6 17 21 →= 35 21 17 5 2 6 , 38 33 5 6 17 5 →= 37 27 17 5 2 2 , 38 33 5 6 17 21 →= 37 27 17 5 2 6 , 20 17 5 6 18 24 →= 1 6 17 5 6 17 , 20 17 5 6 18 25 →= 1 6 17 5 6 18 , 6 17 5 6 18 24 →= 2 6 17 5 6 17 , 6 17 5 6 18 25 →= 2 6 17 5 6 18 , 21 17 5 6 18 24 →= 5 6 17 5 6 17 , 21 17 5 6 18 25 →= 5 6 17 5 6 18 , 22 17 5 6 18 24 →= 10 6 17 5 6 17 , 22 17 5 6 18 25 →= 10 6 17 5 6 18 , 23 17 5 6 18 24 →= 14 6 17 5 6 17 , 23 17 5 6 18 25 →= 14 6 17 5 6 18 , 27 17 5 6 18 24 →= 26 6 17 5 6 17 , 27 17 5 6 18 25 →= 26 6 17 5 6 18 , 29 17 5 6 18 24 →= 28 6 17 5 6 17 , 29 17 5 6 18 25 →= 28 6 17 5 6 18 , 30 24 5 6 18 24 →= 4 21 17 5 6 17 , 30 24 5 6 18 25 →= 4 21 17 5 6 18 , 31 24 5 6 18 24 →= 12 21 17 5 6 17 , 31 24 5 6 18 25 →= 12 21 17 5 6 18 , 32 24 5 6 18 24 →= 16 21 17 5 6 17 , 32 24 5 6 18 25 →= 16 21 17 5 6 18 , 18 24 5 6 18 24 →= 17 21 17 5 6 17 , 18 24 5 6 18 25 →= 17 21 17 5 6 18 , 25 24 5 6 18 24 →= 24 21 17 5 6 17 , 25 24 5 6 18 25 →= 24 21 17 5 6 18 , 34 24 5 6 18 24 →= 33 21 17 5 6 17 , 34 24 5 6 18 25 →= 33 21 17 5 6 18 , 36 24 5 6 18 24 →= 35 21 17 5 6 17 , 36 24 5 6 18 25 →= 35 21 17 5 6 18 , 38 33 5 6 18 24 →= 37 27 17 5 6 17 , 38 33 5 6 18 25 →= 37 27 17 5 6 18 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 8 ↦ 7, 9 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 7 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 211-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 0 1 2 2 2 7 ⟶ 3 4 5 2 2 7 , 8 9 2 2 2 2 ⟶ 10 11 5 2 2 2 , 8 9 2 2 2 6 ⟶ 10 11 5 2 2 6 , 8 9 2 2 2 12 ⟶ 10 11 5 2 2 12 , 8 9 2 2 2 7 ⟶ 10 11 5 2 2 7 , 13 14 2 2 2 2 ⟶ 15 16 5 2 2 2 , 13 14 2 2 2 6 ⟶ 15 16 5 2 2 6 , 13 14 2 2 2 12 ⟶ 15 16 5 2 2 12 , 13 14 2 2 2 7 ⟶ 15 16 5 2 2 7 , 0 1 2 2 6 17 ⟶ 3 4 5 2 6 17 , 0 1 2 2 6 18 ⟶ 3 4 5 2 6 18 , 0 1 2 2 6 19 ⟶ 3 4 5 2 6 19 , 8 9 2 2 6 17 ⟶ 10 11 5 2 6 17 , 8 9 2 2 6 18 ⟶ 10 11 5 2 6 18 , 8 9 2 2 6 19 ⟶ 10 11 5 2 6 19 , 13 14 2 2 6 17 ⟶ 15 16 5 2 6 17 , 13 14 2 2 6 18 ⟶ 15 16 5 2 6 18 , 13 14 2 2 6 19 ⟶ 15 16 5 2 6 19 , 3 4 5 6 17 5 ⟶ 0 20 17 5 2 2 , 3 4 5 6 17 21 ⟶ 0 20 17 5 2 6 , 10 11 5 6 17 5 ⟶ 8 22 17 5 2 2 , 10 11 5 6 17 21 ⟶ 8 22 17 5 2 6 , 15 16 5 6 17 5 ⟶ 13 23 17 5 2 2 , 15 16 5 6 17 21 ⟶ 13 23 17 5 2 6 , 3 4 5 6 18 24 ⟶ 0 20 17 5 6 17 , 3 4 5 6 18 25 ⟶ 0 20 17 5 6 18 , 10 11 5 6 18 24 ⟶ 8 22 17 5 6 17 , 10 11 5 6 18 25 ⟶ 8 22 17 5 6 18 , 15 16 5 6 18 24 ⟶ 13 23 17 5 6 17 , 15 16 5 6 18 25 ⟶ 13 23 17 5 6 18 , 1 2 2 2 2 2 →= 20 17 5 2 2 2 , 1 2 2 2 2 6 →= 20 17 5 2 2 6 , 1 2 2 2 2 12 →= 20 17 5 2 2 12 , 1 2 2 2 2 7 →= 20 17 5 2 2 7 , 2 2 2 2 2 2 →= 6 17 5 2 2 2 , 2 2 2 2 2 6 →= 6 17 5 2 2 6 , 2 2 2 2 2 12 →= 6 17 5 2 2 12 , 2 2 2 2 2 7 →= 6 17 5 2 2 7 , 5 2 2 2 2 2 →= 21 17 5 2 2 2 , 5 2 2 2 2 6 →= 21 17 5 2 2 6 , 5 2 2 2 2 12 →= 21 17 5 2 2 12 , 5 2 2 2 2 7 →= 21 17 5 2 2 7 , 9 2 2 2 2 2 →= 22 17 5 2 2 2 , 9 2 2 2 2 6 →= 22 17 5 2 2 6 , 9 2 2 2 2 12 →= 22 17 5 2 2 12 , 9 2 2 2 2 7 →= 22 17 5 2 2 7 , 14 2 2 2 2 2 →= 23 17 5 2 2 2 , 14 2 2 2 2 6 →= 23 17 5 2 2 6 , 14 2 2 2 2 12 →= 23 17 5 2 2 12 , 14 2 2 2 2 7 →= 23 17 5 2 2 7 , 26 2 2 2 2 2 →= 27 17 5 2 2 2 , 26 2 2 2 2 6 →= 27 17 5 2 2 6 , 26 2 2 2 2 12 →= 27 17 5 2 2 12 , 26 2 2 2 2 7 →= 27 17 5 2 2 7 , 28 2 2 2 2 2 →= 29 17 5 2 2 2 , 28 2 2 2 2 6 →= 29 17 5 2 2 6 , 28 2 2 2 2 12 →= 29 17 5 2 2 12 , 28 2 2 2 2 7 →= 29 17 5 2 2 7 , 4 5 2 2 2 2 →= 30 24 5 2 2 2 , 4 5 2 2 2 6 →= 30 24 5 2 2 6 , 4 5 2 2 2 12 →= 30 24 5 2 2 12 , 4 5 2 2 2 7 →= 30 24 5 2 2 7 , 11 5 2 2 2 2 →= 31 24 5 2 2 2 , 11 5 2 2 2 6 →= 31 24 5 2 2 6 , 11 5 2 2 2 12 →= 31 24 5 2 2 12 , 11 5 2 2 2 7 →= 31 24 5 2 2 7 , 16 5 2 2 2 2 →= 32 24 5 2 2 2 , 16 5 2 2 2 6 →= 32 24 5 2 2 6 , 16 5 2 2 2 12 →= 32 24 5 2 2 12 , 16 5 2 2 2 7 →= 32 24 5 2 2 7 , 17 5 2 2 2 2 →= 18 24 5 2 2 2 , 17 5 2 2 2 6 →= 18 24 5 2 2 6 , 17 5 2 2 2 12 →= 18 24 5 2 2 12 , 17 5 2 2 2 7 →= 18 24 5 2 2 7 , 24 5 2 2 2 2 →= 25 24 5 2 2 2 , 24 5 2 2 2 6 →= 25 24 5 2 2 6 , 24 5 2 2 2 12 →= 25 24 5 2 2 12 , 24 5 2 2 2 7 →= 25 24 5 2 2 7 , 33 5 2 2 2 2 →= 34 24 5 2 2 2 , 33 5 2 2 2 6 →= 34 24 5 2 2 6 , 33 5 2 2 2 12 →= 34 24 5 2 2 12 , 33 5 2 2 2 7 →= 34 24 5 2 2 7 , 35 5 2 2 2 2 →= 36 24 5 2 2 2 , 35 5 2 2 2 6 →= 36 24 5 2 2 6 , 35 5 2 2 2 12 →= 36 24 5 2 2 12 , 35 5 2 2 2 7 →= 36 24 5 2 2 7 , 37 26 2 2 2 2 →= 38 33 5 2 2 2 , 37 26 2 2 2 6 →= 38 33 5 2 2 6 , 37 26 2 2 2 12 →= 38 33 5 2 2 12 , 37 26 2 2 2 7 →= 38 33 5 2 2 7 , 1 2 2 2 6 17 →= 20 17 5 2 6 17 , 1 2 2 2 6 18 →= 20 17 5 2 6 18 , 1 2 2 2 6 19 →= 20 17 5 2 6 19 , 2 2 2 2 6 17 →= 6 17 5 2 6 17 , 2 2 2 2 6 18 →= 6 17 5 2 6 18 , 2 2 2 2 6 19 →= 6 17 5 2 6 19 , 5 2 2 2 6 17 →= 21 17 5 2 6 17 , 5 2 2 2 6 18 →= 21 17 5 2 6 18 , 5 2 2 2 6 19 →= 21 17 5 2 6 19 , 9 2 2 2 6 17 →= 22 17 5 2 6 17 , 9 2 2 2 6 18 →= 22 17 5 2 6 18 , 9 2 2 2 6 19 →= 22 17 5 2 6 19 , 14 2 2 2 6 17 →= 23 17 5 2 6 17 , 14 2 2 2 6 18 →= 23 17 5 2 6 18 , 14 2 2 2 6 19 →= 23 17 5 2 6 19 , 26 2 2 2 6 17 →= 27 17 5 2 6 17 , 26 2 2 2 6 18 →= 27 17 5 2 6 18 , 26 2 2 2 6 19 →= 27 17 5 2 6 19 , 28 2 2 2 6 17 →= 29 17 5 2 6 17 , 28 2 2 2 6 18 →= 29 17 5 2 6 18 , 28 2 2 2 6 19 →= 29 17 5 2 6 19 , 4 5 2 2 6 17 →= 30 24 5 2 6 17 , 4 5 2 2 6 18 →= 30 24 5 2 6 18 , 4 5 2 2 6 19 →= 30 24 5 2 6 19 , 11 5 2 2 6 17 →= 31 24 5 2 6 17 , 11 5 2 2 6 18 →= 31 24 5 2 6 18 , 11 5 2 2 6 19 →= 31 24 5 2 6 19 , 16 5 2 2 6 17 →= 32 24 5 2 6 17 , 16 5 2 2 6 18 →= 32 24 5 2 6 18 , 16 5 2 2 6 19 →= 32 24 5 2 6 19 , 17 5 2 2 6 17 →= 18 24 5 2 6 17 , 17 5 2 2 6 18 →= 18 24 5 2 6 18 , 17 5 2 2 6 19 →= 18 24 5 2 6 19 , 24 5 2 2 6 17 →= 25 24 5 2 6 17 , 24 5 2 2 6 18 →= 25 24 5 2 6 18 , 24 5 2 2 6 19 →= 25 24 5 2 6 19 , 33 5 2 2 6 17 →= 34 24 5 2 6 17 , 33 5 2 2 6 18 →= 34 24 5 2 6 18 , 33 5 2 2 6 19 →= 34 24 5 2 6 19 , 35 5 2 2 6 17 →= 36 24 5 2 6 17 , 35 5 2 2 6 18 →= 36 24 5 2 6 18 , 35 5 2 2 6 19 →= 36 24 5 2 6 19 , 37 26 2 2 6 17 →= 38 33 5 2 6 17 , 37 26 2 2 6 18 →= 38 33 5 2 6 18 , 37 26 2 2 6 19 →= 38 33 5 2 6 19 , 1 2 2 2 12 39 →= 20 17 5 2 12 39 , 2 2 2 2 12 39 →= 6 17 5 2 12 39 , 5 2 2 2 12 39 →= 21 17 5 2 12 39 , 9 2 2 2 12 39 →= 22 17 5 2 12 39 , 14 2 2 2 12 39 →= 23 17 5 2 12 39 , 26 2 2 2 12 39 →= 27 17 5 2 12 39 , 28 2 2 2 12 39 →= 29 17 5 2 12 39 , 4 5 2 2 12 39 →= 30 24 5 2 12 39 , 11 5 2 2 12 39 →= 31 24 5 2 12 39 , 16 5 2 2 12 39 →= 32 24 5 2 12 39 , 17 5 2 2 12 39 →= 18 24 5 2 12 39 , 24 5 2 2 12 39 →= 25 24 5 2 12 39 , 33 5 2 2 12 39 →= 34 24 5 2 12 39 , 35 5 2 2 12 39 →= 36 24 5 2 12 39 , 20 17 5 6 17 5 →= 1 6 17 5 2 2 , 20 17 5 6 17 21 →= 1 6 17 5 2 6 , 6 17 5 6 17 5 →= 2 6 17 5 2 2 , 6 17 5 6 17 21 →= 2 6 17 5 2 6 , 21 17 5 6 17 5 →= 5 6 17 5 2 2 , 21 17 5 6 17 21 →= 5 6 17 5 2 6 , 22 17 5 6 17 5 →= 9 6 17 5 2 2 , 22 17 5 6 17 21 →= 9 6 17 5 2 6 , 23 17 5 6 17 5 →= 14 6 17 5 2 2 , 23 17 5 6 17 21 →= 14 6 17 5 2 6 , 27 17 5 6 17 5 →= 26 6 17 5 2 2 , 27 17 5 6 17 21 →= 26 6 17 5 2 6 , 29 17 5 6 17 5 →= 28 6 17 5 2 2 , 29 17 5 6 17 21 →= 28 6 17 5 2 6 , 30 24 5 6 17 5 →= 4 21 17 5 2 2 , 30 24 5 6 17 21 →= 4 21 17 5 2 6 , 31 24 5 6 17 5 →= 11 21 17 5 2 2 , 31 24 5 6 17 21 →= 11 21 17 5 2 6 , 32 24 5 6 17 5 →= 16 21 17 5 2 2 , 32 24 5 6 17 21 →= 16 21 17 5 2 6 , 18 24 5 6 17 5 →= 17 21 17 5 2 2 , 18 24 5 6 17 21 →= 17 21 17 5 2 6 , 25 24 5 6 17 5 →= 24 21 17 5 2 2 , 25 24 5 6 17 21 →= 24 21 17 5 2 6 , 34 24 5 6 17 5 →= 33 21 17 5 2 2 , 34 24 5 6 17 21 →= 33 21 17 5 2 6 , 36 24 5 6 17 5 →= 35 21 17 5 2 2 , 36 24 5 6 17 21 →= 35 21 17 5 2 6 , 38 33 5 6 17 5 →= 37 27 17 5 2 2 , 38 33 5 6 17 21 →= 37 27 17 5 2 6 , 20 17 5 6 18 24 →= 1 6 17 5 6 17 , 20 17 5 6 18 25 →= 1 6 17 5 6 18 , 6 17 5 6 18 24 →= 2 6 17 5 6 17 , 6 17 5 6 18 25 →= 2 6 17 5 6 18 , 21 17 5 6 18 24 →= 5 6 17 5 6 17 , 21 17 5 6 18 25 →= 5 6 17 5 6 18 , 22 17 5 6 18 24 →= 9 6 17 5 6 17 , 22 17 5 6 18 25 →= 9 6 17 5 6 18 , 23 17 5 6 18 24 →= 14 6 17 5 6 17 , 23 17 5 6 18 25 →= 14 6 17 5 6 18 , 27 17 5 6 18 24 →= 26 6 17 5 6 17 , 27 17 5 6 18 25 →= 26 6 17 5 6 18 , 29 17 5 6 18 24 →= 28 6 17 5 6 17 , 29 17 5 6 18 25 →= 28 6 17 5 6 18 , 30 24 5 6 18 24 →= 4 21 17 5 6 17 , 30 24 5 6 18 25 →= 4 21 17 5 6 18 , 31 24 5 6 18 24 →= 11 21 17 5 6 17 , 31 24 5 6 18 25 →= 11 21 17 5 6 18 , 32 24 5 6 18 24 →= 16 21 17 5 6 17 , 32 24 5 6 18 25 →= 16 21 17 5 6 18 , 18 24 5 6 18 24 →= 17 21 17 5 6 17 , 18 24 5 6 18 25 →= 17 21 17 5 6 18 , 25 24 5 6 18 24 →= 24 21 17 5 6 17 , 25 24 5 6 18 25 →= 24 21 17 5 6 18 , 34 24 5 6 18 24 →= 33 21 17 5 6 17 , 34 24 5 6 18 25 →= 33 21 17 5 6 18 , 36 24 5 6 18 24 →= 35 21 17 5 6 17 , 36 24 5 6 18 25 →= 35 21 17 5 6 18 , 38 33 5 6 18 24 →= 37 27 17 5 6 17 , 38 33 5 6 18 25 →= 37 27 17 5 6 18 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 8 ↦ 7, 9 ↦ 8, 10 ↦ 9, 11 ↦ 10, 12 ↦ 11, 7 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 210-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 7 8 2 2 2 11 ⟶ 9 10 5 2 2 11 , 7 8 2 2 2 12 ⟶ 9 10 5 2 2 12 , 13 14 2 2 2 2 ⟶ 15 16 5 2 2 2 , 13 14 2 2 2 6 ⟶ 15 16 5 2 2 6 , 13 14 2 2 2 11 ⟶ 15 16 5 2 2 11 , 13 14 2 2 2 12 ⟶ 15 16 5 2 2 12 , 0 1 2 2 6 17 ⟶ 3 4 5 2 6 17 , 0 1 2 2 6 18 ⟶ 3 4 5 2 6 18 , 0 1 2 2 6 19 ⟶ 3 4 5 2 6 19 , 7 8 2 2 6 17 ⟶ 9 10 5 2 6 17 , 7 8 2 2 6 18 ⟶ 9 10 5 2 6 18 , 7 8 2 2 6 19 ⟶ 9 10 5 2 6 19 , 13 14 2 2 6 17 ⟶ 15 16 5 2 6 17 , 13 14 2 2 6 18 ⟶ 15 16 5 2 6 18 , 13 14 2 2 6 19 ⟶ 15 16 5 2 6 19 , 3 4 5 6 17 5 ⟶ 0 20 17 5 2 2 , 3 4 5 6 17 21 ⟶ 0 20 17 5 2 6 , 9 10 5 6 17 5 ⟶ 7 22 17 5 2 2 , 9 10 5 6 17 21 ⟶ 7 22 17 5 2 6 , 15 16 5 6 17 5 ⟶ 13 23 17 5 2 2 , 15 16 5 6 17 21 ⟶ 13 23 17 5 2 6 , 3 4 5 6 18 24 ⟶ 0 20 17 5 6 17 , 3 4 5 6 18 25 ⟶ 0 20 17 5 6 18 , 9 10 5 6 18 24 ⟶ 7 22 17 5 6 17 , 9 10 5 6 18 25 ⟶ 7 22 17 5 6 18 , 15 16 5 6 18 24 ⟶ 13 23 17 5 6 17 , 15 16 5 6 18 25 ⟶ 13 23 17 5 6 18 , 1 2 2 2 2 2 →= 20 17 5 2 2 2 , 1 2 2 2 2 6 →= 20 17 5 2 2 6 , 1 2 2 2 2 11 →= 20 17 5 2 2 11 , 1 2 2 2 2 12 →= 20 17 5 2 2 12 , 2 2 2 2 2 2 →= 6 17 5 2 2 2 , 2 2 2 2 2 6 →= 6 17 5 2 2 6 , 2 2 2 2 2 11 →= 6 17 5 2 2 11 , 2 2 2 2 2 12 →= 6 17 5 2 2 12 , 5 2 2 2 2 2 →= 21 17 5 2 2 2 , 5 2 2 2 2 6 →= 21 17 5 2 2 6 , 5 2 2 2 2 11 →= 21 17 5 2 2 11 , 5 2 2 2 2 12 →= 21 17 5 2 2 12 , 8 2 2 2 2 2 →= 22 17 5 2 2 2 , 8 2 2 2 2 6 →= 22 17 5 2 2 6 , 8 2 2 2 2 11 →= 22 17 5 2 2 11 , 8 2 2 2 2 12 →= 22 17 5 2 2 12 , 14 2 2 2 2 2 →= 23 17 5 2 2 2 , 14 2 2 2 2 6 →= 23 17 5 2 2 6 , 14 2 2 2 2 11 →= 23 17 5 2 2 11 , 14 2 2 2 2 12 →= 23 17 5 2 2 12 , 26 2 2 2 2 2 →= 27 17 5 2 2 2 , 26 2 2 2 2 6 →= 27 17 5 2 2 6 , 26 2 2 2 2 11 →= 27 17 5 2 2 11 , 26 2 2 2 2 12 →= 27 17 5 2 2 12 , 28 2 2 2 2 2 →= 29 17 5 2 2 2 , 28 2 2 2 2 6 →= 29 17 5 2 2 6 , 28 2 2 2 2 11 →= 29 17 5 2 2 11 , 28 2 2 2 2 12 →= 29 17 5 2 2 12 , 4 5 2 2 2 2 →= 30 24 5 2 2 2 , 4 5 2 2 2 6 →= 30 24 5 2 2 6 , 4 5 2 2 2 11 →= 30 24 5 2 2 11 , 4 5 2 2 2 12 →= 30 24 5 2 2 12 , 10 5 2 2 2 2 →= 31 24 5 2 2 2 , 10 5 2 2 2 6 →= 31 24 5 2 2 6 , 10 5 2 2 2 11 →= 31 24 5 2 2 11 , 10 5 2 2 2 12 →= 31 24 5 2 2 12 , 16 5 2 2 2 2 →= 32 24 5 2 2 2 , 16 5 2 2 2 6 →= 32 24 5 2 2 6 , 16 5 2 2 2 11 →= 32 24 5 2 2 11 , 16 5 2 2 2 12 →= 32 24 5 2 2 12 , 17 5 2 2 2 2 →= 18 24 5 2 2 2 , 17 5 2 2 2 6 →= 18 24 5 2 2 6 , 17 5 2 2 2 11 →= 18 24 5 2 2 11 , 17 5 2 2 2 12 →= 18 24 5 2 2 12 , 24 5 2 2 2 2 →= 25 24 5 2 2 2 , 24 5 2 2 2 6 →= 25 24 5 2 2 6 , 24 5 2 2 2 11 →= 25 24 5 2 2 11 , 24 5 2 2 2 12 →= 25 24 5 2 2 12 , 33 5 2 2 2 2 →= 34 24 5 2 2 2 , 33 5 2 2 2 6 →= 34 24 5 2 2 6 , 33 5 2 2 2 11 →= 34 24 5 2 2 11 , 33 5 2 2 2 12 →= 34 24 5 2 2 12 , 35 5 2 2 2 2 →= 36 24 5 2 2 2 , 35 5 2 2 2 6 →= 36 24 5 2 2 6 , 35 5 2 2 2 11 →= 36 24 5 2 2 11 , 35 5 2 2 2 12 →= 36 24 5 2 2 12 , 37 26 2 2 2 2 →= 38 33 5 2 2 2 , 37 26 2 2 2 6 →= 38 33 5 2 2 6 , 37 26 2 2 2 11 →= 38 33 5 2 2 11 , 37 26 2 2 2 12 →= 38 33 5 2 2 12 , 1 2 2 2 6 17 →= 20 17 5 2 6 17 , 1 2 2 2 6 18 →= 20 17 5 2 6 18 , 1 2 2 2 6 19 →= 20 17 5 2 6 19 , 2 2 2 2 6 17 →= 6 17 5 2 6 17 , 2 2 2 2 6 18 →= 6 17 5 2 6 18 , 2 2 2 2 6 19 →= 6 17 5 2 6 19 , 5 2 2 2 6 17 →= 21 17 5 2 6 17 , 5 2 2 2 6 18 →= 21 17 5 2 6 18 , 5 2 2 2 6 19 →= 21 17 5 2 6 19 , 8 2 2 2 6 17 →= 22 17 5 2 6 17 , 8 2 2 2 6 18 →= 22 17 5 2 6 18 , 8 2 2 2 6 19 →= 22 17 5 2 6 19 , 14 2 2 2 6 17 →= 23 17 5 2 6 17 , 14 2 2 2 6 18 →= 23 17 5 2 6 18 , 14 2 2 2 6 19 →= 23 17 5 2 6 19 , 26 2 2 2 6 17 →= 27 17 5 2 6 17 , 26 2 2 2 6 18 →= 27 17 5 2 6 18 , 26 2 2 2 6 19 →= 27 17 5 2 6 19 , 28 2 2 2 6 17 →= 29 17 5 2 6 17 , 28 2 2 2 6 18 →= 29 17 5 2 6 18 , 28 2 2 2 6 19 →= 29 17 5 2 6 19 , 4 5 2 2 6 17 →= 30 24 5 2 6 17 , 4 5 2 2 6 18 →= 30 24 5 2 6 18 , 4 5 2 2 6 19 →= 30 24 5 2 6 19 , 10 5 2 2 6 17 →= 31 24 5 2 6 17 , 10 5 2 2 6 18 →= 31 24 5 2 6 18 , 10 5 2 2 6 19 →= 31 24 5 2 6 19 , 16 5 2 2 6 17 →= 32 24 5 2 6 17 , 16 5 2 2 6 18 →= 32 24 5 2 6 18 , 16 5 2 2 6 19 →= 32 24 5 2 6 19 , 17 5 2 2 6 17 →= 18 24 5 2 6 17 , 17 5 2 2 6 18 →= 18 24 5 2 6 18 , 17 5 2 2 6 19 →= 18 24 5 2 6 19 , 24 5 2 2 6 17 →= 25 24 5 2 6 17 , 24 5 2 2 6 18 →= 25 24 5 2 6 18 , 24 5 2 2 6 19 →= 25 24 5 2 6 19 , 33 5 2 2 6 17 →= 34 24 5 2 6 17 , 33 5 2 2 6 18 →= 34 24 5 2 6 18 , 33 5 2 2 6 19 →= 34 24 5 2 6 19 , 35 5 2 2 6 17 →= 36 24 5 2 6 17 , 35 5 2 2 6 18 →= 36 24 5 2 6 18 , 35 5 2 2 6 19 →= 36 24 5 2 6 19 , 37 26 2 2 6 17 →= 38 33 5 2 6 17 , 37 26 2 2 6 18 →= 38 33 5 2 6 18 , 37 26 2 2 6 19 →= 38 33 5 2 6 19 , 1 2 2 2 11 39 →= 20 17 5 2 11 39 , 2 2 2 2 11 39 →= 6 17 5 2 11 39 , 5 2 2 2 11 39 →= 21 17 5 2 11 39 , 8 2 2 2 11 39 →= 22 17 5 2 11 39 , 14 2 2 2 11 39 →= 23 17 5 2 11 39 , 26 2 2 2 11 39 →= 27 17 5 2 11 39 , 28 2 2 2 11 39 →= 29 17 5 2 11 39 , 4 5 2 2 11 39 →= 30 24 5 2 11 39 , 10 5 2 2 11 39 →= 31 24 5 2 11 39 , 16 5 2 2 11 39 →= 32 24 5 2 11 39 , 17 5 2 2 11 39 →= 18 24 5 2 11 39 , 24 5 2 2 11 39 →= 25 24 5 2 11 39 , 33 5 2 2 11 39 →= 34 24 5 2 11 39 , 35 5 2 2 11 39 →= 36 24 5 2 11 39 , 20 17 5 6 17 5 →= 1 6 17 5 2 2 , 20 17 5 6 17 21 →= 1 6 17 5 2 6 , 6 17 5 6 17 5 →= 2 6 17 5 2 2 , 6 17 5 6 17 21 →= 2 6 17 5 2 6 , 21 17 5 6 17 5 →= 5 6 17 5 2 2 , 21 17 5 6 17 21 →= 5 6 17 5 2 6 , 22 17 5 6 17 5 →= 8 6 17 5 2 2 , 22 17 5 6 17 21 →= 8 6 17 5 2 6 , 23 17 5 6 17 5 →= 14 6 17 5 2 2 , 23 17 5 6 17 21 →= 14 6 17 5 2 6 , 27 17 5 6 17 5 →= 26 6 17 5 2 2 , 27 17 5 6 17 21 →= 26 6 17 5 2 6 , 29 17 5 6 17 5 →= 28 6 17 5 2 2 , 29 17 5 6 17 21 →= 28 6 17 5 2 6 , 30 24 5 6 17 5 →= 4 21 17 5 2 2 , 30 24 5 6 17 21 →= 4 21 17 5 2 6 , 31 24 5 6 17 5 →= 10 21 17 5 2 2 , 31 24 5 6 17 21 →= 10 21 17 5 2 6 , 32 24 5 6 17 5 →= 16 21 17 5 2 2 , 32 24 5 6 17 21 →= 16 21 17 5 2 6 , 18 24 5 6 17 5 →= 17 21 17 5 2 2 , 18 24 5 6 17 21 →= 17 21 17 5 2 6 , 25 24 5 6 17 5 →= 24 21 17 5 2 2 , 25 24 5 6 17 21 →= 24 21 17 5 2 6 , 34 24 5 6 17 5 →= 33 21 17 5 2 2 , 34 24 5 6 17 21 →= 33 21 17 5 2 6 , 36 24 5 6 17 5 →= 35 21 17 5 2 2 , 36 24 5 6 17 21 →= 35 21 17 5 2 6 , 38 33 5 6 17 5 →= 37 27 17 5 2 2 , 38 33 5 6 17 21 →= 37 27 17 5 2 6 , 20 17 5 6 18 24 →= 1 6 17 5 6 17 , 20 17 5 6 18 25 →= 1 6 17 5 6 18 , 6 17 5 6 18 24 →= 2 6 17 5 6 17 , 6 17 5 6 18 25 →= 2 6 17 5 6 18 , 21 17 5 6 18 24 →= 5 6 17 5 6 17 , 21 17 5 6 18 25 →= 5 6 17 5 6 18 , 22 17 5 6 18 24 →= 8 6 17 5 6 17 , 22 17 5 6 18 25 →= 8 6 17 5 6 18 , 23 17 5 6 18 24 →= 14 6 17 5 6 17 , 23 17 5 6 18 25 →= 14 6 17 5 6 18 , 27 17 5 6 18 24 →= 26 6 17 5 6 17 , 27 17 5 6 18 25 →= 26 6 17 5 6 18 , 29 17 5 6 18 24 →= 28 6 17 5 6 17 , 29 17 5 6 18 25 →= 28 6 17 5 6 18 , 30 24 5 6 18 24 →= 4 21 17 5 6 17 , 30 24 5 6 18 25 →= 4 21 17 5 6 18 , 31 24 5 6 18 24 →= 10 21 17 5 6 17 , 31 24 5 6 18 25 →= 10 21 17 5 6 18 , 32 24 5 6 18 24 →= 16 21 17 5 6 17 , 32 24 5 6 18 25 →= 16 21 17 5 6 18 , 18 24 5 6 18 24 →= 17 21 17 5 6 17 , 18 24 5 6 18 25 →= 17 21 17 5 6 18 , 25 24 5 6 18 24 →= 24 21 17 5 6 17 , 25 24 5 6 18 25 →= 24 21 17 5 6 18 , 34 24 5 6 18 24 →= 33 21 17 5 6 17 , 34 24 5 6 18 25 →= 33 21 17 5 6 18 , 36 24 5 6 18 24 →= 35 21 17 5 6 17 , 36 24 5 6 18 25 →= 35 21 17 5 6 18 , 38 33 5 6 18 24 →= 37 27 17 5 6 17 , 38 33 5 6 18 25 →= 37 27 17 5 6 18 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 12 ↦ 11, 13 ↦ 12, 14 ↦ 13, 15 ↦ 14, 16 ↦ 15, 11 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 209-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 7 8 2 2 2 11 ⟶ 9 10 5 2 2 11 , 12 13 2 2 2 2 ⟶ 14 15 5 2 2 2 , 12 13 2 2 2 6 ⟶ 14 15 5 2 2 6 , 12 13 2 2 2 16 ⟶ 14 15 5 2 2 16 , 12 13 2 2 2 11 ⟶ 14 15 5 2 2 11 , 0 1 2 2 6 17 ⟶ 3 4 5 2 6 17 , 0 1 2 2 6 18 ⟶ 3 4 5 2 6 18 , 0 1 2 2 6 19 ⟶ 3 4 5 2 6 19 , 7 8 2 2 6 17 ⟶ 9 10 5 2 6 17 , 7 8 2 2 6 18 ⟶ 9 10 5 2 6 18 , 7 8 2 2 6 19 ⟶ 9 10 5 2 6 19 , 12 13 2 2 6 17 ⟶ 14 15 5 2 6 17 , 12 13 2 2 6 18 ⟶ 14 15 5 2 6 18 , 12 13 2 2 6 19 ⟶ 14 15 5 2 6 19 , 3 4 5 6 17 5 ⟶ 0 20 17 5 2 2 , 3 4 5 6 17 21 ⟶ 0 20 17 5 2 6 , 9 10 5 6 17 5 ⟶ 7 22 17 5 2 2 , 9 10 5 6 17 21 ⟶ 7 22 17 5 2 6 , 14 15 5 6 17 5 ⟶ 12 23 17 5 2 2 , 14 15 5 6 17 21 ⟶ 12 23 17 5 2 6 , 3 4 5 6 18 24 ⟶ 0 20 17 5 6 17 , 3 4 5 6 18 25 ⟶ 0 20 17 5 6 18 , 9 10 5 6 18 24 ⟶ 7 22 17 5 6 17 , 9 10 5 6 18 25 ⟶ 7 22 17 5 6 18 , 14 15 5 6 18 24 ⟶ 12 23 17 5 6 17 , 14 15 5 6 18 25 ⟶ 12 23 17 5 6 18 , 1 2 2 2 2 2 →= 20 17 5 2 2 2 , 1 2 2 2 2 6 →= 20 17 5 2 2 6 , 1 2 2 2 2 16 →= 20 17 5 2 2 16 , 1 2 2 2 2 11 →= 20 17 5 2 2 11 , 2 2 2 2 2 2 →= 6 17 5 2 2 2 , 2 2 2 2 2 6 →= 6 17 5 2 2 6 , 2 2 2 2 2 16 →= 6 17 5 2 2 16 , 2 2 2 2 2 11 →= 6 17 5 2 2 11 , 5 2 2 2 2 2 →= 21 17 5 2 2 2 , 5 2 2 2 2 6 →= 21 17 5 2 2 6 , 5 2 2 2 2 16 →= 21 17 5 2 2 16 , 5 2 2 2 2 11 →= 21 17 5 2 2 11 , 8 2 2 2 2 2 →= 22 17 5 2 2 2 , 8 2 2 2 2 6 →= 22 17 5 2 2 6 , 8 2 2 2 2 16 →= 22 17 5 2 2 16 , 8 2 2 2 2 11 →= 22 17 5 2 2 11 , 13 2 2 2 2 2 →= 23 17 5 2 2 2 , 13 2 2 2 2 6 →= 23 17 5 2 2 6 , 13 2 2 2 2 16 →= 23 17 5 2 2 16 , 13 2 2 2 2 11 →= 23 17 5 2 2 11 , 26 2 2 2 2 2 →= 27 17 5 2 2 2 , 26 2 2 2 2 6 →= 27 17 5 2 2 6 , 26 2 2 2 2 16 →= 27 17 5 2 2 16 , 26 2 2 2 2 11 →= 27 17 5 2 2 11 , 28 2 2 2 2 2 →= 29 17 5 2 2 2 , 28 2 2 2 2 6 →= 29 17 5 2 2 6 , 28 2 2 2 2 16 →= 29 17 5 2 2 16 , 28 2 2 2 2 11 →= 29 17 5 2 2 11 , 4 5 2 2 2 2 →= 30 24 5 2 2 2 , 4 5 2 2 2 6 →= 30 24 5 2 2 6 , 4 5 2 2 2 16 →= 30 24 5 2 2 16 , 4 5 2 2 2 11 →= 30 24 5 2 2 11 , 10 5 2 2 2 2 →= 31 24 5 2 2 2 , 10 5 2 2 2 6 →= 31 24 5 2 2 6 , 10 5 2 2 2 16 →= 31 24 5 2 2 16 , 10 5 2 2 2 11 →= 31 24 5 2 2 11 , 15 5 2 2 2 2 →= 32 24 5 2 2 2 , 15 5 2 2 2 6 →= 32 24 5 2 2 6 , 15 5 2 2 2 16 →= 32 24 5 2 2 16 , 15 5 2 2 2 11 →= 32 24 5 2 2 11 , 17 5 2 2 2 2 →= 18 24 5 2 2 2 , 17 5 2 2 2 6 →= 18 24 5 2 2 6 , 17 5 2 2 2 16 →= 18 24 5 2 2 16 , 17 5 2 2 2 11 →= 18 24 5 2 2 11 , 24 5 2 2 2 2 →= 25 24 5 2 2 2 , 24 5 2 2 2 6 →= 25 24 5 2 2 6 , 24 5 2 2 2 16 →= 25 24 5 2 2 16 , 24 5 2 2 2 11 →= 25 24 5 2 2 11 , 33 5 2 2 2 2 →= 34 24 5 2 2 2 , 33 5 2 2 2 6 →= 34 24 5 2 2 6 , 33 5 2 2 2 16 →= 34 24 5 2 2 16 , 33 5 2 2 2 11 →= 34 24 5 2 2 11 , 35 5 2 2 2 2 →= 36 24 5 2 2 2 , 35 5 2 2 2 6 →= 36 24 5 2 2 6 , 35 5 2 2 2 16 →= 36 24 5 2 2 16 , 35 5 2 2 2 11 →= 36 24 5 2 2 11 , 37 26 2 2 2 2 →= 38 33 5 2 2 2 , 37 26 2 2 2 6 →= 38 33 5 2 2 6 , 37 26 2 2 2 16 →= 38 33 5 2 2 16 , 37 26 2 2 2 11 →= 38 33 5 2 2 11 , 1 2 2 2 6 17 →= 20 17 5 2 6 17 , 1 2 2 2 6 18 →= 20 17 5 2 6 18 , 1 2 2 2 6 19 →= 20 17 5 2 6 19 , 2 2 2 2 6 17 →= 6 17 5 2 6 17 , 2 2 2 2 6 18 →= 6 17 5 2 6 18 , 2 2 2 2 6 19 →= 6 17 5 2 6 19 , 5 2 2 2 6 17 →= 21 17 5 2 6 17 , 5 2 2 2 6 18 →= 21 17 5 2 6 18 , 5 2 2 2 6 19 →= 21 17 5 2 6 19 , 8 2 2 2 6 17 →= 22 17 5 2 6 17 , 8 2 2 2 6 18 →= 22 17 5 2 6 18 , 8 2 2 2 6 19 →= 22 17 5 2 6 19 , 13 2 2 2 6 17 →= 23 17 5 2 6 17 , 13 2 2 2 6 18 →= 23 17 5 2 6 18 , 13 2 2 2 6 19 →= 23 17 5 2 6 19 , 26 2 2 2 6 17 →= 27 17 5 2 6 17 , 26 2 2 2 6 18 →= 27 17 5 2 6 18 , 26 2 2 2 6 19 →= 27 17 5 2 6 19 , 28 2 2 2 6 17 →= 29 17 5 2 6 17 , 28 2 2 2 6 18 →= 29 17 5 2 6 18 , 28 2 2 2 6 19 →= 29 17 5 2 6 19 , 4 5 2 2 6 17 →= 30 24 5 2 6 17 , 4 5 2 2 6 18 →= 30 24 5 2 6 18 , 4 5 2 2 6 19 →= 30 24 5 2 6 19 , 10 5 2 2 6 17 →= 31 24 5 2 6 17 , 10 5 2 2 6 18 →= 31 24 5 2 6 18 , 10 5 2 2 6 19 →= 31 24 5 2 6 19 , 15 5 2 2 6 17 →= 32 24 5 2 6 17 , 15 5 2 2 6 18 →= 32 24 5 2 6 18 , 15 5 2 2 6 19 →= 32 24 5 2 6 19 , 17 5 2 2 6 17 →= 18 24 5 2 6 17 , 17 5 2 2 6 18 →= 18 24 5 2 6 18 , 17 5 2 2 6 19 →= 18 24 5 2 6 19 , 24 5 2 2 6 17 →= 25 24 5 2 6 17 , 24 5 2 2 6 18 →= 25 24 5 2 6 18 , 24 5 2 2 6 19 →= 25 24 5 2 6 19 , 33 5 2 2 6 17 →= 34 24 5 2 6 17 , 33 5 2 2 6 18 →= 34 24 5 2 6 18 , 33 5 2 2 6 19 →= 34 24 5 2 6 19 , 35 5 2 2 6 17 →= 36 24 5 2 6 17 , 35 5 2 2 6 18 →= 36 24 5 2 6 18 , 35 5 2 2 6 19 →= 36 24 5 2 6 19 , 37 26 2 2 6 17 →= 38 33 5 2 6 17 , 37 26 2 2 6 18 →= 38 33 5 2 6 18 , 37 26 2 2 6 19 →= 38 33 5 2 6 19 , 1 2 2 2 16 39 →= 20 17 5 2 16 39 , 2 2 2 2 16 39 →= 6 17 5 2 16 39 , 5 2 2 2 16 39 →= 21 17 5 2 16 39 , 8 2 2 2 16 39 →= 22 17 5 2 16 39 , 13 2 2 2 16 39 →= 23 17 5 2 16 39 , 26 2 2 2 16 39 →= 27 17 5 2 16 39 , 28 2 2 2 16 39 →= 29 17 5 2 16 39 , 4 5 2 2 16 39 →= 30 24 5 2 16 39 , 10 5 2 2 16 39 →= 31 24 5 2 16 39 , 15 5 2 2 16 39 →= 32 24 5 2 16 39 , 17 5 2 2 16 39 →= 18 24 5 2 16 39 , 24 5 2 2 16 39 →= 25 24 5 2 16 39 , 33 5 2 2 16 39 →= 34 24 5 2 16 39 , 35 5 2 2 16 39 →= 36 24 5 2 16 39 , 20 17 5 6 17 5 →= 1 6 17 5 2 2 , 20 17 5 6 17 21 →= 1 6 17 5 2 6 , 6 17 5 6 17 5 →= 2 6 17 5 2 2 , 6 17 5 6 17 21 →= 2 6 17 5 2 6 , 21 17 5 6 17 5 →= 5 6 17 5 2 2 , 21 17 5 6 17 21 →= 5 6 17 5 2 6 , 22 17 5 6 17 5 →= 8 6 17 5 2 2 , 22 17 5 6 17 21 →= 8 6 17 5 2 6 , 23 17 5 6 17 5 →= 13 6 17 5 2 2 , 23 17 5 6 17 21 →= 13 6 17 5 2 6 , 27 17 5 6 17 5 →= 26 6 17 5 2 2 , 27 17 5 6 17 21 →= 26 6 17 5 2 6 , 29 17 5 6 17 5 →= 28 6 17 5 2 2 , 29 17 5 6 17 21 →= 28 6 17 5 2 6 , 30 24 5 6 17 5 →= 4 21 17 5 2 2 , 30 24 5 6 17 21 →= 4 21 17 5 2 6 , 31 24 5 6 17 5 →= 10 21 17 5 2 2 , 31 24 5 6 17 21 →= 10 21 17 5 2 6 , 32 24 5 6 17 5 →= 15 21 17 5 2 2 , 32 24 5 6 17 21 →= 15 21 17 5 2 6 , 18 24 5 6 17 5 →= 17 21 17 5 2 2 , 18 24 5 6 17 21 →= 17 21 17 5 2 6 , 25 24 5 6 17 5 →= 24 21 17 5 2 2 , 25 24 5 6 17 21 →= 24 21 17 5 2 6 , 34 24 5 6 17 5 →= 33 21 17 5 2 2 , 34 24 5 6 17 21 →= 33 21 17 5 2 6 , 36 24 5 6 17 5 →= 35 21 17 5 2 2 , 36 24 5 6 17 21 →= 35 21 17 5 2 6 , 38 33 5 6 17 5 →= 37 27 17 5 2 2 , 38 33 5 6 17 21 →= 37 27 17 5 2 6 , 20 17 5 6 18 24 →= 1 6 17 5 6 17 , 20 17 5 6 18 25 →= 1 6 17 5 6 18 , 6 17 5 6 18 24 →= 2 6 17 5 6 17 , 6 17 5 6 18 25 →= 2 6 17 5 6 18 , 21 17 5 6 18 24 →= 5 6 17 5 6 17 , 21 17 5 6 18 25 →= 5 6 17 5 6 18 , 22 17 5 6 18 24 →= 8 6 17 5 6 17 , 22 17 5 6 18 25 →= 8 6 17 5 6 18 , 23 17 5 6 18 24 →= 13 6 17 5 6 17 , 23 17 5 6 18 25 →= 13 6 17 5 6 18 , 27 17 5 6 18 24 →= 26 6 17 5 6 17 , 27 17 5 6 18 25 →= 26 6 17 5 6 18 , 29 17 5 6 18 24 →= 28 6 17 5 6 17 , 29 17 5 6 18 25 →= 28 6 17 5 6 18 , 30 24 5 6 18 24 →= 4 21 17 5 6 17 , 30 24 5 6 18 25 →= 4 21 17 5 6 18 , 31 24 5 6 18 24 →= 10 21 17 5 6 17 , 31 24 5 6 18 25 →= 10 21 17 5 6 18 , 32 24 5 6 18 24 →= 15 21 17 5 6 17 , 32 24 5 6 18 25 →= 15 21 17 5 6 18 , 18 24 5 6 18 24 →= 17 21 17 5 6 17 , 18 24 5 6 18 25 →= 17 21 17 5 6 18 , 25 24 5 6 18 24 →= 24 21 17 5 6 17 , 25 24 5 6 18 25 →= 24 21 17 5 6 18 , 34 24 5 6 18 24 →= 33 21 17 5 6 17 , 34 24 5 6 18 25 →= 33 21 17 5 6 18 , 36 24 5 6 18 24 →= 35 21 17 5 6 17 , 36 24 5 6 18 25 →= 35 21 17 5 6 18 , 38 33 5 6 18 24 →= 37 27 17 5 6 17 , 38 33 5 6 18 25 →= 37 27 17 5 6 18 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 12 ↦ 11, 13 ↦ 12, 14 ↦ 13, 15 ↦ 14, 16 ↦ 15, 11 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 208-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 11 12 2 2 2 15 ⟶ 13 14 5 2 2 15 , 11 12 2 2 2 16 ⟶ 13 14 5 2 2 16 , 0 1 2 2 6 17 ⟶ 3 4 5 2 6 17 , 0 1 2 2 6 18 ⟶ 3 4 5 2 6 18 , 0 1 2 2 6 19 ⟶ 3 4 5 2 6 19 , 7 8 2 2 6 17 ⟶ 9 10 5 2 6 17 , 7 8 2 2 6 18 ⟶ 9 10 5 2 6 18 , 7 8 2 2 6 19 ⟶ 9 10 5 2 6 19 , 11 12 2 2 6 17 ⟶ 13 14 5 2 6 17 , 11 12 2 2 6 18 ⟶ 13 14 5 2 6 18 , 11 12 2 2 6 19 ⟶ 13 14 5 2 6 19 , 3 4 5 6 17 5 ⟶ 0 20 17 5 2 2 , 3 4 5 6 17 21 ⟶ 0 20 17 5 2 6 , 9 10 5 6 17 5 ⟶ 7 22 17 5 2 2 , 9 10 5 6 17 21 ⟶ 7 22 17 5 2 6 , 13 14 5 6 17 5 ⟶ 11 23 17 5 2 2 , 13 14 5 6 17 21 ⟶ 11 23 17 5 2 6 , 3 4 5 6 18 24 ⟶ 0 20 17 5 6 17 , 3 4 5 6 18 25 ⟶ 0 20 17 5 6 18 , 9 10 5 6 18 24 ⟶ 7 22 17 5 6 17 , 9 10 5 6 18 25 ⟶ 7 22 17 5 6 18 , 13 14 5 6 18 24 ⟶ 11 23 17 5 6 17 , 13 14 5 6 18 25 ⟶ 11 23 17 5 6 18 , 1 2 2 2 2 2 →= 20 17 5 2 2 2 , 1 2 2 2 2 6 →= 20 17 5 2 2 6 , 1 2 2 2 2 15 →= 20 17 5 2 2 15 , 1 2 2 2 2 16 →= 20 17 5 2 2 16 , 2 2 2 2 2 2 →= 6 17 5 2 2 2 , 2 2 2 2 2 6 →= 6 17 5 2 2 6 , 2 2 2 2 2 15 →= 6 17 5 2 2 15 , 2 2 2 2 2 16 →= 6 17 5 2 2 16 , 5 2 2 2 2 2 →= 21 17 5 2 2 2 , 5 2 2 2 2 6 →= 21 17 5 2 2 6 , 5 2 2 2 2 15 →= 21 17 5 2 2 15 , 5 2 2 2 2 16 →= 21 17 5 2 2 16 , 8 2 2 2 2 2 →= 22 17 5 2 2 2 , 8 2 2 2 2 6 →= 22 17 5 2 2 6 , 8 2 2 2 2 15 →= 22 17 5 2 2 15 , 8 2 2 2 2 16 →= 22 17 5 2 2 16 , 12 2 2 2 2 2 →= 23 17 5 2 2 2 , 12 2 2 2 2 6 →= 23 17 5 2 2 6 , 12 2 2 2 2 15 →= 23 17 5 2 2 15 , 12 2 2 2 2 16 →= 23 17 5 2 2 16 , 26 2 2 2 2 2 →= 27 17 5 2 2 2 , 26 2 2 2 2 6 →= 27 17 5 2 2 6 , 26 2 2 2 2 15 →= 27 17 5 2 2 15 , 26 2 2 2 2 16 →= 27 17 5 2 2 16 , 28 2 2 2 2 2 →= 29 17 5 2 2 2 , 28 2 2 2 2 6 →= 29 17 5 2 2 6 , 28 2 2 2 2 15 →= 29 17 5 2 2 15 , 28 2 2 2 2 16 →= 29 17 5 2 2 16 , 4 5 2 2 2 2 →= 30 24 5 2 2 2 , 4 5 2 2 2 6 →= 30 24 5 2 2 6 , 4 5 2 2 2 15 →= 30 24 5 2 2 15 , 4 5 2 2 2 16 →= 30 24 5 2 2 16 , 10 5 2 2 2 2 →= 31 24 5 2 2 2 , 10 5 2 2 2 6 →= 31 24 5 2 2 6 , 10 5 2 2 2 15 →= 31 24 5 2 2 15 , 10 5 2 2 2 16 →= 31 24 5 2 2 16 , 14 5 2 2 2 2 →= 32 24 5 2 2 2 , 14 5 2 2 2 6 →= 32 24 5 2 2 6 , 14 5 2 2 2 15 →= 32 24 5 2 2 15 , 14 5 2 2 2 16 →= 32 24 5 2 2 16 , 17 5 2 2 2 2 →= 18 24 5 2 2 2 , 17 5 2 2 2 6 →= 18 24 5 2 2 6 , 17 5 2 2 2 15 →= 18 24 5 2 2 15 , 17 5 2 2 2 16 →= 18 24 5 2 2 16 , 24 5 2 2 2 2 →= 25 24 5 2 2 2 , 24 5 2 2 2 6 →= 25 24 5 2 2 6 , 24 5 2 2 2 15 →= 25 24 5 2 2 15 , 24 5 2 2 2 16 →= 25 24 5 2 2 16 , 33 5 2 2 2 2 →= 34 24 5 2 2 2 , 33 5 2 2 2 6 →= 34 24 5 2 2 6 , 33 5 2 2 2 15 →= 34 24 5 2 2 15 , 33 5 2 2 2 16 →= 34 24 5 2 2 16 , 35 5 2 2 2 2 →= 36 24 5 2 2 2 , 35 5 2 2 2 6 →= 36 24 5 2 2 6 , 35 5 2 2 2 15 →= 36 24 5 2 2 15 , 35 5 2 2 2 16 →= 36 24 5 2 2 16 , 37 26 2 2 2 2 →= 38 33 5 2 2 2 , 37 26 2 2 2 6 →= 38 33 5 2 2 6 , 37 26 2 2 2 15 →= 38 33 5 2 2 15 , 37 26 2 2 2 16 →= 38 33 5 2 2 16 , 1 2 2 2 6 17 →= 20 17 5 2 6 17 , 1 2 2 2 6 18 →= 20 17 5 2 6 18 , 1 2 2 2 6 19 →= 20 17 5 2 6 19 , 2 2 2 2 6 17 →= 6 17 5 2 6 17 , 2 2 2 2 6 18 →= 6 17 5 2 6 18 , 2 2 2 2 6 19 →= 6 17 5 2 6 19 , 5 2 2 2 6 17 →= 21 17 5 2 6 17 , 5 2 2 2 6 18 →= 21 17 5 2 6 18 , 5 2 2 2 6 19 →= 21 17 5 2 6 19 , 8 2 2 2 6 17 →= 22 17 5 2 6 17 , 8 2 2 2 6 18 →= 22 17 5 2 6 18 , 8 2 2 2 6 19 →= 22 17 5 2 6 19 , 12 2 2 2 6 17 →= 23 17 5 2 6 17 , 12 2 2 2 6 18 →= 23 17 5 2 6 18 , 12 2 2 2 6 19 →= 23 17 5 2 6 19 , 26 2 2 2 6 17 →= 27 17 5 2 6 17 , 26 2 2 2 6 18 →= 27 17 5 2 6 18 , 26 2 2 2 6 19 →= 27 17 5 2 6 19 , 28 2 2 2 6 17 →= 29 17 5 2 6 17 , 28 2 2 2 6 18 →= 29 17 5 2 6 18 , 28 2 2 2 6 19 →= 29 17 5 2 6 19 , 4 5 2 2 6 17 →= 30 24 5 2 6 17 , 4 5 2 2 6 18 →= 30 24 5 2 6 18 , 4 5 2 2 6 19 →= 30 24 5 2 6 19 , 10 5 2 2 6 17 →= 31 24 5 2 6 17 , 10 5 2 2 6 18 →= 31 24 5 2 6 18 , 10 5 2 2 6 19 →= 31 24 5 2 6 19 , 14 5 2 2 6 17 →= 32 24 5 2 6 17 , 14 5 2 2 6 18 →= 32 24 5 2 6 18 , 14 5 2 2 6 19 →= 32 24 5 2 6 19 , 17 5 2 2 6 17 →= 18 24 5 2 6 17 , 17 5 2 2 6 18 →= 18 24 5 2 6 18 , 17 5 2 2 6 19 →= 18 24 5 2 6 19 , 24 5 2 2 6 17 →= 25 24 5 2 6 17 , 24 5 2 2 6 18 →= 25 24 5 2 6 18 , 24 5 2 2 6 19 →= 25 24 5 2 6 19 , 33 5 2 2 6 17 →= 34 24 5 2 6 17 , 33 5 2 2 6 18 →= 34 24 5 2 6 18 , 33 5 2 2 6 19 →= 34 24 5 2 6 19 , 35 5 2 2 6 17 →= 36 24 5 2 6 17 , 35 5 2 2 6 18 →= 36 24 5 2 6 18 , 35 5 2 2 6 19 →= 36 24 5 2 6 19 , 37 26 2 2 6 17 →= 38 33 5 2 6 17 , 37 26 2 2 6 18 →= 38 33 5 2 6 18 , 37 26 2 2 6 19 →= 38 33 5 2 6 19 , 1 2 2 2 15 39 →= 20 17 5 2 15 39 , 2 2 2 2 15 39 →= 6 17 5 2 15 39 , 5 2 2 2 15 39 →= 21 17 5 2 15 39 , 8 2 2 2 15 39 →= 22 17 5 2 15 39 , 12 2 2 2 15 39 →= 23 17 5 2 15 39 , 26 2 2 2 15 39 →= 27 17 5 2 15 39 , 28 2 2 2 15 39 →= 29 17 5 2 15 39 , 4 5 2 2 15 39 →= 30 24 5 2 15 39 , 10 5 2 2 15 39 →= 31 24 5 2 15 39 , 14 5 2 2 15 39 →= 32 24 5 2 15 39 , 17 5 2 2 15 39 →= 18 24 5 2 15 39 , 24 5 2 2 15 39 →= 25 24 5 2 15 39 , 33 5 2 2 15 39 →= 34 24 5 2 15 39 , 35 5 2 2 15 39 →= 36 24 5 2 15 39 , 20 17 5 6 17 5 →= 1 6 17 5 2 2 , 20 17 5 6 17 21 →= 1 6 17 5 2 6 , 6 17 5 6 17 5 →= 2 6 17 5 2 2 , 6 17 5 6 17 21 →= 2 6 17 5 2 6 , 21 17 5 6 17 5 →= 5 6 17 5 2 2 , 21 17 5 6 17 21 →= 5 6 17 5 2 6 , 22 17 5 6 17 5 →= 8 6 17 5 2 2 , 22 17 5 6 17 21 →= 8 6 17 5 2 6 , 23 17 5 6 17 5 →= 12 6 17 5 2 2 , 23 17 5 6 17 21 →= 12 6 17 5 2 6 , 27 17 5 6 17 5 →= 26 6 17 5 2 2 , 27 17 5 6 17 21 →= 26 6 17 5 2 6 , 29 17 5 6 17 5 →= 28 6 17 5 2 2 , 29 17 5 6 17 21 →= 28 6 17 5 2 6 , 30 24 5 6 17 5 →= 4 21 17 5 2 2 , 30 24 5 6 17 21 →= 4 21 17 5 2 6 , 31 24 5 6 17 5 →= 10 21 17 5 2 2 , 31 24 5 6 17 21 →= 10 21 17 5 2 6 , 32 24 5 6 17 5 →= 14 21 17 5 2 2 , 32 24 5 6 17 21 →= 14 21 17 5 2 6 , 18 24 5 6 17 5 →= 17 21 17 5 2 2 , 18 24 5 6 17 21 →= 17 21 17 5 2 6 , 25 24 5 6 17 5 →= 24 21 17 5 2 2 , 25 24 5 6 17 21 →= 24 21 17 5 2 6 , 34 24 5 6 17 5 →= 33 21 17 5 2 2 , 34 24 5 6 17 21 →= 33 21 17 5 2 6 , 36 24 5 6 17 5 →= 35 21 17 5 2 2 , 36 24 5 6 17 21 →= 35 21 17 5 2 6 , 38 33 5 6 17 5 →= 37 27 17 5 2 2 , 38 33 5 6 17 21 →= 37 27 17 5 2 6 , 20 17 5 6 18 24 →= 1 6 17 5 6 17 , 20 17 5 6 18 25 →= 1 6 17 5 6 18 , 6 17 5 6 18 24 →= 2 6 17 5 6 17 , 6 17 5 6 18 25 →= 2 6 17 5 6 18 , 21 17 5 6 18 24 →= 5 6 17 5 6 17 , 21 17 5 6 18 25 →= 5 6 17 5 6 18 , 22 17 5 6 18 24 →= 8 6 17 5 6 17 , 22 17 5 6 18 25 →= 8 6 17 5 6 18 , 23 17 5 6 18 24 →= 12 6 17 5 6 17 , 23 17 5 6 18 25 →= 12 6 17 5 6 18 , 27 17 5 6 18 24 →= 26 6 17 5 6 17 , 27 17 5 6 18 25 →= 26 6 17 5 6 18 , 29 17 5 6 18 24 →= 28 6 17 5 6 17 , 29 17 5 6 18 25 →= 28 6 17 5 6 18 , 30 24 5 6 18 24 →= 4 21 17 5 6 17 , 30 24 5 6 18 25 →= 4 21 17 5 6 18 , 31 24 5 6 18 24 →= 10 21 17 5 6 17 , 31 24 5 6 18 25 →= 10 21 17 5 6 18 , 32 24 5 6 18 24 →= 14 21 17 5 6 17 , 32 24 5 6 18 25 →= 14 21 17 5 6 18 , 18 24 5 6 18 24 →= 17 21 17 5 6 17 , 18 24 5 6 18 25 →= 17 21 17 5 6 18 , 25 24 5 6 18 24 →= 24 21 17 5 6 17 , 25 24 5 6 18 25 →= 24 21 17 5 6 18 , 34 24 5 6 18 24 →= 33 21 17 5 6 17 , 34 24 5 6 18 25 →= 33 21 17 5 6 18 , 36 24 5 6 18 24 →= 35 21 17 5 6 17 , 36 24 5 6 18 25 →= 35 21 17 5 6 18 , 38 33 5 6 18 24 →= 37 27 17 5 6 17 , 38 33 5 6 18 25 →= 37 27 17 5 6 18 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 16 ↦ 15, 17 ↦ 16, 18 ↦ 17, 19 ↦ 18, 20 ↦ 19, 21 ↦ 20, 22 ↦ 21, 23 ↦ 22, 24 ↦ 23, 25 ↦ 24, 15 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 207-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 11 12 2 2 2 15 ⟶ 13 14 5 2 2 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 0 1 2 2 6 17 ⟶ 3 4 5 2 6 17 , 0 1 2 2 6 18 ⟶ 3 4 5 2 6 18 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 7 8 2 2 6 17 ⟶ 9 10 5 2 6 17 , 7 8 2 2 6 18 ⟶ 9 10 5 2 6 18 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 11 12 2 2 6 17 ⟶ 13 14 5 2 6 17 , 11 12 2 2 6 18 ⟶ 13 14 5 2 6 18 , 3 4 5 6 16 5 ⟶ 0 19 16 5 2 2 , 3 4 5 6 16 20 ⟶ 0 19 16 5 2 6 , 9 10 5 6 16 5 ⟶ 7 21 16 5 2 2 , 9 10 5 6 16 20 ⟶ 7 21 16 5 2 6 , 13 14 5 6 16 5 ⟶ 11 22 16 5 2 2 , 13 14 5 6 16 20 ⟶ 11 22 16 5 2 6 , 3 4 5 6 17 23 ⟶ 0 19 16 5 6 16 , 3 4 5 6 17 24 ⟶ 0 19 16 5 6 17 , 9 10 5 6 17 23 ⟶ 7 21 16 5 6 16 , 9 10 5 6 17 24 ⟶ 7 21 16 5 6 17 , 13 14 5 6 17 23 ⟶ 11 22 16 5 6 16 , 13 14 5 6 17 24 ⟶ 11 22 16 5 6 17 , 1 2 2 2 2 2 →= 19 16 5 2 2 2 , 1 2 2 2 2 6 →= 19 16 5 2 2 6 , 1 2 2 2 2 25 →= 19 16 5 2 2 25 , 1 2 2 2 2 15 →= 19 16 5 2 2 15 , 2 2 2 2 2 2 →= 6 16 5 2 2 2 , 2 2 2 2 2 6 →= 6 16 5 2 2 6 , 2 2 2 2 2 25 →= 6 16 5 2 2 25 , 2 2 2 2 2 15 →= 6 16 5 2 2 15 , 5 2 2 2 2 2 →= 20 16 5 2 2 2 , 5 2 2 2 2 6 →= 20 16 5 2 2 6 , 5 2 2 2 2 25 →= 20 16 5 2 2 25 , 5 2 2 2 2 15 →= 20 16 5 2 2 15 , 8 2 2 2 2 2 →= 21 16 5 2 2 2 , 8 2 2 2 2 6 →= 21 16 5 2 2 6 , 8 2 2 2 2 25 →= 21 16 5 2 2 25 , 8 2 2 2 2 15 →= 21 16 5 2 2 15 , 12 2 2 2 2 2 →= 22 16 5 2 2 2 , 12 2 2 2 2 6 →= 22 16 5 2 2 6 , 12 2 2 2 2 25 →= 22 16 5 2 2 25 , 12 2 2 2 2 15 →= 22 16 5 2 2 15 , 26 2 2 2 2 2 →= 27 16 5 2 2 2 , 26 2 2 2 2 6 →= 27 16 5 2 2 6 , 26 2 2 2 2 25 →= 27 16 5 2 2 25 , 26 2 2 2 2 15 →= 27 16 5 2 2 15 , 28 2 2 2 2 2 →= 29 16 5 2 2 2 , 28 2 2 2 2 6 →= 29 16 5 2 2 6 , 28 2 2 2 2 25 →= 29 16 5 2 2 25 , 28 2 2 2 2 15 →= 29 16 5 2 2 15 , 4 5 2 2 2 2 →= 30 23 5 2 2 2 , 4 5 2 2 2 6 →= 30 23 5 2 2 6 , 4 5 2 2 2 25 →= 30 23 5 2 2 25 , 4 5 2 2 2 15 →= 30 23 5 2 2 15 , 10 5 2 2 2 2 →= 31 23 5 2 2 2 , 10 5 2 2 2 6 →= 31 23 5 2 2 6 , 10 5 2 2 2 25 →= 31 23 5 2 2 25 , 10 5 2 2 2 15 →= 31 23 5 2 2 15 , 14 5 2 2 2 2 →= 32 23 5 2 2 2 , 14 5 2 2 2 6 →= 32 23 5 2 2 6 , 14 5 2 2 2 25 →= 32 23 5 2 2 25 , 14 5 2 2 2 15 →= 32 23 5 2 2 15 , 16 5 2 2 2 2 →= 17 23 5 2 2 2 , 16 5 2 2 2 6 →= 17 23 5 2 2 6 , 16 5 2 2 2 25 →= 17 23 5 2 2 25 , 16 5 2 2 2 15 →= 17 23 5 2 2 15 , 23 5 2 2 2 2 →= 24 23 5 2 2 2 , 23 5 2 2 2 6 →= 24 23 5 2 2 6 , 23 5 2 2 2 25 →= 24 23 5 2 2 25 , 23 5 2 2 2 15 →= 24 23 5 2 2 15 , 33 5 2 2 2 2 →= 34 23 5 2 2 2 , 33 5 2 2 2 6 →= 34 23 5 2 2 6 , 33 5 2 2 2 25 →= 34 23 5 2 2 25 , 33 5 2 2 2 15 →= 34 23 5 2 2 15 , 35 5 2 2 2 2 →= 36 23 5 2 2 2 , 35 5 2 2 2 6 →= 36 23 5 2 2 6 , 35 5 2 2 2 25 →= 36 23 5 2 2 25 , 35 5 2 2 2 15 →= 36 23 5 2 2 15 , 37 26 2 2 2 2 →= 38 33 5 2 2 2 , 37 26 2 2 2 6 →= 38 33 5 2 2 6 , 37 26 2 2 2 25 →= 38 33 5 2 2 25 , 37 26 2 2 2 15 →= 38 33 5 2 2 15 , 1 2 2 2 6 16 →= 19 16 5 2 6 16 , 1 2 2 2 6 17 →= 19 16 5 2 6 17 , 1 2 2 2 6 18 →= 19 16 5 2 6 18 , 2 2 2 2 6 16 →= 6 16 5 2 6 16 , 2 2 2 2 6 17 →= 6 16 5 2 6 17 , 2 2 2 2 6 18 →= 6 16 5 2 6 18 , 5 2 2 2 6 16 →= 20 16 5 2 6 16 , 5 2 2 2 6 17 →= 20 16 5 2 6 17 , 5 2 2 2 6 18 →= 20 16 5 2 6 18 , 8 2 2 2 6 16 →= 21 16 5 2 6 16 , 8 2 2 2 6 17 →= 21 16 5 2 6 17 , 8 2 2 2 6 18 →= 21 16 5 2 6 18 , 12 2 2 2 6 16 →= 22 16 5 2 6 16 , 12 2 2 2 6 17 →= 22 16 5 2 6 17 , 12 2 2 2 6 18 →= 22 16 5 2 6 18 , 26 2 2 2 6 16 →= 27 16 5 2 6 16 , 26 2 2 2 6 17 →= 27 16 5 2 6 17 , 26 2 2 2 6 18 →= 27 16 5 2 6 18 , 28 2 2 2 6 16 →= 29 16 5 2 6 16 , 28 2 2 2 6 17 →= 29 16 5 2 6 17 , 28 2 2 2 6 18 →= 29 16 5 2 6 18 , 4 5 2 2 6 16 →= 30 23 5 2 6 16 , 4 5 2 2 6 17 →= 30 23 5 2 6 17 , 4 5 2 2 6 18 →= 30 23 5 2 6 18 , 10 5 2 2 6 16 →= 31 23 5 2 6 16 , 10 5 2 2 6 17 →= 31 23 5 2 6 17 , 10 5 2 2 6 18 →= 31 23 5 2 6 18 , 14 5 2 2 6 16 →= 32 23 5 2 6 16 , 14 5 2 2 6 17 →= 32 23 5 2 6 17 , 14 5 2 2 6 18 →= 32 23 5 2 6 18 , 16 5 2 2 6 16 →= 17 23 5 2 6 16 , 16 5 2 2 6 17 →= 17 23 5 2 6 17 , 16 5 2 2 6 18 →= 17 23 5 2 6 18 , 23 5 2 2 6 16 →= 24 23 5 2 6 16 , 23 5 2 2 6 17 →= 24 23 5 2 6 17 , 23 5 2 2 6 18 →= 24 23 5 2 6 18 , 33 5 2 2 6 16 →= 34 23 5 2 6 16 , 33 5 2 2 6 17 →= 34 23 5 2 6 17 , 33 5 2 2 6 18 →= 34 23 5 2 6 18 , 35 5 2 2 6 16 →= 36 23 5 2 6 16 , 35 5 2 2 6 17 →= 36 23 5 2 6 17 , 35 5 2 2 6 18 →= 36 23 5 2 6 18 , 37 26 2 2 6 16 →= 38 33 5 2 6 16 , 37 26 2 2 6 17 →= 38 33 5 2 6 17 , 37 26 2 2 6 18 →= 38 33 5 2 6 18 , 1 2 2 2 25 39 →= 19 16 5 2 25 39 , 2 2 2 2 25 39 →= 6 16 5 2 25 39 , 5 2 2 2 25 39 →= 20 16 5 2 25 39 , 8 2 2 2 25 39 →= 21 16 5 2 25 39 , 12 2 2 2 25 39 →= 22 16 5 2 25 39 , 26 2 2 2 25 39 →= 27 16 5 2 25 39 , 28 2 2 2 25 39 →= 29 16 5 2 25 39 , 4 5 2 2 25 39 →= 30 23 5 2 25 39 , 10 5 2 2 25 39 →= 31 23 5 2 25 39 , 14 5 2 2 25 39 →= 32 23 5 2 25 39 , 16 5 2 2 25 39 →= 17 23 5 2 25 39 , 23 5 2 2 25 39 →= 24 23 5 2 25 39 , 33 5 2 2 25 39 →= 34 23 5 2 25 39 , 35 5 2 2 25 39 →= 36 23 5 2 25 39 , 19 16 5 6 16 5 →= 1 6 16 5 2 2 , 19 16 5 6 16 20 →= 1 6 16 5 2 6 , 6 16 5 6 16 5 →= 2 6 16 5 2 2 , 6 16 5 6 16 20 →= 2 6 16 5 2 6 , 20 16 5 6 16 5 →= 5 6 16 5 2 2 , 20 16 5 6 16 20 →= 5 6 16 5 2 6 , 21 16 5 6 16 5 →= 8 6 16 5 2 2 , 21 16 5 6 16 20 →= 8 6 16 5 2 6 , 22 16 5 6 16 5 →= 12 6 16 5 2 2 , 22 16 5 6 16 20 →= 12 6 16 5 2 6 , 27 16 5 6 16 5 →= 26 6 16 5 2 2 , 27 16 5 6 16 20 →= 26 6 16 5 2 6 , 29 16 5 6 16 5 →= 28 6 16 5 2 2 , 29 16 5 6 16 20 →= 28 6 16 5 2 6 , 30 23 5 6 16 5 →= 4 20 16 5 2 2 , 30 23 5 6 16 20 →= 4 20 16 5 2 6 , 31 23 5 6 16 5 →= 10 20 16 5 2 2 , 31 23 5 6 16 20 →= 10 20 16 5 2 6 , 32 23 5 6 16 5 →= 14 20 16 5 2 2 , 32 23 5 6 16 20 →= 14 20 16 5 2 6 , 17 23 5 6 16 5 →= 16 20 16 5 2 2 , 17 23 5 6 16 20 →= 16 20 16 5 2 6 , 24 23 5 6 16 5 →= 23 20 16 5 2 2 , 24 23 5 6 16 20 →= 23 20 16 5 2 6 , 34 23 5 6 16 5 →= 33 20 16 5 2 2 , 34 23 5 6 16 20 →= 33 20 16 5 2 6 , 36 23 5 6 16 5 →= 35 20 16 5 2 2 , 36 23 5 6 16 20 →= 35 20 16 5 2 6 , 38 33 5 6 16 5 →= 37 27 16 5 2 2 , 38 33 5 6 16 20 →= 37 27 16 5 2 6 , 19 16 5 6 17 23 →= 1 6 16 5 6 16 , 19 16 5 6 17 24 →= 1 6 16 5 6 17 , 6 16 5 6 17 23 →= 2 6 16 5 6 16 , 6 16 5 6 17 24 →= 2 6 16 5 6 17 , 20 16 5 6 17 23 →= 5 6 16 5 6 16 , 20 16 5 6 17 24 →= 5 6 16 5 6 17 , 21 16 5 6 17 23 →= 8 6 16 5 6 16 , 21 16 5 6 17 24 →= 8 6 16 5 6 17 , 22 16 5 6 17 23 →= 12 6 16 5 6 16 , 22 16 5 6 17 24 →= 12 6 16 5 6 17 , 27 16 5 6 17 23 →= 26 6 16 5 6 16 , 27 16 5 6 17 24 →= 26 6 16 5 6 17 , 29 16 5 6 17 23 →= 28 6 16 5 6 16 , 29 16 5 6 17 24 →= 28 6 16 5 6 17 , 30 23 5 6 17 23 →= 4 20 16 5 6 16 , 30 23 5 6 17 24 →= 4 20 16 5 6 17 , 31 23 5 6 17 23 →= 10 20 16 5 6 16 , 31 23 5 6 17 24 →= 10 20 16 5 6 17 , 32 23 5 6 17 23 →= 14 20 16 5 6 16 , 32 23 5 6 17 24 →= 14 20 16 5 6 17 , 17 23 5 6 17 23 →= 16 20 16 5 6 16 , 17 23 5 6 17 24 →= 16 20 16 5 6 17 , 24 23 5 6 17 23 →= 23 20 16 5 6 16 , 24 23 5 6 17 24 →= 23 20 16 5 6 17 , 34 23 5 6 17 23 →= 33 20 16 5 6 16 , 34 23 5 6 17 24 →= 33 20 16 5 6 17 , 36 23 5 6 17 23 →= 35 20 16 5 6 16 , 36 23 5 6 17 24 →= 35 20 16 5 6 17 , 38 33 5 6 17 23 →= 37 27 16 5 6 16 , 38 33 5 6 17 24 →= 37 27 16 5 6 17 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 16 ↦ 15, 17 ↦ 16, 18 ↦ 17, 19 ↦ 18, 20 ↦ 19, 21 ↦ 20, 22 ↦ 21, 23 ↦ 22, 24 ↦ 23, 25 ↦ 24, 15 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 206-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 0 1 2 2 6 17 ⟶ 3 4 5 2 6 17 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 7 8 2 2 6 17 ⟶ 9 10 5 2 6 17 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 11 12 2 2 6 17 ⟶ 13 14 5 2 6 17 , 3 4 5 6 15 5 ⟶ 0 18 15 5 2 2 , 3 4 5 6 15 19 ⟶ 0 18 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 20 15 5 2 2 , 9 10 5 6 15 19 ⟶ 7 20 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 21 15 5 2 2 , 13 14 5 6 15 19 ⟶ 11 21 15 5 2 6 , 3 4 5 6 16 22 ⟶ 0 18 15 5 6 15 , 3 4 5 6 16 23 ⟶ 0 18 15 5 6 16 , 9 10 5 6 16 22 ⟶ 7 20 15 5 6 15 , 9 10 5 6 16 23 ⟶ 7 20 15 5 6 16 , 13 14 5 6 16 22 ⟶ 11 21 15 5 6 15 , 13 14 5 6 16 23 ⟶ 11 21 15 5 6 16 , 1 2 2 2 2 2 →= 18 15 5 2 2 2 , 1 2 2 2 2 6 →= 18 15 5 2 2 6 , 1 2 2 2 2 24 →= 18 15 5 2 2 24 , 1 2 2 2 2 25 →= 18 15 5 2 2 25 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 2 2 2 2 2 25 →= 6 15 5 2 2 25 , 5 2 2 2 2 2 →= 19 15 5 2 2 2 , 5 2 2 2 2 6 →= 19 15 5 2 2 6 , 5 2 2 2 2 24 →= 19 15 5 2 2 24 , 5 2 2 2 2 25 →= 19 15 5 2 2 25 , 8 2 2 2 2 2 →= 20 15 5 2 2 2 , 8 2 2 2 2 6 →= 20 15 5 2 2 6 , 8 2 2 2 2 24 →= 20 15 5 2 2 24 , 8 2 2 2 2 25 →= 20 15 5 2 2 25 , 12 2 2 2 2 2 →= 21 15 5 2 2 2 , 12 2 2 2 2 6 →= 21 15 5 2 2 6 , 12 2 2 2 2 24 →= 21 15 5 2 2 24 , 12 2 2 2 2 25 →= 21 15 5 2 2 25 , 26 2 2 2 2 2 →= 27 15 5 2 2 2 , 26 2 2 2 2 6 →= 27 15 5 2 2 6 , 26 2 2 2 2 24 →= 27 15 5 2 2 24 , 26 2 2 2 2 25 →= 27 15 5 2 2 25 , 28 2 2 2 2 2 →= 29 15 5 2 2 2 , 28 2 2 2 2 6 →= 29 15 5 2 2 6 , 28 2 2 2 2 24 →= 29 15 5 2 2 24 , 28 2 2 2 2 25 →= 29 15 5 2 2 25 , 4 5 2 2 2 2 →= 30 22 5 2 2 2 , 4 5 2 2 2 6 →= 30 22 5 2 2 6 , 4 5 2 2 2 24 →= 30 22 5 2 2 24 , 4 5 2 2 2 25 →= 30 22 5 2 2 25 , 10 5 2 2 2 2 →= 31 22 5 2 2 2 , 10 5 2 2 2 6 →= 31 22 5 2 2 6 , 10 5 2 2 2 24 →= 31 22 5 2 2 24 , 10 5 2 2 2 25 →= 31 22 5 2 2 25 , 14 5 2 2 2 2 →= 32 22 5 2 2 2 , 14 5 2 2 2 6 →= 32 22 5 2 2 6 , 14 5 2 2 2 24 →= 32 22 5 2 2 24 , 14 5 2 2 2 25 →= 32 22 5 2 2 25 , 15 5 2 2 2 2 →= 16 22 5 2 2 2 , 15 5 2 2 2 6 →= 16 22 5 2 2 6 , 15 5 2 2 2 24 →= 16 22 5 2 2 24 , 15 5 2 2 2 25 →= 16 22 5 2 2 25 , 22 5 2 2 2 2 →= 23 22 5 2 2 2 , 22 5 2 2 2 6 →= 23 22 5 2 2 6 , 22 5 2 2 2 24 →= 23 22 5 2 2 24 , 22 5 2 2 2 25 →= 23 22 5 2 2 25 , 33 5 2 2 2 2 →= 34 22 5 2 2 2 , 33 5 2 2 2 6 →= 34 22 5 2 2 6 , 33 5 2 2 2 24 →= 34 22 5 2 2 24 , 33 5 2 2 2 25 →= 34 22 5 2 2 25 , 35 5 2 2 2 2 →= 36 22 5 2 2 2 , 35 5 2 2 2 6 →= 36 22 5 2 2 6 , 35 5 2 2 2 24 →= 36 22 5 2 2 24 , 35 5 2 2 2 25 →= 36 22 5 2 2 25 , 37 26 2 2 2 2 →= 38 33 5 2 2 2 , 37 26 2 2 2 6 →= 38 33 5 2 2 6 , 37 26 2 2 2 24 →= 38 33 5 2 2 24 , 37 26 2 2 2 25 →= 38 33 5 2 2 25 , 1 2 2 2 6 15 →= 18 15 5 2 6 15 , 1 2 2 2 6 16 →= 18 15 5 2 6 16 , 1 2 2 2 6 17 →= 18 15 5 2 6 17 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 17 →= 6 15 5 2 6 17 , 5 2 2 2 6 15 →= 19 15 5 2 6 15 , 5 2 2 2 6 16 →= 19 15 5 2 6 16 , 5 2 2 2 6 17 →= 19 15 5 2 6 17 , 8 2 2 2 6 15 →= 20 15 5 2 6 15 , 8 2 2 2 6 16 →= 20 15 5 2 6 16 , 8 2 2 2 6 17 →= 20 15 5 2 6 17 , 12 2 2 2 6 15 →= 21 15 5 2 6 15 , 12 2 2 2 6 16 →= 21 15 5 2 6 16 , 12 2 2 2 6 17 →= 21 15 5 2 6 17 , 26 2 2 2 6 15 →= 27 15 5 2 6 15 , 26 2 2 2 6 16 →= 27 15 5 2 6 16 , 26 2 2 2 6 17 →= 27 15 5 2 6 17 , 28 2 2 2 6 15 →= 29 15 5 2 6 15 , 28 2 2 2 6 16 →= 29 15 5 2 6 16 , 28 2 2 2 6 17 →= 29 15 5 2 6 17 , 4 5 2 2 6 15 →= 30 22 5 2 6 15 , 4 5 2 2 6 16 →= 30 22 5 2 6 16 , 4 5 2 2 6 17 →= 30 22 5 2 6 17 , 10 5 2 2 6 15 →= 31 22 5 2 6 15 , 10 5 2 2 6 16 →= 31 22 5 2 6 16 , 10 5 2 2 6 17 →= 31 22 5 2 6 17 , 14 5 2 2 6 15 →= 32 22 5 2 6 15 , 14 5 2 2 6 16 →= 32 22 5 2 6 16 , 14 5 2 2 6 17 →= 32 22 5 2 6 17 , 15 5 2 2 6 15 →= 16 22 5 2 6 15 , 15 5 2 2 6 16 →= 16 22 5 2 6 16 , 15 5 2 2 6 17 →= 16 22 5 2 6 17 , 22 5 2 2 6 15 →= 23 22 5 2 6 15 , 22 5 2 2 6 16 →= 23 22 5 2 6 16 , 22 5 2 2 6 17 →= 23 22 5 2 6 17 , 33 5 2 2 6 15 →= 34 22 5 2 6 15 , 33 5 2 2 6 16 →= 34 22 5 2 6 16 , 33 5 2 2 6 17 →= 34 22 5 2 6 17 , 35 5 2 2 6 15 →= 36 22 5 2 6 15 , 35 5 2 2 6 16 →= 36 22 5 2 6 16 , 35 5 2 2 6 17 →= 36 22 5 2 6 17 , 37 26 2 2 6 15 →= 38 33 5 2 6 15 , 37 26 2 2 6 16 →= 38 33 5 2 6 16 , 37 26 2 2 6 17 →= 38 33 5 2 6 17 , 1 2 2 2 24 39 →= 18 15 5 2 24 39 , 2 2 2 2 24 39 →= 6 15 5 2 24 39 , 5 2 2 2 24 39 →= 19 15 5 2 24 39 , 8 2 2 2 24 39 →= 20 15 5 2 24 39 , 12 2 2 2 24 39 →= 21 15 5 2 24 39 , 26 2 2 2 24 39 →= 27 15 5 2 24 39 , 28 2 2 2 24 39 →= 29 15 5 2 24 39 , 4 5 2 2 24 39 →= 30 22 5 2 24 39 , 10 5 2 2 24 39 →= 31 22 5 2 24 39 , 14 5 2 2 24 39 →= 32 22 5 2 24 39 , 15 5 2 2 24 39 →= 16 22 5 2 24 39 , 22 5 2 2 24 39 →= 23 22 5 2 24 39 , 33 5 2 2 24 39 →= 34 22 5 2 24 39 , 35 5 2 2 24 39 →= 36 22 5 2 24 39 , 18 15 5 6 15 5 →= 1 6 15 5 2 2 , 18 15 5 6 15 19 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 19 →= 2 6 15 5 2 6 , 19 15 5 6 15 5 →= 5 6 15 5 2 2 , 19 15 5 6 15 19 →= 5 6 15 5 2 6 , 20 15 5 6 15 5 →= 8 6 15 5 2 2 , 20 15 5 6 15 19 →= 8 6 15 5 2 6 , 21 15 5 6 15 5 →= 12 6 15 5 2 2 , 21 15 5 6 15 19 →= 12 6 15 5 2 6 , 27 15 5 6 15 5 →= 26 6 15 5 2 2 , 27 15 5 6 15 19 →= 26 6 15 5 2 6 , 29 15 5 6 15 5 →= 28 6 15 5 2 2 , 29 15 5 6 15 19 →= 28 6 15 5 2 6 , 30 22 5 6 15 5 →= 4 19 15 5 2 2 , 30 22 5 6 15 19 →= 4 19 15 5 2 6 , 31 22 5 6 15 5 →= 10 19 15 5 2 2 , 31 22 5 6 15 19 →= 10 19 15 5 2 6 , 32 22 5 6 15 5 →= 14 19 15 5 2 2 , 32 22 5 6 15 19 →= 14 19 15 5 2 6 , 16 22 5 6 15 5 →= 15 19 15 5 2 2 , 16 22 5 6 15 19 →= 15 19 15 5 2 6 , 23 22 5 6 15 5 →= 22 19 15 5 2 2 , 23 22 5 6 15 19 →= 22 19 15 5 2 6 , 34 22 5 6 15 5 →= 33 19 15 5 2 2 , 34 22 5 6 15 19 →= 33 19 15 5 2 6 , 36 22 5 6 15 5 →= 35 19 15 5 2 2 , 36 22 5 6 15 19 →= 35 19 15 5 2 6 , 38 33 5 6 15 5 →= 37 27 15 5 2 2 , 38 33 5 6 15 19 →= 37 27 15 5 2 6 , 18 15 5 6 16 22 →= 1 6 15 5 6 15 , 18 15 5 6 16 23 →= 1 6 15 5 6 16 , 6 15 5 6 16 22 →= 2 6 15 5 6 15 , 6 15 5 6 16 23 →= 2 6 15 5 6 16 , 19 15 5 6 16 22 →= 5 6 15 5 6 15 , 19 15 5 6 16 23 →= 5 6 15 5 6 16 , 20 15 5 6 16 22 →= 8 6 15 5 6 15 , 20 15 5 6 16 23 →= 8 6 15 5 6 16 , 21 15 5 6 16 22 →= 12 6 15 5 6 15 , 21 15 5 6 16 23 →= 12 6 15 5 6 16 , 27 15 5 6 16 22 →= 26 6 15 5 6 15 , 27 15 5 6 16 23 →= 26 6 15 5 6 16 , 29 15 5 6 16 22 →= 28 6 15 5 6 15 , 29 15 5 6 16 23 →= 28 6 15 5 6 16 , 30 22 5 6 16 22 →= 4 19 15 5 6 15 , 30 22 5 6 16 23 →= 4 19 15 5 6 16 , 31 22 5 6 16 22 →= 10 19 15 5 6 15 , 31 22 5 6 16 23 →= 10 19 15 5 6 16 , 32 22 5 6 16 22 →= 14 19 15 5 6 15 , 32 22 5 6 16 23 →= 14 19 15 5 6 16 , 16 22 5 6 16 22 →= 15 19 15 5 6 15 , 16 22 5 6 16 23 →= 15 19 15 5 6 16 , 23 22 5 6 16 22 →= 22 19 15 5 6 15 , 23 22 5 6 16 23 →= 22 19 15 5 6 16 , 34 22 5 6 16 22 →= 33 19 15 5 6 15 , 34 22 5 6 16 23 →= 33 19 15 5 6 16 , 36 22 5 6 16 22 →= 35 19 15 5 6 15 , 36 22 5 6 16 23 →= 35 19 15 5 6 16 , 38 33 5 6 16 22 →= 37 27 15 5 6 15 , 38 33 5 6 16 23 →= 37 27 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 205-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 7 8 2 2 6 17 ⟶ 9 10 5 2 6 17 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 11 12 2 2 6 17 ⟶ 13 14 5 2 6 17 , 3 4 5 6 15 5 ⟶ 0 18 15 5 2 2 , 3 4 5 6 15 19 ⟶ 0 18 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 20 15 5 2 2 , 9 10 5 6 15 19 ⟶ 7 20 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 21 15 5 2 2 , 13 14 5 6 15 19 ⟶ 11 21 15 5 2 6 , 3 4 5 6 16 22 ⟶ 0 18 15 5 6 15 , 3 4 5 6 16 23 ⟶ 0 18 15 5 6 16 , 9 10 5 6 16 22 ⟶ 7 20 15 5 6 15 , 9 10 5 6 16 23 ⟶ 7 20 15 5 6 16 , 13 14 5 6 16 22 ⟶ 11 21 15 5 6 15 , 13 14 5 6 16 23 ⟶ 11 21 15 5 6 16 , 1 2 2 2 2 2 →= 18 15 5 2 2 2 , 1 2 2 2 2 6 →= 18 15 5 2 2 6 , 1 2 2 2 2 24 →= 18 15 5 2 2 24 , 1 2 2 2 2 25 →= 18 15 5 2 2 25 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 2 2 2 2 2 25 →= 6 15 5 2 2 25 , 5 2 2 2 2 2 →= 19 15 5 2 2 2 , 5 2 2 2 2 6 →= 19 15 5 2 2 6 , 5 2 2 2 2 24 →= 19 15 5 2 2 24 , 5 2 2 2 2 25 →= 19 15 5 2 2 25 , 8 2 2 2 2 2 →= 20 15 5 2 2 2 , 8 2 2 2 2 6 →= 20 15 5 2 2 6 , 8 2 2 2 2 24 →= 20 15 5 2 2 24 , 8 2 2 2 2 25 →= 20 15 5 2 2 25 , 12 2 2 2 2 2 →= 21 15 5 2 2 2 , 12 2 2 2 2 6 →= 21 15 5 2 2 6 , 12 2 2 2 2 24 →= 21 15 5 2 2 24 , 12 2 2 2 2 25 →= 21 15 5 2 2 25 , 26 2 2 2 2 2 →= 27 15 5 2 2 2 , 26 2 2 2 2 6 →= 27 15 5 2 2 6 , 26 2 2 2 2 24 →= 27 15 5 2 2 24 , 26 2 2 2 2 25 →= 27 15 5 2 2 25 , 28 2 2 2 2 2 →= 29 15 5 2 2 2 , 28 2 2 2 2 6 →= 29 15 5 2 2 6 , 28 2 2 2 2 24 →= 29 15 5 2 2 24 , 28 2 2 2 2 25 →= 29 15 5 2 2 25 , 4 5 2 2 2 2 →= 30 22 5 2 2 2 , 4 5 2 2 2 6 →= 30 22 5 2 2 6 , 4 5 2 2 2 24 →= 30 22 5 2 2 24 , 4 5 2 2 2 25 →= 30 22 5 2 2 25 , 10 5 2 2 2 2 →= 31 22 5 2 2 2 , 10 5 2 2 2 6 →= 31 22 5 2 2 6 , 10 5 2 2 2 24 →= 31 22 5 2 2 24 , 10 5 2 2 2 25 →= 31 22 5 2 2 25 , 14 5 2 2 2 2 →= 32 22 5 2 2 2 , 14 5 2 2 2 6 →= 32 22 5 2 2 6 , 14 5 2 2 2 24 →= 32 22 5 2 2 24 , 14 5 2 2 2 25 →= 32 22 5 2 2 25 , 15 5 2 2 2 2 →= 16 22 5 2 2 2 , 15 5 2 2 2 6 →= 16 22 5 2 2 6 , 15 5 2 2 2 24 →= 16 22 5 2 2 24 , 15 5 2 2 2 25 →= 16 22 5 2 2 25 , 22 5 2 2 2 2 →= 23 22 5 2 2 2 , 22 5 2 2 2 6 →= 23 22 5 2 2 6 , 22 5 2 2 2 24 →= 23 22 5 2 2 24 , 22 5 2 2 2 25 →= 23 22 5 2 2 25 , 33 5 2 2 2 2 →= 34 22 5 2 2 2 , 33 5 2 2 2 6 →= 34 22 5 2 2 6 , 33 5 2 2 2 24 →= 34 22 5 2 2 24 , 33 5 2 2 2 25 →= 34 22 5 2 2 25 , 35 5 2 2 2 2 →= 36 22 5 2 2 2 , 35 5 2 2 2 6 →= 36 22 5 2 2 6 , 35 5 2 2 2 24 →= 36 22 5 2 2 24 , 35 5 2 2 2 25 →= 36 22 5 2 2 25 , 37 26 2 2 2 2 →= 38 33 5 2 2 2 , 37 26 2 2 2 6 →= 38 33 5 2 2 6 , 37 26 2 2 2 24 →= 38 33 5 2 2 24 , 37 26 2 2 2 25 →= 38 33 5 2 2 25 , 1 2 2 2 6 15 →= 18 15 5 2 6 15 , 1 2 2 2 6 16 →= 18 15 5 2 6 16 , 1 2 2 2 6 17 →= 18 15 5 2 6 17 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 17 →= 6 15 5 2 6 17 , 5 2 2 2 6 15 →= 19 15 5 2 6 15 , 5 2 2 2 6 16 →= 19 15 5 2 6 16 , 5 2 2 2 6 17 →= 19 15 5 2 6 17 , 8 2 2 2 6 15 →= 20 15 5 2 6 15 , 8 2 2 2 6 16 →= 20 15 5 2 6 16 , 8 2 2 2 6 17 →= 20 15 5 2 6 17 , 12 2 2 2 6 15 →= 21 15 5 2 6 15 , 12 2 2 2 6 16 →= 21 15 5 2 6 16 , 12 2 2 2 6 17 →= 21 15 5 2 6 17 , 26 2 2 2 6 15 →= 27 15 5 2 6 15 , 26 2 2 2 6 16 →= 27 15 5 2 6 16 , 26 2 2 2 6 17 →= 27 15 5 2 6 17 , 28 2 2 2 6 15 →= 29 15 5 2 6 15 , 28 2 2 2 6 16 →= 29 15 5 2 6 16 , 28 2 2 2 6 17 →= 29 15 5 2 6 17 , 4 5 2 2 6 15 →= 30 22 5 2 6 15 , 4 5 2 2 6 16 →= 30 22 5 2 6 16 , 4 5 2 2 6 17 →= 30 22 5 2 6 17 , 10 5 2 2 6 15 →= 31 22 5 2 6 15 , 10 5 2 2 6 16 →= 31 22 5 2 6 16 , 10 5 2 2 6 17 →= 31 22 5 2 6 17 , 14 5 2 2 6 15 →= 32 22 5 2 6 15 , 14 5 2 2 6 16 →= 32 22 5 2 6 16 , 14 5 2 2 6 17 →= 32 22 5 2 6 17 , 15 5 2 2 6 15 →= 16 22 5 2 6 15 , 15 5 2 2 6 16 →= 16 22 5 2 6 16 , 15 5 2 2 6 17 →= 16 22 5 2 6 17 , 22 5 2 2 6 15 →= 23 22 5 2 6 15 , 22 5 2 2 6 16 →= 23 22 5 2 6 16 , 22 5 2 2 6 17 →= 23 22 5 2 6 17 , 33 5 2 2 6 15 →= 34 22 5 2 6 15 , 33 5 2 2 6 16 →= 34 22 5 2 6 16 , 33 5 2 2 6 17 →= 34 22 5 2 6 17 , 35 5 2 2 6 15 →= 36 22 5 2 6 15 , 35 5 2 2 6 16 →= 36 22 5 2 6 16 , 35 5 2 2 6 17 →= 36 22 5 2 6 17 , 37 26 2 2 6 15 →= 38 33 5 2 6 15 , 37 26 2 2 6 16 →= 38 33 5 2 6 16 , 37 26 2 2 6 17 →= 38 33 5 2 6 17 , 1 2 2 2 24 39 →= 18 15 5 2 24 39 , 2 2 2 2 24 39 →= 6 15 5 2 24 39 , 5 2 2 2 24 39 →= 19 15 5 2 24 39 , 8 2 2 2 24 39 →= 20 15 5 2 24 39 , 12 2 2 2 24 39 →= 21 15 5 2 24 39 , 26 2 2 2 24 39 →= 27 15 5 2 24 39 , 28 2 2 2 24 39 →= 29 15 5 2 24 39 , 4 5 2 2 24 39 →= 30 22 5 2 24 39 , 10 5 2 2 24 39 →= 31 22 5 2 24 39 , 14 5 2 2 24 39 →= 32 22 5 2 24 39 , 15 5 2 2 24 39 →= 16 22 5 2 24 39 , 22 5 2 2 24 39 →= 23 22 5 2 24 39 , 33 5 2 2 24 39 →= 34 22 5 2 24 39 , 35 5 2 2 24 39 →= 36 22 5 2 24 39 , 18 15 5 6 15 5 →= 1 6 15 5 2 2 , 18 15 5 6 15 19 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 19 →= 2 6 15 5 2 6 , 19 15 5 6 15 5 →= 5 6 15 5 2 2 , 19 15 5 6 15 19 →= 5 6 15 5 2 6 , 20 15 5 6 15 5 →= 8 6 15 5 2 2 , 20 15 5 6 15 19 →= 8 6 15 5 2 6 , 21 15 5 6 15 5 →= 12 6 15 5 2 2 , 21 15 5 6 15 19 →= 12 6 15 5 2 6 , 27 15 5 6 15 5 →= 26 6 15 5 2 2 , 27 15 5 6 15 19 →= 26 6 15 5 2 6 , 29 15 5 6 15 5 →= 28 6 15 5 2 2 , 29 15 5 6 15 19 →= 28 6 15 5 2 6 , 30 22 5 6 15 5 →= 4 19 15 5 2 2 , 30 22 5 6 15 19 →= 4 19 15 5 2 6 , 31 22 5 6 15 5 →= 10 19 15 5 2 2 , 31 22 5 6 15 19 →= 10 19 15 5 2 6 , 32 22 5 6 15 5 →= 14 19 15 5 2 2 , 32 22 5 6 15 19 →= 14 19 15 5 2 6 , 16 22 5 6 15 5 →= 15 19 15 5 2 2 , 16 22 5 6 15 19 →= 15 19 15 5 2 6 , 23 22 5 6 15 5 →= 22 19 15 5 2 2 , 23 22 5 6 15 19 →= 22 19 15 5 2 6 , 34 22 5 6 15 5 →= 33 19 15 5 2 2 , 34 22 5 6 15 19 →= 33 19 15 5 2 6 , 36 22 5 6 15 5 →= 35 19 15 5 2 2 , 36 22 5 6 15 19 →= 35 19 15 5 2 6 , 38 33 5 6 15 5 →= 37 27 15 5 2 2 , 38 33 5 6 15 19 →= 37 27 15 5 2 6 , 18 15 5 6 16 22 →= 1 6 15 5 6 15 , 18 15 5 6 16 23 →= 1 6 15 5 6 16 , 6 15 5 6 16 22 →= 2 6 15 5 6 15 , 6 15 5 6 16 23 →= 2 6 15 5 6 16 , 19 15 5 6 16 22 →= 5 6 15 5 6 15 , 19 15 5 6 16 23 →= 5 6 15 5 6 16 , 20 15 5 6 16 22 →= 8 6 15 5 6 15 , 20 15 5 6 16 23 →= 8 6 15 5 6 16 , 21 15 5 6 16 22 →= 12 6 15 5 6 15 , 21 15 5 6 16 23 →= 12 6 15 5 6 16 , 27 15 5 6 16 22 →= 26 6 15 5 6 15 , 27 15 5 6 16 23 →= 26 6 15 5 6 16 , 29 15 5 6 16 22 →= 28 6 15 5 6 15 , 29 15 5 6 16 23 →= 28 6 15 5 6 16 , 30 22 5 6 16 22 →= 4 19 15 5 6 15 , 30 22 5 6 16 23 →= 4 19 15 5 6 16 , 31 22 5 6 16 22 →= 10 19 15 5 6 15 , 31 22 5 6 16 23 →= 10 19 15 5 6 16 , 32 22 5 6 16 22 →= 14 19 15 5 6 15 , 32 22 5 6 16 23 →= 14 19 15 5 6 16 , 16 22 5 6 16 22 →= 15 19 15 5 6 15 , 16 22 5 6 16 23 →= 15 19 15 5 6 16 , 23 22 5 6 16 22 →= 22 19 15 5 6 15 , 23 22 5 6 16 23 →= 22 19 15 5 6 16 , 34 22 5 6 16 22 →= 33 19 15 5 6 15 , 34 22 5 6 16 23 →= 33 19 15 5 6 16 , 36 22 5 6 16 22 →= 35 19 15 5 6 15 , 36 22 5 6 16 23 →= 35 19 15 5 6 16 , 38 33 5 6 16 22 →= 37 27 15 5 6 15 , 38 33 5 6 16 23 →= 37 27 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 204-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 11 12 2 2 6 17 ⟶ 13 14 5 2 6 17 , 3 4 5 6 15 5 ⟶ 0 18 15 5 2 2 , 3 4 5 6 15 19 ⟶ 0 18 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 20 15 5 2 2 , 9 10 5 6 15 19 ⟶ 7 20 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 21 15 5 2 2 , 13 14 5 6 15 19 ⟶ 11 21 15 5 2 6 , 3 4 5 6 16 22 ⟶ 0 18 15 5 6 15 , 3 4 5 6 16 23 ⟶ 0 18 15 5 6 16 , 9 10 5 6 16 22 ⟶ 7 20 15 5 6 15 , 9 10 5 6 16 23 ⟶ 7 20 15 5 6 16 , 13 14 5 6 16 22 ⟶ 11 21 15 5 6 15 , 13 14 5 6 16 23 ⟶ 11 21 15 5 6 16 , 1 2 2 2 2 2 →= 18 15 5 2 2 2 , 1 2 2 2 2 6 →= 18 15 5 2 2 6 , 1 2 2 2 2 24 →= 18 15 5 2 2 24 , 1 2 2 2 2 25 →= 18 15 5 2 2 25 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 2 2 2 2 2 25 →= 6 15 5 2 2 25 , 5 2 2 2 2 2 →= 19 15 5 2 2 2 , 5 2 2 2 2 6 →= 19 15 5 2 2 6 , 5 2 2 2 2 24 →= 19 15 5 2 2 24 , 5 2 2 2 2 25 →= 19 15 5 2 2 25 , 8 2 2 2 2 2 →= 20 15 5 2 2 2 , 8 2 2 2 2 6 →= 20 15 5 2 2 6 , 8 2 2 2 2 24 →= 20 15 5 2 2 24 , 8 2 2 2 2 25 →= 20 15 5 2 2 25 , 12 2 2 2 2 2 →= 21 15 5 2 2 2 , 12 2 2 2 2 6 →= 21 15 5 2 2 6 , 12 2 2 2 2 24 →= 21 15 5 2 2 24 , 12 2 2 2 2 25 →= 21 15 5 2 2 25 , 26 2 2 2 2 2 →= 27 15 5 2 2 2 , 26 2 2 2 2 6 →= 27 15 5 2 2 6 , 26 2 2 2 2 24 →= 27 15 5 2 2 24 , 26 2 2 2 2 25 →= 27 15 5 2 2 25 , 28 2 2 2 2 2 →= 29 15 5 2 2 2 , 28 2 2 2 2 6 →= 29 15 5 2 2 6 , 28 2 2 2 2 24 →= 29 15 5 2 2 24 , 28 2 2 2 2 25 →= 29 15 5 2 2 25 , 4 5 2 2 2 2 →= 30 22 5 2 2 2 , 4 5 2 2 2 6 →= 30 22 5 2 2 6 , 4 5 2 2 2 24 →= 30 22 5 2 2 24 , 4 5 2 2 2 25 →= 30 22 5 2 2 25 , 10 5 2 2 2 2 →= 31 22 5 2 2 2 , 10 5 2 2 2 6 →= 31 22 5 2 2 6 , 10 5 2 2 2 24 →= 31 22 5 2 2 24 , 10 5 2 2 2 25 →= 31 22 5 2 2 25 , 14 5 2 2 2 2 →= 32 22 5 2 2 2 , 14 5 2 2 2 6 →= 32 22 5 2 2 6 , 14 5 2 2 2 24 →= 32 22 5 2 2 24 , 14 5 2 2 2 25 →= 32 22 5 2 2 25 , 15 5 2 2 2 2 →= 16 22 5 2 2 2 , 15 5 2 2 2 6 →= 16 22 5 2 2 6 , 15 5 2 2 2 24 →= 16 22 5 2 2 24 , 15 5 2 2 2 25 →= 16 22 5 2 2 25 , 22 5 2 2 2 2 →= 23 22 5 2 2 2 , 22 5 2 2 2 6 →= 23 22 5 2 2 6 , 22 5 2 2 2 24 →= 23 22 5 2 2 24 , 22 5 2 2 2 25 →= 23 22 5 2 2 25 , 33 5 2 2 2 2 →= 34 22 5 2 2 2 , 33 5 2 2 2 6 →= 34 22 5 2 2 6 , 33 5 2 2 2 24 →= 34 22 5 2 2 24 , 33 5 2 2 2 25 →= 34 22 5 2 2 25 , 35 5 2 2 2 2 →= 36 22 5 2 2 2 , 35 5 2 2 2 6 →= 36 22 5 2 2 6 , 35 5 2 2 2 24 →= 36 22 5 2 2 24 , 35 5 2 2 2 25 →= 36 22 5 2 2 25 , 37 26 2 2 2 2 →= 38 33 5 2 2 2 , 37 26 2 2 2 6 →= 38 33 5 2 2 6 , 37 26 2 2 2 24 →= 38 33 5 2 2 24 , 37 26 2 2 2 25 →= 38 33 5 2 2 25 , 1 2 2 2 6 15 →= 18 15 5 2 6 15 , 1 2 2 2 6 16 →= 18 15 5 2 6 16 , 1 2 2 2 6 17 →= 18 15 5 2 6 17 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 17 →= 6 15 5 2 6 17 , 5 2 2 2 6 15 →= 19 15 5 2 6 15 , 5 2 2 2 6 16 →= 19 15 5 2 6 16 , 5 2 2 2 6 17 →= 19 15 5 2 6 17 , 8 2 2 2 6 15 →= 20 15 5 2 6 15 , 8 2 2 2 6 16 →= 20 15 5 2 6 16 , 8 2 2 2 6 17 →= 20 15 5 2 6 17 , 12 2 2 2 6 15 →= 21 15 5 2 6 15 , 12 2 2 2 6 16 →= 21 15 5 2 6 16 , 12 2 2 2 6 17 →= 21 15 5 2 6 17 , 26 2 2 2 6 15 →= 27 15 5 2 6 15 , 26 2 2 2 6 16 →= 27 15 5 2 6 16 , 26 2 2 2 6 17 →= 27 15 5 2 6 17 , 28 2 2 2 6 15 →= 29 15 5 2 6 15 , 28 2 2 2 6 16 →= 29 15 5 2 6 16 , 28 2 2 2 6 17 →= 29 15 5 2 6 17 , 4 5 2 2 6 15 →= 30 22 5 2 6 15 , 4 5 2 2 6 16 →= 30 22 5 2 6 16 , 4 5 2 2 6 17 →= 30 22 5 2 6 17 , 10 5 2 2 6 15 →= 31 22 5 2 6 15 , 10 5 2 2 6 16 →= 31 22 5 2 6 16 , 10 5 2 2 6 17 →= 31 22 5 2 6 17 , 14 5 2 2 6 15 →= 32 22 5 2 6 15 , 14 5 2 2 6 16 →= 32 22 5 2 6 16 , 14 5 2 2 6 17 →= 32 22 5 2 6 17 , 15 5 2 2 6 15 →= 16 22 5 2 6 15 , 15 5 2 2 6 16 →= 16 22 5 2 6 16 , 15 5 2 2 6 17 →= 16 22 5 2 6 17 , 22 5 2 2 6 15 →= 23 22 5 2 6 15 , 22 5 2 2 6 16 →= 23 22 5 2 6 16 , 22 5 2 2 6 17 →= 23 22 5 2 6 17 , 33 5 2 2 6 15 →= 34 22 5 2 6 15 , 33 5 2 2 6 16 →= 34 22 5 2 6 16 , 33 5 2 2 6 17 →= 34 22 5 2 6 17 , 35 5 2 2 6 15 →= 36 22 5 2 6 15 , 35 5 2 2 6 16 →= 36 22 5 2 6 16 , 35 5 2 2 6 17 →= 36 22 5 2 6 17 , 37 26 2 2 6 15 →= 38 33 5 2 6 15 , 37 26 2 2 6 16 →= 38 33 5 2 6 16 , 37 26 2 2 6 17 →= 38 33 5 2 6 17 , 1 2 2 2 24 39 →= 18 15 5 2 24 39 , 2 2 2 2 24 39 →= 6 15 5 2 24 39 , 5 2 2 2 24 39 →= 19 15 5 2 24 39 , 8 2 2 2 24 39 →= 20 15 5 2 24 39 , 12 2 2 2 24 39 →= 21 15 5 2 24 39 , 26 2 2 2 24 39 →= 27 15 5 2 24 39 , 28 2 2 2 24 39 →= 29 15 5 2 24 39 , 4 5 2 2 24 39 →= 30 22 5 2 24 39 , 10 5 2 2 24 39 →= 31 22 5 2 24 39 , 14 5 2 2 24 39 →= 32 22 5 2 24 39 , 15 5 2 2 24 39 →= 16 22 5 2 24 39 , 22 5 2 2 24 39 →= 23 22 5 2 24 39 , 33 5 2 2 24 39 →= 34 22 5 2 24 39 , 35 5 2 2 24 39 →= 36 22 5 2 24 39 , 18 15 5 6 15 5 →= 1 6 15 5 2 2 , 18 15 5 6 15 19 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 19 →= 2 6 15 5 2 6 , 19 15 5 6 15 5 →= 5 6 15 5 2 2 , 19 15 5 6 15 19 →= 5 6 15 5 2 6 , 20 15 5 6 15 5 →= 8 6 15 5 2 2 , 20 15 5 6 15 19 →= 8 6 15 5 2 6 , 21 15 5 6 15 5 →= 12 6 15 5 2 2 , 21 15 5 6 15 19 →= 12 6 15 5 2 6 , 27 15 5 6 15 5 →= 26 6 15 5 2 2 , 27 15 5 6 15 19 →= 26 6 15 5 2 6 , 29 15 5 6 15 5 →= 28 6 15 5 2 2 , 29 15 5 6 15 19 →= 28 6 15 5 2 6 , 30 22 5 6 15 5 →= 4 19 15 5 2 2 , 30 22 5 6 15 19 →= 4 19 15 5 2 6 , 31 22 5 6 15 5 →= 10 19 15 5 2 2 , 31 22 5 6 15 19 →= 10 19 15 5 2 6 , 32 22 5 6 15 5 →= 14 19 15 5 2 2 , 32 22 5 6 15 19 →= 14 19 15 5 2 6 , 16 22 5 6 15 5 →= 15 19 15 5 2 2 , 16 22 5 6 15 19 →= 15 19 15 5 2 6 , 23 22 5 6 15 5 →= 22 19 15 5 2 2 , 23 22 5 6 15 19 →= 22 19 15 5 2 6 , 34 22 5 6 15 5 →= 33 19 15 5 2 2 , 34 22 5 6 15 19 →= 33 19 15 5 2 6 , 36 22 5 6 15 5 →= 35 19 15 5 2 2 , 36 22 5 6 15 19 →= 35 19 15 5 2 6 , 38 33 5 6 15 5 →= 37 27 15 5 2 2 , 38 33 5 6 15 19 →= 37 27 15 5 2 6 , 18 15 5 6 16 22 →= 1 6 15 5 6 15 , 18 15 5 6 16 23 →= 1 6 15 5 6 16 , 6 15 5 6 16 22 →= 2 6 15 5 6 15 , 6 15 5 6 16 23 →= 2 6 15 5 6 16 , 19 15 5 6 16 22 →= 5 6 15 5 6 15 , 19 15 5 6 16 23 →= 5 6 15 5 6 16 , 20 15 5 6 16 22 →= 8 6 15 5 6 15 , 20 15 5 6 16 23 →= 8 6 15 5 6 16 , 21 15 5 6 16 22 →= 12 6 15 5 6 15 , 21 15 5 6 16 23 →= 12 6 15 5 6 16 , 27 15 5 6 16 22 →= 26 6 15 5 6 15 , 27 15 5 6 16 23 →= 26 6 15 5 6 16 , 29 15 5 6 16 22 →= 28 6 15 5 6 15 , 29 15 5 6 16 23 →= 28 6 15 5 6 16 , 30 22 5 6 16 22 →= 4 19 15 5 6 15 , 30 22 5 6 16 23 →= 4 19 15 5 6 16 , 31 22 5 6 16 22 →= 10 19 15 5 6 15 , 31 22 5 6 16 23 →= 10 19 15 5 6 16 , 32 22 5 6 16 22 →= 14 19 15 5 6 15 , 32 22 5 6 16 23 →= 14 19 15 5 6 16 , 16 22 5 6 16 22 →= 15 19 15 5 6 15 , 16 22 5 6 16 23 →= 15 19 15 5 6 16 , 23 22 5 6 16 22 →= 22 19 15 5 6 15 , 23 22 5 6 16 23 →= 22 19 15 5 6 16 , 34 22 5 6 16 22 →= 33 19 15 5 6 15 , 34 22 5 6 16 23 →= 33 19 15 5 6 16 , 36 22 5 6 16 22 →= 35 19 15 5 6 15 , 36 22 5 6 16 23 →= 35 19 15 5 6 16 , 38 33 5 6 16 22 →= 37 27 15 5 6 15 , 38 33 5 6 16 23 →= 37 27 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 18 ↦ 17, 19 ↦ 18, 20 ↦ 19, 21 ↦ 20, 22 ↦ 21, 23 ↦ 22, 24 ↦ 23, 25 ↦ 24, 26 ↦ 25, 27 ↦ 26, 28 ↦ 27, 29 ↦ 28, 30 ↦ 29, 31 ↦ 30, 32 ↦ 31, 33 ↦ 32, 34 ↦ 33, 35 ↦ 34, 36 ↦ 35, 37 ↦ 36, 38 ↦ 37, 17 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 203-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 1 2 2 2 2 23 →= 17 15 5 2 2 23 , 1 2 2 2 2 24 →= 17 15 5 2 2 24 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 8 2 2 2 2 23 →= 19 15 5 2 2 23 , 8 2 2 2 2 24 →= 19 15 5 2 2 24 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 12 2 2 2 2 23 →= 20 15 5 2 2 23 , 12 2 2 2 2 24 →= 20 15 5 2 2 24 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 25 2 2 2 2 23 →= 26 15 5 2 2 23 , 25 2 2 2 2 24 →= 26 15 5 2 2 24 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 27 2 2 2 2 23 →= 28 15 5 2 2 23 , 27 2 2 2 2 24 →= 28 15 5 2 2 24 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 34 5 2 2 2 23 →= 35 21 5 2 2 23 , 34 5 2 2 2 24 →= 35 21 5 2 2 24 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 36 25 2 2 2 23 →= 37 32 5 2 2 23 , 36 25 2 2 2 24 →= 37 32 5 2 2 24 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 1 2 2 2 6 38 →= 17 15 5 2 6 38 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 24 ↦ 23, 23 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 202-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 1 2 2 2 2 23 →= 17 15 5 2 2 23 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 8 2 2 2 2 24 →= 19 15 5 2 2 24 , 8 2 2 2 2 23 →= 19 15 5 2 2 23 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 12 2 2 2 2 24 →= 20 15 5 2 2 24 , 12 2 2 2 2 23 →= 20 15 5 2 2 23 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 25 2 2 2 2 24 →= 26 15 5 2 2 24 , 25 2 2 2 2 23 →= 26 15 5 2 2 23 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 27 2 2 2 2 24 →= 28 15 5 2 2 24 , 27 2 2 2 2 23 →= 28 15 5 2 2 23 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 34 5 2 2 2 24 →= 35 21 5 2 2 24 , 34 5 2 2 2 23 →= 35 21 5 2 2 23 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 36 25 2 2 2 24 →= 37 32 5 2 2 24 , 36 25 2 2 2 23 →= 37 32 5 2 2 23 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 1 2 2 2 6 38 →= 17 15 5 2 6 38 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 24 39 →= 17 15 5 2 24 39 , 2 2 2 2 24 39 →= 6 15 5 2 24 39 , 5 2 2 2 24 39 →= 18 15 5 2 24 39 , 8 2 2 2 24 39 →= 19 15 5 2 24 39 , 12 2 2 2 24 39 →= 20 15 5 2 24 39 , 25 2 2 2 24 39 →= 26 15 5 2 24 39 , 27 2 2 2 24 39 →= 28 15 5 2 24 39 , 4 5 2 2 24 39 →= 29 21 5 2 24 39 , 10 5 2 2 24 39 →= 30 21 5 2 24 39 , 14 5 2 2 24 39 →= 31 21 5 2 24 39 , 15 5 2 2 24 39 →= 16 21 5 2 24 39 , 21 5 2 2 24 39 →= 22 21 5 2 24 39 , 32 5 2 2 24 39 →= 33 21 5 2 24 39 , 34 5 2 2 24 39 →= 35 21 5 2 24 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 24 ↦ 23, 23 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 201-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 8 2 2 2 2 23 →= 19 15 5 2 2 23 , 8 2 2 2 2 24 →= 19 15 5 2 2 24 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 12 2 2 2 2 23 →= 20 15 5 2 2 23 , 12 2 2 2 2 24 →= 20 15 5 2 2 24 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 25 2 2 2 2 23 →= 26 15 5 2 2 23 , 25 2 2 2 2 24 →= 26 15 5 2 2 24 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 27 2 2 2 2 23 →= 28 15 5 2 2 23 , 27 2 2 2 2 24 →= 28 15 5 2 2 24 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 34 5 2 2 2 23 →= 35 21 5 2 2 23 , 34 5 2 2 2 24 →= 35 21 5 2 2 24 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 36 25 2 2 2 23 →= 37 32 5 2 2 23 , 36 25 2 2 2 24 →= 37 32 5 2 2 24 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 1 2 2 2 6 38 →= 17 15 5 2 6 38 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 200-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 8 2 2 2 2 24 →= 19 15 5 2 2 24 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 12 2 2 2 2 23 →= 20 15 5 2 2 23 , 12 2 2 2 2 24 →= 20 15 5 2 2 24 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 25 2 2 2 2 23 →= 26 15 5 2 2 23 , 25 2 2 2 2 24 →= 26 15 5 2 2 24 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 27 2 2 2 2 23 →= 28 15 5 2 2 23 , 27 2 2 2 2 24 →= 28 15 5 2 2 24 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 34 5 2 2 2 23 →= 35 21 5 2 2 23 , 34 5 2 2 2 24 →= 35 21 5 2 2 24 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 36 25 2 2 2 23 →= 37 32 5 2 2 23 , 36 25 2 2 2 24 →= 37 32 5 2 2 24 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 1 2 2 2 6 38 →= 17 15 5 2 6 38 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 199-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 12 2 2 2 2 23 →= 20 15 5 2 2 23 , 12 2 2 2 2 24 →= 20 15 5 2 2 24 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 25 2 2 2 2 23 →= 26 15 5 2 2 23 , 25 2 2 2 2 24 →= 26 15 5 2 2 24 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 27 2 2 2 2 23 →= 28 15 5 2 2 23 , 27 2 2 2 2 24 →= 28 15 5 2 2 24 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 34 5 2 2 2 23 →= 35 21 5 2 2 23 , 34 5 2 2 2 24 →= 35 21 5 2 2 24 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 36 25 2 2 2 23 →= 37 32 5 2 2 23 , 36 25 2 2 2 24 →= 37 32 5 2 2 24 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 1 2 2 2 6 38 →= 17 15 5 2 6 38 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 198-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 12 2 2 2 2 24 →= 20 15 5 2 2 24 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 25 2 2 2 2 23 →= 26 15 5 2 2 23 , 25 2 2 2 2 24 →= 26 15 5 2 2 24 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 27 2 2 2 2 23 →= 28 15 5 2 2 23 , 27 2 2 2 2 24 →= 28 15 5 2 2 24 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 34 5 2 2 2 23 →= 35 21 5 2 2 23 , 34 5 2 2 2 24 →= 35 21 5 2 2 24 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 36 25 2 2 2 23 →= 37 32 5 2 2 23 , 36 25 2 2 2 24 →= 37 32 5 2 2 24 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 1 2 2 2 6 38 →= 17 15 5 2 6 38 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 197-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 25 2 2 2 2 23 →= 26 15 5 2 2 23 , 25 2 2 2 2 24 →= 26 15 5 2 2 24 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 27 2 2 2 2 23 →= 28 15 5 2 2 23 , 27 2 2 2 2 24 →= 28 15 5 2 2 24 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 34 5 2 2 2 23 →= 35 21 5 2 2 23 , 34 5 2 2 2 24 →= 35 21 5 2 2 24 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 36 25 2 2 2 23 →= 37 32 5 2 2 23 , 36 25 2 2 2 24 →= 37 32 5 2 2 24 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 1 2 2 2 6 38 →= 17 15 5 2 6 38 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 196-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 25 2 2 2 2 24 →= 26 15 5 2 2 24 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 27 2 2 2 2 23 →= 28 15 5 2 2 23 , 27 2 2 2 2 24 →= 28 15 5 2 2 24 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 34 5 2 2 2 23 →= 35 21 5 2 2 23 , 34 5 2 2 2 24 →= 35 21 5 2 2 24 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 36 25 2 2 2 23 →= 37 32 5 2 2 23 , 36 25 2 2 2 24 →= 37 32 5 2 2 24 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 1 2 2 2 6 38 →= 17 15 5 2 6 38 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 195-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 27 2 2 2 2 23 →= 28 15 5 2 2 23 , 27 2 2 2 2 24 →= 28 15 5 2 2 24 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 34 5 2 2 2 23 →= 35 21 5 2 2 23 , 34 5 2 2 2 24 →= 35 21 5 2 2 24 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 36 25 2 2 2 23 →= 37 32 5 2 2 23 , 36 25 2 2 2 24 →= 37 32 5 2 2 24 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 1 2 2 2 6 38 →= 17 15 5 2 6 38 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 194-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 27 2 2 2 2 24 →= 28 15 5 2 2 24 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 34 5 2 2 2 23 →= 35 21 5 2 2 23 , 34 5 2 2 2 24 →= 35 21 5 2 2 24 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 36 25 2 2 2 23 →= 37 32 5 2 2 23 , 36 25 2 2 2 24 →= 37 32 5 2 2 24 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 1 2 2 2 6 38 →= 17 15 5 2 6 38 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 193-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 34 5 2 2 2 23 →= 35 21 5 2 2 23 , 34 5 2 2 2 24 →= 35 21 5 2 2 24 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 36 25 2 2 2 23 →= 37 32 5 2 2 23 , 36 25 2 2 2 24 →= 37 32 5 2 2 24 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 1 2 2 2 6 38 →= 17 15 5 2 6 38 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 192-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 34 5 2 2 2 24 →= 35 21 5 2 2 24 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 36 25 2 2 2 23 →= 37 32 5 2 2 23 , 36 25 2 2 2 24 →= 37 32 5 2 2 24 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 1 2 2 2 6 38 →= 17 15 5 2 6 38 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 191-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 36 25 2 2 2 23 →= 37 32 5 2 2 23 , 36 25 2 2 2 24 →= 37 32 5 2 2 24 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 1 2 2 2 6 38 →= 17 15 5 2 6 38 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 190-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 36 25 2 2 2 24 →= 37 32 5 2 2 24 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 1 2 2 2 6 38 →= 17 15 5 2 6 38 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 189-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 1 2 2 2 6 38 →= 17 15 5 2 6 38 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 188-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 8 2 2 2 6 38 →= 19 15 5 2 6 38 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 187-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 12 2 2 2 6 38 →= 20 15 5 2 6 38 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 186-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 25 2 2 2 6 38 →= 26 15 5 2 6 38 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 185-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 27 2 2 2 6 38 →= 28 15 5 2 6 38 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 184-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 34 5 2 2 6 38 →= 35 21 5 2 6 38 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 183-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 36 25 2 2 6 38 →= 37 32 5 2 6 38 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 182-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 1 2 2 2 23 39 →= 17 15 5 2 23 39 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 181-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 8 2 2 2 23 39 →= 19 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 180-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 12 2 2 2 23 39 →= 20 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 179-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 25 2 2 2 23 39 →= 26 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 178-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 27 2 2 2 23 39 →= 28 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 177-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 4 5 2 2 23 39 →= 29 21 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 176-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 10 5 2 2 23 39 →= 30 21 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 175-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 14 5 2 2 23 39 →= 31 21 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 174-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 32 5 2 2 23 39 →= 33 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 173-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 34 5 2 2 23 39 →= 35 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 1 0 0 ⎟ ⎜ 0 0 0 0 0 1 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 1 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 1 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 ⎟ ⎜ 0 1 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5, 6 ↦ 6, 7 ↦ 7, 8 ↦ 8, 9 ↦ 9, 10 ↦ 10, 11 ↦ 11, 12 ↦ 12, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19, 20 ↦ 20, 21 ↦ 21, 22 ↦ 22, 23 ↦ 23, 24 ↦ 24, 25 ↦ 25, 26 ↦ 26, 27 ↦ 27, 28 ↦ 28, 29 ↦ 29, 30 ↦ 30, 31 ↦ 31, 32 ↦ 32, 33 ↦ 33, 34 ↦ 34, 35 ↦ 35, 36 ↦ 36, 37 ↦ 37, 38 ↦ 38, 39 ↦ 39 }, it remains to prove termination of the 172-rule system { 0 1 2 2 2 2 ⟶ 3 4 5 2 2 2 , 0 1 2 2 2 6 ⟶ 3 4 5 2 2 6 , 7 8 2 2 2 2 ⟶ 9 10 5 2 2 2 , 7 8 2 2 2 6 ⟶ 9 10 5 2 2 6 , 11 12 2 2 2 2 ⟶ 13 14 5 2 2 2 , 11 12 2 2 2 6 ⟶ 13 14 5 2 2 6 , 0 1 2 2 6 15 ⟶ 3 4 5 2 6 15 , 0 1 2 2 6 16 ⟶ 3 4 5 2 6 16 , 7 8 2 2 6 15 ⟶ 9 10 5 2 6 15 , 7 8 2 2 6 16 ⟶ 9 10 5 2 6 16 , 11 12 2 2 6 15 ⟶ 13 14 5 2 6 15 , 11 12 2 2 6 16 ⟶ 13 14 5 2 6 16 , 3 4 5 6 15 5 ⟶ 0 17 15 5 2 2 , 3 4 5 6 15 18 ⟶ 0 17 15 5 2 6 , 9 10 5 6 15 5 ⟶ 7 19 15 5 2 2 , 9 10 5 6 15 18 ⟶ 7 19 15 5 2 6 , 13 14 5 6 15 5 ⟶ 11 20 15 5 2 2 , 13 14 5 6 15 18 ⟶ 11 20 15 5 2 6 , 3 4 5 6 16 21 ⟶ 0 17 15 5 6 15 , 3 4 5 6 16 22 ⟶ 0 17 15 5 6 16 , 9 10 5 6 16 21 ⟶ 7 19 15 5 6 15 , 9 10 5 6 16 22 ⟶ 7 19 15 5 6 16 , 13 14 5 6 16 21 ⟶ 11 20 15 5 6 15 , 13 14 5 6 16 22 ⟶ 11 20 15 5 6 16 , 1 2 2 2 2 2 →= 17 15 5 2 2 2 , 1 2 2 2 2 6 →= 17 15 5 2 2 6 , 2 2 2 2 2 2 →= 6 15 5 2 2 2 , 2 2 2 2 2 6 →= 6 15 5 2 2 6 , 2 2 2 2 2 23 →= 6 15 5 2 2 23 , 2 2 2 2 2 24 →= 6 15 5 2 2 24 , 5 2 2 2 2 2 →= 18 15 5 2 2 2 , 5 2 2 2 2 6 →= 18 15 5 2 2 6 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 5 2 2 2 2 24 →= 18 15 5 2 2 24 , 8 2 2 2 2 2 →= 19 15 5 2 2 2 , 8 2 2 2 2 6 →= 19 15 5 2 2 6 , 12 2 2 2 2 2 →= 20 15 5 2 2 2 , 12 2 2 2 2 6 →= 20 15 5 2 2 6 , 25 2 2 2 2 2 →= 26 15 5 2 2 2 , 25 2 2 2 2 6 →= 26 15 5 2 2 6 , 27 2 2 2 2 2 →= 28 15 5 2 2 2 , 27 2 2 2 2 6 →= 28 15 5 2 2 6 , 4 5 2 2 2 2 →= 29 21 5 2 2 2 , 4 5 2 2 2 6 →= 29 21 5 2 2 6 , 4 5 2 2 2 23 →= 29 21 5 2 2 23 , 4 5 2 2 2 24 →= 29 21 5 2 2 24 , 10 5 2 2 2 2 →= 30 21 5 2 2 2 , 10 5 2 2 2 6 →= 30 21 5 2 2 6 , 10 5 2 2 2 23 →= 30 21 5 2 2 23 , 10 5 2 2 2 24 →= 30 21 5 2 2 24 , 14 5 2 2 2 2 →= 31 21 5 2 2 2 , 14 5 2 2 2 6 →= 31 21 5 2 2 6 , 14 5 2 2 2 23 →= 31 21 5 2 2 23 , 14 5 2 2 2 24 →= 31 21 5 2 2 24 , 15 5 2 2 2 2 →= 16 21 5 2 2 2 , 15 5 2 2 2 6 →= 16 21 5 2 2 6 , 15 5 2 2 2 23 →= 16 21 5 2 2 23 , 15 5 2 2 2 24 →= 16 21 5 2 2 24 , 21 5 2 2 2 2 →= 22 21 5 2 2 2 , 21 5 2 2 2 6 →= 22 21 5 2 2 6 , 21 5 2 2 2 23 →= 22 21 5 2 2 23 , 21 5 2 2 2 24 →= 22 21 5 2 2 24 , 32 5 2 2 2 2 →= 33 21 5 2 2 2 , 32 5 2 2 2 6 →= 33 21 5 2 2 6 , 32 5 2 2 2 23 →= 33 21 5 2 2 23 , 32 5 2 2 2 24 →= 33 21 5 2 2 24 , 34 5 2 2 2 2 →= 35 21 5 2 2 2 , 34 5 2 2 2 6 →= 35 21 5 2 2 6 , 36 25 2 2 2 2 →= 37 32 5 2 2 2 , 36 25 2 2 2 6 →= 37 32 5 2 2 6 , 1 2 2 2 6 15 →= 17 15 5 2 6 15 , 1 2 2 2 6 16 →= 17 15 5 2 6 16 , 2 2 2 2 6 15 →= 6 15 5 2 6 15 , 2 2 2 2 6 16 →= 6 15 5 2 6 16 , 2 2 2 2 6 38 →= 6 15 5 2 6 38 , 5 2 2 2 6 15 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 38 →= 18 15 5 2 6 38 , 8 2 2 2 6 15 →= 19 15 5 2 6 15 , 8 2 2 2 6 16 →= 19 15 5 2 6 16 , 12 2 2 2 6 15 →= 20 15 5 2 6 15 , 12 2 2 2 6 16 →= 20 15 5 2 6 16 , 25 2 2 2 6 15 →= 26 15 5 2 6 15 , 25 2 2 2 6 16 →= 26 15 5 2 6 16 , 27 2 2 2 6 15 →= 28 15 5 2 6 15 , 27 2 2 2 6 16 →= 28 15 5 2 6 16 , 4 5 2 2 6 15 →= 29 21 5 2 6 15 , 4 5 2 2 6 16 →= 29 21 5 2 6 16 , 4 5 2 2 6 38 →= 29 21 5 2 6 38 , 10 5 2 2 6 15 →= 30 21 5 2 6 15 , 10 5 2 2 6 16 →= 30 21 5 2 6 16 , 10 5 2 2 6 38 →= 30 21 5 2 6 38 , 14 5 2 2 6 15 →= 31 21 5 2 6 15 , 14 5 2 2 6 16 →= 31 21 5 2 6 16 , 14 5 2 2 6 38 →= 31 21 5 2 6 38 , 15 5 2 2 6 15 →= 16 21 5 2 6 15 , 15 5 2 2 6 16 →= 16 21 5 2 6 16 , 15 5 2 2 6 38 →= 16 21 5 2 6 38 , 21 5 2 2 6 15 →= 22 21 5 2 6 15 , 21 5 2 2 6 16 →= 22 21 5 2 6 16 , 21 5 2 2 6 38 →= 22 21 5 2 6 38 , 32 5 2 2 6 15 →= 33 21 5 2 6 15 , 32 5 2 2 6 16 →= 33 21 5 2 6 16 , 32 5 2 2 6 38 →= 33 21 5 2 6 38 , 34 5 2 2 6 15 →= 35 21 5 2 6 15 , 34 5 2 2 6 16 →= 35 21 5 2 6 16 , 36 25 2 2 6 15 →= 37 32 5 2 6 15 , 36 25 2 2 6 16 →= 37 32 5 2 6 16 , 2 2 2 2 23 39 →= 6 15 5 2 23 39 , 5 2 2 2 23 39 →= 18 15 5 2 23 39 , 15 5 2 2 23 39 →= 16 21 5 2 23 39 , 21 5 2 2 23 39 →= 22 21 5 2 23 39 , 17 15 5 6 15 5 →= 1 6 15 5 2 2 , 17 15 5 6 15 18 →= 1 6 15 5 2 6 , 6 15 5 6 15 5 →= 2 6 15 5 2 2 , 6 15 5 6 15 18 →= 2 6 15 5 2 6 , 18 15 5 6 15 5 →= 5 6 15 5 2 2 , 18 15 5 6 15 18 →= 5 6 15 5 2 6 , 19 15 5 6 15 5 →= 8 6 15 5 2 2 , 19 15 5 6 15 18 →= 8 6 15 5 2 6 , 20 15 5 6 15 5 →= 12 6 15 5 2 2 , 20 15 5 6 15 18 →= 12 6 15 5 2 6 , 26 15 5 6 15 5 →= 25 6 15 5 2 2 , 26 15 5 6 15 18 →= 25 6 15 5 2 6 , 28 15 5 6 15 5 →= 27 6 15 5 2 2 , 28 15 5 6 15 18 →= 27 6 15 5 2 6 , 29 21 5 6 15 5 →= 4 18 15 5 2 2 , 29 21 5 6 15 18 →= 4 18 15 5 2 6 , 30 21 5 6 15 5 →= 10 18 15 5 2 2 , 30 21 5 6 15 18 →= 10 18 15 5 2 6 , 31 21 5 6 15 5 →= 14 18 15 5 2 2 , 31 21 5 6 15 18 →= 14 18 15 5 2 6 , 16 21 5 6 15 5 →= 15 18 15 5 2 2 , 16 21 5 6 15 18 →= 15 18 15 5 2 6 , 22 21 5 6 15 5 →= 21 18 15 5 2 2 , 22 21 5 6 15 18 →= 21 18 15 5 2 6 , 33 21 5 6 15 5 →= 32 18 15 5 2 2 , 33 21 5 6 15 18 →= 32 18 15 5 2 6 , 35 21 5 6 15 5 →= 34 18 15 5 2 2 , 35 21 5 6 15 18 →= 34 18 15 5 2 6 , 37 32 5 6 15 5 →= 36 26 15 5 2 2 , 37 32 5 6 15 18 →= 36 26 15 5 2 6 , 17 15 5 6 16 21 →= 1 6 15 5 6 15 , 17 15 5 6 16 22 →= 1 6 15 5 6 16 , 6 15 5 6 16 21 →= 2 6 15 5 6 15 , 6 15 5 6 16 22 →= 2 6 15 5 6 16 , 18 15 5 6 16 21 →= 5 6 15 5 6 15 , 18 15 5 6 16 22 →= 5 6 15 5 6 16 , 19 15 5 6 16 21 →= 8 6 15 5 6 15 , 19 15 5 6 16 22 →= 8 6 15 5 6 16 , 20 15 5 6 16 21 →= 12 6 15 5 6 15 , 20 15 5 6 16 22 →= 12 6 15 5 6 16 , 26 15 5 6 16 21 →= 25 6 15 5 6 15 , 26 15 5 6 16 22 →= 25 6 15 5 6 16 , 28 15 5 6 16 21 →= 27 6 15 5 6 15 , 28 15 5 6 16 22 →= 27 6 15 5 6 16 , 29 21 5 6 16 21 →= 4 18 15 5 6 15 , 29 21 5 6 16 22 →= 4 18 15 5 6 16 , 30 21 5 6 16 21 →= 10 18 15 5 6 15 , 30 21 5 6 16 22 →= 10 18 15 5 6 16 , 31 21 5 6 16 21 →= 14 18 15 5 6 15 , 31 21 5 6 16 22 →= 14 18 15 5 6 16 , 16 21 5 6 16 21 →= 15 18 15 5 6 15 , 16 21 5 6 16 22 →= 15 18 15 5 6 16 , 22 21 5 6 16 21 →= 21 18 15 5 6 15 , 22 21 5 6 16 22 →= 21 18 15 5 6 16 , 33 21 5 6 16 21 →= 32 18 15 5 6 15 , 33 21 5 6 16 22 →= 32 18 15 5 6 16 , 35 21 5 6 16 21 →= 34 18 15 5 6 15 , 35 21 5 6 16 22 →= 34 18 15 5 6 16 , 37 32 5 6 16 21 →= 36 26 15 5 6 15 , 37 32 5 6 16 22 →= 36 26 15 5 6 16 } Applying sparse tiling TROC(2) [Geser/Hofbauer/Waldmann, FSCD 2019]. After renaming modulo the bijection { (40,0) ↦ 0, (0,1) ↦ 1, (1,2) ↦ 2, (2,2) ↦ 3, (40,3) ↦ 4, (3,4) ↦ 5, (4,5) ↦ 6, (5,2) ↦ 7, (2,6) ↦ 8, (2,23) ↦ 9, (2,24) ↦ 10, (2,41) ↦ 11, (6,16) ↦ 12, (6,38) ↦ 13, (6,41) ↦ 14, (6,15) ↦ 15, (40,7) ↦ 16, (7,8) ↦ 17, (8,2) ↦ 18, (40,9) ↦ 19, (9,10) ↦ 20, (10,5) ↦ 21, (40,11) ↦ 22, (11,12) ↦ 23, (12,2) ↦ 24, (40,13) ↦ 25, (13,14) ↦ 26, (14,5) ↦ 27, (15,18) ↦ 28, (15,5) ↦ 29, (15,41) ↦ 30, (16,21) ↦ 31, (16,22) ↦ 32, (16,41) ↦ 33, (5,6) ↦ 34, (0,17) ↦ 35, (17,15) ↦ 36, (18,16) ↦ 37, (18,15) ↦ 38, (7,19) ↦ 39, (19,15) ↦ 40, (11,20) ↦ 41, (20,15) ↦ 42, (21,18) ↦ 43, (21,5) ↦ 44, (22,21) ↦ 45, (22,22) ↦ 46, (40,1) ↦ 47, (40,17) ↦ 48, (1,6) ↦ 49, (8,6) ↦ 50, (40,2) ↦ 51, (40,6) ↦ 52, (25,2) ↦ 53, (25,6) ↦ 54, (27,2) ↦ 55, (27,6) ↦ 56, (12,6) ↦ 57, (23,39) ↦ 58, (23,41) ↦ 59, (24,41) ↦ 60, (32,5) ↦ 61, (32,18) ↦ 62, (34,5) ↦ 63, (34,18) ↦ 64, (4,18) ↦ 65, (40,5) ↦ 66, (40,18) ↦ 67, (10,18) ↦ 68, (14,18) ↦ 69, (40,8) ↦ 70, (40,19) ↦ 71, (40,12) ↦ 72, (40,20) ↦ 73, (36,25) ↦ 74, (36,26) ↦ 75, (26,15) ↦ 76, (40,25) ↦ 77, (40,26) ↦ 78, (40,27) ↦ 79, (40,28) ↦ 80, (28,15) ↦ 81, (3,29) ↦ 82, (29,21) ↦ 83, (40,4) ↦ 84, (40,29) ↦ 85, (40,10) ↦ 86, (40,30) ↦ 87, (30,21) ↦ 88, (9,30) ↦ 89, (40,14) ↦ 90, (40,31) ↦ 91, (31,21) ↦ 92, (13,31) ↦ 93, (17,16) ↦ 94, (19,16) ↦ 95, (20,16) ↦ 96, (40,15) ↦ 97, (40,16) ↦ 98, (26,16) ↦ 99, (28,16) ↦ 100, (33,21) ↦ 101, (33,22) ↦ 102, (35,21) ↦ 103, (35,22) ↦ 104, (40,21) ↦ 105, (40,22) ↦ 106, (29,22) ↦ 107, (30,22) ↦ 108, (31,22) ↦ 109, (37,32) ↦ 110, (37,33) ↦ 111, (40,32) ↦ 112, (40,33) ↦ 113, (40,34) ↦ 114, (40,35) ↦ 115, (40,36) ↦ 116, (40,37) ↦ 117, (38,41) ↦ 118, (39,41) ↦ 119 }, it remains to prove termination of the 1434-rule system { 0 1 2 3 3 3 3 ⟶ 4 5 6 7 3 3 3 , 0 1 2 3 3 3 8 ⟶ 4 5 6 7 3 3 8 , 0 1 2 3 3 3 9 ⟶ 4 5 6 7 3 3 9 , 0 1 2 3 3 3 10 ⟶ 4 5 6 7 3 3 10 , 0 1 2 3 3 3 11 ⟶ 4 5 6 7 3 3 11 , 0 1 2 3 3 8 12 ⟶ 4 5 6 7 3 8 12 , 0 1 2 3 3 8 13 ⟶ 4 5 6 7 3 8 13 , 0 1 2 3 3 8 14 ⟶ 4 5 6 7 3 8 14 , 0 1 2 3 3 8 15 ⟶ 4 5 6 7 3 8 15 , 16 17 18 3 3 3 3 ⟶ 19 20 21 7 3 3 3 , 16 17 18 3 3 3 8 ⟶ 19 20 21 7 3 3 8 , 16 17 18 3 3 3 9 ⟶ 19 20 21 7 3 3 9 , 16 17 18 3 3 3 10 ⟶ 19 20 21 7 3 3 10 , 16 17 18 3 3 3 11 ⟶ 19 20 21 7 3 3 11 , 16 17 18 3 3 8 12 ⟶ 19 20 21 7 3 8 12 , 16 17 18 3 3 8 13 ⟶ 19 20 21 7 3 8 13 , 16 17 18 3 3 8 14 ⟶ 19 20 21 7 3 8 14 , 16 17 18 3 3 8 15 ⟶ 19 20 21 7 3 8 15 , 22 23 24 3 3 3 3 ⟶ 25 26 27 7 3 3 3 , 22 23 24 3 3 3 8 ⟶ 25 26 27 7 3 3 8 , 22 23 24 3 3 3 9 ⟶ 25 26 27 7 3 3 9 , 22 23 24 3 3 3 10 ⟶ 25 26 27 7 3 3 10 , 22 23 24 3 3 3 11 ⟶ 25 26 27 7 3 3 11 , 22 23 24 3 3 8 12 ⟶ 25 26 27 7 3 8 12 , 22 23 24 3 3 8 13 ⟶ 25 26 27 7 3 8 13 , 22 23 24 3 3 8 14 ⟶ 25 26 27 7 3 8 14 , 22 23 24 3 3 8 15 ⟶ 25 26 27 7 3 8 15 , 0 1 2 3 8 15 28 ⟶ 4 5 6 7 8 15 28 , 0 1 2 3 8 15 29 ⟶ 4 5 6 7 8 15 29 , 0 1 2 3 8 15 30 ⟶ 4 5 6 7 8 15 30 , 0 1 2 3 8 12 31 ⟶ 4 5 6 7 8 12 31 , 0 1 2 3 8 12 32 ⟶ 4 5 6 7 8 12 32 , 0 1 2 3 8 12 33 ⟶ 4 5 6 7 8 12 33 , 16 17 18 3 8 15 28 ⟶ 19 20 21 7 8 15 28 , 16 17 18 3 8 15 29 ⟶ 19 20 21 7 8 15 29 , 16 17 18 3 8 15 30 ⟶ 19 20 21 7 8 15 30 , 16 17 18 3 8 12 31 ⟶ 19 20 21 7 8 12 31 , 16 17 18 3 8 12 32 ⟶ 19 20 21 7 8 12 32 , 16 17 18 3 8 12 33 ⟶ 19 20 21 7 8 12 33 , 22 23 24 3 8 15 28 ⟶ 25 26 27 7 8 15 28 , 22 23 24 3 8 15 29 ⟶ 25 26 27 7 8 15 29 , 22 23 24 3 8 15 30 ⟶ 25 26 27 7 8 15 30 , 22 23 24 3 8 12 31 ⟶ 25 26 27 7 8 12 31 , 22 23 24 3 8 12 32 ⟶ 25 26 27 7 8 12 32 , 22 23 24 3 8 12 33 ⟶ 25 26 27 7 8 12 33 , 4 5 6 34 15 29 7 ⟶ 0 35 36 29 7 3 3 , 4 5 6 34 15 29 34 ⟶ 0 35 36 29 7 3 8 , 4 5 6 34 15 28 37 ⟶ 0 35 36 29 7 8 12 , 4 5 6 34 15 28 38 ⟶ 0 35 36 29 7 8 15 , 19 20 21 34 15 29 7 ⟶ 16 39 40 29 7 3 3 , 19 20 21 34 15 29 34 ⟶ 16 39 40 29 7 3 8 , 19 20 21 34 15 28 37 ⟶ 16 39 40 29 7 8 12 , 19 20 21 34 15 28 38 ⟶ 16 39 40 29 7 8 15 , 25 26 27 34 15 29 7 ⟶ 22 41 42 29 7 3 3 , 25 26 27 34 15 29 34 ⟶ 22 41 42 29 7 3 8 , 25 26 27 34 15 28 37 ⟶ 22 41 42 29 7 8 12 , 25 26 27 34 15 28 38 ⟶ 22 41 42 29 7 8 15 , 4 5 6 34 12 31 43 ⟶ 0 35 36 29 34 15 28 , 4 5 6 34 12 31 44 ⟶ 0 35 36 29 34 15 29 , 4 5 6 34 12 32 45 ⟶ 0 35 36 29 34 12 31 , 4 5 6 34 12 32 46 ⟶ 0 35 36 29 34 12 32 , 19 20 21 34 12 31 43 ⟶ 16 39 40 29 34 15 28 , 19 20 21 34 12 31 44 ⟶ 16 39 40 29 34 15 29 , 19 20 21 34 12 32 45 ⟶ 16 39 40 29 34 12 31 , 19 20 21 34 12 32 46 ⟶ 16 39 40 29 34 12 32 , 25 26 27 34 12 31 43 ⟶ 22 41 42 29 34 15 28 , 25 26 27 34 12 31 44 ⟶ 22 41 42 29 34 15 29 , 25 26 27 34 12 32 45 ⟶ 22 41 42 29 34 12 31 , 25 26 27 34 12 32 46 ⟶ 22 41 42 29 34 12 32 , 1 2 3 3 3 3 3 →= 35 36 29 7 3 3 3 , 1 2 3 3 3 3 8 →= 35 36 29 7 3 3 8 , 1 2 3 3 3 3 9 →= 35 36 29 7 3 3 9 , 1 2 3 3 3 3 10 →= 35 36 29 7 3 3 10 , 1 2 3 3 3 3 11 →= 35 36 29 7 3 3 11 , 47 2 3 3 3 3 3 →= 48 36 29 7 3 3 3 , 47 2 3 3 3 3 8 →= 48 36 29 7 3 3 8 , 47 2 3 3 3 3 9 →= 48 36 29 7 3 3 9 , 47 2 3 3 3 3 10 →= 48 36 29 7 3 3 10 , 47 2 3 3 3 3 11 →= 48 36 29 7 3 3 11 , 1 2 3 3 3 8 12 →= 35 36 29 7 3 8 12 , 1 2 3 3 3 8 13 →= 35 36 29 7 3 8 13 , 1 2 3 3 3 8 14 →= 35 36 29 7 3 8 14 , 1 2 3 3 3 8 15 →= 35 36 29 7 3 8 15 , 47 2 3 3 3 8 12 →= 48 36 29 7 3 8 12 , 47 2 3 3 3 8 13 →= 48 36 29 7 3 8 13 , 47 2 3 3 3 8 14 →= 48 36 29 7 3 8 14 , 47 2 3 3 3 8 15 →= 48 36 29 7 3 8 15 , 2 3 3 3 3 3 3 →= 49 15 29 7 3 3 3 , 2 3 3 3 3 3 8 →= 49 15 29 7 3 3 8 , 2 3 3 3 3 3 9 →= 49 15 29 7 3 3 9 , 2 3 3 3 3 3 10 →= 49 15 29 7 3 3 10 , 2 3 3 3 3 3 11 →= 49 15 29 7 3 3 11 , 3 3 3 3 3 3 3 →= 8 15 29 7 3 3 3 , 3 3 3 3 3 3 8 →= 8 15 29 7 3 3 8 , 3 3 3 3 3 3 9 →= 8 15 29 7 3 3 9 , 3 3 3 3 3 3 10 →= 8 15 29 7 3 3 10 , 3 3 3 3 3 3 11 →= 8 15 29 7 3 3 11 , 7 3 3 3 3 3 3 →= 34 15 29 7 3 3 3 , 7 3 3 3 3 3 8 →= 34 15 29 7 3 3 8 , 7 3 3 3 3 3 9 →= 34 15 29 7 3 3 9 , 7 3 3 3 3 3 10 →= 34 15 29 7 3 3 10 , 7 3 3 3 3 3 11 →= 34 15 29 7 3 3 11 , 18 3 3 3 3 3 3 →= 50 15 29 7 3 3 3 , 18 3 3 3 3 3 8 →= 50 15 29 7 3 3 8 , 18 3 3 3 3 3 9 →= 50 15 29 7 3 3 9 , 18 3 3 3 3 3 10 →= 50 15 29 7 3 3 10 , 18 3 3 3 3 3 11 →= 50 15 29 7 3 3 11 , 51 3 3 3 3 3 3 →= 52 15 29 7 3 3 3 , 51 3 3 3 3 3 8 →= 52 15 29 7 3 3 8 , 51 3 3 3 3 3 9 →= 52 15 29 7 3 3 9 , 51 3 3 3 3 3 10 →= 52 15 29 7 3 3 10 , 51 3 3 3 3 3 11 →= 52 15 29 7 3 3 11 , 53 3 3 3 3 3 3 →= 54 15 29 7 3 3 3 , 53 3 3 3 3 3 8 →= 54 15 29 7 3 3 8 , 53 3 3 3 3 3 9 →= 54 15 29 7 3 3 9 , 53 3 3 3 3 3 10 →= 54 15 29 7 3 3 10 , 53 3 3 3 3 3 11 →= 54 15 29 7 3 3 11 , 55 3 3 3 3 3 3 →= 56 15 29 7 3 3 3 , 55 3 3 3 3 3 8 →= 56 15 29 7 3 3 8 , 55 3 3 3 3 3 9 →= 56 15 29 7 3 3 9 , 55 3 3 3 3 3 10 →= 56 15 29 7 3 3 10 , 55 3 3 3 3 3 11 →= 56 15 29 7 3 3 11 , 24 3 3 3 3 3 3 →= 57 15 29 7 3 3 3 , 24 3 3 3 3 3 8 →= 57 15 29 7 3 3 8 , 24 3 3 3 3 3 9 →= 57 15 29 7 3 3 9 , 24 3 3 3 3 3 10 →= 57 15 29 7 3 3 10 , 24 3 3 3 3 3 11 →= 57 15 29 7 3 3 11 , 2 3 3 3 3 8 12 →= 49 15 29 7 3 8 12 , 2 3 3 3 3 8 13 →= 49 15 29 7 3 8 13 , 2 3 3 3 3 8 14 →= 49 15 29 7 3 8 14 , 2 3 3 3 3 8 15 →= 49 15 29 7 3 8 15 , 3 3 3 3 3 8 12 →= 8 15 29 7 3 8 12 , 3 3 3 3 3 8 13 →= 8 15 29 7 3 8 13 , 3 3 3 3 3 8 14 →= 8 15 29 7 3 8 14 , 3 3 3 3 3 8 15 →= 8 15 29 7 3 8 15 , 7 3 3 3 3 8 12 →= 34 15 29 7 3 8 12 , 7 3 3 3 3 8 13 →= 34 15 29 7 3 8 13 , 7 3 3 3 3 8 14 →= 34 15 29 7 3 8 14 , 7 3 3 3 3 8 15 →= 34 15 29 7 3 8 15 , 18 3 3 3 3 8 12 →= 50 15 29 7 3 8 12 , 18 3 3 3 3 8 13 →= 50 15 29 7 3 8 13 , 18 3 3 3 3 8 14 →= 50 15 29 7 3 8 14 , 18 3 3 3 3 8 15 →= 50 15 29 7 3 8 15 , 51 3 3 3 3 8 12 →= 52 15 29 7 3 8 12 , 51 3 3 3 3 8 13 →= 52 15 29 7 3 8 13 , 51 3 3 3 3 8 14 →= 52 15 29 7 3 8 14 , 51 3 3 3 3 8 15 →= 52 15 29 7 3 8 15 , 53 3 3 3 3 8 12 →= 54 15 29 7 3 8 12 , 53 3 3 3 3 8 13 →= 54 15 29 7 3 8 13 , 53 3 3 3 3 8 14 →= 54 15 29 7 3 8 14 , 53 3 3 3 3 8 15 →= 54 15 29 7 3 8 15 , 55 3 3 3 3 8 12 →= 56 15 29 7 3 8 12 , 55 3 3 3 3 8 13 →= 56 15 29 7 3 8 13 , 55 3 3 3 3 8 14 →= 56 15 29 7 3 8 14 , 55 3 3 3 3 8 15 →= 56 15 29 7 3 8 15 , 24 3 3 3 3 8 12 →= 57 15 29 7 3 8 12 , 24 3 3 3 3 8 13 →= 57 15 29 7 3 8 13 , 24 3 3 3 3 8 14 →= 57 15 29 7 3 8 14 , 24 3 3 3 3 8 15 →= 57 15 29 7 3 8 15 , 2 3 3 3 3 9 58 →= 49 15 29 7 3 9 58 , 2 3 3 3 3 9 59 →= 49 15 29 7 3 9 59 , 3 3 3 3 3 9 58 →= 8 15 29 7 3 9 58 , 3 3 3 3 3 9 59 →= 8 15 29 7 3 9 59 , 7 3 3 3 3 9 58 →= 34 15 29 7 3 9 58 , 7 3 3 3 3 9 59 →= 34 15 29 7 3 9 59 , 18 3 3 3 3 9 58 →= 50 15 29 7 3 9 58 , 18 3 3 3 3 9 59 →= 50 15 29 7 3 9 59 , 51 3 3 3 3 9 58 →= 52 15 29 7 3 9 58 , 51 3 3 3 3 9 59 →= 52 15 29 7 3 9 59 , 53 3 3 3 3 9 58 →= 54 15 29 7 3 9 58 , 53 3 3 3 3 9 59 →= 54 15 29 7 3 9 59 , 55 3 3 3 3 9 58 →= 56 15 29 7 3 9 58 , 55 3 3 3 3 9 59 →= 56 15 29 7 3 9 59 , 24 3 3 3 3 9 58 →= 57 15 29 7 3 9 58 , 24 3 3 3 3 9 59 →= 57 15 29 7 3 9 59 , 2 3 3 3 3 10 60 →= 49 15 29 7 3 10 60 , 3 3 3 3 3 10 60 →= 8 15 29 7 3 10 60 , 7 3 3 3 3 10 60 →= 34 15 29 7 3 10 60 , 18 3 3 3 3 10 60 →= 50 15 29 7 3 10 60 , 51 3 3 3 3 10 60 →= 52 15 29 7 3 10 60 , 53 3 3 3 3 10 60 →= 54 15 29 7 3 10 60 , 55 3 3 3 3 10 60 →= 56 15 29 7 3 10 60 , 24 3 3 3 3 10 60 →= 57 15 29 7 3 10 60 , 61 7 3 3 3 3 3 →= 62 38 29 7 3 3 3 , 61 7 3 3 3 3 8 →= 62 38 29 7 3 3 8 , 61 7 3 3 3 3 9 →= 62 38 29 7 3 3 9 , 61 7 3 3 3 3 10 →= 62 38 29 7 3 3 10 , 61 7 3 3 3 3 11 →= 62 38 29 7 3 3 11 , 63 7 3 3 3 3 3 →= 64 38 29 7 3 3 3 , 63 7 3 3 3 3 8 →= 64 38 29 7 3 3 8 , 63 7 3 3 3 3 9 →= 64 38 29 7 3 3 9 , 63 7 3 3 3 3 10 →= 64 38 29 7 3 3 10 , 63 7 3 3 3 3 11 →= 64 38 29 7 3 3 11 , 6 7 3 3 3 3 3 →= 65 38 29 7 3 3 3 , 6 7 3 3 3 3 8 →= 65 38 29 7 3 3 8 , 6 7 3 3 3 3 9 →= 65 38 29 7 3 3 9 , 6 7 3 3 3 3 10 →= 65 38 29 7 3 3 10 , 6 7 3 3 3 3 11 →= 65 38 29 7 3 3 11 , 44 7 3 3 3 3 3 →= 43 38 29 7 3 3 3 , 44 7 3 3 3 3 8 →= 43 38 29 7 3 3 8 , 44 7 3 3 3 3 9 →= 43 38 29 7 3 3 9 , 44 7 3 3 3 3 10 →= 43 38 29 7 3 3 10 , 44 7 3 3 3 3 11 →= 43 38 29 7 3 3 11 , 66 7 3 3 3 3 3 →= 67 38 29 7 3 3 3 , 66 7 3 3 3 3 8 →= 67 38 29 7 3 3 8 , 66 7 3 3 3 3 9 →= 67 38 29 7 3 3 9 , 66 7 3 3 3 3 10 →= 67 38 29 7 3 3 10 , 66 7 3 3 3 3 11 →= 67 38 29 7 3 3 11 , 21 7 3 3 3 3 3 →= 68 38 29 7 3 3 3 , 21 7 3 3 3 3 8 →= 68 38 29 7 3 3 8 , 21 7 3 3 3 3 9 →= 68 38 29 7 3 3 9 , 21 7 3 3 3 3 10 →= 68 38 29 7 3 3 10 , 21 7 3 3 3 3 11 →= 68 38 29 7 3 3 11 , 27 7 3 3 3 3 3 →= 69 38 29 7 3 3 3 , 27 7 3 3 3 3 8 →= 69 38 29 7 3 3 8 , 27 7 3 3 3 3 9 →= 69 38 29 7 3 3 9 , 27 7 3 3 3 3 10 →= 69 38 29 7 3 3 10 , 27 7 3 3 3 3 11 →= 69 38 29 7 3 3 11 , 29 7 3 3 3 3 3 →= 28 38 29 7 3 3 3 , 29 7 3 3 3 3 8 →= 28 38 29 7 3 3 8 , 29 7 3 3 3 3 9 →= 28 38 29 7 3 3 9 , 29 7 3 3 3 3 10 →= 28 38 29 7 3 3 10 , 29 7 3 3 3 3 11 →= 28 38 29 7 3 3 11 , 61 7 3 3 3 8 12 →= 62 38 29 7 3 8 12 , 61 7 3 3 3 8 13 →= 62 38 29 7 3 8 13 , 61 7 3 3 3 8 14 →= 62 38 29 7 3 8 14 , 61 7 3 3 3 8 15 →= 62 38 29 7 3 8 15 , 63 7 3 3 3 8 12 →= 64 38 29 7 3 8 12 , 63 7 3 3 3 8 13 →= 64 38 29 7 3 8 13 , 63 7 3 3 3 8 14 →= 64 38 29 7 3 8 14 , 63 7 3 3 3 8 15 →= 64 38 29 7 3 8 15 , 6 7 3 3 3 8 12 →= 65 38 29 7 3 8 12 , 6 7 3 3 3 8 13 →= 65 38 29 7 3 8 13 , 6 7 3 3 3 8 14 →= 65 38 29 7 3 8 14 , 6 7 3 3 3 8 15 →= 65 38 29 7 3 8 15 , 44 7 3 3 3 8 12 →= 43 38 29 7 3 8 12 , 44 7 3 3 3 8 13 →= 43 38 29 7 3 8 13 , 44 7 3 3 3 8 14 →= 43 38 29 7 3 8 14 , 44 7 3 3 3 8 15 →= 43 38 29 7 3 8 15 , 66 7 3 3 3 8 12 →= 67 38 29 7 3 8 12 , 66 7 3 3 3 8 13 →= 67 38 29 7 3 8 13 , 66 7 3 3 3 8 14 →= 67 38 29 7 3 8 14 , 66 7 3 3 3 8 15 →= 67 38 29 7 3 8 15 , 21 7 3 3 3 8 12 →= 68 38 29 7 3 8 12 , 21 7 3 3 3 8 13 →= 68 38 29 7 3 8 13 , 21 7 3 3 3 8 14 →= 68 38 29 7 3 8 14 , 21 7 3 3 3 8 15 →= 68 38 29 7 3 8 15 , 27 7 3 3 3 8 12 →= 69 38 29 7 3 8 12 , 27 7 3 3 3 8 13 →= 69 38 29 7 3 8 13 , 27 7 3 3 3 8 14 →= 69 38 29 7 3 8 14 , 27 7 3 3 3 8 15 →= 69 38 29 7 3 8 15 , 29 7 3 3 3 8 12 →= 28 38 29 7 3 8 12 , 29 7 3 3 3 8 13 →= 28 38 29 7 3 8 13 , 29 7 3 3 3 8 14 →= 28 38 29 7 3 8 14 , 29 7 3 3 3 8 15 →= 28 38 29 7 3 8 15 , 61 7 3 3 3 9 58 →= 62 38 29 7 3 9 58 , 61 7 3 3 3 9 59 →= 62 38 29 7 3 9 59 , 63 7 3 3 3 9 58 →= 64 38 29 7 3 9 58 , 63 7 3 3 3 9 59 →= 64 38 29 7 3 9 59 , 6 7 3 3 3 9 58 →= 65 38 29 7 3 9 58 , 6 7 3 3 3 9 59 →= 65 38 29 7 3 9 59 , 44 7 3 3 3 9 58 →= 43 38 29 7 3 9 58 , 44 7 3 3 3 9 59 →= 43 38 29 7 3 9 59 , 66 7 3 3 3 9 58 →= 67 38 29 7 3 9 58 , 66 7 3 3 3 9 59 →= 67 38 29 7 3 9 59 , 21 7 3 3 3 9 58 →= 68 38 29 7 3 9 58 , 21 7 3 3 3 9 59 →= 68 38 29 7 3 9 59 , 27 7 3 3 3 9 58 →= 69 38 29 7 3 9 58 , 27 7 3 3 3 9 59 →= 69 38 29 7 3 9 59 , 29 7 3 3 3 9 58 →= 28 38 29 7 3 9 58 , 29 7 3 3 3 9 59 →= 28 38 29 7 3 9 59 , 61 7 3 3 3 10 60 →= 62 38 29 7 3 10 60 , 63 7 3 3 3 10 60 →= 64 38 29 7 3 10 60 , 6 7 3 3 3 10 60 →= 65 38 29 7 3 10 60 , 44 7 3 3 3 10 60 →= 43 38 29 7 3 10 60 , 66 7 3 3 3 10 60 →= 67 38 29 7 3 10 60 , 21 7 3 3 3 10 60 →= 68 38 29 7 3 10 60 , 27 7 3 3 3 10 60 →= 69 38 29 7 3 10 60 , 29 7 3 3 3 10 60 →= 28 38 29 7 3 10 60 , 17 18 3 3 3 3 3 →= 39 40 29 7 3 3 3 , 17 18 3 3 3 3 8 →= 39 40 29 7 3 3 8 , 17 18 3 3 3 3 9 →= 39 40 29 7 3 3 9 , 17 18 3 3 3 3 10 →= 39 40 29 7 3 3 10 , 17 18 3 3 3 3 11 →= 39 40 29 7 3 3 11 , 70 18 3 3 3 3 3 →= 71 40 29 7 3 3 3 , 70 18 3 3 3 3 8 →= 71 40 29 7 3 3 8 , 70 18 3 3 3 3 9 →= 71 40 29 7 3 3 9 , 70 18 3 3 3 3 10 →= 71 40 29 7 3 3 10 , 70 18 3 3 3 3 11 →= 71 40 29 7 3 3 11 , 17 18 3 3 3 8 12 →= 39 40 29 7 3 8 12 , 17 18 3 3 3 8 13 →= 39 40 29 7 3 8 13 , 17 18 3 3 3 8 14 →= 39 40 29 7 3 8 14 , 17 18 3 3 3 8 15 →= 39 40 29 7 3 8 15 , 70 18 3 3 3 8 12 →= 71 40 29 7 3 8 12 , 70 18 3 3 3 8 13 →= 71 40 29 7 3 8 13 , 70 18 3 3 3 8 14 →= 71 40 29 7 3 8 14 , 70 18 3 3 3 8 15 →= 71 40 29 7 3 8 15 , 72 24 3 3 3 3 3 →= 73 42 29 7 3 3 3 , 72 24 3 3 3 3 8 →= 73 42 29 7 3 3 8 , 72 24 3 3 3 3 9 →= 73 42 29 7 3 3 9 , 72 24 3 3 3 3 10 →= 73 42 29 7 3 3 10 , 72 24 3 3 3 3 11 →= 73 42 29 7 3 3 11 , 23 24 3 3 3 3 3 →= 41 42 29 7 3 3 3 , 23 24 3 3 3 3 8 →= 41 42 29 7 3 3 8 , 23 24 3 3 3 3 9 →= 41 42 29 7 3 3 9 , 23 24 3 3 3 3 10 →= 41 42 29 7 3 3 10 , 23 24 3 3 3 3 11 →= 41 42 29 7 3 3 11 , 72 24 3 3 3 8 12 →= 73 42 29 7 3 8 12 , 72 24 3 3 3 8 13 →= 73 42 29 7 3 8 13 , 72 24 3 3 3 8 14 →= 73 42 29 7 3 8 14 , 72 24 3 3 3 8 15 →= 73 42 29 7 3 8 15 , 23 24 3 3 3 8 12 →= 41 42 29 7 3 8 12 , 23 24 3 3 3 8 13 →= 41 42 29 7 3 8 13 , 23 24 3 3 3 8 14 →= 41 42 29 7 3 8 14 , 23 24 3 3 3 8 15 →= 41 42 29 7 3 8 15 , 74 53 3 3 3 3 3 →= 75 76 29 7 3 3 3 , 74 53 3 3 3 3 8 →= 75 76 29 7 3 3 8 , 74 53 3 3 3 3 9 →= 75 76 29 7 3 3 9 , 74 53 3 3 3 3 10 →= 75 76 29 7 3 3 10 , 74 53 3 3 3 3 11 →= 75 76 29 7 3 3 11 , 77 53 3 3 3 3 3 →= 78 76 29 7 3 3 3 , 77 53 3 3 3 3 8 →= 78 76 29 7 3 3 8 , 77 53 3 3 3 3 9 →= 78 76 29 7 3 3 9 , 77 53 3 3 3 3 10 →= 78 76 29 7 3 3 10 , 77 53 3 3 3 3 11 →= 78 76 29 7 3 3 11 , 74 53 3 3 3 8 12 →= 75 76 29 7 3 8 12 , 74 53 3 3 3 8 13 →= 75 76 29 7 3 8 13 , 74 53 3 3 3 8 14 →= 75 76 29 7 3 8 14 , 74 53 3 3 3 8 15 →= 75 76 29 7 3 8 15 , 77 53 3 3 3 8 12 →= 78 76 29 7 3 8 12 , 77 53 3 3 3 8 13 →= 78 76 29 7 3 8 13 , 77 53 3 3 3 8 14 →= 78 76 29 7 3 8 14 , 77 53 3 3 3 8 15 →= 78 76 29 7 3 8 15 , 79 55 3 3 3 3 3 →= 80 81 29 7 3 3 3 , 79 55 3 3 3 3 8 →= 80 81 29 7 3 3 8 , 79 55 3 3 3 3 9 →= 80 81 29 7 3 3 9 , 79 55 3 3 3 3 10 →= 80 81 29 7 3 3 10 , 79 55 3 3 3 3 11 →= 80 81 29 7 3 3 11 , 79 55 3 3 3 8 12 →= 80 81 29 7 3 8 12 , 79 55 3 3 3 8 13 →= 80 81 29 7 3 8 13 , 79 55 3 3 3 8 14 →= 80 81 29 7 3 8 14 , 79 55 3 3 3 8 15 →= 80 81 29 7 3 8 15 , 5 6 7 3 3 3 3 →= 82 83 44 7 3 3 3 , 5 6 7 3 3 3 8 →= 82 83 44 7 3 3 8 , 5 6 7 3 3 3 9 →= 82 83 44 7 3 3 9 , 5 6 7 3 3 3 10 →= 82 83 44 7 3 3 10 , 5 6 7 3 3 3 11 →= 82 83 44 7 3 3 11 , 84 6 7 3 3 3 3 →= 85 83 44 7 3 3 3 , 84 6 7 3 3 3 8 →= 85 83 44 7 3 3 8 , 84 6 7 3 3 3 9 →= 85 83 44 7 3 3 9 , 84 6 7 3 3 3 10 →= 85 83 44 7 3 3 10 , 84 6 7 3 3 3 11 →= 85 83 44 7 3 3 11 , 5 6 7 3 3 8 12 →= 82 83 44 7 3 8 12 , 5 6 7 3 3 8 13 →= 82 83 44 7 3 8 13 , 5 6 7 3 3 8 14 →= 82 83 44 7 3 8 14 , 5 6 7 3 3 8 15 →= 82 83 44 7 3 8 15 , 84 6 7 3 3 8 12 →= 85 83 44 7 3 8 12 , 84 6 7 3 3 8 13 →= 85 83 44 7 3 8 13 , 84 6 7 3 3 8 14 →= 85 83 44 7 3 8 14 , 84 6 7 3 3 8 15 →= 85 83 44 7 3 8 15 , 5 6 7 3 3 9 58 →= 82 83 44 7 3 9 58 , 5 6 7 3 3 9 59 →= 82 83 44 7 3 9 59 , 84 6 7 3 3 9 58 →= 85 83 44 7 3 9 58 , 84 6 7 3 3 9 59 →= 85 83 44 7 3 9 59 , 5 6 7 3 3 10 60 →= 82 83 44 7 3 10 60 , 84 6 7 3 3 10 60 →= 85 83 44 7 3 10 60 , 86 21 7 3 3 3 3 →= 87 88 44 7 3 3 3 , 86 21 7 3 3 3 8 →= 87 88 44 7 3 3 8 , 86 21 7 3 3 3 9 →= 87 88 44 7 3 3 9 , 86 21 7 3 3 3 10 →= 87 88 44 7 3 3 10 , 86 21 7 3 3 3 11 →= 87 88 44 7 3 3 11 , 20 21 7 3 3 3 3 →= 89 88 44 7 3 3 3 , 20 21 7 3 3 3 8 →= 89 88 44 7 3 3 8 , 20 21 7 3 3 3 9 →= 89 88 44 7 3 3 9 , 20 21 7 3 3 3 10 →= 89 88 44 7 3 3 10 , 20 21 7 3 3 3 11 →= 89 88 44 7 3 3 11 , 86 21 7 3 3 8 12 →= 87 88 44 7 3 8 12 , 86 21 7 3 3 8 13 →= 87 88 44 7 3 8 13 , 86 21 7 3 3 8 14 →= 87 88 44 7 3 8 14 , 86 21 7 3 3 8 15 →= 87 88 44 7 3 8 15 , 20 21 7 3 3 8 12 →= 89 88 44 7 3 8 12 , 20 21 7 3 3 8 13 →= 89 88 44 7 3 8 13 , 20 21 7 3 3 8 14 →= 89 88 44 7 3 8 14 , 20 21 7 3 3 8 15 →= 89 88 44 7 3 8 15 , 86 21 7 3 3 9 58 →= 87 88 44 7 3 9 58 , 86 21 7 3 3 9 59 →= 87 88 44 7 3 9 59 , 20 21 7 3 3 9 58 →= 89 88 44 7 3 9 58 , 20 21 7 3 3 9 59 →= 89 88 44 7 3 9 59 , 86 21 7 3 3 10 60 →= 87 88 44 7 3 10 60 , 20 21 7 3 3 10 60 →= 89 88 44 7 3 10 60 , 90 27 7 3 3 3 3 →= 91 92 44 7 3 3 3 , 90 27 7 3 3 3 8 →= 91 92 44 7 3 3 8 , 90 27 7 3 3 3 9 →= 91 92 44 7 3 3 9 , 90 27 7 3 3 3 10 →= 91 92 44 7 3 3 10 , 90 27 7 3 3 3 11 →= 91 92 44 7 3 3 11 , 26 27 7 3 3 3 3 →= 93 92 44 7 3 3 3 , 26 27 7 3 3 3 8 →= 93 92 44 7 3 3 8 , 26 27 7 3 3 3 9 →= 93 92 44 7 3 3 9 , 26 27 7 3 3 3 10 →= 93 92 44 7 3 3 10 , 26 27 7 3 3 3 11 →= 93 92 44 7 3 3 11 , 90 27 7 3 3 8 12 →= 91 92 44 7 3 8 12 , 90 27 7 3 3 8 13 →= 91 92 44 7 3 8 13 , 90 27 7 3 3 8 14 →= 91 92 44 7 3 8 14 , 90 27 7 3 3 8 15 →= 91 92 44 7 3 8 15 , 26 27 7 3 3 8 12 →= 93 92 44 7 3 8 12 , 26 27 7 3 3 8 13 →= 93 92 44 7 3 8 13 , 26 27 7 3 3 8 14 →= 93 92 44 7 3 8 14 , 26 27 7 3 3 8 15 →= 93 92 44 7 3 8 15 , 90 27 7 3 3 9 58 →= 91 92 44 7 3 9 58 , 90 27 7 3 3 9 59 →= 91 92 44 7 3 9 59 , 26 27 7 3 3 9 58 →= 93 92 44 7 3 9 58 , 26 27 7 3 3 9 59 →= 93 92 44 7 3 9 59 , 90 27 7 3 3 10 60 →= 91 92 44 7 3 10 60 , 26 27 7 3 3 10 60 →= 93 92 44 7 3 10 60 , 36 29 7 3 3 3 3 →= 94 31 44 7 3 3 3 , 36 29 7 3 3 3 8 →= 94 31 44 7 3 3 8 , 36 29 7 3 3 3 9 →= 94 31 44 7 3 3 9 , 36 29 7 3 3 3 10 →= 94 31 44 7 3 3 10 , 36 29 7 3 3 3 11 →= 94 31 44 7 3 3 11 , 38 29 7 3 3 3 3 →= 37 31 44 7 3 3 3 , 38 29 7 3 3 3 8 →= 37 31 44 7 3 3 8 , 38 29 7 3 3 3 9 →= 37 31 44 7 3 3 9 , 38 29 7 3 3 3 10 →= 37 31 44 7 3 3 10 , 38 29 7 3 3 3 11 →= 37 31 44 7 3 3 11 , 40 29 7 3 3 3 3 →= 95 31 44 7 3 3 3 , 40 29 7 3 3 3 8 →= 95 31 44 7 3 3 8 , 40 29 7 3 3 3 9 →= 95 31 44 7 3 3 9 , 40 29 7 3 3 3 10 →= 95 31 44 7 3 3 10 , 40 29 7 3 3 3 11 →= 95 31 44 7 3 3 11 , 42 29 7 3 3 3 3 →= 96 31 44 7 3 3 3 , 42 29 7 3 3 3 8 →= 96 31 44 7 3 3 8 , 42 29 7 3 3 3 9 →= 96 31 44 7 3 3 9 , 42 29 7 3 3 3 10 →= 96 31 44 7 3 3 10 , 42 29 7 3 3 3 11 →= 96 31 44 7 3 3 11 , 15 29 7 3 3 3 3 →= 12 31 44 7 3 3 3 , 15 29 7 3 3 3 8 →= 12 31 44 7 3 3 8 , 15 29 7 3 3 3 9 →= 12 31 44 7 3 3 9 , 15 29 7 3 3 3 10 →= 12 31 44 7 3 3 10 , 15 29 7 3 3 3 11 →= 12 31 44 7 3 3 11 , 97 29 7 3 3 3 3 →= 98 31 44 7 3 3 3 , 97 29 7 3 3 3 8 →= 98 31 44 7 3 3 8 , 97 29 7 3 3 3 9 →= 98 31 44 7 3 3 9 , 97 29 7 3 3 3 10 →= 98 31 44 7 3 3 10 , 97 29 7 3 3 3 11 →= 98 31 44 7 3 3 11 , 76 29 7 3 3 3 3 →= 99 31 44 7 3 3 3 , 76 29 7 3 3 3 8 →= 99 31 44 7 3 3 8 , 76 29 7 3 3 3 9 →= 99 31 44 7 3 3 9 , 76 29 7 3 3 3 10 →= 99 31 44 7 3 3 10 , 76 29 7 3 3 3 11 →= 99 31 44 7 3 3 11 , 81 29 7 3 3 3 3 →= 100 31 44 7 3 3 3 , 81 29 7 3 3 3 8 →= 100 31 44 7 3 3 8 , 81 29 7 3 3 3 9 →= 100 31 44 7 3 3 9 , 81 29 7 3 3 3 10 →= 100 31 44 7 3 3 10 , 81 29 7 3 3 3 11 →= 100 31 44 7 3 3 11 , 36 29 7 3 3 8 12 →= 94 31 44 7 3 8 12 , 36 29 7 3 3 8 13 →= 94 31 44 7 3 8 13 , 36 29 7 3 3 8 14 →= 94 31 44 7 3 8 14 , 36 29 7 3 3 8 15 →= 94 31 44 7 3 8 15 , 38 29 7 3 3 8 12 →= 37 31 44 7 3 8 12 , 38 29 7 3 3 8 13 →= 37 31 44 7 3 8 13 , 38 29 7 3 3 8 14 →= 37 31 44 7 3 8 14 , 38 29 7 3 3 8 15 →= 37 31 44 7 3 8 15 , 40 29 7 3 3 8 12 →= 95 31 44 7 3 8 12 , 40 29 7 3 3 8 13 →= 95 31 44 7 3 8 13 , 40 29 7 3 3 8 14 →= 95 31 44 7 3 8 14 , 40 29 7 3 3 8 15 →= 95 31 44 7 3 8 15 , 42 29 7 3 3 8 12 →= 96 31 44 7 3 8 12 , 42 29 7 3 3 8 13 →= 96 31 44 7 3 8 13 , 42 29 7 3 3 8 14 →= 96 31 44 7 3 8 14 , 42 29 7 3 3 8 15 →= 96 31 44 7 3 8 15 , 15 29 7 3 3 8 12 →= 12 31 44 7 3 8 12 , 15 29 7 3 3 8 13 →= 12 31 44 7 3 8 13 , 15 29 7 3 3 8 14 →= 12 31 44 7 3 8 14 , 15 29 7 3 3 8 15 →= 12 31 44 7 3 8 15 , 97 29 7 3 3 8 12 →= 98 31 44 7 3 8 12 , 97 29 7 3 3 8 13 →= 98 31 44 7 3 8 13 , 97 29 7 3 3 8 14 →= 98 31 44 7 3 8 14 , 97 29 7 3 3 8 15 →= 98 31 44 7 3 8 15 , 76 29 7 3 3 8 12 →= 99 31 44 7 3 8 12 , 76 29 7 3 3 8 13 →= 99 31 44 7 3 8 13 , 76 29 7 3 3 8 14 →= 99 31 44 7 3 8 14 , 76 29 7 3 3 8 15 →= 99 31 44 7 3 8 15 , 81 29 7 3 3 8 12 →= 100 31 44 7 3 8 12 , 81 29 7 3 3 8 13 →= 100 31 44 7 3 8 13 , 81 29 7 3 3 8 14 →= 100 31 44 7 3 8 14 , 81 29 7 3 3 8 15 →= 100 31 44 7 3 8 15 , 36 29 7 3 3 9 58 →= 94 31 44 7 3 9 58 , 36 29 7 3 3 9 59 →= 94 31 44 7 3 9 59 , 38 29 7 3 3 9 58 →= 37 31 44 7 3 9 58 , 38 29 7 3 3 9 59 →= 37 31 44 7 3 9 59 , 40 29 7 3 3 9 58 →= 95 31 44 7 3 9 58 , 40 29 7 3 3 9 59 →= 95 31 44 7 3 9 59 , 42 29 7 3 3 9 58 →= 96 31 44 7 3 9 58 , 42 29 7 3 3 9 59 →= 96 31 44 7 3 9 59 , 15 29 7 3 3 9 58 →= 12 31 44 7 3 9 58 , 15 29 7 3 3 9 59 →= 12 31 44 7 3 9 59 , 97 29 7 3 3 9 58 →= 98 31 44 7 3 9 58 , 97 29 7 3 3 9 59 →= 98 31 44 7 3 9 59 , 76 29 7 3 3 9 58 →= 99 31 44 7 3 9 58 , 76 29 7 3 3 9 59 →= 99 31 44 7 3 9 59 , 81 29 7 3 3 9 58 →= 100 31 44 7 3 9 58 , 81 29 7 3 3 9 59 →= 100 31 44 7 3 9 59 , 36 29 7 3 3 10 60 →= 94 31 44 7 3 10 60 , 38 29 7 3 3 10 60 →= 37 31 44 7 3 10 60 , 40 29 7 3 3 10 60 →= 95 31 44 7 3 10 60 , 42 29 7 3 3 10 60 →= 96 31 44 7 3 10 60 , 15 29 7 3 3 10 60 →= 12 31 44 7 3 10 60 , 97 29 7 3 3 10 60 →= 98 31 44 7 3 10 60 , 76 29 7 3 3 10 60 →= 99 31 44 7 3 10 60 , 81 29 7 3 3 10 60 →= 100 31 44 7 3 10 60 , 31 44 7 3 3 3 3 →= 32 45 44 7 3 3 3 , 31 44 7 3 3 3 8 →= 32 45 44 7 3 3 8 , 31 44 7 3 3 3 9 →= 32 45 44 7 3 3 9 , 31 44 7 3 3 3 10 →= 32 45 44 7 3 3 10 , 31 44 7 3 3 3 11 →= 32 45 44 7 3 3 11 , 101 44 7 3 3 3 3 →= 102 45 44 7 3 3 3 , 101 44 7 3 3 3 8 →= 102 45 44 7 3 3 8 , 101 44 7 3 3 3 9 →= 102 45 44 7 3 3 9 , 101 44 7 3 3 3 10 →= 102 45 44 7 3 3 10 , 101 44 7 3 3 3 11 →= 102 45 44 7 3 3 11 , 103 44 7 3 3 3 3 →= 104 45 44 7 3 3 3 , 103 44 7 3 3 3 8 →= 104 45 44 7 3 3 8 , 103 44 7 3 3 3 9 →= 104 45 44 7 3 3 9 , 103 44 7 3 3 3 10 →= 104 45 44 7 3 3 10 , 103 44 7 3 3 3 11 →= 104 45 44 7 3 3 11 , 45 44 7 3 3 3 3 →= 46 45 44 7 3 3 3 , 45 44 7 3 3 3 8 →= 46 45 44 7 3 3 8 , 45 44 7 3 3 3 9 →= 46 45 44 7 3 3 9 , 45 44 7 3 3 3 10 →= 46 45 44 7 3 3 10 , 45 44 7 3 3 3 11 →= 46 45 44 7 3 3 11 , 105 44 7 3 3 3 3 →= 106 45 44 7 3 3 3 , 105 44 7 3 3 3 8 →= 106 45 44 7 3 3 8 , 105 44 7 3 3 3 9 →= 106 45 44 7 3 3 9 , 105 44 7 3 3 3 10 →= 106 45 44 7 3 3 10 , 105 44 7 3 3 3 11 →= 106 45 44 7 3 3 11 , 83 44 7 3 3 3 3 →= 107 45 44 7 3 3 3 , 83 44 7 3 3 3 8 →= 107 45 44 7 3 3 8 , 83 44 7 3 3 3 9 →= 107 45 44 7 3 3 9 , 83 44 7 3 3 3 10 →= 107 45 44 7 3 3 10 , 83 44 7 3 3 3 11 →= 107 45 44 7 3 3 11 , 88 44 7 3 3 3 3 →= 108 45 44 7 3 3 3 , 88 44 7 3 3 3 8 →= 108 45 44 7 3 3 8 , 88 44 7 3 3 3 9 →= 108 45 44 7 3 3 9 , 88 44 7 3 3 3 10 →= 108 45 44 7 3 3 10 , 88 44 7 3 3 3 11 →= 108 45 44 7 3 3 11 , 92 44 7 3 3 3 3 →= 109 45 44 7 3 3 3 , 92 44 7 3 3 3 8 →= 109 45 44 7 3 3 8 , 92 44 7 3 3 3 9 →= 109 45 44 7 3 3 9 , 92 44 7 3 3 3 10 →= 109 45 44 7 3 3 10 , 92 44 7 3 3 3 11 →= 109 45 44 7 3 3 11 , 31 44 7 3 3 8 12 →= 32 45 44 7 3 8 12 , 31 44 7 3 3 8 13 →= 32 45 44 7 3 8 13 , 31 44 7 3 3 8 14 →= 32 45 44 7 3 8 14 , 31 44 7 3 3 8 15 →= 32 45 44 7 3 8 15 , 101 44 7 3 3 8 12 →= 102 45 44 7 3 8 12 , 101 44 7 3 3 8 13 →= 102 45 44 7 3 8 13 , 101 44 7 3 3 8 14 →= 102 45 44 7 3 8 14 , 101 44 7 3 3 8 15 →= 102 45 44 7 3 8 15 , 103 44 7 3 3 8 12 →= 104 45 44 7 3 8 12 , 103 44 7 3 3 8 13 →= 104 45 44 7 3 8 13 , 103 44 7 3 3 8 14 →= 104 45 44 7 3 8 14 , 103 44 7 3 3 8 15 →= 104 45 44 7 3 8 15 , 45 44 7 3 3 8 12 →= 46 45 44 7 3 8 12 , 45 44 7 3 3 8 13 →= 46 45 44 7 3 8 13 , 45 44 7 3 3 8 14 →= 46 45 44 7 3 8 14 , 45 44 7 3 3 8 15 →= 46 45 44 7 3 8 15 , 105 44 7 3 3 8 12 →= 106 45 44 7 3 8 12 , 105 44 7 3 3 8 13 →= 106 45 44 7 3 8 13 , 105 44 7 3 3 8 14 →= 106 45 44 7 3 8 14 , 105 44 7 3 3 8 15 →= 106 45 44 7 3 8 15 , 83 44 7 3 3 8 12 →= 107 45 44 7 3 8 12 , 83 44 7 3 3 8 13 →= 107 45 44 7 3 8 13 , 83 44 7 3 3 8 14 →= 107 45 44 7 3 8 14 , 83 44 7 3 3 8 15 →= 107 45 44 7 3 8 15 , 88 44 7 3 3 8 12 →= 108 45 44 7 3 8 12 , 88 44 7 3 3 8 13 →= 108 45 44 7 3 8 13 , 88 44 7 3 3 8 14 →= 108 45 44 7 3 8 14 , 88 44 7 3 3 8 15 →= 108 45 44 7 3 8 15 , 92 44 7 3 3 8 12 →= 109 45 44 7 3 8 12 , 92 44 7 3 3 8 13 →= 109 45 44 7 3 8 13 , 92 44 7 3 3 8 14 →= 109 45 44 7 3 8 14 , 92 44 7 3 3 8 15 →= 109 45 44 7 3 8 15 , 31 44 7 3 3 9 58 →= 32 45 44 7 3 9 58 , 31 44 7 3 3 9 59 →= 32 45 44 7 3 9 59 , 101 44 7 3 3 9 58 →= 102 45 44 7 3 9 58 , 101 44 7 3 3 9 59 →= 102 45 44 7 3 9 59 , 103 44 7 3 3 9 58 →= 104 45 44 7 3 9 58 , 103 44 7 3 3 9 59 →= 104 45 44 7 3 9 59 , 45 44 7 3 3 9 58 →= 46 45 44 7 3 9 58 , 45 44 7 3 3 9 59 →= 46 45 44 7 3 9 59 , 105 44 7 3 3 9 58 →= 106 45 44 7 3 9 58 , 105 44 7 3 3 9 59 →= 106 45 44 7 3 9 59 , 83 44 7 3 3 9 58 →= 107 45 44 7 3 9 58 , 83 44 7 3 3 9 59 →= 107 45 44 7 3 9 59 , 88 44 7 3 3 9 58 →= 108 45 44 7 3 9 58 , 88 44 7 3 3 9 59 →= 108 45 44 7 3 9 59 , 92 44 7 3 3 9 58 →= 109 45 44 7 3 9 58 , 92 44 7 3 3 9 59 →= 109 45 44 7 3 9 59 , 31 44 7 3 3 10 60 →= 32 45 44 7 3 10 60 , 101 44 7 3 3 10 60 →= 102 45 44 7 3 10 60 , 103 44 7 3 3 10 60 →= 104 45 44 7 3 10 60 , 45 44 7 3 3 10 60 →= 46 45 44 7 3 10 60 , 105 44 7 3 3 10 60 →= 106 45 44 7 3 10 60 , 83 44 7 3 3 10 60 →= 107 45 44 7 3 10 60 , 88 44 7 3 3 10 60 →= 108 45 44 7 3 10 60 , 92 44 7 3 3 10 60 →= 109 45 44 7 3 10 60 , 110 61 7 3 3 3 3 →= 111 101 44 7 3 3 3 , 110 61 7 3 3 3 8 →= 111 101 44 7 3 3 8 , 110 61 7 3 3 3 9 →= 111 101 44 7 3 3 9 , 110 61 7 3 3 3 10 →= 111 101 44 7 3 3 10 , 110 61 7 3 3 3 11 →= 111 101 44 7 3 3 11 , 112 61 7 3 3 3 3 →= 113 101 44 7 3 3 3 , 112 61 7 3 3 3 8 →= 113 101 44 7 3 3 8 , 112 61 7 3 3 3 9 →= 113 101 44 7 3 3 9 , 112 61 7 3 3 3 10 →= 113 101 44 7 3 3 10 , 112 61 7 3 3 3 11 →= 113 101 44 7 3 3 11 , 110 61 7 3 3 8 12 →= 111 101 44 7 3 8 12 , 110 61 7 3 3 8 13 →= 111 101 44 7 3 8 13 , 110 61 7 3 3 8 14 →= 111 101 44 7 3 8 14 , 110 61 7 3 3 8 15 →= 111 101 44 7 3 8 15 , 112 61 7 3 3 8 12 →= 113 101 44 7 3 8 12 , 112 61 7 3 3 8 13 →= 113 101 44 7 3 8 13 , 112 61 7 3 3 8 14 →= 113 101 44 7 3 8 14 , 112 61 7 3 3 8 15 →= 113 101 44 7 3 8 15 , 110 61 7 3 3 9 58 →= 111 101 44 7 3 9 58 , 110 61 7 3 3 9 59 →= 111 101 44 7 3 9 59 , 112 61 7 3 3 9 58 →= 113 101 44 7 3 9 58 , 112 61 7 3 3 9 59 →= 113 101 44 7 3 9 59 , 110 61 7 3 3 10 60 →= 111 101 44 7 3 10 60 , 112 61 7 3 3 10 60 →= 113 101 44 7 3 10 60 , 114 63 7 3 3 3 3 →= 115 103 44 7 3 3 3 , 114 63 7 3 3 3 8 →= 115 103 44 7 3 3 8 , 114 63 7 3 3 3 9 →= 115 103 44 7 3 3 9 , 114 63 7 3 3 3 10 →= 115 103 44 7 3 3 10 , 114 63 7 3 3 3 11 →= 115 103 44 7 3 3 11 , 114 63 7 3 3 8 12 →= 115 103 44 7 3 8 12 , 114 63 7 3 3 8 13 →= 115 103 44 7 3 8 13 , 114 63 7 3 3 8 14 →= 115 103 44 7 3 8 14 , 114 63 7 3 3 8 15 →= 115 103 44 7 3 8 15 , 116 74 53 3 3 3 3 →= 117 110 61 7 3 3 3 , 116 74 53 3 3 3 8 →= 117 110 61 7 3 3 8 , 116 74 53 3 3 3 9 →= 117 110 61 7 3 3 9 , 116 74 53 3 3 3 10 →= 117 110 61 7 3 3 10 , 116 74 53 3 3 3 11 →= 117 110 61 7 3 3 11 , 116 74 53 3 3 8 12 →= 117 110 61 7 3 8 12 , 116 74 53 3 3 8 13 →= 117 110 61 7 3 8 13 , 116 74 53 3 3 8 14 →= 117 110 61 7 3 8 14 , 116 74 53 3 3 8 15 →= 117 110 61 7 3 8 15 , 1 2 3 3 8 15 28 →= 35 36 29 7 8 15 28 , 1 2 3 3 8 15 29 →= 35 36 29 7 8 15 29 , 1 2 3 3 8 15 30 →= 35 36 29 7 8 15 30 , 47 2 3 3 8 15 28 →= 48 36 29 7 8 15 28 , 47 2 3 3 8 15 29 →= 48 36 29 7 8 15 29 , 47 2 3 3 8 15 30 →= 48 36 29 7 8 15 30 , 1 2 3 3 8 12 31 →= 35 36 29 7 8 12 31 , 1 2 3 3 8 12 32 →= 35 36 29 7 8 12 32 , 1 2 3 3 8 12 33 →= 35 36 29 7 8 12 33 , 47 2 3 3 8 12 31 →= 48 36 29 7 8 12 31 , 47 2 3 3 8 12 32 →= 48 36 29 7 8 12 32 , 47 2 3 3 8 12 33 →= 48 36 29 7 8 12 33 , 2 3 3 3 8 15 28 →= 49 15 29 7 8 15 28 , 2 3 3 3 8 15 29 →= 49 15 29 7 8 15 29 , 2 3 3 3 8 15 30 →= 49 15 29 7 8 15 30 , 3 3 3 3 8 15 28 →= 8 15 29 7 8 15 28 , 3 3 3 3 8 15 29 →= 8 15 29 7 8 15 29 , 3 3 3 3 8 15 30 →= 8 15 29 7 8 15 30 , 7 3 3 3 8 15 28 →= 34 15 29 7 8 15 28 , 7 3 3 3 8 15 29 →= 34 15 29 7 8 15 29 , 7 3 3 3 8 15 30 →= 34 15 29 7 8 15 30 , 18 3 3 3 8 15 28 →= 50 15 29 7 8 15 28 , 18 3 3 3 8 15 29 →= 50 15 29 7 8 15 29 , 18 3 3 3 8 15 30 →= 50 15 29 7 8 15 30 , 51 3 3 3 8 15 28 →= 52 15 29 7 8 15 28 , 51 3 3 3 8 15 29 →= 52 15 29 7 8 15 29 , 51 3 3 3 8 15 30 →= 52 15 29 7 8 15 30 , 53 3 3 3 8 15 28 →= 54 15 29 7 8 15 28 , 53 3 3 3 8 15 29 →= 54 15 29 7 8 15 29 , 53 3 3 3 8 15 30 →= 54 15 29 7 8 15 30 , 55 3 3 3 8 15 28 →= 56 15 29 7 8 15 28 , 55 3 3 3 8 15 29 →= 56 15 29 7 8 15 29 , 55 3 3 3 8 15 30 →= 56 15 29 7 8 15 30 , 24 3 3 3 8 15 28 →= 57 15 29 7 8 15 28 , 24 3 3 3 8 15 29 →= 57 15 29 7 8 15 29 , 24 3 3 3 8 15 30 →= 57 15 29 7 8 15 30 , 2 3 3 3 8 12 31 →= 49 15 29 7 8 12 31 , 2 3 3 3 8 12 32 →= 49 15 29 7 8 12 32 , 2 3 3 3 8 12 33 →= 49 15 29 7 8 12 33 , 3 3 3 3 8 12 31 →= 8 15 29 7 8 12 31 , 3 3 3 3 8 12 32 →= 8 15 29 7 8 12 32 , 3 3 3 3 8 12 33 →= 8 15 29 7 8 12 33 , 7 3 3 3 8 12 31 →= 34 15 29 7 8 12 31 , 7 3 3 3 8 12 32 →= 34 15 29 7 8 12 32 , 7 3 3 3 8 12 33 →= 34 15 29 7 8 12 33 , 18 3 3 3 8 12 31 →= 50 15 29 7 8 12 31 , 18 3 3 3 8 12 32 →= 50 15 29 7 8 12 32 , 18 3 3 3 8 12 33 →= 50 15 29 7 8 12 33 , 51 3 3 3 8 12 31 →= 52 15 29 7 8 12 31 , 51 3 3 3 8 12 32 →= 52 15 29 7 8 12 32 , 51 3 3 3 8 12 33 →= 52 15 29 7 8 12 33 , 53 3 3 3 8 12 31 →= 54 15 29 7 8 12 31 , 53 3 3 3 8 12 32 →= 54 15 29 7 8 12 32 , 53 3 3 3 8 12 33 →= 54 15 29 7 8 12 33 , 55 3 3 3 8 12 31 →= 56 15 29 7 8 12 31 , 55 3 3 3 8 12 32 →= 56 15 29 7 8 12 32 , 55 3 3 3 8 12 33 →= 56 15 29 7 8 12 33 , 24 3 3 3 8 12 31 →= 57 15 29 7 8 12 31 , 24 3 3 3 8 12 32 →= 57 15 29 7 8 12 32 , 24 3 3 3 8 12 33 →= 57 15 29 7 8 12 33 , 2 3 3 3 8 13 118 →= 49 15 29 7 8 13 118 , 3 3 3 3 8 13 118 →= 8 15 29 7 8 13 118 , 7 3 3 3 8 13 118 →= 34 15 29 7 8 13 118 , 18 3 3 3 8 13 118 →= 50 15 29 7 8 13 118 , 51 3 3 3 8 13 118 →= 52 15 29 7 8 13 118 , 53 3 3 3 8 13 118 →= 54 15 29 7 8 13 118 , 55 3 3 3 8 13 118 →= 56 15 29 7 8 13 118 , 24 3 3 3 8 13 118 →= 57 15 29 7 8 13 118 , 61 7 3 3 8 15 28 →= 62 38 29 7 8 15 28 , 61 7 3 3 8 15 29 →= 62 38 29 7 8 15 29 , 61 7 3 3 8 15 30 →= 62 38 29 7 8 15 30 , 63 7 3 3 8 15 28 →= 64 38 29 7 8 15 28 , 63 7 3 3 8 15 29 →= 64 38 29 7 8 15 29 , 63 7 3 3 8 15 30 →= 64 38 29 7 8 15 30 , 6 7 3 3 8 15 28 →= 65 38 29 7 8 15 28 , 6 7 3 3 8 15 29 →= 65 38 29 7 8 15 29 , 6 7 3 3 8 15 30 →= 65 38 29 7 8 15 30 , 44 7 3 3 8 15 28 →= 43 38 29 7 8 15 28 , 44 7 3 3 8 15 29 →= 43 38 29 7 8 15 29 , 44 7 3 3 8 15 30 →= 43 38 29 7 8 15 30 , 66 7 3 3 8 15 28 →= 67 38 29 7 8 15 28 , 66 7 3 3 8 15 29 →= 67 38 29 7 8 15 29 , 66 7 3 3 8 15 30 →= 67 38 29 7 8 15 30 , 21 7 3 3 8 15 28 →= 68 38 29 7 8 15 28 , 21 7 3 3 8 15 29 →= 68 38 29 7 8 15 29 , 21 7 3 3 8 15 30 →= 68 38 29 7 8 15 30 , 27 7 3 3 8 15 28 →= 69 38 29 7 8 15 28 , 27 7 3 3 8 15 29 →= 69 38 29 7 8 15 29 , 27 7 3 3 8 15 30 →= 69 38 29 7 8 15 30 , 29 7 3 3 8 15 28 →= 28 38 29 7 8 15 28 , 29 7 3 3 8 15 29 →= 28 38 29 7 8 15 29 , 29 7 3 3 8 15 30 →= 28 38 29 7 8 15 30 , 61 7 3 3 8 12 31 →= 62 38 29 7 8 12 31 , 61 7 3 3 8 12 32 →= 62 38 29 7 8 12 32 , 61 7 3 3 8 12 33 →= 62 38 29 7 8 12 33 , 63 7 3 3 8 12 31 →= 64 38 29 7 8 12 31 , 63 7 3 3 8 12 32 →= 64 38 29 7 8 12 32 , 63 7 3 3 8 12 33 →= 64 38 29 7 8 12 33 , 6 7 3 3 8 12 31 →= 65 38 29 7 8 12 31 , 6 7 3 3 8 12 32 →= 65 38 29 7 8 12 32 , 6 7 3 3 8 12 33 →= 65 38 29 7 8 12 33 , 44 7 3 3 8 12 31 →= 43 38 29 7 8 12 31 , 44 7 3 3 8 12 32 →= 43 38 29 7 8 12 32 , 44 7 3 3 8 12 33 →= 43 38 29 7 8 12 33 , 66 7 3 3 8 12 31 →= 67 38 29 7 8 12 31 , 66 7 3 3 8 12 32 →= 67 38 29 7 8 12 32 , 66 7 3 3 8 12 33 →= 67 38 29 7 8 12 33 , 21 7 3 3 8 12 31 →= 68 38 29 7 8 12 31 , 21 7 3 3 8 12 32 →= 68 38 29 7 8 12 32 , 21 7 3 3 8 12 33 →= 68 38 29 7 8 12 33 , 27 7 3 3 8 12 31 →= 69 38 29 7 8 12 31 , 27 7 3 3 8 12 32 →= 69 38 29 7 8 12 32 , 27 7 3 3 8 12 33 →= 69 38 29 7 8 12 33 , 29 7 3 3 8 12 31 →= 28 38 29 7 8 12 31 , 29 7 3 3 8 12 32 →= 28 38 29 7 8 12 32 , 29 7 3 3 8 12 33 →= 28 38 29 7 8 12 33 , 61 7 3 3 8 13 118 →= 62 38 29 7 8 13 118 , 63 7 3 3 8 13 118 →= 64 38 29 7 8 13 118 , 6 7 3 3 8 13 118 →= 65 38 29 7 8 13 118 , 44 7 3 3 8 13 118 →= 43 38 29 7 8 13 118 , 66 7 3 3 8 13 118 →= 67 38 29 7 8 13 118 , 21 7 3 3 8 13 118 →= 68 38 29 7 8 13 118 , 27 7 3 3 8 13 118 →= 69 38 29 7 8 13 118 , 29 7 3 3 8 13 118 →= 28 38 29 7 8 13 118 , 17 18 3 3 8 15 28 →= 39 40 29 7 8 15 28 , 17 18 3 3 8 15 29 →= 39 40 29 7 8 15 29 , 17 18 3 3 8 15 30 →= 39 40 29 7 8 15 30 , 70 18 3 3 8 15 28 →= 71 40 29 7 8 15 28 , 70 18 3 3 8 15 29 →= 71 40 29 7 8 15 29 , 70 18 3 3 8 15 30 →= 71 40 29 7 8 15 30 , 17 18 3 3 8 12 31 →= 39 40 29 7 8 12 31 , 17 18 3 3 8 12 32 →= 39 40 29 7 8 12 32 , 17 18 3 3 8 12 33 →= 39 40 29 7 8 12 33 , 70 18 3 3 8 12 31 →= 71 40 29 7 8 12 31 , 70 18 3 3 8 12 32 →= 71 40 29 7 8 12 32 , 70 18 3 3 8 12 33 →= 71 40 29 7 8 12 33 , 72 24 3 3 8 15 28 →= 73 42 29 7 8 15 28 , 72 24 3 3 8 15 29 →= 73 42 29 7 8 15 29 , 72 24 3 3 8 15 30 →= 73 42 29 7 8 15 30 , 23 24 3 3 8 15 28 →= 41 42 29 7 8 15 28 , 23 24 3 3 8 15 29 →= 41 42 29 7 8 15 29 , 23 24 3 3 8 15 30 →= 41 42 29 7 8 15 30 , 72 24 3 3 8 12 31 →= 73 42 29 7 8 12 31 , 72 24 3 3 8 12 32 →= 73 42 29 7 8 12 32 , 72 24 3 3 8 12 33 →= 73 42 29 7 8 12 33 , 23 24 3 3 8 12 31 →= 41 42 29 7 8 12 31 , 23 24 3 3 8 12 32 →= 41 42 29 7 8 12 32 , 23 24 3 3 8 12 33 →= 41 42 29 7 8 12 33 , 74 53 3 3 8 15 28 →= 75 76 29 7 8 15 28 , 74 53 3 3 8 15 29 →= 75 76 29 7 8 15 29 , 74 53 3 3 8 15 30 →= 75 76 29 7 8 15 30 , 77 53 3 3 8 15 28 →= 78 76 29 7 8 15 28 , 77 53 3 3 8 15 29 →= 78 76 29 7 8 15 29 , 77 53 3 3 8 15 30 →= 78 76 29 7 8 15 30 , 74 53 3 3 8 12 31 →= 75 76 29 7 8 12 31 , 74 53 3 3 8 12 32 →= 75 76 29 7 8 12 32 , 74 53 3 3 8 12 33 →= 75 76 29 7 8 12 33 , 77 53 3 3 8 12 31 →= 78 76 29 7 8 12 31 , 77 53 3 3 8 12 32 →= 78 76 29 7 8 12 32 , 77 53 3 3 8 12 33 →= 78 76 29 7 8 12 33 , 79 55 3 3 8 15 28 →= 80 81 29 7 8 15 28 , 79 55 3 3 8 15 29 →= 80 81 29 7 8 15 29 , 79 55 3 3 8 15 30 →= 80 81 29 7 8 15 30 , 79 55 3 3 8 12 31 →= 80 81 29 7 8 12 31 , 79 55 3 3 8 12 32 →= 80 81 29 7 8 12 32 , 79 55 3 3 8 12 33 →= 80 81 29 7 8 12 33 , 5 6 7 3 8 15 28 →= 82 83 44 7 8 15 28 , 5 6 7 3 8 15 29 →= 82 83 44 7 8 15 29 , 5 6 7 3 8 15 30 →= 82 83 44 7 8 15 30 , 84 6 7 3 8 15 28 →= 85 83 44 7 8 15 28 , 84 6 7 3 8 15 29 →= 85 83 44 7 8 15 29 , 84 6 7 3 8 15 30 →= 85 83 44 7 8 15 30 , 5 6 7 3 8 12 31 →= 82 83 44 7 8 12 31 , 5 6 7 3 8 12 32 →= 82 83 44 7 8 12 32 , 5 6 7 3 8 12 33 →= 82 83 44 7 8 12 33 , 84 6 7 3 8 12 31 →= 85 83 44 7 8 12 31 , 84 6 7 3 8 12 32 →= 85 83 44 7 8 12 32 , 84 6 7 3 8 12 33 →= 85 83 44 7 8 12 33 , 5 6 7 3 8 13 118 →= 82 83 44 7 8 13 118 , 84 6 7 3 8 13 118 →= 85 83 44 7 8 13 118 , 86 21 7 3 8 15 28 →= 87 88 44 7 8 15 28 , 86 21 7 3 8 15 29 →= 87 88 44 7 8 15 29 , 86 21 7 3 8 15 30 →= 87 88 44 7 8 15 30 , 20 21 7 3 8 15 28 →= 89 88 44 7 8 15 28 , 20 21 7 3 8 15 29 →= 89 88 44 7 8 15 29 , 20 21 7 3 8 15 30 →= 89 88 44 7 8 15 30 , 86 21 7 3 8 12 31 →= 87 88 44 7 8 12 31 , 86 21 7 3 8 12 32 →= 87 88 44 7 8 12 32 , 86 21 7 3 8 12 33 →= 87 88 44 7 8 12 33 , 20 21 7 3 8 12 31 →= 89 88 44 7 8 12 31 , 20 21 7 3 8 12 32 →= 89 88 44 7 8 12 32 , 20 21 7 3 8 12 33 →= 89 88 44 7 8 12 33 , 86 21 7 3 8 13 118 →= 87 88 44 7 8 13 118 , 20 21 7 3 8 13 118 →= 89 88 44 7 8 13 118 , 90 27 7 3 8 15 28 →= 91 92 44 7 8 15 28 , 90 27 7 3 8 15 29 →= 91 92 44 7 8 15 29 , 90 27 7 3 8 15 30 →= 91 92 44 7 8 15 30 , 26 27 7 3 8 15 28 →= 93 92 44 7 8 15 28 , 26 27 7 3 8 15 29 →= 93 92 44 7 8 15 29 , 26 27 7 3 8 15 30 →= 93 92 44 7 8 15 30 , 90 27 7 3 8 12 31 →= 91 92 44 7 8 12 31 , 90 27 7 3 8 12 32 →= 91 92 44 7 8 12 32 , 90 27 7 3 8 12 33 →= 91 92 44 7 8 12 33 , 26 27 7 3 8 12 31 →= 93 92 44 7 8 12 31 , 26 27 7 3 8 12 32 →= 93 92 44 7 8 12 32 , 26 27 7 3 8 12 33 →= 93 92 44 7 8 12 33 , 90 27 7 3 8 13 118 →= 91 92 44 7 8 13 118 , 26 27 7 3 8 13 118 →= 93 92 44 7 8 13 118 , 36 29 7 3 8 15 28 →= 94 31 44 7 8 15 28 , 36 29 7 3 8 15 29 →= 94 31 44 7 8 15 29 , 36 29 7 3 8 15 30 →= 94 31 44 7 8 15 30 , 38 29 7 3 8 15 28 →= 37 31 44 7 8 15 28 , 38 29 7 3 8 15 29 →= 37 31 44 7 8 15 29 , 38 29 7 3 8 15 30 →= 37 31 44 7 8 15 30 , 40 29 7 3 8 15 28 →= 95 31 44 7 8 15 28 , 40 29 7 3 8 15 29 →= 95 31 44 7 8 15 29 , 40 29 7 3 8 15 30 →= 95 31 44 7 8 15 30 , 42 29 7 3 8 15 28 →= 96 31 44 7 8 15 28 , 42 29 7 3 8 15 29 →= 96 31 44 7 8 15 29 , 42 29 7 3 8 15 30 →= 96 31 44 7 8 15 30 , 15 29 7 3 8 15 28 →= 12 31 44 7 8 15 28 , 15 29 7 3 8 15 29 →= 12 31 44 7 8 15 29 , 15 29 7 3 8 15 30 →= 12 31 44 7 8 15 30 , 97 29 7 3 8 15 28 →= 98 31 44 7 8 15 28 , 97 29 7 3 8 15 29 →= 98 31 44 7 8 15 29 , 97 29 7 3 8 15 30 →= 98 31 44 7 8 15 30 , 76 29 7 3 8 15 28 →= 99 31 44 7 8 15 28 , 76 29 7 3 8 15 29 →= 99 31 44 7 8 15 29 , 76 29 7 3 8 15 30 →= 99 31 44 7 8 15 30 , 81 29 7 3 8 15 28 →= 100 31 44 7 8 15 28 , 81 29 7 3 8 15 29 →= 100 31 44 7 8 15 29 , 81 29 7 3 8 15 30 →= 100 31 44 7 8 15 30 , 36 29 7 3 8 12 31 →= 94 31 44 7 8 12 31 , 36 29 7 3 8 12 32 →= 94 31 44 7 8 12 32 , 36 29 7 3 8 12 33 →= 94 31 44 7 8 12 33 , 38 29 7 3 8 12 31 →= 37 31 44 7 8 12 31 , 38 29 7 3 8 12 32 →= 37 31 44 7 8 12 32 , 38 29 7 3 8 12 33 →= 37 31 44 7 8 12 33 , 40 29 7 3 8 12 31 →= 95 31 44 7 8 12 31 , 40 29 7 3 8 12 32 →= 95 31 44 7 8 12 32 , 40 29 7 3 8 12 33 →= 95 31 44 7 8 12 33 , 42 29 7 3 8 12 31 →= 96 31 44 7 8 12 31 , 42 29 7 3 8 12 32 →= 96 31 44 7 8 12 32 , 42 29 7 3 8 12 33 →= 96 31 44 7 8 12 33 , 15 29 7 3 8 12 31 →= 12 31 44 7 8 12 31 , 15 29 7 3 8 12 32 →= 12 31 44 7 8 12 32 , 15 29 7 3 8 12 33 →= 12 31 44 7 8 12 33 , 97 29 7 3 8 12 31 →= 98 31 44 7 8 12 31 , 97 29 7 3 8 12 32 →= 98 31 44 7 8 12 32 , 97 29 7 3 8 12 33 →= 98 31 44 7 8 12 33 , 76 29 7 3 8 12 31 →= 99 31 44 7 8 12 31 , 76 29 7 3 8 12 32 →= 99 31 44 7 8 12 32 , 76 29 7 3 8 12 33 →= 99 31 44 7 8 12 33 , 81 29 7 3 8 12 31 →= 100 31 44 7 8 12 31 , 81 29 7 3 8 12 32 →= 100 31 44 7 8 12 32 , 81 29 7 3 8 12 33 →= 100 31 44 7 8 12 33 , 36 29 7 3 8 13 118 →= 94 31 44 7 8 13 118 , 38 29 7 3 8 13 118 →= 37 31 44 7 8 13 118 , 40 29 7 3 8 13 118 →= 95 31 44 7 8 13 118 , 42 29 7 3 8 13 118 →= 96 31 44 7 8 13 118 , 15 29 7 3 8 13 118 →= 12 31 44 7 8 13 118 , 97 29 7 3 8 13 118 →= 98 31 44 7 8 13 118 , 76 29 7 3 8 13 118 →= 99 31 44 7 8 13 118 , 81 29 7 3 8 13 118 →= 100 31 44 7 8 13 118 , 31 44 7 3 8 15 28 →= 32 45 44 7 8 15 28 , 31 44 7 3 8 15 29 →= 32 45 44 7 8 15 29 , 31 44 7 3 8 15 30 →= 32 45 44 7 8 15 30 , 101 44 7 3 8 15 28 →= 102 45 44 7 8 15 28 , 101 44 7 3 8 15 29 →= 102 45 44 7 8 15 29 , 101 44 7 3 8 15 30 →= 102 45 44 7 8 15 30 , 103 44 7 3 8 15 28 →= 104 45 44 7 8 15 28 , 103 44 7 3 8 15 29 →= 104 45 44 7 8 15 29 , 103 44 7 3 8 15 30 →= 104 45 44 7 8 15 30 , 45 44 7 3 8 15 28 →= 46 45 44 7 8 15 28 , 45 44 7 3 8 15 29 →= 46 45 44 7 8 15 29 , 45 44 7 3 8 15 30 →= 46 45 44 7 8 15 30 , 105 44 7 3 8 15 28 →= 106 45 44 7 8 15 28 , 105 44 7 3 8 15 29 →= 106 45 44 7 8 15 29 , 105 44 7 3 8 15 30 →= 106 45 44 7 8 15 30 , 83 44 7 3 8 15 28 →= 107 45 44 7 8 15 28 , 83 44 7 3 8 15 29 →= 107 45 44 7 8 15 29 , 83 44 7 3 8 15 30 →= 107 45 44 7 8 15 30 , 88 44 7 3 8 15 28 →= 108 45 44 7 8 15 28 , 88 44 7 3 8 15 29 →= 108 45 44 7 8 15 29 , 88 44 7 3 8 15 30 →= 108 45 44 7 8 15 30 , 92 44 7 3 8 15 28 →= 109 45 44 7 8 15 28 , 92 44 7 3 8 15 29 →= 109 45 44 7 8 15 29 , 92 44 7 3 8 15 30 →= 109 45 44 7 8 15 30 , 31 44 7 3 8 12 31 →= 32 45 44 7 8 12 31 , 31 44 7 3 8 12 32 →= 32 45 44 7 8 12 32 , 31 44 7 3 8 12 33 →= 32 45 44 7 8 12 33 , 101 44 7 3 8 12 31 →= 102 45 44 7 8 12 31 , 101 44 7 3 8 12 32 →= 102 45 44 7 8 12 32 , 101 44 7 3 8 12 33 →= 102 45 44 7 8 12 33 , 103 44 7 3 8 12 31 →= 104 45 44 7 8 12 31 , 103 44 7 3 8 12 32 →= 104 45 44 7 8 12 32 , 103 44 7 3 8 12 33 →= 104 45 44 7 8 12 33 , 45 44 7 3 8 12 31 →= 46 45 44 7 8 12 31 , 45 44 7 3 8 12 32 →= 46 45 44 7 8 12 32 , 45 44 7 3 8 12 33 →= 46 45 44 7 8 12 33 , 105 44 7 3 8 12 31 →= 106 45 44 7 8 12 31 , 105 44 7 3 8 12 32 →= 106 45 44 7 8 12 32 , 105 44 7 3 8 12 33 →= 106 45 44 7 8 12 33 , 83 44 7 3 8 12 31 →= 107 45 44 7 8 12 31 , 83 44 7 3 8 12 32 →= 107 45 44 7 8 12 32 , 83 44 7 3 8 12 33 →= 107 45 44 7 8 12 33 , 88 44 7 3 8 12 31 →= 108 45 44 7 8 12 31 , 88 44 7 3 8 12 32 →= 108 45 44 7 8 12 32 , 88 44 7 3 8 12 33 →= 108 45 44 7 8 12 33 , 92 44 7 3 8 12 31 →= 109 45 44 7 8 12 31 , 92 44 7 3 8 12 32 →= 109 45 44 7 8 12 32 , 92 44 7 3 8 12 33 →= 109 45 44 7 8 12 33 , 31 44 7 3 8 13 118 →= 32 45 44 7 8 13 118 , 101 44 7 3 8 13 118 →= 102 45 44 7 8 13 118 , 103 44 7 3 8 13 118 →= 104 45 44 7 8 13 118 , 45 44 7 3 8 13 118 →= 46 45 44 7 8 13 118 , 105 44 7 3 8 13 118 →= 106 45 44 7 8 13 118 , 83 44 7 3 8 13 118 →= 107 45 44 7 8 13 118 , 88 44 7 3 8 13 118 →= 108 45 44 7 8 13 118 , 92 44 7 3 8 13 118 →= 109 45 44 7 8 13 118 , 110 61 7 3 8 15 28 →= 111 101 44 7 8 15 28 , 110 61 7 3 8 15 29 →= 111 101 44 7 8 15 29 , 110 61 7 3 8 15 30 →= 111 101 44 7 8 15 30 , 112 61 7 3 8 15 28 →= 113 101 44 7 8 15 28 , 112 61 7 3 8 15 29 →= 113 101 44 7 8 15 29 , 112 61 7 3 8 15 30 →= 113 101 44 7 8 15 30 , 110 61 7 3 8 12 31 →= 111 101 44 7 8 12 31 , 110 61 7 3 8 12 32 →= 111 101 44 7 8 12 32 , 110 61 7 3 8 12 33 →= 111 101 44 7 8 12 33 , 112 61 7 3 8 12 31 →= 113 101 44 7 8 12 31 , 112 61 7 3 8 12 32 →= 113 101 44 7 8 12 32 , 112 61 7 3 8 12 33 →= 113 101 44 7 8 12 33 , 110 61 7 3 8 13 118 →= 111 101 44 7 8 13 118 , 112 61 7 3 8 13 118 →= 113 101 44 7 8 13 118 , 114 63 7 3 8 15 28 →= 115 103 44 7 8 15 28 , 114 63 7 3 8 15 29 →= 115 103 44 7 8 15 29 , 114 63 7 3 8 15 30 →= 115 103 44 7 8 15 30 , 114 63 7 3 8 12 31 →= 115 103 44 7 8 12 31 , 114 63 7 3 8 12 32 →= 115 103 44 7 8 12 32 , 114 63 7 3 8 12 33 →= 115 103 44 7 8 12 33 , 116 74 53 3 8 15 28 →= 117 110 61 7 8 15 28 , 116 74 53 3 8 15 29 →= 117 110 61 7 8 15 29 , 116 74 53 3 8 15 30 →= 117 110 61 7 8 15 30 , 116 74 53 3 8 12 31 →= 117 110 61 7 8 12 31 , 116 74 53 3 8 12 32 →= 117 110 61 7 8 12 32 , 116 74 53 3 8 12 33 →= 117 110 61 7 8 12 33 , 2 3 3 3 9 58 119 →= 49 15 29 7 9 58 119 , 3 3 3 3 9 58 119 →= 8 15 29 7 9 58 119 , 7 3 3 3 9 58 119 →= 34 15 29 7 9 58 119 , 18 3 3 3 9 58 119 →= 50 15 29 7 9 58 119 , 51 3 3 3 9 58 119 →= 52 15 29 7 9 58 119 , 53 3 3 3 9 58 119 →= 54 15 29 7 9 58 119 , 55 3 3 3 9 58 119 →= 56 15 29 7 9 58 119 , 24 3 3 3 9 58 119 →= 57 15 29 7 9 58 119 , 61 7 3 3 9 58 119 →= 62 38 29 7 9 58 119 , 63 7 3 3 9 58 119 →= 64 38 29 7 9 58 119 , 6 7 3 3 9 58 119 →= 65 38 29 7 9 58 119 , 44 7 3 3 9 58 119 →= 43 38 29 7 9 58 119 , 66 7 3 3 9 58 119 →= 67 38 29 7 9 58 119 , 21 7 3 3 9 58 119 →= 68 38 29 7 9 58 119 , 27 7 3 3 9 58 119 →= 69 38 29 7 9 58 119 , 29 7 3 3 9 58 119 →= 28 38 29 7 9 58 119 , 36 29 7 3 9 58 119 →= 94 31 44 7 9 58 119 , 38 29 7 3 9 58 119 →= 37 31 44 7 9 58 119 , 40 29 7 3 9 58 119 →= 95 31 44 7 9 58 119 , 42 29 7 3 9 58 119 →= 96 31 44 7 9 58 119 , 15 29 7 3 9 58 119 →= 12 31 44 7 9 58 119 , 97 29 7 3 9 58 119 →= 98 31 44 7 9 58 119 , 76 29 7 3 9 58 119 →= 99 31 44 7 9 58 119 , 81 29 7 3 9 58 119 →= 100 31 44 7 9 58 119 , 31 44 7 3 9 58 119 →= 32 45 44 7 9 58 119 , 101 44 7 3 9 58 119 →= 102 45 44 7 9 58 119 , 103 44 7 3 9 58 119 →= 104 45 44 7 9 58 119 , 45 44 7 3 9 58 119 →= 46 45 44 7 9 58 119 , 105 44 7 3 9 58 119 →= 106 45 44 7 9 58 119 , 83 44 7 3 9 58 119 →= 107 45 44 7 9 58 119 , 88 44 7 3 9 58 119 →= 108 45 44 7 9 58 119 , 92 44 7 3 9 58 119 →= 109 45 44 7 9 58 119 , 35 36 29 34 15 29 7 →= 1 49 15 29 7 3 3 , 35 36 29 34 15 29 34 →= 1 49 15 29 7 3 8 , 48 36 29 34 15 29 7 →= 47 49 15 29 7 3 3 , 48 36 29 34 15 29 34 →= 47 49 15 29 7 3 8 , 35 36 29 34 15 28 37 →= 1 49 15 29 7 8 12 , 35 36 29 34 15 28 38 →= 1 49 15 29 7 8 15 , 48 36 29 34 15 28 37 →= 47 49 15 29 7 8 12 , 48 36 29 34 15 28 38 →= 47 49 15 29 7 8 15 , 49 15 29 34 15 29 7 →= 2 8 15 29 7 3 3 , 49 15 29 34 15 29 34 →= 2 8 15 29 7 3 8 , 8 15 29 34 15 29 7 →= 3 8 15 29 7 3 3 , 8 15 29 34 15 29 34 →= 3 8 15 29 7 3 8 , 34 15 29 34 15 29 7 →= 7 8 15 29 7 3 3 , 34 15 29 34 15 29 34 →= 7 8 15 29 7 3 8 , 50 15 29 34 15 29 7 →= 18 8 15 29 7 3 3 , 50 15 29 34 15 29 34 →= 18 8 15 29 7 3 8 , 52 15 29 34 15 29 7 →= 51 8 15 29 7 3 3 , 52 15 29 34 15 29 34 →= 51 8 15 29 7 3 8 , 54 15 29 34 15 29 7 →= 53 8 15 29 7 3 3 , 54 15 29 34 15 29 34 →= 53 8 15 29 7 3 8 , 56 15 29 34 15 29 7 →= 55 8 15 29 7 3 3 , 56 15 29 34 15 29 34 →= 55 8 15 29 7 3 8 , 57 15 29 34 15 29 7 →= 24 8 15 29 7 3 3 , 57 15 29 34 15 29 34 →= 24 8 15 29 7 3 8 , 49 15 29 34 15 28 37 →= 2 8 15 29 7 8 12 , 49 15 29 34 15 28 38 →= 2 8 15 29 7 8 15 , 8 15 29 34 15 28 37 →= 3 8 15 29 7 8 12 , 8 15 29 34 15 28 38 →= 3 8 15 29 7 8 15 , 34 15 29 34 15 28 37 →= 7 8 15 29 7 8 12 , 34 15 29 34 15 28 38 →= 7 8 15 29 7 8 15 , 50 15 29 34 15 28 37 →= 18 8 15 29 7 8 12 , 50 15 29 34 15 28 38 →= 18 8 15 29 7 8 15 , 52 15 29 34 15 28 37 →= 51 8 15 29 7 8 12 , 52 15 29 34 15 28 38 →= 51 8 15 29 7 8 15 , 54 15 29 34 15 28 37 →= 53 8 15 29 7 8 12 , 54 15 29 34 15 28 38 →= 53 8 15 29 7 8 15 , 56 15 29 34 15 28 37 →= 55 8 15 29 7 8 12 , 56 15 29 34 15 28 38 →= 55 8 15 29 7 8 15 , 57 15 29 34 15 28 37 →= 24 8 15 29 7 8 12 , 57 15 29 34 15 28 38 →= 24 8 15 29 7 8 15 , 62 38 29 34 15 29 7 →= 61 34 15 29 7 3 3 , 62 38 29 34 15 29 34 →= 61 34 15 29 7 3 8 , 64 38 29 34 15 29 7 →= 63 34 15 29 7 3 3 , 64 38 29 34 15 29 34 →= 63 34 15 29 7 3 8 , 65 38 29 34 15 29 7 →= 6 34 15 29 7 3 3 , 65 38 29 34 15 29 34 →= 6 34 15 29 7 3 8 , 43 38 29 34 15 29 7 →= 44 34 15 29 7 3 3 , 43 38 29 34 15 29 34 →= 44 34 15 29 7 3 8 , 67 38 29 34 15 29 7 →= 66 34 15 29 7 3 3 , 67 38 29 34 15 29 34 →= 66 34 15 29 7 3 8 , 68 38 29 34 15 29 7 →= 21 34 15 29 7 3 3 , 68 38 29 34 15 29 34 →= 21 34 15 29 7 3 8 , 69 38 29 34 15 29 7 →= 27 34 15 29 7 3 3 , 69 38 29 34 15 29 34 →= 27 34 15 29 7 3 8 , 28 38 29 34 15 29 7 →= 29 34 15 29 7 3 3 , 28 38 29 34 15 29 34 →= 29 34 15 29 7 3 8 , 62 38 29 34 15 28 37 →= 61 34 15 29 7 8 12 , 62 38 29 34 15 28 38 →= 61 34 15 29 7 8 15 , 64 38 29 34 15 28 37 →= 63 34 15 29 7 8 12 , 64 38 29 34 15 28 38 →= 63 34 15 29 7 8 15 , 65 38 29 34 15 28 37 →= 6 34 15 29 7 8 12 , 65 38 29 34 15 28 38 →= 6 34 15 29 7 8 15 , 43 38 29 34 15 28 37 →= 44 34 15 29 7 8 12 , 43 38 29 34 15 28 38 →= 44 34 15 29 7 8 15 , 67 38 29 34 15 28 37 →= 66 34 15 29 7 8 12 , 67 38 29 34 15 28 38 →= 66 34 15 29 7 8 15 , 68 38 29 34 15 28 37 →= 21 34 15 29 7 8 12 , 68 38 29 34 15 28 38 →= 21 34 15 29 7 8 15 , 69 38 29 34 15 28 37 →= 27 34 15 29 7 8 12 , 69 38 29 34 15 28 38 →= 27 34 15 29 7 8 15 , 28 38 29 34 15 28 37 →= 29 34 15 29 7 8 12 , 28 38 29 34 15 28 38 →= 29 34 15 29 7 8 15 , 39 40 29 34 15 29 7 →= 17 50 15 29 7 3 3 , 39 40 29 34 15 29 34 →= 17 50 15 29 7 3 8 , 71 40 29 34 15 29 7 →= 70 50 15 29 7 3 3 , 71 40 29 34 15 29 34 →= 70 50 15 29 7 3 8 , 39 40 29 34 15 28 37 →= 17 50 15 29 7 8 12 , 39 40 29 34 15 28 38 →= 17 50 15 29 7 8 15 , 71 40 29 34 15 28 37 →= 70 50 15 29 7 8 12 , 71 40 29 34 15 28 38 →= 70 50 15 29 7 8 15 , 73 42 29 34 15 29 7 →= 72 57 15 29 7 3 3 , 73 42 29 34 15 29 34 →= 72 57 15 29 7 3 8 , 41 42 29 34 15 29 7 →= 23 57 15 29 7 3 3 , 41 42 29 34 15 29 34 →= 23 57 15 29 7 3 8 , 73 42 29 34 15 28 37 →= 72 57 15 29 7 8 12 , 73 42 29 34 15 28 38 →= 72 57 15 29 7 8 15 , 41 42 29 34 15 28 37 →= 23 57 15 29 7 8 12 , 41 42 29 34 15 28 38 →= 23 57 15 29 7 8 15 , 75 76 29 34 15 29 7 →= 74 54 15 29 7 3 3 , 75 76 29 34 15 29 34 →= 74 54 15 29 7 3 8 , 78 76 29 34 15 29 7 →= 77 54 15 29 7 3 3 , 78 76 29 34 15 29 34 →= 77 54 15 29 7 3 8 , 75 76 29 34 15 28 37 →= 74 54 15 29 7 8 12 , 75 76 29 34 15 28 38 →= 74 54 15 29 7 8 15 , 78 76 29 34 15 28 37 →= 77 54 15 29 7 8 12 , 78 76 29 34 15 28 38 →= 77 54 15 29 7 8 15 , 80 81 29 34 15 29 7 →= 79 56 15 29 7 3 3 , 80 81 29 34 15 29 34 →= 79 56 15 29 7 3 8 , 80 81 29 34 15 28 37 →= 79 56 15 29 7 8 12 , 80 81 29 34 15 28 38 →= 79 56 15 29 7 8 15 , 82 83 44 34 15 29 7 →= 5 65 38 29 7 3 3 , 82 83 44 34 15 29 34 →= 5 65 38 29 7 3 8 , 85 83 44 34 15 29 7 →= 84 65 38 29 7 3 3 , 85 83 44 34 15 29 34 →= 84 65 38 29 7 3 8 , 82 83 44 34 15 28 37 →= 5 65 38 29 7 8 12 , 82 83 44 34 15 28 38 →= 5 65 38 29 7 8 15 , 85 83 44 34 15 28 37 →= 84 65 38 29 7 8 12 , 85 83 44 34 15 28 38 →= 84 65 38 29 7 8 15 , 87 88 44 34 15 29 7 →= 86 68 38 29 7 3 3 , 87 88 44 34 15 29 34 →= 86 68 38 29 7 3 8 , 89 88 44 34 15 29 7 →= 20 68 38 29 7 3 3 , 89 88 44 34 15 29 34 →= 20 68 38 29 7 3 8 , 87 88 44 34 15 28 37 →= 86 68 38 29 7 8 12 , 87 88 44 34 15 28 38 →= 86 68 38 29 7 8 15 , 89 88 44 34 15 28 37 →= 20 68 38 29 7 8 12 , 89 88 44 34 15 28 38 →= 20 68 38 29 7 8 15 , 91 92 44 34 15 29 7 →= 90 69 38 29 7 3 3 , 91 92 44 34 15 29 34 →= 90 69 38 29 7 3 8 , 93 92 44 34 15 29 7 →= 26 69 38 29 7 3 3 , 93 92 44 34 15 29 34 →= 26 69 38 29 7 3 8 , 91 92 44 34 15 28 37 →= 90 69 38 29 7 8 12 , 91 92 44 34 15 28 38 →= 90 69 38 29 7 8 15 , 93 92 44 34 15 28 37 →= 26 69 38 29 7 8 12 , 93 92 44 34 15 28 38 →= 26 69 38 29 7 8 15 , 94 31 44 34 15 29 7 →= 36 28 38 29 7 3 3 , 94 31 44 34 15 29 34 →= 36 28 38 29 7 3 8 , 37 31 44 34 15 29 7 →= 38 28 38 29 7 3 3 , 37 31 44 34 15 29 34 →= 38 28 38 29 7 3 8 , 95 31 44 34 15 29 7 →= 40 28 38 29 7 3 3 , 95 31 44 34 15 29 34 →= 40 28 38 29 7 3 8 , 96 31 44 34 15 29 7 →= 42 28 38 29 7 3 3 , 96 31 44 34 15 29 34 →= 42 28 38 29 7 3 8 , 12 31 44 34 15 29 7 →= 15 28 38 29 7 3 3 , 12 31 44 34 15 29 34 →= 15 28 38 29 7 3 8 , 98 31 44 34 15 29 7 →= 97 28 38 29 7 3 3 , 98 31 44 34 15 29 34 →= 97 28 38 29 7 3 8 , 99 31 44 34 15 29 7 →= 76 28 38 29 7 3 3 , 99 31 44 34 15 29 34 →= 76 28 38 29 7 3 8 , 100 31 44 34 15 29 7 →= 81 28 38 29 7 3 3 , 100 31 44 34 15 29 34 →= 81 28 38 29 7 3 8 , 94 31 44 34 15 28 37 →= 36 28 38 29 7 8 12 , 94 31 44 34 15 28 38 →= 36 28 38 29 7 8 15 , 37 31 44 34 15 28 37 →= 38 28 38 29 7 8 12 , 37 31 44 34 15 28 38 →= 38 28 38 29 7 8 15 , 95 31 44 34 15 28 37 →= 40 28 38 29 7 8 12 , 95 31 44 34 15 28 38 →= 40 28 38 29 7 8 15 , 96 31 44 34 15 28 37 →= 42 28 38 29 7 8 12 , 96 31 44 34 15 28 38 →= 42 28 38 29 7 8 15 , 12 31 44 34 15 28 37 →= 15 28 38 29 7 8 12 , 12 31 44 34 15 28 38 →= 15 28 38 29 7 8 15 , 98 31 44 34 15 28 37 →= 97 28 38 29 7 8 12 , 98 31 44 34 15 28 38 →= 97 28 38 29 7 8 15 , 99 31 44 34 15 28 37 →= 76 28 38 29 7 8 12 , 99 31 44 34 15 28 38 →= 76 28 38 29 7 8 15 , 100 31 44 34 15 28 37 →= 81 28 38 29 7 8 12 , 100 31 44 34 15 28 38 →= 81 28 38 29 7 8 15 , 32 45 44 34 15 29 7 →= 31 43 38 29 7 3 3 , 32 45 44 34 15 29 34 →= 31 43 38 29 7 3 8 , 102 45 44 34 15 29 7 →= 101 43 38 29 7 3 3 , 102 45 44 34 15 29 34 →= 101 43 38 29 7 3 8 , 104 45 44 34 15 29 7 →= 103 43 38 29 7 3 3 , 104 45 44 34 15 29 34 →= 103 43 38 29 7 3 8 , 46 45 44 34 15 29 7 →= 45 43 38 29 7 3 3 , 46 45 44 34 15 29 34 →= 45 43 38 29 7 3 8 , 106 45 44 34 15 29 7 →= 105 43 38 29 7 3 3 , 106 45 44 34 15 29 34 →= 105 43 38 29 7 3 8 , 107 45 44 34 15 29 7 →= 83 43 38 29 7 3 3 , 107 45 44 34 15 29 34 →= 83 43 38 29 7 3 8 , 108 45 44 34 15 29 7 →= 88 43 38 29 7 3 3 , 108 45 44 34 15 29 34 →= 88 43 38 29 7 3 8 , 109 45 44 34 15 29 7 →= 92 43 38 29 7 3 3 , 109 45 44 34 15 29 34 →= 92 43 38 29 7 3 8 , 32 45 44 34 15 28 37 →= 31 43 38 29 7 8 12 , 32 45 44 34 15 28 38 →= 31 43 38 29 7 8 15 , 102 45 44 34 15 28 37 →= 101 43 38 29 7 8 12 , 102 45 44 34 15 28 38 →= 101 43 38 29 7 8 15 , 104 45 44 34 15 28 37 →= 103 43 38 29 7 8 12 , 104 45 44 34 15 28 38 →= 103 43 38 29 7 8 15 , 46 45 44 34 15 28 37 →= 45 43 38 29 7 8 12 , 46 45 44 34 15 28 38 →= 45 43 38 29 7 8 15 , 106 45 44 34 15 28 37 →= 105 43 38 29 7 8 12 , 106 45 44 34 15 28 38 →= 105 43 38 29 7 8 15 , 107 45 44 34 15 28 37 →= 83 43 38 29 7 8 12 , 107 45 44 34 15 28 38 →= 83 43 38 29 7 8 15 , 108 45 44 34 15 28 37 →= 88 43 38 29 7 8 12 , 108 45 44 34 15 28 38 →= 88 43 38 29 7 8 15 , 109 45 44 34 15 28 37 →= 92 43 38 29 7 8 12 , 109 45 44 34 15 28 38 →= 92 43 38 29 7 8 15 , 111 101 44 34 15 29 7 →= 110 62 38 29 7 3 3 , 111 101 44 34 15 29 34 →= 110 62 38 29 7 3 8 , 113 101 44 34 15 29 7 →= 112 62 38 29 7 3 3 , 113 101 44 34 15 29 34 →= 112 62 38 29 7 3 8 , 111 101 44 34 15 28 37 →= 110 62 38 29 7 8 12 , 111 101 44 34 15 28 38 →= 110 62 38 29 7 8 15 , 113 101 44 34 15 28 37 →= 112 62 38 29 7 8 12 , 113 101 44 34 15 28 38 →= 112 62 38 29 7 8 15 , 115 103 44 34 15 29 7 →= 114 64 38 29 7 3 3 , 115 103 44 34 15 29 34 →= 114 64 38 29 7 3 8 , 115 103 44 34 15 28 37 →= 114 64 38 29 7 8 12 , 115 103 44 34 15 28 38 →= 114 64 38 29 7 8 15 , 117 110 61 34 15 29 7 →= 116 75 76 29 7 3 3 , 117 110 61 34 15 29 34 →= 116 75 76 29 7 3 8 , 117 110 61 34 15 28 37 →= 116 75 76 29 7 8 12 , 117 110 61 34 15 28 38 →= 116 75 76 29 7 8 15 , 35 36 29 34 12 31 43 →= 1 49 15 29 34 15 28 , 35 36 29 34 12 31 44 →= 1 49 15 29 34 15 29 , 48 36 29 34 12 31 43 →= 47 49 15 29 34 15 28 , 48 36 29 34 12 31 44 →= 47 49 15 29 34 15 29 , 35 36 29 34 12 32 45 →= 1 49 15 29 34 12 31 , 35 36 29 34 12 32 46 →= 1 49 15 29 34 12 32 , 48 36 29 34 12 32 45 →= 47 49 15 29 34 12 31 , 48 36 29 34 12 32 46 →= 47 49 15 29 34 12 32 , 49 15 29 34 12 31 43 →= 2 8 15 29 34 15 28 , 49 15 29 34 12 31 44 →= 2 8 15 29 34 15 29 , 8 15 29 34 12 31 43 →= 3 8 15 29 34 15 28 , 8 15 29 34 12 31 44 →= 3 8 15 29 34 15 29 , 34 15 29 34 12 31 43 →= 7 8 15 29 34 15 28 , 34 15 29 34 12 31 44 →= 7 8 15 29 34 15 29 , 50 15 29 34 12 31 43 →= 18 8 15 29 34 15 28 , 50 15 29 34 12 31 44 →= 18 8 15 29 34 15 29 , 52 15 29 34 12 31 43 →= 51 8 15 29 34 15 28 , 52 15 29 34 12 31 44 →= 51 8 15 29 34 15 29 , 54 15 29 34 12 31 43 →= 53 8 15 29 34 15 28 , 54 15 29 34 12 31 44 →= 53 8 15 29 34 15 29 , 56 15 29 34 12 31 43 →= 55 8 15 29 34 15 28 , 56 15 29 34 12 31 44 →= 55 8 15 29 34 15 29 , 57 15 29 34 12 31 43 →= 24 8 15 29 34 15 28 , 57 15 29 34 12 31 44 →= 24 8 15 29 34 15 29 , 49 15 29 34 12 32 45 →= 2 8 15 29 34 12 31 , 49 15 29 34 12 32 46 →= 2 8 15 29 34 12 32 , 8 15 29 34 12 32 45 →= 3 8 15 29 34 12 31 , 8 15 29 34 12 32 46 →= 3 8 15 29 34 12 32 , 34 15 29 34 12 32 45 →= 7 8 15 29 34 12 31 , 34 15 29 34 12 32 46 →= 7 8 15 29 34 12 32 , 50 15 29 34 12 32 45 →= 18 8 15 29 34 12 31 , 50 15 29 34 12 32 46 →= 18 8 15 29 34 12 32 , 52 15 29 34 12 32 45 →= 51 8 15 29 34 12 31 , 52 15 29 34 12 32 46 →= 51 8 15 29 34 12 32 , 54 15 29 34 12 32 45 →= 53 8 15 29 34 12 31 , 54 15 29 34 12 32 46 →= 53 8 15 29 34 12 32 , 56 15 29 34 12 32 45 →= 55 8 15 29 34 12 31 , 56 15 29 34 12 32 46 →= 55 8 15 29 34 12 32 , 57 15 29 34 12 32 45 →= 24 8 15 29 34 12 31 , 57 15 29 34 12 32 46 →= 24 8 15 29 34 12 32 , 62 38 29 34 12 31 43 →= 61 34 15 29 34 15 28 , 62 38 29 34 12 31 44 →= 61 34 15 29 34 15 29 , 64 38 29 34 12 31 43 →= 63 34 15 29 34 15 28 , 64 38 29 34 12 31 44 →= 63 34 15 29 34 15 29 , 65 38 29 34 12 31 43 →= 6 34 15 29 34 15 28 , 65 38 29 34 12 31 44 →= 6 34 15 29 34 15 29 , 43 38 29 34 12 31 43 →= 44 34 15 29 34 15 28 , 43 38 29 34 12 31 44 →= 44 34 15 29 34 15 29 , 67 38 29 34 12 31 43 →= 66 34 15 29 34 15 28 , 67 38 29 34 12 31 44 →= 66 34 15 29 34 15 29 , 68 38 29 34 12 31 43 →= 21 34 15 29 34 15 28 , 68 38 29 34 12 31 44 →= 21 34 15 29 34 15 29 , 69 38 29 34 12 31 43 →= 27 34 15 29 34 15 28 , 69 38 29 34 12 31 44 →= 27 34 15 29 34 15 29 , 28 38 29 34 12 31 43 →= 29 34 15 29 34 15 28 , 28 38 29 34 12 31 44 →= 29 34 15 29 34 15 29 , 62 38 29 34 12 32 45 →= 61 34 15 29 34 12 31 , 62 38 29 34 12 32 46 →= 61 34 15 29 34 12 32 , 64 38 29 34 12 32 45 →= 63 34 15 29 34 12 31 , 64 38 29 34 12 32 46 →= 63 34 15 29 34 12 32 , 65 38 29 34 12 32 45 →= 6 34 15 29 34 12 31 , 65 38 29 34 12 32 46 →= 6 34 15 29 34 12 32 , 43 38 29 34 12 32 45 →= 44 34 15 29 34 12 31 , 43 38 29 34 12 32 46 →= 44 34 15 29 34 12 32 , 67 38 29 34 12 32 45 →= 66 34 15 29 34 12 31 , 67 38 29 34 12 32 46 →= 66 34 15 29 34 12 32 , 68 38 29 34 12 32 45 →= 21 34 15 29 34 12 31 , 68 38 29 34 12 32 46 →= 21 34 15 29 34 12 32 , 69 38 29 34 12 32 45 →= 27 34 15 29 34 12 31 , 69 38 29 34 12 32 46 →= 27 34 15 29 34 12 32 , 28 38 29 34 12 32 45 →= 29 34 15 29 34 12 31 , 28 38 29 34 12 32 46 →= 29 34 15 29 34 12 32 , 39 40 29 34 12 31 43 →= 17 50 15 29 34 15 28 , 39 40 29 34 12 31 44 →= 17 50 15 29 34 15 29 , 71 40 29 34 12 31 43 →= 70 50 15 29 34 15 28 , 71 40 29 34 12 31 44 →= 70 50 15 29 34 15 29 , 39 40 29 34 12 32 45 →= 17 50 15 29 34 12 31 , 39 40 29 34 12 32 46 →= 17 50 15 29 34 12 32 , 71 40 29 34 12 32 45 →= 70 50 15 29 34 12 31 , 71 40 29 34 12 32 46 →= 70 50 15 29 34 12 32 , 73 42 29 34 12 31 43 →= 72 57 15 29 34 15 28 , 73 42 29 34 12 31 44 →= 72 57 15 29 34 15 29 , 41 42 29 34 12 31 43 →= 23 57 15 29 34 15 28 , 41 42 29 34 12 31 44 →= 23 57 15 29 34 15 29 , 73 42 29 34 12 32 45 →= 72 57 15 29 34 12 31 , 73 42 29 34 12 32 46 →= 72 57 15 29 34 12 32 , 41 42 29 34 12 32 45 →= 23 57 15 29 34 12 31 , 41 42 29 34 12 32 46 →= 23 57 15 29 34 12 32 , 75 76 29 34 12 31 43 →= 74 54 15 29 34 15 28 , 75 76 29 34 12 31 44 →= 74 54 15 29 34 15 29 , 78 76 29 34 12 31 43 →= 77 54 15 29 34 15 28 , 78 76 29 34 12 31 44 →= 77 54 15 29 34 15 29 , 75 76 29 34 12 32 45 →= 74 54 15 29 34 12 31 , 75 76 29 34 12 32 46 →= 74 54 15 29 34 12 32 , 78 76 29 34 12 32 45 →= 77 54 15 29 34 12 31 , 78 76 29 34 12 32 46 →= 77 54 15 29 34 12 32 , 80 81 29 34 12 31 43 →= 79 56 15 29 34 15 28 , 80 81 29 34 12 31 44 →= 79 56 15 29 34 15 29 , 80 81 29 34 12 32 45 →= 79 56 15 29 34 12 31 , 80 81 29 34 12 32 46 →= 79 56 15 29 34 12 32 , 82 83 44 34 12 31 43 →= 5 65 38 29 34 15 28 , 82 83 44 34 12 31 44 →= 5 65 38 29 34 15 29 , 85 83 44 34 12 31 43 →= 84 65 38 29 34 15 28 , 85 83 44 34 12 31 44 →= 84 65 38 29 34 15 29 , 82 83 44 34 12 32 45 →= 5 65 38 29 34 12 31 , 82 83 44 34 12 32 46 →= 5 65 38 29 34 12 32 , 85 83 44 34 12 32 45 →= 84 65 38 29 34 12 31 , 85 83 44 34 12 32 46 →= 84 65 38 29 34 12 32 , 87 88 44 34 12 31 43 →= 86 68 38 29 34 15 28 , 87 88 44 34 12 31 44 →= 86 68 38 29 34 15 29 , 89 88 44 34 12 31 43 →= 20 68 38 29 34 15 28 , 89 88 44 34 12 31 44 →= 20 68 38 29 34 15 29 , 87 88 44 34 12 32 45 →= 86 68 38 29 34 12 31 , 87 88 44 34 12 32 46 →= 86 68 38 29 34 12 32 , 89 88 44 34 12 32 45 →= 20 68 38 29 34 12 31 , 89 88 44 34 12 32 46 →= 20 68 38 29 34 12 32 , 91 92 44 34 12 31 43 →= 90 69 38 29 34 15 28 , 91 92 44 34 12 31 44 →= 90 69 38 29 34 15 29 , 93 92 44 34 12 31 43 →= 26 69 38 29 34 15 28 , 93 92 44 34 12 31 44 →= 26 69 38 29 34 15 29 , 91 92 44 34 12 32 45 →= 90 69 38 29 34 12 31 , 91 92 44 34 12 32 46 →= 90 69 38 29 34 12 32 , 93 92 44 34 12 32 45 →= 26 69 38 29 34 12 31 , 93 92 44 34 12 32 46 →= 26 69 38 29 34 12 32 , 94 31 44 34 12 31 43 →= 36 28 38 29 34 15 28 , 94 31 44 34 12 31 44 →= 36 28 38 29 34 15 29 , 37 31 44 34 12 31 43 →= 38 28 38 29 34 15 28 , 37 31 44 34 12 31 44 →= 38 28 38 29 34 15 29 , 95 31 44 34 12 31 43 →= 40 28 38 29 34 15 28 , 95 31 44 34 12 31 44 →= 40 28 38 29 34 15 29 , 96 31 44 34 12 31 43 →= 42 28 38 29 34 15 28 , 96 31 44 34 12 31 44 →= 42 28 38 29 34 15 29 , 12 31 44 34 12 31 43 →= 15 28 38 29 34 15 28 , 12 31 44 34 12 31 44 →= 15 28 38 29 34 15 29 , 98 31 44 34 12 31 43 →= 97 28 38 29 34 15 28 , 98 31 44 34 12 31 44 →= 97 28 38 29 34 15 29 , 99 31 44 34 12 31 43 →= 76 28 38 29 34 15 28 , 99 31 44 34 12 31 44 →= 76 28 38 29 34 15 29 , 100 31 44 34 12 31 43 →= 81 28 38 29 34 15 28 , 100 31 44 34 12 31 44 →= 81 28 38 29 34 15 29 , 94 31 44 34 12 32 45 →= 36 28 38 29 34 12 31 , 94 31 44 34 12 32 46 →= 36 28 38 29 34 12 32 , 37 31 44 34 12 32 45 →= 38 28 38 29 34 12 31 , 37 31 44 34 12 32 46 →= 38 28 38 29 34 12 32 , 95 31 44 34 12 32 45 →= 40 28 38 29 34 12 31 , 95 31 44 34 12 32 46 →= 40 28 38 29 34 12 32 , 96 31 44 34 12 32 45 →= 42 28 38 29 34 12 31 , 96 31 44 34 12 32 46 →= 42 28 38 29 34 12 32 , 12 31 44 34 12 32 45 →= 15 28 38 29 34 12 31 , 12 31 44 34 12 32 46 →= 15 28 38 29 34 12 32 , 98 31 44 34 12 32 45 →= 97 28 38 29 34 12 31 , 98 31 44 34 12 32 46 →= 97 28 38 29 34 12 32 , 99 31 44 34 12 32 45 →= 76 28 38 29 34 12 31 , 99 31 44 34 12 32 46 →= 76 28 38 29 34 12 32 , 100 31 44 34 12 32 45 →= 81 28 38 29 34 12 31 , 100 31 44 34 12 32 46 →= 81 28 38 29 34 12 32 , 32 45 44 34 12 31 43 →= 31 43 38 29 34 15 28 , 32 45 44 34 12 31 44 →= 31 43 38 29 34 15 29 , 102 45 44 34 12 31 43 →= 101 43 38 29 34 15 28 , 102 45 44 34 12 31 44 →= 101 43 38 29 34 15 29 , 104 45 44 34 12 31 43 →= 103 43 38 29 34 15 28 , 104 45 44 34 12 31 44 →= 103 43 38 29 34 15 29 , 46 45 44 34 12 31 43 →= 45 43 38 29 34 15 28 , 46 45 44 34 12 31 44 →= 45 43 38 29 34 15 29 , 106 45 44 34 12 31 43 →= 105 43 38 29 34 15 28 , 106 45 44 34 12 31 44 →= 105 43 38 29 34 15 29 , 107 45 44 34 12 31 43 →= 83 43 38 29 34 15 28 , 107 45 44 34 12 31 44 →= 83 43 38 29 34 15 29 , 108 45 44 34 12 31 43 →= 88 43 38 29 34 15 28 , 108 45 44 34 12 31 44 →= 88 43 38 29 34 15 29 , 109 45 44 34 12 31 43 →= 92 43 38 29 34 15 28 , 109 45 44 34 12 31 44 →= 92 43 38 29 34 15 29 , 32 45 44 34 12 32 45 →= 31 43 38 29 34 12 31 , 32 45 44 34 12 32 46 →= 31 43 38 29 34 12 32 , 102 45 44 34 12 32 45 →= 101 43 38 29 34 12 31 , 102 45 44 34 12 32 46 →= 101 43 38 29 34 12 32 , 104 45 44 34 12 32 45 →= 103 43 38 29 34 12 31 , 104 45 44 34 12 32 46 →= 103 43 38 29 34 12 32 , 46 45 44 34 12 32 45 →= 45 43 38 29 34 12 31 , 46 45 44 34 12 32 46 →= 45 43 38 29 34 12 32 , 106 45 44 34 12 32 45 →= 105 43 38 29 34 12 31 , 106 45 44 34 12 32 46 →= 105 43 38 29 34 12 32 , 107 45 44 34 12 32 45 →= 83 43 38 29 34 12 31 , 107 45 44 34 12 32 46 →= 83 43 38 29 34 12 32 , 108 45 44 34 12 32 45 →= 88 43 38 29 34 12 31 , 108 45 44 34 12 32 46 →= 88 43 38 29 34 12 32 , 109 45 44 34 12 32 45 →= 92 43 38 29 34 12 31 , 109 45 44 34 12 32 46 →= 92 43 38 29 34 12 32 , 111 101 44 34 12 31 43 →= 110 62 38 29 34 15 28 , 111 101 44 34 12 31 44 →= 110 62 38 29 34 15 29 , 113 101 44 34 12 31 43 →= 112 62 38 29 34 15 28 , 113 101 44 34 12 31 44 →= 112 62 38 29 34 15 29 , 111 101 44 34 12 32 45 →= 110 62 38 29 34 12 31 , 111 101 44 34 12 32 46 →= 110 62 38 29 34 12 32 , 113 101 44 34 12 32 45 →= 112 62 38 29 34 12 31 , 113 101 44 34 12 32 46 →= 112 62 38 29 34 12 32 , 115 103 44 34 12 31 43 →= 114 64 38 29 34 15 28 , 115 103 44 34 12 31 44 →= 114 64 38 29 34 15 29 , 115 103 44 34 12 32 45 →= 114 64 38 29 34 12 31 , 115 103 44 34 12 32 46 →= 114 64 38 29 34 12 32 , 117 110 61 34 12 31 43 →= 116 75 76 29 34 15 28 , 117 110 61 34 12 31 44 →= 116 75 76 29 34 15 29 , 117 110 61 34 12 32 45 →= 116 75 76 29 34 12 31 , 117 110 61 34 12 32 46 →= 116 75 76 29 34 12 32 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 40 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 41 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 42 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 43 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 44 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 45 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 46 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 47 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 48 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 49 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 50 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 51 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 52 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 53 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 54 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 55 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 56 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 57 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 58 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 59 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 60 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 61 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 62 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 63 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 64 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 65 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 66 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 67 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 68 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 69 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 70 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 71 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 72 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 73 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 74 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 75 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 76 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 77 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 78 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 79 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 80 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 81 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 82 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 83 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 84 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 85 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 86 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 87 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 88 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 89 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 90 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 91 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 92 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 93 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 94 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 95 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 96 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 97 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 98 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 99 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 100 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 101 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 102 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 103 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 104 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 105 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 106 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 107 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 108 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 109 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 110 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 111 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 112 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 113 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 114 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 115 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 116 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 117 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 118 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 119 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ After renaming modulo the bijection { 4 ↦ 0, 5 ↦ 1, 6 ↦ 2, 34 ↦ 3, 15 ↦ 4, 29 ↦ 5, 7 ↦ 6, 0 ↦ 7, 35 ↦ 8, 36 ↦ 9, 3 ↦ 10, 19 ↦ 11, 20 ↦ 12, 21 ↦ 13, 16 ↦ 14, 39 ↦ 15, 40 ↦ 16, 25 ↦ 17, 26 ↦ 18, 27 ↦ 19, 22 ↦ 20, 41 ↦ 21, 42 ↦ 22, 12 ↦ 23, 31 ↦ 24, 43 ↦ 25, 28 ↦ 26, 44 ↦ 27, 32 ↦ 28, 45 ↦ 29, 46 ↦ 30, 8 ↦ 31, 9 ↦ 32, 10 ↦ 33, 11 ↦ 34, 13 ↦ 35, 14 ↦ 36, 58 ↦ 37, 59 ↦ 38, 60 ↦ 39, 61 ↦ 40, 62 ↦ 41, 38 ↦ 42, 63 ↦ 43, 64 ↦ 44, 65 ↦ 45, 66 ↦ 46, 67 ↦ 47, 68 ↦ 48, 69 ↦ 49, 82 ↦ 50, 83 ↦ 51, 84 ↦ 52, 85 ↦ 53, 86 ↦ 54, 87 ↦ 55, 88 ↦ 56, 89 ↦ 57, 90 ↦ 58, 91 ↦ 59, 92 ↦ 60, 93 ↦ 61, 94 ↦ 62, 37 ↦ 63, 95 ↦ 64, 96 ↦ 65, 97 ↦ 66, 98 ↦ 67, 76 ↦ 68, 99 ↦ 69, 81 ↦ 70, 100 ↦ 71, 101 ↦ 72, 102 ↦ 73, 103 ↦ 74, 104 ↦ 75, 105 ↦ 76, 106 ↦ 77, 107 ↦ 78, 108 ↦ 79, 109 ↦ 80, 110 ↦ 81, 111 ↦ 82, 112 ↦ 83, 113 ↦ 84, 114 ↦ 85, 115 ↦ 86, 30 ↦ 87, 33 ↦ 88, 118 ↦ 89, 119 ↦ 90, 1 ↦ 91, 49 ↦ 92, 48 ↦ 93, 47 ↦ 94, 17 ↦ 95, 50 ↦ 96, 71 ↦ 97, 70 ↦ 98, 73 ↦ 99, 72 ↦ 100, 57 ↦ 101, 23 ↦ 102, 75 ↦ 103, 74 ↦ 104, 54 ↦ 105, 78 ↦ 106, 77 ↦ 107, 80 ↦ 108, 79 ↦ 109, 56 ↦ 110, 117 ↦ 111, 116 ↦ 112 }, it remains to prove termination of the 902-rule system { 0 1 2 3 4 5 6 ⟶ 7 8 9 5 6 10 10 , 11 12 13 3 4 5 6 ⟶ 14 15 16 5 6 10 10 , 17 18 19 3 4 5 6 ⟶ 20 21 22 5 6 10 10 , 0 1 2 3 23 24 25 ⟶ 7 8 9 5 3 4 26 , 0 1 2 3 23 24 27 ⟶ 7 8 9 5 3 4 5 , 0 1 2 3 23 28 29 ⟶ 7 8 9 5 3 23 24 , 0 1 2 3 23 28 30 ⟶ 7 8 9 5 3 23 28 , 11 12 13 3 23 24 25 ⟶ 14 15 16 5 3 4 26 , 11 12 13 3 23 24 27 ⟶ 14 15 16 5 3 4 5 , 11 12 13 3 23 28 29 ⟶ 14 15 16 5 3 23 24 , 11 12 13 3 23 28 30 ⟶ 14 15 16 5 3 23 28 , 17 18 19 3 23 24 25 ⟶ 20 21 22 5 3 4 26 , 17 18 19 3 23 24 27 ⟶ 20 21 22 5 3 4 5 , 17 18 19 3 23 28 29 ⟶ 20 21 22 5 3 23 24 , 17 18 19 3 23 28 30 ⟶ 20 21 22 5 3 23 28 , 6 10 10 10 10 10 10 →= 3 4 5 6 10 10 10 , 6 10 10 10 10 10 31 →= 3 4 5 6 10 10 31 , 6 10 10 10 10 10 32 →= 3 4 5 6 10 10 32 , 6 10 10 10 10 10 33 →= 3 4 5 6 10 10 33 , 6 10 10 10 10 10 34 →= 3 4 5 6 10 10 34 , 6 10 10 10 10 31 23 →= 3 4 5 6 10 31 23 , 6 10 10 10 10 31 35 →= 3 4 5 6 10 31 35 , 6 10 10 10 10 31 36 →= 3 4 5 6 10 31 36 , 6 10 10 10 10 31 4 →= 3 4 5 6 10 31 4 , 6 10 10 10 10 32 37 →= 3 4 5 6 10 32 37 , 6 10 10 10 10 32 38 →= 3 4 5 6 10 32 38 , 6 10 10 10 10 33 39 →= 3 4 5 6 10 33 39 , 40 6 10 10 10 10 10 →= 41 42 5 6 10 10 10 , 40 6 10 10 10 10 31 →= 41 42 5 6 10 10 31 , 40 6 10 10 10 10 32 →= 41 42 5 6 10 10 32 , 40 6 10 10 10 10 33 →= 41 42 5 6 10 10 33 , 40 6 10 10 10 10 34 →= 41 42 5 6 10 10 34 , 43 6 10 10 10 10 10 →= 44 42 5 6 10 10 10 , 43 6 10 10 10 10 31 →= 44 42 5 6 10 10 31 , 43 6 10 10 10 10 32 →= 44 42 5 6 10 10 32 , 43 6 10 10 10 10 33 →= 44 42 5 6 10 10 33 , 43 6 10 10 10 10 34 →= 44 42 5 6 10 10 34 , 2 6 10 10 10 10 10 →= 45 42 5 6 10 10 10 , 2 6 10 10 10 10 31 →= 45 42 5 6 10 10 31 , 2 6 10 10 10 10 32 →= 45 42 5 6 10 10 32 , 2 6 10 10 10 10 33 →= 45 42 5 6 10 10 33 , 2 6 10 10 10 10 34 →= 45 42 5 6 10 10 34 , 27 6 10 10 10 10 10 →= 25 42 5 6 10 10 10 , 27 6 10 10 10 10 31 →= 25 42 5 6 10 10 31 , 27 6 10 10 10 10 32 →= 25 42 5 6 10 10 32 , 27 6 10 10 10 10 33 →= 25 42 5 6 10 10 33 , 27 6 10 10 10 10 34 →= 25 42 5 6 10 10 34 , 46 6 10 10 10 10 10 →= 47 42 5 6 10 10 10 , 46 6 10 10 10 10 31 →= 47 42 5 6 10 10 31 , 46 6 10 10 10 10 32 →= 47 42 5 6 10 10 32 , 46 6 10 10 10 10 33 →= 47 42 5 6 10 10 33 , 46 6 10 10 10 10 34 →= 47 42 5 6 10 10 34 , 13 6 10 10 10 10 10 →= 48 42 5 6 10 10 10 , 13 6 10 10 10 10 31 →= 48 42 5 6 10 10 31 , 13 6 10 10 10 10 32 →= 48 42 5 6 10 10 32 , 13 6 10 10 10 10 33 →= 48 42 5 6 10 10 33 , 13 6 10 10 10 10 34 →= 48 42 5 6 10 10 34 , 19 6 10 10 10 10 10 →= 49 42 5 6 10 10 10 , 19 6 10 10 10 10 31 →= 49 42 5 6 10 10 31 , 19 6 10 10 10 10 32 →= 49 42 5 6 10 10 32 , 19 6 10 10 10 10 33 →= 49 42 5 6 10 10 33 , 19 6 10 10 10 10 34 →= 49 42 5 6 10 10 34 , 5 6 10 10 10 10 10 →= 26 42 5 6 10 10 10 , 5 6 10 10 10 10 31 →= 26 42 5 6 10 10 31 , 5 6 10 10 10 10 32 →= 26 42 5 6 10 10 32 , 5 6 10 10 10 10 33 →= 26 42 5 6 10 10 33 , 5 6 10 10 10 10 34 →= 26 42 5 6 10 10 34 , 40 6 10 10 10 31 23 →= 41 42 5 6 10 31 23 , 40 6 10 10 10 31 35 →= 41 42 5 6 10 31 35 , 40 6 10 10 10 31 36 →= 41 42 5 6 10 31 36 , 40 6 10 10 10 31 4 →= 41 42 5 6 10 31 4 , 43 6 10 10 10 31 23 →= 44 42 5 6 10 31 23 , 43 6 10 10 10 31 35 →= 44 42 5 6 10 31 35 , 43 6 10 10 10 31 36 →= 44 42 5 6 10 31 36 , 43 6 10 10 10 31 4 →= 44 42 5 6 10 31 4 , 2 6 10 10 10 31 23 →= 45 42 5 6 10 31 23 , 2 6 10 10 10 31 35 →= 45 42 5 6 10 31 35 , 2 6 10 10 10 31 36 →= 45 42 5 6 10 31 36 , 2 6 10 10 10 31 4 →= 45 42 5 6 10 31 4 , 27 6 10 10 10 31 23 →= 25 42 5 6 10 31 23 , 27 6 10 10 10 31 35 →= 25 42 5 6 10 31 35 , 27 6 10 10 10 31 36 →= 25 42 5 6 10 31 36 , 27 6 10 10 10 31 4 →= 25 42 5 6 10 31 4 , 46 6 10 10 10 31 23 →= 47 42 5 6 10 31 23 , 46 6 10 10 10 31 35 →= 47 42 5 6 10 31 35 , 46 6 10 10 10 31 36 →= 47 42 5 6 10 31 36 , 46 6 10 10 10 31 4 →= 47 42 5 6 10 31 4 , 13 6 10 10 10 31 23 →= 48 42 5 6 10 31 23 , 13 6 10 10 10 31 35 →= 48 42 5 6 10 31 35 , 13 6 10 10 10 31 36 →= 48 42 5 6 10 31 36 , 13 6 10 10 10 31 4 →= 48 42 5 6 10 31 4 , 19 6 10 10 10 31 23 →= 49 42 5 6 10 31 23 , 19 6 10 10 10 31 35 →= 49 42 5 6 10 31 35 , 19 6 10 10 10 31 36 →= 49 42 5 6 10 31 36 , 19 6 10 10 10 31 4 →= 49 42 5 6 10 31 4 , 5 6 10 10 10 31 23 →= 26 42 5 6 10 31 23 , 5 6 10 10 10 31 35 →= 26 42 5 6 10 31 35 , 5 6 10 10 10 31 36 →= 26 42 5 6 10 31 36 , 5 6 10 10 10 31 4 →= 26 42 5 6 10 31 4 , 40 6 10 10 10 32 37 →= 41 42 5 6 10 32 37 , 40 6 10 10 10 32 38 →= 41 42 5 6 10 32 38 , 43 6 10 10 10 32 37 →= 44 42 5 6 10 32 37 , 43 6 10 10 10 32 38 →= 44 42 5 6 10 32 38 , 2 6 10 10 10 32 37 →= 45 42 5 6 10 32 37 , 2 6 10 10 10 32 38 →= 45 42 5 6 10 32 38 , 27 6 10 10 10 32 37 →= 25 42 5 6 10 32 37 , 27 6 10 10 10 32 38 →= 25 42 5 6 10 32 38 , 46 6 10 10 10 32 37 →= 47 42 5 6 10 32 37 , 46 6 10 10 10 32 38 →= 47 42 5 6 10 32 38 , 13 6 10 10 10 32 37 →= 48 42 5 6 10 32 37 , 13 6 10 10 10 32 38 →= 48 42 5 6 10 32 38 , 19 6 10 10 10 32 37 →= 49 42 5 6 10 32 37 , 19 6 10 10 10 32 38 →= 49 42 5 6 10 32 38 , 5 6 10 10 10 32 37 →= 26 42 5 6 10 32 37 , 5 6 10 10 10 32 38 →= 26 42 5 6 10 32 38 , 40 6 10 10 10 33 39 →= 41 42 5 6 10 33 39 , 43 6 10 10 10 33 39 →= 44 42 5 6 10 33 39 , 2 6 10 10 10 33 39 →= 45 42 5 6 10 33 39 , 27 6 10 10 10 33 39 →= 25 42 5 6 10 33 39 , 46 6 10 10 10 33 39 →= 47 42 5 6 10 33 39 , 13 6 10 10 10 33 39 →= 48 42 5 6 10 33 39 , 19 6 10 10 10 33 39 →= 49 42 5 6 10 33 39 , 5 6 10 10 10 33 39 →= 26 42 5 6 10 33 39 , 1 2 6 10 10 10 10 →= 50 51 27 6 10 10 10 , 1 2 6 10 10 10 31 →= 50 51 27 6 10 10 31 , 1 2 6 10 10 10 32 →= 50 51 27 6 10 10 32 , 1 2 6 10 10 10 33 →= 50 51 27 6 10 10 33 , 1 2 6 10 10 10 34 →= 50 51 27 6 10 10 34 , 52 2 6 10 10 10 10 →= 53 51 27 6 10 10 10 , 52 2 6 10 10 10 31 →= 53 51 27 6 10 10 31 , 52 2 6 10 10 10 32 →= 53 51 27 6 10 10 32 , 52 2 6 10 10 10 33 →= 53 51 27 6 10 10 33 , 52 2 6 10 10 10 34 →= 53 51 27 6 10 10 34 , 1 2 6 10 10 31 23 →= 50 51 27 6 10 31 23 , 1 2 6 10 10 31 35 →= 50 51 27 6 10 31 35 , 1 2 6 10 10 31 36 →= 50 51 27 6 10 31 36 , 1 2 6 10 10 31 4 →= 50 51 27 6 10 31 4 , 52 2 6 10 10 31 23 →= 53 51 27 6 10 31 23 , 52 2 6 10 10 31 35 →= 53 51 27 6 10 31 35 , 52 2 6 10 10 31 36 →= 53 51 27 6 10 31 36 , 52 2 6 10 10 31 4 →= 53 51 27 6 10 31 4 , 1 2 6 10 10 32 37 →= 50 51 27 6 10 32 37 , 1 2 6 10 10 32 38 →= 50 51 27 6 10 32 38 , 52 2 6 10 10 32 37 →= 53 51 27 6 10 32 37 , 52 2 6 10 10 32 38 →= 53 51 27 6 10 32 38 , 1 2 6 10 10 33 39 →= 50 51 27 6 10 33 39 , 52 2 6 10 10 33 39 →= 53 51 27 6 10 33 39 , 54 13 6 10 10 10 10 →= 55 56 27 6 10 10 10 , 54 13 6 10 10 10 31 →= 55 56 27 6 10 10 31 , 54 13 6 10 10 10 32 →= 55 56 27 6 10 10 32 , 54 13 6 10 10 10 33 →= 55 56 27 6 10 10 33 , 54 13 6 10 10 10 34 →= 55 56 27 6 10 10 34 , 12 13 6 10 10 10 10 →= 57 56 27 6 10 10 10 , 12 13 6 10 10 10 31 →= 57 56 27 6 10 10 31 , 12 13 6 10 10 10 32 →= 57 56 27 6 10 10 32 , 12 13 6 10 10 10 33 →= 57 56 27 6 10 10 33 , 12 13 6 10 10 10 34 →= 57 56 27 6 10 10 34 , 54 13 6 10 10 31 23 →= 55 56 27 6 10 31 23 , 54 13 6 10 10 31 35 →= 55 56 27 6 10 31 35 , 54 13 6 10 10 31 36 →= 55 56 27 6 10 31 36 , 54 13 6 10 10 31 4 →= 55 56 27 6 10 31 4 , 12 13 6 10 10 31 23 →= 57 56 27 6 10 31 23 , 12 13 6 10 10 31 35 →= 57 56 27 6 10 31 35 , 12 13 6 10 10 31 36 →= 57 56 27 6 10 31 36 , 12 13 6 10 10 31 4 →= 57 56 27 6 10 31 4 , 54 13 6 10 10 32 37 →= 55 56 27 6 10 32 37 , 54 13 6 10 10 32 38 →= 55 56 27 6 10 32 38 , 12 13 6 10 10 32 37 →= 57 56 27 6 10 32 37 , 12 13 6 10 10 32 38 →= 57 56 27 6 10 32 38 , 54 13 6 10 10 33 39 →= 55 56 27 6 10 33 39 , 12 13 6 10 10 33 39 →= 57 56 27 6 10 33 39 , 58 19 6 10 10 10 10 →= 59 60 27 6 10 10 10 , 58 19 6 10 10 10 31 →= 59 60 27 6 10 10 31 , 58 19 6 10 10 10 32 →= 59 60 27 6 10 10 32 , 58 19 6 10 10 10 33 →= 59 60 27 6 10 10 33 , 58 19 6 10 10 10 34 →= 59 60 27 6 10 10 34 , 18 19 6 10 10 10 10 →= 61 60 27 6 10 10 10 , 18 19 6 10 10 10 31 →= 61 60 27 6 10 10 31 , 18 19 6 10 10 10 32 →= 61 60 27 6 10 10 32 , 18 19 6 10 10 10 33 →= 61 60 27 6 10 10 33 , 18 19 6 10 10 10 34 →= 61 60 27 6 10 10 34 , 58 19 6 10 10 31 23 →= 59 60 27 6 10 31 23 , 58 19 6 10 10 31 35 →= 59 60 27 6 10 31 35 , 58 19 6 10 10 31 36 →= 59 60 27 6 10 31 36 , 58 19 6 10 10 31 4 →= 59 60 27 6 10 31 4 , 18 19 6 10 10 31 23 →= 61 60 27 6 10 31 23 , 18 19 6 10 10 31 35 →= 61 60 27 6 10 31 35 , 18 19 6 10 10 31 36 →= 61 60 27 6 10 31 36 , 18 19 6 10 10 31 4 →= 61 60 27 6 10 31 4 , 58 19 6 10 10 32 37 →= 59 60 27 6 10 32 37 , 58 19 6 10 10 32 38 →= 59 60 27 6 10 32 38 , 18 19 6 10 10 32 37 →= 61 60 27 6 10 32 37 , 18 19 6 10 10 32 38 →= 61 60 27 6 10 32 38 , 58 19 6 10 10 33 39 →= 59 60 27 6 10 33 39 , 18 19 6 10 10 33 39 →= 61 60 27 6 10 33 39 , 9 5 6 10 10 10 10 →= 62 24 27 6 10 10 10 , 9 5 6 10 10 10 31 →= 62 24 27 6 10 10 31 , 9 5 6 10 10 10 32 →= 62 24 27 6 10 10 32 , 9 5 6 10 10 10 33 →= 62 24 27 6 10 10 33 , 9 5 6 10 10 10 34 →= 62 24 27 6 10 10 34 , 42 5 6 10 10 10 10 →= 63 24 27 6 10 10 10 , 42 5 6 10 10 10 31 →= 63 24 27 6 10 10 31 , 42 5 6 10 10 10 32 →= 63 24 27 6 10 10 32 , 42 5 6 10 10 10 33 →= 63 24 27 6 10 10 33 , 42 5 6 10 10 10 34 →= 63 24 27 6 10 10 34 , 16 5 6 10 10 10 10 →= 64 24 27 6 10 10 10 , 16 5 6 10 10 10 31 →= 64 24 27 6 10 10 31 , 16 5 6 10 10 10 32 →= 64 24 27 6 10 10 32 , 16 5 6 10 10 10 33 →= 64 24 27 6 10 10 33 , 16 5 6 10 10 10 34 →= 64 24 27 6 10 10 34 , 22 5 6 10 10 10 10 →= 65 24 27 6 10 10 10 , 22 5 6 10 10 10 31 →= 65 24 27 6 10 10 31 , 22 5 6 10 10 10 32 →= 65 24 27 6 10 10 32 , 22 5 6 10 10 10 33 →= 65 24 27 6 10 10 33 , 22 5 6 10 10 10 34 →= 65 24 27 6 10 10 34 , 4 5 6 10 10 10 10 →= 23 24 27 6 10 10 10 , 4 5 6 10 10 10 31 →= 23 24 27 6 10 10 31 , 4 5 6 10 10 10 32 →= 23 24 27 6 10 10 32 , 4 5 6 10 10 10 33 →= 23 24 27 6 10 10 33 , 4 5 6 10 10 10 34 →= 23 24 27 6 10 10 34 , 66 5 6 10 10 10 10 →= 67 24 27 6 10 10 10 , 66 5 6 10 10 10 31 →= 67 24 27 6 10 10 31 , 66 5 6 10 10 10 32 →= 67 24 27 6 10 10 32 , 66 5 6 10 10 10 33 →= 67 24 27 6 10 10 33 , 66 5 6 10 10 10 34 →= 67 24 27 6 10 10 34 , 68 5 6 10 10 10 10 →= 69 24 27 6 10 10 10 , 68 5 6 10 10 10 31 →= 69 24 27 6 10 10 31 , 68 5 6 10 10 10 32 →= 69 24 27 6 10 10 32 , 68 5 6 10 10 10 33 →= 69 24 27 6 10 10 33 , 68 5 6 10 10 10 34 →= 69 24 27 6 10 10 34 , 70 5 6 10 10 10 10 →= 71 24 27 6 10 10 10 , 70 5 6 10 10 10 31 →= 71 24 27 6 10 10 31 , 70 5 6 10 10 10 32 →= 71 24 27 6 10 10 32 , 70 5 6 10 10 10 33 →= 71 24 27 6 10 10 33 , 70 5 6 10 10 10 34 →= 71 24 27 6 10 10 34 , 9 5 6 10 10 31 23 →= 62 24 27 6 10 31 23 , 9 5 6 10 10 31 35 →= 62 24 27 6 10 31 35 , 9 5 6 10 10 31 36 →= 62 24 27 6 10 31 36 , 9 5 6 10 10 31 4 →= 62 24 27 6 10 31 4 , 42 5 6 10 10 31 23 →= 63 24 27 6 10 31 23 , 42 5 6 10 10 31 35 →= 63 24 27 6 10 31 35 , 42 5 6 10 10 31 36 →= 63 24 27 6 10 31 36 , 42 5 6 10 10 31 4 →= 63 24 27 6 10 31 4 , 16 5 6 10 10 31 23 →= 64 24 27 6 10 31 23 , 16 5 6 10 10 31 35 →= 64 24 27 6 10 31 35 , 16 5 6 10 10 31 36 →= 64 24 27 6 10 31 36 , 16 5 6 10 10 31 4 →= 64 24 27 6 10 31 4 , 22 5 6 10 10 31 23 →= 65 24 27 6 10 31 23 , 22 5 6 10 10 31 35 →= 65 24 27 6 10 31 35 , 22 5 6 10 10 31 36 →= 65 24 27 6 10 31 36 , 22 5 6 10 10 31 4 →= 65 24 27 6 10 31 4 , 4 5 6 10 10 31 23 →= 23 24 27 6 10 31 23 , 4 5 6 10 10 31 35 →= 23 24 27 6 10 31 35 , 4 5 6 10 10 31 36 →= 23 24 27 6 10 31 36 , 4 5 6 10 10 31 4 →= 23 24 27 6 10 31 4 , 66 5 6 10 10 31 23 →= 67 24 27 6 10 31 23 , 66 5 6 10 10 31 35 →= 67 24 27 6 10 31 35 , 66 5 6 10 10 31 36 →= 67 24 27 6 10 31 36 , 66 5 6 10 10 31 4 →= 67 24 27 6 10 31 4 , 68 5 6 10 10 31 23 →= 69 24 27 6 10 31 23 , 68 5 6 10 10 31 35 →= 69 24 27 6 10 31 35 , 68 5 6 10 10 31 36 →= 69 24 27 6 10 31 36 , 68 5 6 10 10 31 4 →= 69 24 27 6 10 31 4 , 70 5 6 10 10 31 23 →= 71 24 27 6 10 31 23 , 70 5 6 10 10 31 35 →= 71 24 27 6 10 31 35 , 70 5 6 10 10 31 36 →= 71 24 27 6 10 31 36 , 70 5 6 10 10 31 4 →= 71 24 27 6 10 31 4 , 9 5 6 10 10 32 37 →= 62 24 27 6 10 32 37 , 9 5 6 10 10 32 38 →= 62 24 27 6 10 32 38 , 42 5 6 10 10 32 37 →= 63 24 27 6 10 32 37 , 42 5 6 10 10 32 38 →= 63 24 27 6 10 32 38 , 16 5 6 10 10 32 37 →= 64 24 27 6 10 32 37 , 16 5 6 10 10 32 38 →= 64 24 27 6 10 32 38 , 22 5 6 10 10 32 37 →= 65 24 27 6 10 32 37 , 22 5 6 10 10 32 38 →= 65 24 27 6 10 32 38 , 4 5 6 10 10 32 37 →= 23 24 27 6 10 32 37 , 4 5 6 10 10 32 38 →= 23 24 27 6 10 32 38 , 66 5 6 10 10 32 37 →= 67 24 27 6 10 32 37 , 66 5 6 10 10 32 38 →= 67 24 27 6 10 32 38 , 68 5 6 10 10 32 37 →= 69 24 27 6 10 32 37 , 68 5 6 10 10 32 38 →= 69 24 27 6 10 32 38 , 70 5 6 10 10 32 37 →= 71 24 27 6 10 32 37 , 70 5 6 10 10 32 38 →= 71 24 27 6 10 32 38 , 9 5 6 10 10 33 39 →= 62 24 27 6 10 33 39 , 42 5 6 10 10 33 39 →= 63 24 27 6 10 33 39 , 16 5 6 10 10 33 39 →= 64 24 27 6 10 33 39 , 22 5 6 10 10 33 39 →= 65 24 27 6 10 33 39 , 4 5 6 10 10 33 39 →= 23 24 27 6 10 33 39 , 66 5 6 10 10 33 39 →= 67 24 27 6 10 33 39 , 68 5 6 10 10 33 39 →= 69 24 27 6 10 33 39 , 70 5 6 10 10 33 39 →= 71 24 27 6 10 33 39 , 24 27 6 10 10 10 10 →= 28 29 27 6 10 10 10 , 24 27 6 10 10 10 31 →= 28 29 27 6 10 10 31 , 24 27 6 10 10 10 32 →= 28 29 27 6 10 10 32 , 24 27 6 10 10 10 33 →= 28 29 27 6 10 10 33 , 24 27 6 10 10 10 34 →= 28 29 27 6 10 10 34 , 72 27 6 10 10 10 10 →= 73 29 27 6 10 10 10 , 72 27 6 10 10 10 31 →= 73 29 27 6 10 10 31 , 72 27 6 10 10 10 32 →= 73 29 27 6 10 10 32 , 72 27 6 10 10 10 33 →= 73 29 27 6 10 10 33 , 72 27 6 10 10 10 34 →= 73 29 27 6 10 10 34 , 74 27 6 10 10 10 10 →= 75 29 27 6 10 10 10 , 74 27 6 10 10 10 31 →= 75 29 27 6 10 10 31 , 74 27 6 10 10 10 32 →= 75 29 27 6 10 10 32 , 74 27 6 10 10 10 33 →= 75 29 27 6 10 10 33 , 74 27 6 10 10 10 34 →= 75 29 27 6 10 10 34 , 29 27 6 10 10 10 10 →= 30 29 27 6 10 10 10 , 29 27 6 10 10 10 31 →= 30 29 27 6 10 10 31 , 29 27 6 10 10 10 32 →= 30 29 27 6 10 10 32 , 29 27 6 10 10 10 33 →= 30 29 27 6 10 10 33 , 29 27 6 10 10 10 34 →= 30 29 27 6 10 10 34 , 76 27 6 10 10 10 10 →= 77 29 27 6 10 10 10 , 76 27 6 10 10 10 31 →= 77 29 27 6 10 10 31 , 76 27 6 10 10 10 32 →= 77 29 27 6 10 10 32 , 76 27 6 10 10 10 33 →= 77 29 27 6 10 10 33 , 76 27 6 10 10 10 34 →= 77 29 27 6 10 10 34 , 51 27 6 10 10 10 10 →= 78 29 27 6 10 10 10 , 51 27 6 10 10 10 31 →= 78 29 27 6 10 10 31 , 51 27 6 10 10 10 32 →= 78 29 27 6 10 10 32 , 51 27 6 10 10 10 33 →= 78 29 27 6 10 10 33 , 51 27 6 10 10 10 34 →= 78 29 27 6 10 10 34 , 56 27 6 10 10 10 10 →= 79 29 27 6 10 10 10 , 56 27 6 10 10 10 31 →= 79 29 27 6 10 10 31 , 56 27 6 10 10 10 32 →= 79 29 27 6 10 10 32 , 56 27 6 10 10 10 33 →= 79 29 27 6 10 10 33 , 56 27 6 10 10 10 34 →= 79 29 27 6 10 10 34 , 60 27 6 10 10 10 10 →= 80 29 27 6 10 10 10 , 60 27 6 10 10 10 31 →= 80 29 27 6 10 10 31 , 60 27 6 10 10 10 32 →= 80 29 27 6 10 10 32 , 60 27 6 10 10 10 33 →= 80 29 27 6 10 10 33 , 60 27 6 10 10 10 34 →= 80 29 27 6 10 10 34 , 24 27 6 10 10 31 23 →= 28 29 27 6 10 31 23 , 24 27 6 10 10 31 35 →= 28 29 27 6 10 31 35 , 24 27 6 10 10 31 36 →= 28 29 27 6 10 31 36 , 24 27 6 10 10 31 4 →= 28 29 27 6 10 31 4 , 72 27 6 10 10 31 23 →= 73 29 27 6 10 31 23 , 72 27 6 10 10 31 35 →= 73 29 27 6 10 31 35 , 72 27 6 10 10 31 36 →= 73 29 27 6 10 31 36 , 72 27 6 10 10 31 4 →= 73 29 27 6 10 31 4 , 74 27 6 10 10 31 23 →= 75 29 27 6 10 31 23 , 74 27 6 10 10 31 35 →= 75 29 27 6 10 31 35 , 74 27 6 10 10 31 36 →= 75 29 27 6 10 31 36 , 74 27 6 10 10 31 4 →= 75 29 27 6 10 31 4 , 29 27 6 10 10 31 23 →= 30 29 27 6 10 31 23 , 29 27 6 10 10 31 35 →= 30 29 27 6 10 31 35 , 29 27 6 10 10 31 36 →= 30 29 27 6 10 31 36 , 29 27 6 10 10 31 4 →= 30 29 27 6 10 31 4 , 76 27 6 10 10 31 23 →= 77 29 27 6 10 31 23 , 76 27 6 10 10 31 35 →= 77 29 27 6 10 31 35 , 76 27 6 10 10 31 36 →= 77 29 27 6 10 31 36 , 76 27 6 10 10 31 4 →= 77 29 27 6 10 31 4 , 51 27 6 10 10 31 23 →= 78 29 27 6 10 31 23 , 51 27 6 10 10 31 35 →= 78 29 27 6 10 31 35 , 51 27 6 10 10 31 36 →= 78 29 27 6 10 31 36 , 51 27 6 10 10 31 4 →= 78 29 27 6 10 31 4 , 56 27 6 10 10 31 23 →= 79 29 27 6 10 31 23 , 56 27 6 10 10 31 35 →= 79 29 27 6 10 31 35 , 56 27 6 10 10 31 36 →= 79 29 27 6 10 31 36 , 56 27 6 10 10 31 4 →= 79 29 27 6 10 31 4 , 60 27 6 10 10 31 23 →= 80 29 27 6 10 31 23 , 60 27 6 10 10 31 35 →= 80 29 27 6 10 31 35 , 60 27 6 10 10 31 36 →= 80 29 27 6 10 31 36 , 60 27 6 10 10 31 4 →= 80 29 27 6 10 31 4 , 24 27 6 10 10 32 37 →= 28 29 27 6 10 32 37 , 24 27 6 10 10 32 38 →= 28 29 27 6 10 32 38 , 72 27 6 10 10 32 37 →= 73 29 27 6 10 32 37 , 72 27 6 10 10 32 38 →= 73 29 27 6 10 32 38 , 74 27 6 10 10 32 37 →= 75 29 27 6 10 32 37 , 74 27 6 10 10 32 38 →= 75 29 27 6 10 32 38 , 29 27 6 10 10 32 37 →= 30 29 27 6 10 32 37 , 29 27 6 10 10 32 38 →= 30 29 27 6 10 32 38 , 76 27 6 10 10 32 37 →= 77 29 27 6 10 32 37 , 76 27 6 10 10 32 38 →= 77 29 27 6 10 32 38 , 51 27 6 10 10 32 37 →= 78 29 27 6 10 32 37 , 51 27 6 10 10 32 38 →= 78 29 27 6 10 32 38 , 56 27 6 10 10 32 37 →= 79 29 27 6 10 32 37 , 56 27 6 10 10 32 38 →= 79 29 27 6 10 32 38 , 60 27 6 10 10 32 37 →= 80 29 27 6 10 32 37 , 60 27 6 10 10 32 38 →= 80 29 27 6 10 32 38 , 24 27 6 10 10 33 39 →= 28 29 27 6 10 33 39 , 72 27 6 10 10 33 39 →= 73 29 27 6 10 33 39 , 74 27 6 10 10 33 39 →= 75 29 27 6 10 33 39 , 29 27 6 10 10 33 39 →= 30 29 27 6 10 33 39 , 76 27 6 10 10 33 39 →= 77 29 27 6 10 33 39 , 51 27 6 10 10 33 39 →= 78 29 27 6 10 33 39 , 56 27 6 10 10 33 39 →= 79 29 27 6 10 33 39 , 60 27 6 10 10 33 39 →= 80 29 27 6 10 33 39 , 81 40 6 10 10 10 10 →= 82 72 27 6 10 10 10 , 81 40 6 10 10 10 31 →= 82 72 27 6 10 10 31 , 81 40 6 10 10 10 32 →= 82 72 27 6 10 10 32 , 81 40 6 10 10 10 33 →= 82 72 27 6 10 10 33 , 81 40 6 10 10 10 34 →= 82 72 27 6 10 10 34 , 83 40 6 10 10 10 10 →= 84 72 27 6 10 10 10 , 83 40 6 10 10 10 31 →= 84 72 27 6 10 10 31 , 83 40 6 10 10 10 32 →= 84 72 27 6 10 10 32 , 83 40 6 10 10 10 33 →= 84 72 27 6 10 10 33 , 83 40 6 10 10 10 34 →= 84 72 27 6 10 10 34 , 81 40 6 10 10 31 23 →= 82 72 27 6 10 31 23 , 81 40 6 10 10 31 35 →= 82 72 27 6 10 31 35 , 81 40 6 10 10 31 36 →= 82 72 27 6 10 31 36 , 81 40 6 10 10 31 4 →= 82 72 27 6 10 31 4 , 83 40 6 10 10 31 23 →= 84 72 27 6 10 31 23 , 83 40 6 10 10 31 35 →= 84 72 27 6 10 31 35 , 83 40 6 10 10 31 36 →= 84 72 27 6 10 31 36 , 83 40 6 10 10 31 4 →= 84 72 27 6 10 31 4 , 81 40 6 10 10 32 37 →= 82 72 27 6 10 32 37 , 81 40 6 10 10 32 38 →= 82 72 27 6 10 32 38 , 83 40 6 10 10 32 37 →= 84 72 27 6 10 32 37 , 83 40 6 10 10 32 38 →= 84 72 27 6 10 32 38 , 81 40 6 10 10 33 39 →= 82 72 27 6 10 33 39 , 83 40 6 10 10 33 39 →= 84 72 27 6 10 33 39 , 85 43 6 10 10 10 10 →= 86 74 27 6 10 10 10 , 85 43 6 10 10 10 31 →= 86 74 27 6 10 10 31 , 85 43 6 10 10 10 32 →= 86 74 27 6 10 10 32 , 85 43 6 10 10 10 33 →= 86 74 27 6 10 10 33 , 85 43 6 10 10 10 34 →= 86 74 27 6 10 10 34 , 85 43 6 10 10 31 23 →= 86 74 27 6 10 31 23 , 85 43 6 10 10 31 35 →= 86 74 27 6 10 31 35 , 85 43 6 10 10 31 36 →= 86 74 27 6 10 31 36 , 85 43 6 10 10 31 4 →= 86 74 27 6 10 31 4 , 6 10 10 10 31 4 26 →= 3 4 5 6 31 4 26 , 6 10 10 10 31 4 5 →= 3 4 5 6 31 4 5 , 6 10 10 10 31 4 87 →= 3 4 5 6 31 4 87 , 6 10 10 10 31 23 24 →= 3 4 5 6 31 23 24 , 6 10 10 10 31 23 28 →= 3 4 5 6 31 23 28 , 6 10 10 10 31 23 88 →= 3 4 5 6 31 23 88 , 6 10 10 10 31 35 89 →= 3 4 5 6 31 35 89 , 40 6 10 10 31 4 26 →= 41 42 5 6 31 4 26 , 40 6 10 10 31 4 5 →= 41 42 5 6 31 4 5 , 40 6 10 10 31 4 87 →= 41 42 5 6 31 4 87 , 43 6 10 10 31 4 26 →= 44 42 5 6 31 4 26 , 43 6 10 10 31 4 5 →= 44 42 5 6 31 4 5 , 43 6 10 10 31 4 87 →= 44 42 5 6 31 4 87 , 2 6 10 10 31 4 26 →= 45 42 5 6 31 4 26 , 2 6 10 10 31 4 5 →= 45 42 5 6 31 4 5 , 2 6 10 10 31 4 87 →= 45 42 5 6 31 4 87 , 27 6 10 10 31 4 26 →= 25 42 5 6 31 4 26 , 27 6 10 10 31 4 5 →= 25 42 5 6 31 4 5 , 27 6 10 10 31 4 87 →= 25 42 5 6 31 4 87 , 46 6 10 10 31 4 26 →= 47 42 5 6 31 4 26 , 46 6 10 10 31 4 5 →= 47 42 5 6 31 4 5 , 46 6 10 10 31 4 87 →= 47 42 5 6 31 4 87 , 13 6 10 10 31 4 26 →= 48 42 5 6 31 4 26 , 13 6 10 10 31 4 5 →= 48 42 5 6 31 4 5 , 13 6 10 10 31 4 87 →= 48 42 5 6 31 4 87 , 19 6 10 10 31 4 26 →= 49 42 5 6 31 4 26 , 19 6 10 10 31 4 5 →= 49 42 5 6 31 4 5 , 19 6 10 10 31 4 87 →= 49 42 5 6 31 4 87 , 5 6 10 10 31 4 26 →= 26 42 5 6 31 4 26 , 5 6 10 10 31 4 5 →= 26 42 5 6 31 4 5 , 5 6 10 10 31 4 87 →= 26 42 5 6 31 4 87 , 40 6 10 10 31 23 24 →= 41 42 5 6 31 23 24 , 40 6 10 10 31 23 28 →= 41 42 5 6 31 23 28 , 40 6 10 10 31 23 88 →= 41 42 5 6 31 23 88 , 43 6 10 10 31 23 24 →= 44 42 5 6 31 23 24 , 43 6 10 10 31 23 28 →= 44 42 5 6 31 23 28 , 43 6 10 10 31 23 88 →= 44 42 5 6 31 23 88 , 2 6 10 10 31 23 24 →= 45 42 5 6 31 23 24 , 2 6 10 10 31 23 28 →= 45 42 5 6 31 23 28 , 2 6 10 10 31 23 88 →= 45 42 5 6 31 23 88 , 27 6 10 10 31 23 24 →= 25 42 5 6 31 23 24 , 27 6 10 10 31 23 28 →= 25 42 5 6 31 23 28 , 27 6 10 10 31 23 88 →= 25 42 5 6 31 23 88 , 46 6 10 10 31 23 24 →= 47 42 5 6 31 23 24 , 46 6 10 10 31 23 28 →= 47 42 5 6 31 23 28 , 46 6 10 10 31 23 88 →= 47 42 5 6 31 23 88 , 13 6 10 10 31 23 24 →= 48 42 5 6 31 23 24 , 13 6 10 10 31 23 28 →= 48 42 5 6 31 23 28 , 13 6 10 10 31 23 88 →= 48 42 5 6 31 23 88 , 19 6 10 10 31 23 24 →= 49 42 5 6 31 23 24 , 19 6 10 10 31 23 28 →= 49 42 5 6 31 23 28 , 19 6 10 10 31 23 88 →= 49 42 5 6 31 23 88 , 5 6 10 10 31 23 24 →= 26 42 5 6 31 23 24 , 5 6 10 10 31 23 28 →= 26 42 5 6 31 23 28 , 5 6 10 10 31 23 88 →= 26 42 5 6 31 23 88 , 40 6 10 10 31 35 89 →= 41 42 5 6 31 35 89 , 43 6 10 10 31 35 89 →= 44 42 5 6 31 35 89 , 2 6 10 10 31 35 89 →= 45 42 5 6 31 35 89 , 27 6 10 10 31 35 89 →= 25 42 5 6 31 35 89 , 46 6 10 10 31 35 89 →= 47 42 5 6 31 35 89 , 13 6 10 10 31 35 89 →= 48 42 5 6 31 35 89 , 19 6 10 10 31 35 89 →= 49 42 5 6 31 35 89 , 5 6 10 10 31 35 89 →= 26 42 5 6 31 35 89 , 1 2 6 10 31 4 26 →= 50 51 27 6 31 4 26 , 1 2 6 10 31 4 5 →= 50 51 27 6 31 4 5 , 1 2 6 10 31 4 87 →= 50 51 27 6 31 4 87 , 52 2 6 10 31 4 26 →= 53 51 27 6 31 4 26 , 52 2 6 10 31 4 5 →= 53 51 27 6 31 4 5 , 52 2 6 10 31 4 87 →= 53 51 27 6 31 4 87 , 1 2 6 10 31 23 24 →= 50 51 27 6 31 23 24 , 1 2 6 10 31 23 28 →= 50 51 27 6 31 23 28 , 1 2 6 10 31 23 88 →= 50 51 27 6 31 23 88 , 52 2 6 10 31 23 24 →= 53 51 27 6 31 23 24 , 52 2 6 10 31 23 28 →= 53 51 27 6 31 23 28 , 52 2 6 10 31 23 88 →= 53 51 27 6 31 23 88 , 1 2 6 10 31 35 89 →= 50 51 27 6 31 35 89 , 52 2 6 10 31 35 89 →= 53 51 27 6 31 35 89 , 54 13 6 10 31 4 26 →= 55 56 27 6 31 4 26 , 54 13 6 10 31 4 5 →= 55 56 27 6 31 4 5 , 54 13 6 10 31 4 87 →= 55 56 27 6 31 4 87 , 12 13 6 10 31 4 26 →= 57 56 27 6 31 4 26 , 12 13 6 10 31 4 5 →= 57 56 27 6 31 4 5 , 12 13 6 10 31 4 87 →= 57 56 27 6 31 4 87 , 54 13 6 10 31 23 24 →= 55 56 27 6 31 23 24 , 54 13 6 10 31 23 28 →= 55 56 27 6 31 23 28 , 54 13 6 10 31 23 88 →= 55 56 27 6 31 23 88 , 12 13 6 10 31 23 24 →= 57 56 27 6 31 23 24 , 12 13 6 10 31 23 28 →= 57 56 27 6 31 23 28 , 12 13 6 10 31 23 88 →= 57 56 27 6 31 23 88 , 54 13 6 10 31 35 89 →= 55 56 27 6 31 35 89 , 12 13 6 10 31 35 89 →= 57 56 27 6 31 35 89 , 58 19 6 10 31 4 26 →= 59 60 27 6 31 4 26 , 58 19 6 10 31 4 5 →= 59 60 27 6 31 4 5 , 58 19 6 10 31 4 87 →= 59 60 27 6 31 4 87 , 18 19 6 10 31 4 26 →= 61 60 27 6 31 4 26 , 18 19 6 10 31 4 5 →= 61 60 27 6 31 4 5 , 18 19 6 10 31 4 87 →= 61 60 27 6 31 4 87 , 58 19 6 10 31 23 24 →= 59 60 27 6 31 23 24 , 58 19 6 10 31 23 28 →= 59 60 27 6 31 23 28 , 58 19 6 10 31 23 88 →= 59 60 27 6 31 23 88 , 18 19 6 10 31 23 24 →= 61 60 27 6 31 23 24 , 18 19 6 10 31 23 28 →= 61 60 27 6 31 23 28 , 18 19 6 10 31 23 88 →= 61 60 27 6 31 23 88 , 58 19 6 10 31 35 89 →= 59 60 27 6 31 35 89 , 18 19 6 10 31 35 89 →= 61 60 27 6 31 35 89 , 9 5 6 10 31 4 26 →= 62 24 27 6 31 4 26 , 9 5 6 10 31 4 5 →= 62 24 27 6 31 4 5 , 9 5 6 10 31 4 87 →= 62 24 27 6 31 4 87 , 42 5 6 10 31 4 26 →= 63 24 27 6 31 4 26 , 42 5 6 10 31 4 5 →= 63 24 27 6 31 4 5 , 42 5 6 10 31 4 87 →= 63 24 27 6 31 4 87 , 16 5 6 10 31 4 26 →= 64 24 27 6 31 4 26 , 16 5 6 10 31 4 5 →= 64 24 27 6 31 4 5 , 16 5 6 10 31 4 87 →= 64 24 27 6 31 4 87 , 22 5 6 10 31 4 26 →= 65 24 27 6 31 4 26 , 22 5 6 10 31 4 5 →= 65 24 27 6 31 4 5 , 22 5 6 10 31 4 87 →= 65 24 27 6 31 4 87 , 4 5 6 10 31 4 26 →= 23 24 27 6 31 4 26 , 4 5 6 10 31 4 5 →= 23 24 27 6 31 4 5 , 4 5 6 10 31 4 87 →= 23 24 27 6 31 4 87 , 66 5 6 10 31 4 26 →= 67 24 27 6 31 4 26 , 66 5 6 10 31 4 5 →= 67 24 27 6 31 4 5 , 66 5 6 10 31 4 87 →= 67 24 27 6 31 4 87 , 68 5 6 10 31 4 26 →= 69 24 27 6 31 4 26 , 68 5 6 10 31 4 5 →= 69 24 27 6 31 4 5 , 68 5 6 10 31 4 87 →= 69 24 27 6 31 4 87 , 70 5 6 10 31 4 26 →= 71 24 27 6 31 4 26 , 70 5 6 10 31 4 5 →= 71 24 27 6 31 4 5 , 70 5 6 10 31 4 87 →= 71 24 27 6 31 4 87 , 9 5 6 10 31 23 24 →= 62 24 27 6 31 23 24 , 9 5 6 10 31 23 28 →= 62 24 27 6 31 23 28 , 9 5 6 10 31 23 88 →= 62 24 27 6 31 23 88 , 42 5 6 10 31 23 24 →= 63 24 27 6 31 23 24 , 42 5 6 10 31 23 28 →= 63 24 27 6 31 23 28 , 42 5 6 10 31 23 88 →= 63 24 27 6 31 23 88 , 16 5 6 10 31 23 24 →= 64 24 27 6 31 23 24 , 16 5 6 10 31 23 28 →= 64 24 27 6 31 23 28 , 16 5 6 10 31 23 88 →= 64 24 27 6 31 23 88 , 22 5 6 10 31 23 24 →= 65 24 27 6 31 23 24 , 22 5 6 10 31 23 28 →= 65 24 27 6 31 23 28 , 22 5 6 10 31 23 88 →= 65 24 27 6 31 23 88 , 4 5 6 10 31 23 24 →= 23 24 27 6 31 23 24 , 4 5 6 10 31 23 28 →= 23 24 27 6 31 23 28 , 4 5 6 10 31 23 88 →= 23 24 27 6 31 23 88 , 66 5 6 10 31 23 24 →= 67 24 27 6 31 23 24 , 66 5 6 10 31 23 28 →= 67 24 27 6 31 23 28 , 66 5 6 10 31 23 88 →= 67 24 27 6 31 23 88 , 68 5 6 10 31 23 24 →= 69 24 27 6 31 23 24 , 68 5 6 10 31 23 28 →= 69 24 27 6 31 23 28 , 68 5 6 10 31 23 88 →= 69 24 27 6 31 23 88 , 70 5 6 10 31 23 24 →= 71 24 27 6 31 23 24 , 70 5 6 10 31 23 28 →= 71 24 27 6 31 23 28 , 70 5 6 10 31 23 88 →= 71 24 27 6 31 23 88 , 9 5 6 10 31 35 89 →= 62 24 27 6 31 35 89 , 42 5 6 10 31 35 89 →= 63 24 27 6 31 35 89 , 16 5 6 10 31 35 89 →= 64 24 27 6 31 35 89 , 22 5 6 10 31 35 89 →= 65 24 27 6 31 35 89 , 4 5 6 10 31 35 89 →= 23 24 27 6 31 35 89 , 66 5 6 10 31 35 89 →= 67 24 27 6 31 35 89 , 68 5 6 10 31 35 89 →= 69 24 27 6 31 35 89 , 70 5 6 10 31 35 89 →= 71 24 27 6 31 35 89 , 24 27 6 10 31 4 26 →= 28 29 27 6 31 4 26 , 24 27 6 10 31 4 5 →= 28 29 27 6 31 4 5 , 24 27 6 10 31 4 87 →= 28 29 27 6 31 4 87 , 72 27 6 10 31 4 26 →= 73 29 27 6 31 4 26 , 72 27 6 10 31 4 5 →= 73 29 27 6 31 4 5 , 72 27 6 10 31 4 87 →= 73 29 27 6 31 4 87 , 74 27 6 10 31 4 26 →= 75 29 27 6 31 4 26 , 74 27 6 10 31 4 5 →= 75 29 27 6 31 4 5 , 74 27 6 10 31 4 87 →= 75 29 27 6 31 4 87 , 29 27 6 10 31 4 26 →= 30 29 27 6 31 4 26 , 29 27 6 10 31 4 5 →= 30 29 27 6 31 4 5 , 29 27 6 10 31 4 87 →= 30 29 27 6 31 4 87 , 76 27 6 10 31 4 26 →= 77 29 27 6 31 4 26 , 76 27 6 10 31 4 5 →= 77 29 27 6 31 4 5 , 76 27 6 10 31 4 87 →= 77 29 27 6 31 4 87 , 51 27 6 10 31 4 26 →= 78 29 27 6 31 4 26 , 51 27 6 10 31 4 5 →= 78 29 27 6 31 4 5 , 51 27 6 10 31 4 87 →= 78 29 27 6 31 4 87 , 56 27 6 10 31 4 26 →= 79 29 27 6 31 4 26 , 56 27 6 10 31 4 5 →= 79 29 27 6 31 4 5 , 56 27 6 10 31 4 87 →= 79 29 27 6 31 4 87 , 60 27 6 10 31 4 26 →= 80 29 27 6 31 4 26 , 60 27 6 10 31 4 5 →= 80 29 27 6 31 4 5 , 60 27 6 10 31 4 87 →= 80 29 27 6 31 4 87 , 24 27 6 10 31 23 24 →= 28 29 27 6 31 23 24 , 24 27 6 10 31 23 28 →= 28 29 27 6 31 23 28 , 24 27 6 10 31 23 88 →= 28 29 27 6 31 23 88 , 72 27 6 10 31 23 24 →= 73 29 27 6 31 23 24 , 72 27 6 10 31 23 28 →= 73 29 27 6 31 23 28 , 72 27 6 10 31 23 88 →= 73 29 27 6 31 23 88 , 74 27 6 10 31 23 24 →= 75 29 27 6 31 23 24 , 74 27 6 10 31 23 28 →= 75 29 27 6 31 23 28 , 74 27 6 10 31 23 88 →= 75 29 27 6 31 23 88 , 29 27 6 10 31 23 24 →= 30 29 27 6 31 23 24 , 29 27 6 10 31 23 28 →= 30 29 27 6 31 23 28 , 29 27 6 10 31 23 88 →= 30 29 27 6 31 23 88 , 76 27 6 10 31 23 24 →= 77 29 27 6 31 23 24 , 76 27 6 10 31 23 28 →= 77 29 27 6 31 23 28 , 76 27 6 10 31 23 88 →= 77 29 27 6 31 23 88 , 51 27 6 10 31 23 24 →= 78 29 27 6 31 23 24 , 51 27 6 10 31 23 28 →= 78 29 27 6 31 23 28 , 51 27 6 10 31 23 88 →= 78 29 27 6 31 23 88 , 56 27 6 10 31 23 24 →= 79 29 27 6 31 23 24 , 56 27 6 10 31 23 28 →= 79 29 27 6 31 23 28 , 56 27 6 10 31 23 88 →= 79 29 27 6 31 23 88 , 60 27 6 10 31 23 24 →= 80 29 27 6 31 23 24 , 60 27 6 10 31 23 28 →= 80 29 27 6 31 23 28 , 60 27 6 10 31 23 88 →= 80 29 27 6 31 23 88 , 24 27 6 10 31 35 89 →= 28 29 27 6 31 35 89 , 72 27 6 10 31 35 89 →= 73 29 27 6 31 35 89 , 74 27 6 10 31 35 89 →= 75 29 27 6 31 35 89 , 29 27 6 10 31 35 89 →= 30 29 27 6 31 35 89 , 76 27 6 10 31 35 89 →= 77 29 27 6 31 35 89 , 51 27 6 10 31 35 89 →= 78 29 27 6 31 35 89 , 56 27 6 10 31 35 89 →= 79 29 27 6 31 35 89 , 60 27 6 10 31 35 89 →= 80 29 27 6 31 35 89 , 81 40 6 10 31 4 26 →= 82 72 27 6 31 4 26 , 81 40 6 10 31 4 5 →= 82 72 27 6 31 4 5 , 81 40 6 10 31 4 87 →= 82 72 27 6 31 4 87 , 83 40 6 10 31 4 26 →= 84 72 27 6 31 4 26 , 83 40 6 10 31 4 5 →= 84 72 27 6 31 4 5 , 83 40 6 10 31 4 87 →= 84 72 27 6 31 4 87 , 81 40 6 10 31 23 24 →= 82 72 27 6 31 23 24 , 81 40 6 10 31 23 28 →= 82 72 27 6 31 23 28 , 81 40 6 10 31 23 88 →= 82 72 27 6 31 23 88 , 83 40 6 10 31 23 24 →= 84 72 27 6 31 23 24 , 83 40 6 10 31 23 28 →= 84 72 27 6 31 23 28 , 83 40 6 10 31 23 88 →= 84 72 27 6 31 23 88 , 81 40 6 10 31 35 89 →= 82 72 27 6 31 35 89 , 83 40 6 10 31 35 89 →= 84 72 27 6 31 35 89 , 85 43 6 10 31 4 26 →= 86 74 27 6 31 4 26 , 85 43 6 10 31 4 5 →= 86 74 27 6 31 4 5 , 85 43 6 10 31 4 87 →= 86 74 27 6 31 4 87 , 85 43 6 10 31 23 24 →= 86 74 27 6 31 23 24 , 85 43 6 10 31 23 28 →= 86 74 27 6 31 23 28 , 85 43 6 10 31 23 88 →= 86 74 27 6 31 23 88 , 6 10 10 10 32 37 90 →= 3 4 5 6 32 37 90 , 40 6 10 10 32 37 90 →= 41 42 5 6 32 37 90 , 43 6 10 10 32 37 90 →= 44 42 5 6 32 37 90 , 2 6 10 10 32 37 90 →= 45 42 5 6 32 37 90 , 27 6 10 10 32 37 90 →= 25 42 5 6 32 37 90 , 46 6 10 10 32 37 90 →= 47 42 5 6 32 37 90 , 13 6 10 10 32 37 90 →= 48 42 5 6 32 37 90 , 19 6 10 10 32 37 90 →= 49 42 5 6 32 37 90 , 5 6 10 10 32 37 90 →= 26 42 5 6 32 37 90 , 9 5 6 10 32 37 90 →= 62 24 27 6 32 37 90 , 42 5 6 10 32 37 90 →= 63 24 27 6 32 37 90 , 16 5 6 10 32 37 90 →= 64 24 27 6 32 37 90 , 22 5 6 10 32 37 90 →= 65 24 27 6 32 37 90 , 4 5 6 10 32 37 90 →= 23 24 27 6 32 37 90 , 66 5 6 10 32 37 90 →= 67 24 27 6 32 37 90 , 68 5 6 10 32 37 90 →= 69 24 27 6 32 37 90 , 70 5 6 10 32 37 90 →= 71 24 27 6 32 37 90 , 24 27 6 10 32 37 90 →= 28 29 27 6 32 37 90 , 72 27 6 10 32 37 90 →= 73 29 27 6 32 37 90 , 74 27 6 10 32 37 90 →= 75 29 27 6 32 37 90 , 29 27 6 10 32 37 90 →= 30 29 27 6 32 37 90 , 76 27 6 10 32 37 90 →= 77 29 27 6 32 37 90 , 51 27 6 10 32 37 90 →= 78 29 27 6 32 37 90 , 56 27 6 10 32 37 90 →= 79 29 27 6 32 37 90 , 60 27 6 10 32 37 90 →= 80 29 27 6 32 37 90 , 8 9 5 3 4 5 6 →= 91 92 4 5 6 10 10 , 93 9 5 3 4 5 6 →= 94 92 4 5 6 10 10 , 31 4 5 3 4 5 6 →= 10 31 4 5 6 10 10 , 41 42 5 3 4 5 6 →= 40 3 4 5 6 10 10 , 44 42 5 3 4 5 6 →= 43 3 4 5 6 10 10 , 45 42 5 3 4 5 6 →= 2 3 4 5 6 10 10 , 25 42 5 3 4 5 6 →= 27 3 4 5 6 10 10 , 47 42 5 3 4 5 6 →= 46 3 4 5 6 10 10 , 48 42 5 3 4 5 6 →= 13 3 4 5 6 10 10 , 49 42 5 3 4 5 6 →= 19 3 4 5 6 10 10 , 26 42 5 3 4 5 6 →= 5 3 4 5 6 10 10 , 15 16 5 3 4 5 6 →= 95 96 4 5 6 10 10 , 97 16 5 3 4 5 6 →= 98 96 4 5 6 10 10 , 99 22 5 3 4 5 6 →= 100 101 4 5 6 10 10 , 21 22 5 3 4 5 6 →= 102 101 4 5 6 10 10 , 103 68 5 3 4 5 6 →= 104 105 4 5 6 10 10 , 106 68 5 3 4 5 6 →= 107 105 4 5 6 10 10 , 108 70 5 3 4 5 6 →= 109 110 4 5 6 10 10 , 50 51 27 3 4 5 6 →= 1 45 42 5 6 10 10 , 53 51 27 3 4 5 6 →= 52 45 42 5 6 10 10 , 55 56 27 3 4 5 6 →= 54 48 42 5 6 10 10 , 57 56 27 3 4 5 6 →= 12 48 42 5 6 10 10 , 59 60 27 3 4 5 6 →= 58 49 42 5 6 10 10 , 61 60 27 3 4 5 6 →= 18 49 42 5 6 10 10 , 62 24 27 3 4 5 6 →= 9 26 42 5 6 10 10 , 63 24 27 3 4 5 6 →= 42 26 42 5 6 10 10 , 64 24 27 3 4 5 6 →= 16 26 42 5 6 10 10 , 65 24 27 3 4 5 6 →= 22 26 42 5 6 10 10 , 23 24 27 3 4 5 6 →= 4 26 42 5 6 10 10 , 67 24 27 3 4 5 6 →= 66 26 42 5 6 10 10 , 69 24 27 3 4 5 6 →= 68 26 42 5 6 10 10 , 71 24 27 3 4 5 6 →= 70 26 42 5 6 10 10 , 28 29 27 3 4 5 6 →= 24 25 42 5 6 10 10 , 73 29 27 3 4 5 6 →= 72 25 42 5 6 10 10 , 75 29 27 3 4 5 6 →= 74 25 42 5 6 10 10 , 30 29 27 3 4 5 6 →= 29 25 42 5 6 10 10 , 77 29 27 3 4 5 6 →= 76 25 42 5 6 10 10 , 78 29 27 3 4 5 6 →= 51 25 42 5 6 10 10 , 79 29 27 3 4 5 6 →= 56 25 42 5 6 10 10 , 80 29 27 3 4 5 6 →= 60 25 42 5 6 10 10 , 82 72 27 3 4 5 6 →= 81 41 42 5 6 10 10 , 84 72 27 3 4 5 6 →= 83 41 42 5 6 10 10 , 86 74 27 3 4 5 6 →= 85 44 42 5 6 10 10 , 111 81 40 3 4 5 6 →= 112 103 68 5 6 10 10 , 8 9 5 3 23 24 25 →= 91 92 4 5 3 4 26 , 8 9 5 3 23 24 27 →= 91 92 4 5 3 4 5 , 93 9 5 3 23 24 25 →= 94 92 4 5 3 4 26 , 93 9 5 3 23 24 27 →= 94 92 4 5 3 4 5 , 8 9 5 3 23 28 29 →= 91 92 4 5 3 23 24 , 8 9 5 3 23 28 30 →= 91 92 4 5 3 23 28 , 93 9 5 3 23 28 29 →= 94 92 4 5 3 23 24 , 93 9 5 3 23 28 30 →= 94 92 4 5 3 23 28 , 31 4 5 3 23 24 25 →= 10 31 4 5 3 4 26 , 31 4 5 3 23 24 27 →= 10 31 4 5 3 4 5 , 31 4 5 3 23 28 29 →= 10 31 4 5 3 23 24 , 31 4 5 3 23 28 30 →= 10 31 4 5 3 23 28 , 41 42 5 3 23 24 25 →= 40 3 4 5 3 4 26 , 41 42 5 3 23 24 27 →= 40 3 4 5 3 4 5 , 44 42 5 3 23 24 25 →= 43 3 4 5 3 4 26 , 44 42 5 3 23 24 27 →= 43 3 4 5 3 4 5 , 45 42 5 3 23 24 25 →= 2 3 4 5 3 4 26 , 45 42 5 3 23 24 27 →= 2 3 4 5 3 4 5 , 25 42 5 3 23 24 25 →= 27 3 4 5 3 4 26 , 25 42 5 3 23 24 27 →= 27 3 4 5 3 4 5 , 47 42 5 3 23 24 25 →= 46 3 4 5 3 4 26 , 47 42 5 3 23 24 27 →= 46 3 4 5 3 4 5 , 48 42 5 3 23 24 25 →= 13 3 4 5 3 4 26 , 48 42 5 3 23 24 27 →= 13 3 4 5 3 4 5 , 49 42 5 3 23 24 25 →= 19 3 4 5 3 4 26 , 49 42 5 3 23 24 27 →= 19 3 4 5 3 4 5 , 26 42 5 3 23 24 25 →= 5 3 4 5 3 4 26 , 26 42 5 3 23 24 27 →= 5 3 4 5 3 4 5 , 41 42 5 3 23 28 29 →= 40 3 4 5 3 23 24 , 41 42 5 3 23 28 30 →= 40 3 4 5 3 23 28 , 44 42 5 3 23 28 29 →= 43 3 4 5 3 23 24 , 44 42 5 3 23 28 30 →= 43 3 4 5 3 23 28 , 45 42 5 3 23 28 29 →= 2 3 4 5 3 23 24 , 45 42 5 3 23 28 30 →= 2 3 4 5 3 23 28 , 25 42 5 3 23 28 29 →= 27 3 4 5 3 23 24 , 25 42 5 3 23 28 30 →= 27 3 4 5 3 23 28 , 47 42 5 3 23 28 29 →= 46 3 4 5 3 23 24 , 47 42 5 3 23 28 30 →= 46 3 4 5 3 23 28 , 48 42 5 3 23 28 29 →= 13 3 4 5 3 23 24 , 48 42 5 3 23 28 30 →= 13 3 4 5 3 23 28 , 49 42 5 3 23 28 29 →= 19 3 4 5 3 23 24 , 49 42 5 3 23 28 30 →= 19 3 4 5 3 23 28 , 26 42 5 3 23 28 29 →= 5 3 4 5 3 23 24 , 26 42 5 3 23 28 30 →= 5 3 4 5 3 23 28 , 15 16 5 3 23 24 25 →= 95 96 4 5 3 4 26 , 15 16 5 3 23 24 27 →= 95 96 4 5 3 4 5 , 97 16 5 3 23 24 25 →= 98 96 4 5 3 4 26 , 97 16 5 3 23 24 27 →= 98 96 4 5 3 4 5 , 15 16 5 3 23 28 29 →= 95 96 4 5 3 23 24 , 15 16 5 3 23 28 30 →= 95 96 4 5 3 23 28 , 97 16 5 3 23 28 29 →= 98 96 4 5 3 23 24 , 97 16 5 3 23 28 30 →= 98 96 4 5 3 23 28 , 99 22 5 3 23 24 25 →= 100 101 4 5 3 4 26 , 99 22 5 3 23 24 27 →= 100 101 4 5 3 4 5 , 21 22 5 3 23 24 25 →= 102 101 4 5 3 4 26 , 21 22 5 3 23 24 27 →= 102 101 4 5 3 4 5 , 99 22 5 3 23 28 29 →= 100 101 4 5 3 23 24 , 99 22 5 3 23 28 30 →= 100 101 4 5 3 23 28 , 21 22 5 3 23 28 29 →= 102 101 4 5 3 23 24 , 21 22 5 3 23 28 30 →= 102 101 4 5 3 23 28 , 103 68 5 3 23 24 25 →= 104 105 4 5 3 4 26 , 103 68 5 3 23 24 27 →= 104 105 4 5 3 4 5 , 106 68 5 3 23 24 25 →= 107 105 4 5 3 4 26 , 106 68 5 3 23 24 27 →= 107 105 4 5 3 4 5 , 103 68 5 3 23 28 29 →= 104 105 4 5 3 23 24 , 103 68 5 3 23 28 30 →= 104 105 4 5 3 23 28 , 106 68 5 3 23 28 29 →= 107 105 4 5 3 23 24 , 106 68 5 3 23 28 30 →= 107 105 4 5 3 23 28 , 108 70 5 3 23 24 25 →= 109 110 4 5 3 4 26 , 108 70 5 3 23 24 27 →= 109 110 4 5 3 4 5 , 108 70 5 3 23 28 29 →= 109 110 4 5 3 23 24 , 108 70 5 3 23 28 30 →= 109 110 4 5 3 23 28 , 50 51 27 3 23 24 25 →= 1 45 42 5 3 4 26 , 50 51 27 3 23 24 27 →= 1 45 42 5 3 4 5 , 53 51 27 3 23 24 25 →= 52 45 42 5 3 4 26 , 53 51 27 3 23 24 27 →= 52 45 42 5 3 4 5 , 50 51 27 3 23 28 29 →= 1 45 42 5 3 23 24 , 50 51 27 3 23 28 30 →= 1 45 42 5 3 23 28 , 53 51 27 3 23 28 29 →= 52 45 42 5 3 23 24 , 53 51 27 3 23 28 30 →= 52 45 42 5 3 23 28 , 55 56 27 3 23 24 25 →= 54 48 42 5 3 4 26 , 55 56 27 3 23 24 27 →= 54 48 42 5 3 4 5 , 57 56 27 3 23 24 25 →= 12 48 42 5 3 4 26 , 57 56 27 3 23 24 27 →= 12 48 42 5 3 4 5 , 55 56 27 3 23 28 29 →= 54 48 42 5 3 23 24 , 55 56 27 3 23 28 30 →= 54 48 42 5 3 23 28 , 57 56 27 3 23 28 29 →= 12 48 42 5 3 23 24 , 57 56 27 3 23 28 30 →= 12 48 42 5 3 23 28 , 59 60 27 3 23 24 25 →= 58 49 42 5 3 4 26 , 59 60 27 3 23 24 27 →= 58 49 42 5 3 4 5 , 61 60 27 3 23 24 25 →= 18 49 42 5 3 4 26 , 61 60 27 3 23 24 27 →= 18 49 42 5 3 4 5 , 59 60 27 3 23 28 29 →= 58 49 42 5 3 23 24 , 59 60 27 3 23 28 30 →= 58 49 42 5 3 23 28 , 61 60 27 3 23 28 29 →= 18 49 42 5 3 23 24 , 61 60 27 3 23 28 30 →= 18 49 42 5 3 23 28 , 62 24 27 3 23 24 25 →= 9 26 42 5 3 4 26 , 62 24 27 3 23 24 27 →= 9 26 42 5 3 4 5 , 63 24 27 3 23 24 25 →= 42 26 42 5 3 4 26 , 63 24 27 3 23 24 27 →= 42 26 42 5 3 4 5 , 64 24 27 3 23 24 25 →= 16 26 42 5 3 4 26 , 64 24 27 3 23 24 27 →= 16 26 42 5 3 4 5 , 65 24 27 3 23 24 25 →= 22 26 42 5 3 4 26 , 65 24 27 3 23 24 27 →= 22 26 42 5 3 4 5 , 23 24 27 3 23 24 25 →= 4 26 42 5 3 4 26 , 23 24 27 3 23 24 27 →= 4 26 42 5 3 4 5 , 67 24 27 3 23 24 25 →= 66 26 42 5 3 4 26 , 67 24 27 3 23 24 27 →= 66 26 42 5 3 4 5 , 69 24 27 3 23 24 25 →= 68 26 42 5 3 4 26 , 69 24 27 3 23 24 27 →= 68 26 42 5 3 4 5 , 71 24 27 3 23 24 25 →= 70 26 42 5 3 4 26 , 71 24 27 3 23 24 27 →= 70 26 42 5 3 4 5 , 62 24 27 3 23 28 29 →= 9 26 42 5 3 23 24 , 62 24 27 3 23 28 30 →= 9 26 42 5 3 23 28 , 63 24 27 3 23 28 29 →= 42 26 42 5 3 23 24 , 63 24 27 3 23 28 30 →= 42 26 42 5 3 23 28 , 64 24 27 3 23 28 29 →= 16 26 42 5 3 23 24 , 64 24 27 3 23 28 30 →= 16 26 42 5 3 23 28 , 65 24 27 3 23 28 29 →= 22 26 42 5 3 23 24 , 65 24 27 3 23 28 30 →= 22 26 42 5 3 23 28 , 23 24 27 3 23 28 29 →= 4 26 42 5 3 23 24 , 23 24 27 3 23 28 30 →= 4 26 42 5 3 23 28 , 67 24 27 3 23 28 29 →= 66 26 42 5 3 23 24 , 67 24 27 3 23 28 30 →= 66 26 42 5 3 23 28 , 69 24 27 3 23 28 29 →= 68 26 42 5 3 23 24 , 69 24 27 3 23 28 30 →= 68 26 42 5 3 23 28 , 71 24 27 3 23 28 29 →= 70 26 42 5 3 23 24 , 71 24 27 3 23 28 30 →= 70 26 42 5 3 23 28 , 28 29 27 3 23 24 25 →= 24 25 42 5 3 4 26 , 28 29 27 3 23 24 27 →= 24 25 42 5 3 4 5 , 73 29 27 3 23 24 25 →= 72 25 42 5 3 4 26 , 73 29 27 3 23 24 27 →= 72 25 42 5 3 4 5 , 75 29 27 3 23 24 25 →= 74 25 42 5 3 4 26 , 75 29 27 3 23 24 27 →= 74 25 42 5 3 4 5 , 30 29 27 3 23 24 25 →= 29 25 42 5 3 4 26 , 30 29 27 3 23 24 27 →= 29 25 42 5 3 4 5 , 77 29 27 3 23 24 25 →= 76 25 42 5 3 4 26 , 77 29 27 3 23 24 27 →= 76 25 42 5 3 4 5 , 78 29 27 3 23 24 25 →= 51 25 42 5 3 4 26 , 78 29 27 3 23 24 27 →= 51 25 42 5 3 4 5 , 79 29 27 3 23 24 25 →= 56 25 42 5 3 4 26 , 79 29 27 3 23 24 27 →= 56 25 42 5 3 4 5 , 80 29 27 3 23 24 25 →= 60 25 42 5 3 4 26 , 80 29 27 3 23 24 27 →= 60 25 42 5 3 4 5 , 28 29 27 3 23 28 29 →= 24 25 42 5 3 23 24 , 28 29 27 3 23 28 30 →= 24 25 42 5 3 23 28 , 73 29 27 3 23 28 29 →= 72 25 42 5 3 23 24 , 73 29 27 3 23 28 30 →= 72 25 42 5 3 23 28 , 75 29 27 3 23 28 29 →= 74 25 42 5 3 23 24 , 75 29 27 3 23 28 30 →= 74 25 42 5 3 23 28 , 30 29 27 3 23 28 29 →= 29 25 42 5 3 23 24 , 30 29 27 3 23 28 30 →= 29 25 42 5 3 23 28 , 77 29 27 3 23 28 29 →= 76 25 42 5 3 23 24 , 77 29 27 3 23 28 30 →= 76 25 42 5 3 23 28 , 78 29 27 3 23 28 29 →= 51 25 42 5 3 23 24 , 78 29 27 3 23 28 30 →= 51 25 42 5 3 23 28 , 79 29 27 3 23 28 29 →= 56 25 42 5 3 23 24 , 79 29 27 3 23 28 30 →= 56 25 42 5 3 23 28 , 80 29 27 3 23 28 29 →= 60 25 42 5 3 23 24 , 80 29 27 3 23 28 30 →= 60 25 42 5 3 23 28 , 82 72 27 3 23 24 25 →= 81 41 42 5 3 4 26 , 82 72 27 3 23 24 27 →= 81 41 42 5 3 4 5 , 84 72 27 3 23 24 25 →= 83 41 42 5 3 4 26 , 84 72 27 3 23 24 27 →= 83 41 42 5 3 4 5 , 82 72 27 3 23 28 29 →= 81 41 42 5 3 23 24 , 82 72 27 3 23 28 30 →= 81 41 42 5 3 23 28 , 84 72 27 3 23 28 29 →= 83 41 42 5 3 23 24 , 84 72 27 3 23 28 30 →= 83 41 42 5 3 23 28 , 86 74 27 3 23 24 25 →= 85 44 42 5 3 4 26 , 86 74 27 3 23 24 27 →= 85 44 42 5 3 4 5 , 86 74 27 3 23 28 29 →= 85 44 42 5 3 23 24 , 86 74 27 3 23 28 30 →= 85 44 42 5 3 23 28 , 111 81 40 3 23 24 25 →= 112 103 68 5 3 4 26 , 111 81 40 3 23 24 27 →= 112 103 68 5 3 4 5 , 111 81 40 3 23 28 29 →= 112 103 68 5 3 23 24 , 111 81 40 3 23 28 30 →= 112 103 68 5 3 23 28 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 33 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 34 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 35 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 36 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 37 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 38 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 39 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 40 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 41 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 42 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 43 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 44 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 45 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 46 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 47 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 48 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 49 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 50 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 51 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 52 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 53 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 54 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 55 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 56 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 57 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 58 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 59 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 60 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 61 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 62 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 63 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 64 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 65 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 66 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 67 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 68 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 69 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 70 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 71 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 72 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 73 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 74 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 75 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 76 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 77 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 78 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 79 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 80 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 81 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 82 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 83 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 84 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 85 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 86 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 87 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 88 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 89 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 90 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 91 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 92 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 93 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 94 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 95 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 96 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 97 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 98 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 99 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 100 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 101 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 102 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 103 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 104 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 105 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 106 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 107 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 108 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 109 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 110 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 111 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 112 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ After renaming modulo the bijection { 6 ↦ 0, 10 ↦ 1, 3 ↦ 2, 4 ↦ 3, 5 ↦ 4, 31 ↦ 5, 32 ↦ 6, 33 ↦ 7, 34 ↦ 8, 23 ↦ 9, 35 ↦ 10, 36 ↦ 11, 37 ↦ 12, 38 ↦ 13, 39 ↦ 14, 40 ↦ 15, 41 ↦ 16, 42 ↦ 17, 43 ↦ 18, 44 ↦ 19, 2 ↦ 20, 45 ↦ 21, 27 ↦ 22, 25 ↦ 23, 46 ↦ 24, 47 ↦ 25, 13 ↦ 26, 48 ↦ 27, 19 ↦ 28, 49 ↦ 29, 26 ↦ 30, 1 ↦ 31, 50 ↦ 32, 51 ↦ 33, 52 ↦ 34, 53 ↦ 35, 54 ↦ 36, 55 ↦ 37, 56 ↦ 38, 12 ↦ 39, 57 ↦ 40, 58 ↦ 41, 59 ↦ 42, 60 ↦ 43, 18 ↦ 44, 61 ↦ 45, 9 ↦ 46, 62 ↦ 47, 24 ↦ 48, 63 ↦ 49, 16 ↦ 50, 64 ↦ 51, 22 ↦ 52, 65 ↦ 53, 66 ↦ 54, 67 ↦ 55, 68 ↦ 56, 69 ↦ 57, 70 ↦ 58, 71 ↦ 59, 28 ↦ 60, 29 ↦ 61, 72 ↦ 62, 73 ↦ 63, 74 ↦ 64, 75 ↦ 65, 30 ↦ 66, 76 ↦ 67, 77 ↦ 68, 78 ↦ 69, 79 ↦ 70, 80 ↦ 71, 81 ↦ 72, 82 ↦ 73, 83 ↦ 74, 84 ↦ 75, 85 ↦ 76, 86 ↦ 77, 87 ↦ 78, 88 ↦ 79, 89 ↦ 80, 90 ↦ 81 }, it remains to prove termination of the 837-rule system { 0 1 1 1 1 1 1 →= 2 3 4 0 1 1 1 , 0 1 1 1 1 1 5 →= 2 3 4 0 1 1 5 , 0 1 1 1 1 1 6 →= 2 3 4 0 1 1 6 , 0 1 1 1 1 1 7 →= 2 3 4 0 1 1 7 , 0 1 1 1 1 1 8 →= 2 3 4 0 1 1 8 , 0 1 1 1 1 5 9 →= 2 3 4 0 1 5 9 , 0 1 1 1 1 5 10 →= 2 3 4 0 1 5 10 , 0 1 1 1 1 5 11 →= 2 3 4 0 1 5 11 , 0 1 1 1 1 5 3 →= 2 3 4 0 1 5 3 , 0 1 1 1 1 6 12 →= 2 3 4 0 1 6 12 , 0 1 1 1 1 6 13 →= 2 3 4 0 1 6 13 , 0 1 1 1 1 7 14 →= 2 3 4 0 1 7 14 , 15 0 1 1 1 1 1 →= 16 17 4 0 1 1 1 , 15 0 1 1 1 1 5 →= 16 17 4 0 1 1 5 , 15 0 1 1 1 1 6 →= 16 17 4 0 1 1 6 , 15 0 1 1 1 1 7 →= 16 17 4 0 1 1 7 , 15 0 1 1 1 1 8 →= 16 17 4 0 1 1 8 , 18 0 1 1 1 1 1 →= 19 17 4 0 1 1 1 , 18 0 1 1 1 1 5 →= 19 17 4 0 1 1 5 , 18 0 1 1 1 1 6 →= 19 17 4 0 1 1 6 , 18 0 1 1 1 1 7 →= 19 17 4 0 1 1 7 , 18 0 1 1 1 1 8 →= 19 17 4 0 1 1 8 , 20 0 1 1 1 1 1 →= 21 17 4 0 1 1 1 , 20 0 1 1 1 1 5 →= 21 17 4 0 1 1 5 , 20 0 1 1 1 1 6 →= 21 17 4 0 1 1 6 , 20 0 1 1 1 1 7 →= 21 17 4 0 1 1 7 , 20 0 1 1 1 1 8 →= 21 17 4 0 1 1 8 , 22 0 1 1 1 1 1 →= 23 17 4 0 1 1 1 , 22 0 1 1 1 1 5 →= 23 17 4 0 1 1 5 , 22 0 1 1 1 1 6 →= 23 17 4 0 1 1 6 , 22 0 1 1 1 1 7 →= 23 17 4 0 1 1 7 , 22 0 1 1 1 1 8 →= 23 17 4 0 1 1 8 , 24 0 1 1 1 1 1 →= 25 17 4 0 1 1 1 , 24 0 1 1 1 1 5 →= 25 17 4 0 1 1 5 , 24 0 1 1 1 1 6 →= 25 17 4 0 1 1 6 , 24 0 1 1 1 1 7 →= 25 17 4 0 1 1 7 , 24 0 1 1 1 1 8 →= 25 17 4 0 1 1 8 , 26 0 1 1 1 1 1 →= 27 17 4 0 1 1 1 , 26 0 1 1 1 1 5 →= 27 17 4 0 1 1 5 , 26 0 1 1 1 1 6 →= 27 17 4 0 1 1 6 , 26 0 1 1 1 1 7 →= 27 17 4 0 1 1 7 , 26 0 1 1 1 1 8 →= 27 17 4 0 1 1 8 , 28 0 1 1 1 1 1 →= 29 17 4 0 1 1 1 , 28 0 1 1 1 1 5 →= 29 17 4 0 1 1 5 , 28 0 1 1 1 1 6 →= 29 17 4 0 1 1 6 , 28 0 1 1 1 1 7 →= 29 17 4 0 1 1 7 , 28 0 1 1 1 1 8 →= 29 17 4 0 1 1 8 , 4 0 1 1 1 1 1 →= 30 17 4 0 1 1 1 , 4 0 1 1 1 1 5 →= 30 17 4 0 1 1 5 , 4 0 1 1 1 1 6 →= 30 17 4 0 1 1 6 , 4 0 1 1 1 1 7 →= 30 17 4 0 1 1 7 , 4 0 1 1 1 1 8 →= 30 17 4 0 1 1 8 , 15 0 1 1 1 5 9 →= 16 17 4 0 1 5 9 , 15 0 1 1 1 5 10 →= 16 17 4 0 1 5 10 , 15 0 1 1 1 5 11 →= 16 17 4 0 1 5 11 , 15 0 1 1 1 5 3 →= 16 17 4 0 1 5 3 , 18 0 1 1 1 5 9 →= 19 17 4 0 1 5 9 , 18 0 1 1 1 5 10 →= 19 17 4 0 1 5 10 , 18 0 1 1 1 5 11 →= 19 17 4 0 1 5 11 , 18 0 1 1 1 5 3 →= 19 17 4 0 1 5 3 , 20 0 1 1 1 5 9 →= 21 17 4 0 1 5 9 , 20 0 1 1 1 5 10 →= 21 17 4 0 1 5 10 , 20 0 1 1 1 5 11 →= 21 17 4 0 1 5 11 , 20 0 1 1 1 5 3 →= 21 17 4 0 1 5 3 , 22 0 1 1 1 5 9 →= 23 17 4 0 1 5 9 , 22 0 1 1 1 5 10 →= 23 17 4 0 1 5 10 , 22 0 1 1 1 5 11 →= 23 17 4 0 1 5 11 , 22 0 1 1 1 5 3 →= 23 17 4 0 1 5 3 , 24 0 1 1 1 5 9 →= 25 17 4 0 1 5 9 , 24 0 1 1 1 5 10 →= 25 17 4 0 1 5 10 , 24 0 1 1 1 5 11 →= 25 17 4 0 1 5 11 , 24 0 1 1 1 5 3 →= 25 17 4 0 1 5 3 , 26 0 1 1 1 5 9 →= 27 17 4 0 1 5 9 , 26 0 1 1 1 5 10 →= 27 17 4 0 1 5 10 , 26 0 1 1 1 5 11 →= 27 17 4 0 1 5 11 , 26 0 1 1 1 5 3 →= 27 17 4 0 1 5 3 , 28 0 1 1 1 5 9 →= 29 17 4 0 1 5 9 , 28 0 1 1 1 5 10 →= 29 17 4 0 1 5 10 , 28 0 1 1 1 5 11 →= 29 17 4 0 1 5 11 , 28 0 1 1 1 5 3 →= 29 17 4 0 1 5 3 , 4 0 1 1 1 5 9 →= 30 17 4 0 1 5 9 , 4 0 1 1 1 5 10 →= 30 17 4 0 1 5 10 , 4 0 1 1 1 5 11 →= 30 17 4 0 1 5 11 , 4 0 1 1 1 5 3 →= 30 17 4 0 1 5 3 , 15 0 1 1 1 6 12 →= 16 17 4 0 1 6 12 , 15 0 1 1 1 6 13 →= 16 17 4 0 1 6 13 , 18 0 1 1 1 6 12 →= 19 17 4 0 1 6 12 , 18 0 1 1 1 6 13 →= 19 17 4 0 1 6 13 , 20 0 1 1 1 6 12 →= 21 17 4 0 1 6 12 , 20 0 1 1 1 6 13 →= 21 17 4 0 1 6 13 , 22 0 1 1 1 6 12 →= 23 17 4 0 1 6 12 , 22 0 1 1 1 6 13 →= 23 17 4 0 1 6 13 , 24 0 1 1 1 6 12 →= 25 17 4 0 1 6 12 , 24 0 1 1 1 6 13 →= 25 17 4 0 1 6 13 , 26 0 1 1 1 6 12 →= 27 17 4 0 1 6 12 , 26 0 1 1 1 6 13 →= 27 17 4 0 1 6 13 , 28 0 1 1 1 6 12 →= 29 17 4 0 1 6 12 , 28 0 1 1 1 6 13 →= 29 17 4 0 1 6 13 , 4 0 1 1 1 6 12 →= 30 17 4 0 1 6 12 , 4 0 1 1 1 6 13 →= 30 17 4 0 1 6 13 , 15 0 1 1 1 7 14 →= 16 17 4 0 1 7 14 , 18 0 1 1 1 7 14 →= 19 17 4 0 1 7 14 , 20 0 1 1 1 7 14 →= 21 17 4 0 1 7 14 , 22 0 1 1 1 7 14 →= 23 17 4 0 1 7 14 , 24 0 1 1 1 7 14 →= 25 17 4 0 1 7 14 , 26 0 1 1 1 7 14 →= 27 17 4 0 1 7 14 , 28 0 1 1 1 7 14 →= 29 17 4 0 1 7 14 , 4 0 1 1 1 7 14 →= 30 17 4 0 1 7 14 , 31 20 0 1 1 1 1 →= 32 33 22 0 1 1 1 , 31 20 0 1 1 1 5 →= 32 33 22 0 1 1 5 , 31 20 0 1 1 1 6 →= 32 33 22 0 1 1 6 , 31 20 0 1 1 1 7 →= 32 33 22 0 1 1 7 , 31 20 0 1 1 1 8 →= 32 33 22 0 1 1 8 , 34 20 0 1 1 1 1 →= 35 33 22 0 1 1 1 , 34 20 0 1 1 1 5 →= 35 33 22 0 1 1 5 , 34 20 0 1 1 1 6 →= 35 33 22 0 1 1 6 , 34 20 0 1 1 1 7 →= 35 33 22 0 1 1 7 , 34 20 0 1 1 1 8 →= 35 33 22 0 1 1 8 , 31 20 0 1 1 5 9 →= 32 33 22 0 1 5 9 , 31 20 0 1 1 5 10 →= 32 33 22 0 1 5 10 , 31 20 0 1 1 5 11 →= 32 33 22 0 1 5 11 , 31 20 0 1 1 5 3 →= 32 33 22 0 1 5 3 , 34 20 0 1 1 5 9 →= 35 33 22 0 1 5 9 , 34 20 0 1 1 5 10 →= 35 33 22 0 1 5 10 , 34 20 0 1 1 5 11 →= 35 33 22 0 1 5 11 , 34 20 0 1 1 5 3 →= 35 33 22 0 1 5 3 , 31 20 0 1 1 6 12 →= 32 33 22 0 1 6 12 , 31 20 0 1 1 6 13 →= 32 33 22 0 1 6 13 , 34 20 0 1 1 6 12 →= 35 33 22 0 1 6 12 , 34 20 0 1 1 6 13 →= 35 33 22 0 1 6 13 , 31 20 0 1 1 7 14 →= 32 33 22 0 1 7 14 , 34 20 0 1 1 7 14 →= 35 33 22 0 1 7 14 , 36 26 0 1 1 1 1 →= 37 38 22 0 1 1 1 , 36 26 0 1 1 1 5 →= 37 38 22 0 1 1 5 , 36 26 0 1 1 1 6 →= 37 38 22 0 1 1 6 , 36 26 0 1 1 1 7 →= 37 38 22 0 1 1 7 , 36 26 0 1 1 1 8 →= 37 38 22 0 1 1 8 , 39 26 0 1 1 1 1 →= 40 38 22 0 1 1 1 , 39 26 0 1 1 1 5 →= 40 38 22 0 1 1 5 , 39 26 0 1 1 1 6 →= 40 38 22 0 1 1 6 , 39 26 0 1 1 1 7 →= 40 38 22 0 1 1 7 , 39 26 0 1 1 1 8 →= 40 38 22 0 1 1 8 , 36 26 0 1 1 5 9 →= 37 38 22 0 1 5 9 , 36 26 0 1 1 5 10 →= 37 38 22 0 1 5 10 , 36 26 0 1 1 5 11 →= 37 38 22 0 1 5 11 , 36 26 0 1 1 5 3 →= 37 38 22 0 1 5 3 , 39 26 0 1 1 5 9 →= 40 38 22 0 1 5 9 , 39 26 0 1 1 5 10 →= 40 38 22 0 1 5 10 , 39 26 0 1 1 5 11 →= 40 38 22 0 1 5 11 , 39 26 0 1 1 5 3 →= 40 38 22 0 1 5 3 , 36 26 0 1 1 6 12 →= 37 38 22 0 1 6 12 , 36 26 0 1 1 6 13 →= 37 38 22 0 1 6 13 , 39 26 0 1 1 6 12 →= 40 38 22 0 1 6 12 , 39 26 0 1 1 6 13 →= 40 38 22 0 1 6 13 , 36 26 0 1 1 7 14 →= 37 38 22 0 1 7 14 , 39 26 0 1 1 7 14 →= 40 38 22 0 1 7 14 , 41 28 0 1 1 1 1 →= 42 43 22 0 1 1 1 , 41 28 0 1 1 1 5 →= 42 43 22 0 1 1 5 , 41 28 0 1 1 1 6 →= 42 43 22 0 1 1 6 , 41 28 0 1 1 1 7 →= 42 43 22 0 1 1 7 , 41 28 0 1 1 1 8 →= 42 43 22 0 1 1 8 , 44 28 0 1 1 1 1 →= 45 43 22 0 1 1 1 , 44 28 0 1 1 1 5 →= 45 43 22 0 1 1 5 , 44 28 0 1 1 1 6 →= 45 43 22 0 1 1 6 , 44 28 0 1 1 1 7 →= 45 43 22 0 1 1 7 , 44 28 0 1 1 1 8 →= 45 43 22 0 1 1 8 , 41 28 0 1 1 5 9 →= 42 43 22 0 1 5 9 , 41 28 0 1 1 5 10 →= 42 43 22 0 1 5 10 , 41 28 0 1 1 5 11 →= 42 43 22 0 1 5 11 , 41 28 0 1 1 5 3 →= 42 43 22 0 1 5 3 , 44 28 0 1 1 5 9 →= 45 43 22 0 1 5 9 , 44 28 0 1 1 5 10 →= 45 43 22 0 1 5 10 , 44 28 0 1 1 5 11 →= 45 43 22 0 1 5 11 , 44 28 0 1 1 5 3 →= 45 43 22 0 1 5 3 , 41 28 0 1 1 6 12 →= 42 43 22 0 1 6 12 , 41 28 0 1 1 6 13 →= 42 43 22 0 1 6 13 , 44 28 0 1 1 6 12 →= 45 43 22 0 1 6 12 , 44 28 0 1 1 6 13 →= 45 43 22 0 1 6 13 , 41 28 0 1 1 7 14 →= 42 43 22 0 1 7 14 , 44 28 0 1 1 7 14 →= 45 43 22 0 1 7 14 , 46 4 0 1 1 1 1 →= 47 48 22 0 1 1 1 , 46 4 0 1 1 1 5 →= 47 48 22 0 1 1 5 , 46 4 0 1 1 1 6 →= 47 48 22 0 1 1 6 , 46 4 0 1 1 1 7 →= 47 48 22 0 1 1 7 , 46 4 0 1 1 1 8 →= 47 48 22 0 1 1 8 , 17 4 0 1 1 1 1 →= 49 48 22 0 1 1 1 , 17 4 0 1 1 1 5 →= 49 48 22 0 1 1 5 , 17 4 0 1 1 1 6 →= 49 48 22 0 1 1 6 , 17 4 0 1 1 1 7 →= 49 48 22 0 1 1 7 , 17 4 0 1 1 1 8 →= 49 48 22 0 1 1 8 , 50 4 0 1 1 1 1 →= 51 48 22 0 1 1 1 , 50 4 0 1 1 1 5 →= 51 48 22 0 1 1 5 , 50 4 0 1 1 1 6 →= 51 48 22 0 1 1 6 , 50 4 0 1 1 1 7 →= 51 48 22 0 1 1 7 , 50 4 0 1 1 1 8 →= 51 48 22 0 1 1 8 , 52 4 0 1 1 1 1 →= 53 48 22 0 1 1 1 , 52 4 0 1 1 1 5 →= 53 48 22 0 1 1 5 , 52 4 0 1 1 1 6 →= 53 48 22 0 1 1 6 , 52 4 0 1 1 1 7 →= 53 48 22 0 1 1 7 , 52 4 0 1 1 1 8 →= 53 48 22 0 1 1 8 , 3 4 0 1 1 1 1 →= 9 48 22 0 1 1 1 , 3 4 0 1 1 1 5 →= 9 48 22 0 1 1 5 , 3 4 0 1 1 1 6 →= 9 48 22 0 1 1 6 , 3 4 0 1 1 1 7 →= 9 48 22 0 1 1 7 , 3 4 0 1 1 1 8 →= 9 48 22 0 1 1 8 , 54 4 0 1 1 1 1 →= 55 48 22 0 1 1 1 , 54 4 0 1 1 1 5 →= 55 48 22 0 1 1 5 , 54 4 0 1 1 1 6 →= 55 48 22 0 1 1 6 , 54 4 0 1 1 1 7 →= 55 48 22 0 1 1 7 , 54 4 0 1 1 1 8 →= 55 48 22 0 1 1 8 , 56 4 0 1 1 1 1 →= 57 48 22 0 1 1 1 , 56 4 0 1 1 1 5 →= 57 48 22 0 1 1 5 , 56 4 0 1 1 1 6 →= 57 48 22 0 1 1 6 , 56 4 0 1 1 1 7 →= 57 48 22 0 1 1 7 , 56 4 0 1 1 1 8 →= 57 48 22 0 1 1 8 , 58 4 0 1 1 1 1 →= 59 48 22 0 1 1 1 , 58 4 0 1 1 1 5 →= 59 48 22 0 1 1 5 , 58 4 0 1 1 1 6 →= 59 48 22 0 1 1 6 , 58 4 0 1 1 1 7 →= 59 48 22 0 1 1 7 , 58 4 0 1 1 1 8 →= 59 48 22 0 1 1 8 , 46 4 0 1 1 5 9 →= 47 48 22 0 1 5 9 , 46 4 0 1 1 5 10 →= 47 48 22 0 1 5 10 , 46 4 0 1 1 5 11 →= 47 48 22 0 1 5 11 , 46 4 0 1 1 5 3 →= 47 48 22 0 1 5 3 , 17 4 0 1 1 5 9 →= 49 48 22 0 1 5 9 , 17 4 0 1 1 5 10 →= 49 48 22 0 1 5 10 , 17 4 0 1 1 5 11 →= 49 48 22 0 1 5 11 , 17 4 0 1 1 5 3 →= 49 48 22 0 1 5 3 , 50 4 0 1 1 5 9 →= 51 48 22 0 1 5 9 , 50 4 0 1 1 5 10 →= 51 48 22 0 1 5 10 , 50 4 0 1 1 5 11 →= 51 48 22 0 1 5 11 , 50 4 0 1 1 5 3 →= 51 48 22 0 1 5 3 , 52 4 0 1 1 5 9 →= 53 48 22 0 1 5 9 , 52 4 0 1 1 5 10 →= 53 48 22 0 1 5 10 , 52 4 0 1 1 5 11 →= 53 48 22 0 1 5 11 , 52 4 0 1 1 5 3 →= 53 48 22 0 1 5 3 , 3 4 0 1 1 5 9 →= 9 48 22 0 1 5 9 , 3 4 0 1 1 5 10 →= 9 48 22 0 1 5 10 , 3 4 0 1 1 5 11 →= 9 48 22 0 1 5 11 , 3 4 0 1 1 5 3 →= 9 48 22 0 1 5 3 , 54 4 0 1 1 5 9 →= 55 48 22 0 1 5 9 , 54 4 0 1 1 5 10 →= 55 48 22 0 1 5 10 , 54 4 0 1 1 5 11 →= 55 48 22 0 1 5 11 , 54 4 0 1 1 5 3 →= 55 48 22 0 1 5 3 , 56 4 0 1 1 5 9 →= 57 48 22 0 1 5 9 , 56 4 0 1 1 5 10 →= 57 48 22 0 1 5 10 , 56 4 0 1 1 5 11 →= 57 48 22 0 1 5 11 , 56 4 0 1 1 5 3 →= 57 48 22 0 1 5 3 , 58 4 0 1 1 5 9 →= 59 48 22 0 1 5 9 , 58 4 0 1 1 5 10 →= 59 48 22 0 1 5 10 , 58 4 0 1 1 5 11 →= 59 48 22 0 1 5 11 , 58 4 0 1 1 5 3 →= 59 48 22 0 1 5 3 , 46 4 0 1 1 6 12 →= 47 48 22 0 1 6 12 , 46 4 0 1 1 6 13 →= 47 48 22 0 1 6 13 , 17 4 0 1 1 6 12 →= 49 48 22 0 1 6 12 , 17 4 0 1 1 6 13 →= 49 48 22 0 1 6 13 , 50 4 0 1 1 6 12 →= 51 48 22 0 1 6 12 , 50 4 0 1 1 6 13 →= 51 48 22 0 1 6 13 , 52 4 0 1 1 6 12 →= 53 48 22 0 1 6 12 , 52 4 0 1 1 6 13 →= 53 48 22 0 1 6 13 , 3 4 0 1 1 6 12 →= 9 48 22 0 1 6 12 , 3 4 0 1 1 6 13 →= 9 48 22 0 1 6 13 , 54 4 0 1 1 6 12 →= 55 48 22 0 1 6 12 , 54 4 0 1 1 6 13 →= 55 48 22 0 1 6 13 , 56 4 0 1 1 6 12 →= 57 48 22 0 1 6 12 , 56 4 0 1 1 6 13 →= 57 48 22 0 1 6 13 , 58 4 0 1 1 6 12 →= 59 48 22 0 1 6 12 , 58 4 0 1 1 6 13 →= 59 48 22 0 1 6 13 , 46 4 0 1 1 7 14 →= 47 48 22 0 1 7 14 , 17 4 0 1 1 7 14 →= 49 48 22 0 1 7 14 , 50 4 0 1 1 7 14 →= 51 48 22 0 1 7 14 , 52 4 0 1 1 7 14 →= 53 48 22 0 1 7 14 , 3 4 0 1 1 7 14 →= 9 48 22 0 1 7 14 , 54 4 0 1 1 7 14 →= 55 48 22 0 1 7 14 , 56 4 0 1 1 7 14 →= 57 48 22 0 1 7 14 , 58 4 0 1 1 7 14 →= 59 48 22 0 1 7 14 , 48 22 0 1 1 1 1 →= 60 61 22 0 1 1 1 , 48 22 0 1 1 1 5 →= 60 61 22 0 1 1 5 , 48 22 0 1 1 1 6 →= 60 61 22 0 1 1 6 , 48 22 0 1 1 1 7 →= 60 61 22 0 1 1 7 , 48 22 0 1 1 1 8 →= 60 61 22 0 1 1 8 , 62 22 0 1 1 1 1 →= 63 61 22 0 1 1 1 , 62 22 0 1 1 1 5 →= 63 61 22 0 1 1 5 , 62 22 0 1 1 1 6 →= 63 61 22 0 1 1 6 , 62 22 0 1 1 1 7 →= 63 61 22 0 1 1 7 , 62 22 0 1 1 1 8 →= 63 61 22 0 1 1 8 , 64 22 0 1 1 1 1 →= 65 61 22 0 1 1 1 , 64 22 0 1 1 1 5 →= 65 61 22 0 1 1 5 , 64 22 0 1 1 1 6 →= 65 61 22 0 1 1 6 , 64 22 0 1 1 1 7 →= 65 61 22 0 1 1 7 , 64 22 0 1 1 1 8 →= 65 61 22 0 1 1 8 , 61 22 0 1 1 1 1 →= 66 61 22 0 1 1 1 , 61 22 0 1 1 1 5 →= 66 61 22 0 1 1 5 , 61 22 0 1 1 1 6 →= 66 61 22 0 1 1 6 , 61 22 0 1 1 1 7 →= 66 61 22 0 1 1 7 , 61 22 0 1 1 1 8 →= 66 61 22 0 1 1 8 , 67 22 0 1 1 1 1 →= 68 61 22 0 1 1 1 , 67 22 0 1 1 1 5 →= 68 61 22 0 1 1 5 , 67 22 0 1 1 1 6 →= 68 61 22 0 1 1 6 , 67 22 0 1 1 1 7 →= 68 61 22 0 1 1 7 , 67 22 0 1 1 1 8 →= 68 61 22 0 1 1 8 , 33 22 0 1 1 1 1 →= 69 61 22 0 1 1 1 , 33 22 0 1 1 1 5 →= 69 61 22 0 1 1 5 , 33 22 0 1 1 1 6 →= 69 61 22 0 1 1 6 , 33 22 0 1 1 1 7 →= 69 61 22 0 1 1 7 , 33 22 0 1 1 1 8 →= 69 61 22 0 1 1 8 , 38 22 0 1 1 1 1 →= 70 61 22 0 1 1 1 , 38 22 0 1 1 1 5 →= 70 61 22 0 1 1 5 , 38 22 0 1 1 1 6 →= 70 61 22 0 1 1 6 , 38 22 0 1 1 1 7 →= 70 61 22 0 1 1 7 , 38 22 0 1 1 1 8 →= 70 61 22 0 1 1 8 , 43 22 0 1 1 1 1 →= 71 61 22 0 1 1 1 , 43 22 0 1 1 1 5 →= 71 61 22 0 1 1 5 , 43 22 0 1 1 1 6 →= 71 61 22 0 1 1 6 , 43 22 0 1 1 1 7 →= 71 61 22 0 1 1 7 , 43 22 0 1 1 1 8 →= 71 61 22 0 1 1 8 , 48 22 0 1 1 5 9 →= 60 61 22 0 1 5 9 , 48 22 0 1 1 5 10 →= 60 61 22 0 1 5 10 , 48 22 0 1 1 5 11 →= 60 61 22 0 1 5 11 , 48 22 0 1 1 5 3 →= 60 61 22 0 1 5 3 , 62 22 0 1 1 5 9 →= 63 61 22 0 1 5 9 , 62 22 0 1 1 5 10 →= 63 61 22 0 1 5 10 , 62 22 0 1 1 5 11 →= 63 61 22 0 1 5 11 , 62 22 0 1 1 5 3 →= 63 61 22 0 1 5 3 , 64 22 0 1 1 5 9 →= 65 61 22 0 1 5 9 , 64 22 0 1 1 5 10 →= 65 61 22 0 1 5 10 , 64 22 0 1 1 5 11 →= 65 61 22 0 1 5 11 , 64 22 0 1 1 5 3 →= 65 61 22 0 1 5 3 , 61 22 0 1 1 5 9 →= 66 61 22 0 1 5 9 , 61 22 0 1 1 5 10 →= 66 61 22 0 1 5 10 , 61 22 0 1 1 5 11 →= 66 61 22 0 1 5 11 , 61 22 0 1 1 5 3 →= 66 61 22 0 1 5 3 , 67 22 0 1 1 5 9 →= 68 61 22 0 1 5 9 , 67 22 0 1 1 5 10 →= 68 61 22 0 1 5 10 , 67 22 0 1 1 5 11 →= 68 61 22 0 1 5 11 , 67 22 0 1 1 5 3 →= 68 61 22 0 1 5 3 , 33 22 0 1 1 5 9 →= 69 61 22 0 1 5 9 , 33 22 0 1 1 5 10 →= 69 61 22 0 1 5 10 , 33 22 0 1 1 5 11 →= 69 61 22 0 1 5 11 , 33 22 0 1 1 5 3 →= 69 61 22 0 1 5 3 , 38 22 0 1 1 5 9 →= 70 61 22 0 1 5 9 , 38 22 0 1 1 5 10 →= 70 61 22 0 1 5 10 , 38 22 0 1 1 5 11 →= 70 61 22 0 1 5 11 , 38 22 0 1 1 5 3 →= 70 61 22 0 1 5 3 , 43 22 0 1 1 5 9 →= 71 61 22 0 1 5 9 , 43 22 0 1 1 5 10 →= 71 61 22 0 1 5 10 , 43 22 0 1 1 5 11 →= 71 61 22 0 1 5 11 , 43 22 0 1 1 5 3 →= 71 61 22 0 1 5 3 , 48 22 0 1 1 6 12 →= 60 61 22 0 1 6 12 , 48 22 0 1 1 6 13 →= 60 61 22 0 1 6 13 , 62 22 0 1 1 6 12 →= 63 61 22 0 1 6 12 , 62 22 0 1 1 6 13 →= 63 61 22 0 1 6 13 , 64 22 0 1 1 6 12 →= 65 61 22 0 1 6 12 , 64 22 0 1 1 6 13 →= 65 61 22 0 1 6 13 , 61 22 0 1 1 6 12 →= 66 61 22 0 1 6 12 , 61 22 0 1 1 6 13 →= 66 61 22 0 1 6 13 , 67 22 0 1 1 6 12 →= 68 61 22 0 1 6 12 , 67 22 0 1 1 6 13 →= 68 61 22 0 1 6 13 , 33 22 0 1 1 6 12 →= 69 61 22 0 1 6 12 , 33 22 0 1 1 6 13 →= 69 61 22 0 1 6 13 , 38 22 0 1 1 6 12 →= 70 61 22 0 1 6 12 , 38 22 0 1 1 6 13 →= 70 61 22 0 1 6 13 , 43 22 0 1 1 6 12 →= 71 61 22 0 1 6 12 , 43 22 0 1 1 6 13 →= 71 61 22 0 1 6 13 , 48 22 0 1 1 7 14 →= 60 61 22 0 1 7 14 , 62 22 0 1 1 7 14 →= 63 61 22 0 1 7 14 , 64 22 0 1 1 7 14 →= 65 61 22 0 1 7 14 , 61 22 0 1 1 7 14 →= 66 61 22 0 1 7 14 , 67 22 0 1 1 7 14 →= 68 61 22 0 1 7 14 , 33 22 0 1 1 7 14 →= 69 61 22 0 1 7 14 , 38 22 0 1 1 7 14 →= 70 61 22 0 1 7 14 , 43 22 0 1 1 7 14 →= 71 61 22 0 1 7 14 , 72 15 0 1 1 1 1 →= 73 62 22 0 1 1 1 , 72 15 0 1 1 1 5 →= 73 62 22 0 1 1 5 , 72 15 0 1 1 1 6 →= 73 62 22 0 1 1 6 , 72 15 0 1 1 1 7 →= 73 62 22 0 1 1 7 , 72 15 0 1 1 1 8 →= 73 62 22 0 1 1 8 , 74 15 0 1 1 1 1 →= 75 62 22 0 1 1 1 , 74 15 0 1 1 1 5 →= 75 62 22 0 1 1 5 , 74 15 0 1 1 1 6 →= 75 62 22 0 1 1 6 , 74 15 0 1 1 1 7 →= 75 62 22 0 1 1 7 , 74 15 0 1 1 1 8 →= 75 62 22 0 1 1 8 , 72 15 0 1 1 5 9 →= 73 62 22 0 1 5 9 , 72 15 0 1 1 5 10 →= 73 62 22 0 1 5 10 , 72 15 0 1 1 5 11 →= 73 62 22 0 1 5 11 , 72 15 0 1 1 5 3 →= 73 62 22 0 1 5 3 , 74 15 0 1 1 5 9 →= 75 62 22 0 1 5 9 , 74 15 0 1 1 5 10 →= 75 62 22 0 1 5 10 , 74 15 0 1 1 5 11 →= 75 62 22 0 1 5 11 , 74 15 0 1 1 5 3 →= 75 62 22 0 1 5 3 , 72 15 0 1 1 6 12 →= 73 62 22 0 1 6 12 , 72 15 0 1 1 6 13 →= 73 62 22 0 1 6 13 , 74 15 0 1 1 6 12 →= 75 62 22 0 1 6 12 , 74 15 0 1 1 6 13 →= 75 62 22 0 1 6 13 , 72 15 0 1 1 7 14 →= 73 62 22 0 1 7 14 , 74 15 0 1 1 7 14 →= 75 62 22 0 1 7 14 , 76 18 0 1 1 1 1 →= 77 64 22 0 1 1 1 , 76 18 0 1 1 1 5 →= 77 64 22 0 1 1 5 , 76 18 0 1 1 1 6 →= 77 64 22 0 1 1 6 , 76 18 0 1 1 1 7 →= 77 64 22 0 1 1 7 , 76 18 0 1 1 1 8 →= 77 64 22 0 1 1 8 , 76 18 0 1 1 5 9 →= 77 64 22 0 1 5 9 , 76 18 0 1 1 5 10 →= 77 64 22 0 1 5 10 , 76 18 0 1 1 5 11 →= 77 64 22 0 1 5 11 , 76 18 0 1 1 5 3 →= 77 64 22 0 1 5 3 , 0 1 1 1 5 3 30 →= 2 3 4 0 5 3 30 , 0 1 1 1 5 3 4 →= 2 3 4 0 5 3 4 , 0 1 1 1 5 3 78 →= 2 3 4 0 5 3 78 , 0 1 1 1 5 9 48 →= 2 3 4 0 5 9 48 , 0 1 1 1 5 9 60 →= 2 3 4 0 5 9 60 , 0 1 1 1 5 9 79 →= 2 3 4 0 5 9 79 , 0 1 1 1 5 10 80 →= 2 3 4 0 5 10 80 , 15 0 1 1 5 3 30 →= 16 17 4 0 5 3 30 , 15 0 1 1 5 3 4 →= 16 17 4 0 5 3 4 , 15 0 1 1 5 3 78 →= 16 17 4 0 5 3 78 , 18 0 1 1 5 3 30 →= 19 17 4 0 5 3 30 , 18 0 1 1 5 3 4 →= 19 17 4 0 5 3 4 , 18 0 1 1 5 3 78 →= 19 17 4 0 5 3 78 , 20 0 1 1 5 3 30 →= 21 17 4 0 5 3 30 , 20 0 1 1 5 3 4 →= 21 17 4 0 5 3 4 , 20 0 1 1 5 3 78 →= 21 17 4 0 5 3 78 , 22 0 1 1 5 3 30 →= 23 17 4 0 5 3 30 , 22 0 1 1 5 3 4 →= 23 17 4 0 5 3 4 , 22 0 1 1 5 3 78 →= 23 17 4 0 5 3 78 , 24 0 1 1 5 3 30 →= 25 17 4 0 5 3 30 , 24 0 1 1 5 3 4 →= 25 17 4 0 5 3 4 , 24 0 1 1 5 3 78 →= 25 17 4 0 5 3 78 , 26 0 1 1 5 3 30 →= 27 17 4 0 5 3 30 , 26 0 1 1 5 3 4 →= 27 17 4 0 5 3 4 , 26 0 1 1 5 3 78 →= 27 17 4 0 5 3 78 , 28 0 1 1 5 3 30 →= 29 17 4 0 5 3 30 , 28 0 1 1 5 3 4 →= 29 17 4 0 5 3 4 , 28 0 1 1 5 3 78 →= 29 17 4 0 5 3 78 , 4 0 1 1 5 3 30 →= 30 17 4 0 5 3 30 , 4 0 1 1 5 3 4 →= 30 17 4 0 5 3 4 , 4 0 1 1 5 3 78 →= 30 17 4 0 5 3 78 , 15 0 1 1 5 9 48 →= 16 17 4 0 5 9 48 , 15 0 1 1 5 9 60 →= 16 17 4 0 5 9 60 , 15 0 1 1 5 9 79 →= 16 17 4 0 5 9 79 , 18 0 1 1 5 9 48 →= 19 17 4 0 5 9 48 , 18 0 1 1 5 9 60 →= 19 17 4 0 5 9 60 , 18 0 1 1 5 9 79 →= 19 17 4 0 5 9 79 , 20 0 1 1 5 9 48 →= 21 17 4 0 5 9 48 , 20 0 1 1 5 9 60 →= 21 17 4 0 5 9 60 , 20 0 1 1 5 9 79 →= 21 17 4 0 5 9 79 , 22 0 1 1 5 9 48 →= 23 17 4 0 5 9 48 , 22 0 1 1 5 9 60 →= 23 17 4 0 5 9 60 , 22 0 1 1 5 9 79 →= 23 17 4 0 5 9 79 , 24 0 1 1 5 9 48 →= 25 17 4 0 5 9 48 , 24 0 1 1 5 9 60 →= 25 17 4 0 5 9 60 , 24 0 1 1 5 9 79 →= 25 17 4 0 5 9 79 , 26 0 1 1 5 9 48 →= 27 17 4 0 5 9 48 , 26 0 1 1 5 9 60 →= 27 17 4 0 5 9 60 , 26 0 1 1 5 9 79 →= 27 17 4 0 5 9 79 , 28 0 1 1 5 9 48 →= 29 17 4 0 5 9 48 , 28 0 1 1 5 9 60 →= 29 17 4 0 5 9 60 , 28 0 1 1 5 9 79 →= 29 17 4 0 5 9 79 , 4 0 1 1 5 9 48 →= 30 17 4 0 5 9 48 , 4 0 1 1 5 9 60 →= 30 17 4 0 5 9 60 , 4 0 1 1 5 9 79 →= 30 17 4 0 5 9 79 , 15 0 1 1 5 10 80 →= 16 17 4 0 5 10 80 , 18 0 1 1 5 10 80 →= 19 17 4 0 5 10 80 , 20 0 1 1 5 10 80 →= 21 17 4 0 5 10 80 , 22 0 1 1 5 10 80 →= 23 17 4 0 5 10 80 , 24 0 1 1 5 10 80 →= 25 17 4 0 5 10 80 , 26 0 1 1 5 10 80 →= 27 17 4 0 5 10 80 , 28 0 1 1 5 10 80 →= 29 17 4 0 5 10 80 , 4 0 1 1 5 10 80 →= 30 17 4 0 5 10 80 , 31 20 0 1 5 3 30 →= 32 33 22 0 5 3 30 , 31 20 0 1 5 3 4 →= 32 33 22 0 5 3 4 , 31 20 0 1 5 3 78 →= 32 33 22 0 5 3 78 , 34 20 0 1 5 3 30 →= 35 33 22 0 5 3 30 , 34 20 0 1 5 3 4 →= 35 33 22 0 5 3 4 , 34 20 0 1 5 3 78 →= 35 33 22 0 5 3 78 , 31 20 0 1 5 9 48 →= 32 33 22 0 5 9 48 , 31 20 0 1 5 9 60 →= 32 33 22 0 5 9 60 , 31 20 0 1 5 9 79 →= 32 33 22 0 5 9 79 , 34 20 0 1 5 9 48 →= 35 33 22 0 5 9 48 , 34 20 0 1 5 9 60 →= 35 33 22 0 5 9 60 , 34 20 0 1 5 9 79 →= 35 33 22 0 5 9 79 , 31 20 0 1 5 10 80 →= 32 33 22 0 5 10 80 , 34 20 0 1 5 10 80 →= 35 33 22 0 5 10 80 , 36 26 0 1 5 3 30 →= 37 38 22 0 5 3 30 , 36 26 0 1 5 3 4 →= 37 38 22 0 5 3 4 , 36 26 0 1 5 3 78 →= 37 38 22 0 5 3 78 , 39 26 0 1 5 3 30 →= 40 38 22 0 5 3 30 , 39 26 0 1 5 3 4 →= 40 38 22 0 5 3 4 , 39 26 0 1 5 3 78 →= 40 38 22 0 5 3 78 , 36 26 0 1 5 9 48 →= 37 38 22 0 5 9 48 , 36 26 0 1 5 9 60 →= 37 38 22 0 5 9 60 , 36 26 0 1 5 9 79 →= 37 38 22 0 5 9 79 , 39 26 0 1 5 9 48 →= 40 38 22 0 5 9 48 , 39 26 0 1 5 9 60 →= 40 38 22 0 5 9 60 , 39 26 0 1 5 9 79 →= 40 38 22 0 5 9 79 , 36 26 0 1 5 10 80 →= 37 38 22 0 5 10 80 , 39 26 0 1 5 10 80 →= 40 38 22 0 5 10 80 , 41 28 0 1 5 3 30 →= 42 43 22 0 5 3 30 , 41 28 0 1 5 3 4 →= 42 43 22 0 5 3 4 , 41 28 0 1 5 3 78 →= 42 43 22 0 5 3 78 , 44 28 0 1 5 3 30 →= 45 43 22 0 5 3 30 , 44 28 0 1 5 3 4 →= 45 43 22 0 5 3 4 , 44 28 0 1 5 3 78 →= 45 43 22 0 5 3 78 , 41 28 0 1 5 9 48 →= 42 43 22 0 5 9 48 , 41 28 0 1 5 9 60 →= 42 43 22 0 5 9 60 , 41 28 0 1 5 9 79 →= 42 43 22 0 5 9 79 , 44 28 0 1 5 9 48 →= 45 43 22 0 5 9 48 , 44 28 0 1 5 9 60 →= 45 43 22 0 5 9 60 , 44 28 0 1 5 9 79 →= 45 43 22 0 5 9 79 , 41 28 0 1 5 10 80 →= 42 43 22 0 5 10 80 , 44 28 0 1 5 10 80 →= 45 43 22 0 5 10 80 , 46 4 0 1 5 3 30 →= 47 48 22 0 5 3 30 , 46 4 0 1 5 3 4 →= 47 48 22 0 5 3 4 , 46 4 0 1 5 3 78 →= 47 48 22 0 5 3 78 , 17 4 0 1 5 3 30 →= 49 48 22 0 5 3 30 , 17 4 0 1 5 3 4 →= 49 48 22 0 5 3 4 , 17 4 0 1 5 3 78 →= 49 48 22 0 5 3 78 , 50 4 0 1 5 3 30 →= 51 48 22 0 5 3 30 , 50 4 0 1 5 3 4 →= 51 48 22 0 5 3 4 , 50 4 0 1 5 3 78 →= 51 48 22 0 5 3 78 , 52 4 0 1 5 3 30 →= 53 48 22 0 5 3 30 , 52 4 0 1 5 3 4 →= 53 48 22 0 5 3 4 , 52 4 0 1 5 3 78 →= 53 48 22 0 5 3 78 , 3 4 0 1 5 3 30 →= 9 48 22 0 5 3 30 , 3 4 0 1 5 3 4 →= 9 48 22 0 5 3 4 , 3 4 0 1 5 3 78 →= 9 48 22 0 5 3 78 , 54 4 0 1 5 3 30 →= 55 48 22 0 5 3 30 , 54 4 0 1 5 3 4 →= 55 48 22 0 5 3 4 , 54 4 0 1 5 3 78 →= 55 48 22 0 5 3 78 , 56 4 0 1 5 3 30 →= 57 48 22 0 5 3 30 , 56 4 0 1 5 3 4 →= 57 48 22 0 5 3 4 , 56 4 0 1 5 3 78 →= 57 48 22 0 5 3 78 , 58 4 0 1 5 3 30 →= 59 48 22 0 5 3 30 , 58 4 0 1 5 3 4 →= 59 48 22 0 5 3 4 , 58 4 0 1 5 3 78 →= 59 48 22 0 5 3 78 , 46 4 0 1 5 9 48 →= 47 48 22 0 5 9 48 , 46 4 0 1 5 9 60 →= 47 48 22 0 5 9 60 , 46 4 0 1 5 9 79 →= 47 48 22 0 5 9 79 , 17 4 0 1 5 9 48 →= 49 48 22 0 5 9 48 , 17 4 0 1 5 9 60 →= 49 48 22 0 5 9 60 , 17 4 0 1 5 9 79 →= 49 48 22 0 5 9 79 , 50 4 0 1 5 9 48 →= 51 48 22 0 5 9 48 , 50 4 0 1 5 9 60 →= 51 48 22 0 5 9 60 , 50 4 0 1 5 9 79 →= 51 48 22 0 5 9 79 , 52 4 0 1 5 9 48 →= 53 48 22 0 5 9 48 , 52 4 0 1 5 9 60 →= 53 48 22 0 5 9 60 , 52 4 0 1 5 9 79 →= 53 48 22 0 5 9 79 , 3 4 0 1 5 9 48 →= 9 48 22 0 5 9 48 , 3 4 0 1 5 9 60 →= 9 48 22 0 5 9 60 , 3 4 0 1 5 9 79 →= 9 48 22 0 5 9 79 , 54 4 0 1 5 9 48 →= 55 48 22 0 5 9 48 , 54 4 0 1 5 9 60 →= 55 48 22 0 5 9 60 , 54 4 0 1 5 9 79 →= 55 48 22 0 5 9 79 , 56 4 0 1 5 9 48 →= 57 48 22 0 5 9 48 , 56 4 0 1 5 9 60 →= 57 48 22 0 5 9 60 , 56 4 0 1 5 9 79 →= 57 48 22 0 5 9 79 , 58 4 0 1 5 9 48 →= 59 48 22 0 5 9 48 , 58 4 0 1 5 9 60 →= 59 48 22 0 5 9 60 , 58 4 0 1 5 9 79 →= 59 48 22 0 5 9 79 , 46 4 0 1 5 10 80 →= 47 48 22 0 5 10 80 , 17 4 0 1 5 10 80 →= 49 48 22 0 5 10 80 , 50 4 0 1 5 10 80 →= 51 48 22 0 5 10 80 , 52 4 0 1 5 10 80 →= 53 48 22 0 5 10 80 , 3 4 0 1 5 10 80 →= 9 48 22 0 5 10 80 , 54 4 0 1 5 10 80 →= 55 48 22 0 5 10 80 , 56 4 0 1 5 10 80 →= 57 48 22 0 5 10 80 , 58 4 0 1 5 10 80 →= 59 48 22 0 5 10 80 , 48 22 0 1 5 3 30 →= 60 61 22 0 5 3 30 , 48 22 0 1 5 3 4 →= 60 61 22 0 5 3 4 , 48 22 0 1 5 3 78 →= 60 61 22 0 5 3 78 , 62 22 0 1 5 3 30 →= 63 61 22 0 5 3 30 , 62 22 0 1 5 3 4 →= 63 61 22 0 5 3 4 , 62 22 0 1 5 3 78 →= 63 61 22 0 5 3 78 , 64 22 0 1 5 3 30 →= 65 61 22 0 5 3 30 , 64 22 0 1 5 3 4 →= 65 61 22 0 5 3 4 , 64 22 0 1 5 3 78 →= 65 61 22 0 5 3 78 , 61 22 0 1 5 3 30 →= 66 61 22 0 5 3 30 , 61 22 0 1 5 3 4 →= 66 61 22 0 5 3 4 , 61 22 0 1 5 3 78 →= 66 61 22 0 5 3 78 , 67 22 0 1 5 3 30 →= 68 61 22 0 5 3 30 , 67 22 0 1 5 3 4 →= 68 61 22 0 5 3 4 , 67 22 0 1 5 3 78 →= 68 61 22 0 5 3 78 , 33 22 0 1 5 3 30 →= 69 61 22 0 5 3 30 , 33 22 0 1 5 3 4 →= 69 61 22 0 5 3 4 , 33 22 0 1 5 3 78 →= 69 61 22 0 5 3 78 , 38 22 0 1 5 3 30 →= 70 61 22 0 5 3 30 , 38 22 0 1 5 3 4 →= 70 61 22 0 5 3 4 , 38 22 0 1 5 3 78 →= 70 61 22 0 5 3 78 , 43 22 0 1 5 3 30 →= 71 61 22 0 5 3 30 , 43 22 0 1 5 3 4 →= 71 61 22 0 5 3 4 , 43 22 0 1 5 3 78 →= 71 61 22 0 5 3 78 , 48 22 0 1 5 9 48 →= 60 61 22 0 5 9 48 , 48 22 0 1 5 9 60 →= 60 61 22 0 5 9 60 , 48 22 0 1 5 9 79 →= 60 61 22 0 5 9 79 , 62 22 0 1 5 9 48 →= 63 61 22 0 5 9 48 , 62 22 0 1 5 9 60 →= 63 61 22 0 5 9 60 , 62 22 0 1 5 9 79 →= 63 61 22 0 5 9 79 , 64 22 0 1 5 9 48 →= 65 61 22 0 5 9 48 , 64 22 0 1 5 9 60 →= 65 61 22 0 5 9 60 , 64 22 0 1 5 9 79 →= 65 61 22 0 5 9 79 , 61 22 0 1 5 9 48 →= 66 61 22 0 5 9 48 , 61 22 0 1 5 9 60 →= 66 61 22 0 5 9 60 , 61 22 0 1 5 9 79 →= 66 61 22 0 5 9 79 , 67 22 0 1 5 9 48 →= 68 61 22 0 5 9 48 , 67 22 0 1 5 9 60 →= 68 61 22 0 5 9 60 , 67 22 0 1 5 9 79 →= 68 61 22 0 5 9 79 , 33 22 0 1 5 9 48 →= 69 61 22 0 5 9 48 , 33 22 0 1 5 9 60 →= 69 61 22 0 5 9 60 , 33 22 0 1 5 9 79 →= 69 61 22 0 5 9 79 , 38 22 0 1 5 9 48 →= 70 61 22 0 5 9 48 , 38 22 0 1 5 9 60 →= 70 61 22 0 5 9 60 , 38 22 0 1 5 9 79 →= 70 61 22 0 5 9 79 , 43 22 0 1 5 9 48 →= 71 61 22 0 5 9 48 , 43 22 0 1 5 9 60 →= 71 61 22 0 5 9 60 , 43 22 0 1 5 9 79 →= 71 61 22 0 5 9 79 , 48 22 0 1 5 10 80 →= 60 61 22 0 5 10 80 , 62 22 0 1 5 10 80 →= 63 61 22 0 5 10 80 , 64 22 0 1 5 10 80 →= 65 61 22 0 5 10 80 , 61 22 0 1 5 10 80 →= 66 61 22 0 5 10 80 , 67 22 0 1 5 10 80 →= 68 61 22 0 5 10 80 , 33 22 0 1 5 10 80 →= 69 61 22 0 5 10 80 , 38 22 0 1 5 10 80 →= 70 61 22 0 5 10 80 , 43 22 0 1 5 10 80 →= 71 61 22 0 5 10 80 , 72 15 0 1 5 3 30 →= 73 62 22 0 5 3 30 , 72 15 0 1 5 3 4 →= 73 62 22 0 5 3 4 , 72 15 0 1 5 3 78 →= 73 62 22 0 5 3 78 , 74 15 0 1 5 3 30 →= 75 62 22 0 5 3 30 , 74 15 0 1 5 3 4 →= 75 62 22 0 5 3 4 , 74 15 0 1 5 3 78 →= 75 62 22 0 5 3 78 , 72 15 0 1 5 9 48 →= 73 62 22 0 5 9 48 , 72 15 0 1 5 9 60 →= 73 62 22 0 5 9 60 , 72 15 0 1 5 9 79 →= 73 62 22 0 5 9 79 , 74 15 0 1 5 9 48 →= 75 62 22 0 5 9 48 , 74 15 0 1 5 9 60 →= 75 62 22 0 5 9 60 , 74 15 0 1 5 9 79 →= 75 62 22 0 5 9 79 , 72 15 0 1 5 10 80 →= 73 62 22 0 5 10 80 , 74 15 0 1 5 10 80 →= 75 62 22 0 5 10 80 , 76 18 0 1 5 3 30 →= 77 64 22 0 5 3 30 , 76 18 0 1 5 3 4 →= 77 64 22 0 5 3 4 , 76 18 0 1 5 3 78 →= 77 64 22 0 5 3 78 , 76 18 0 1 5 9 48 →= 77 64 22 0 5 9 48 , 76 18 0 1 5 9 60 →= 77 64 22 0 5 9 60 , 76 18 0 1 5 9 79 →= 77 64 22 0 5 9 79 , 0 1 1 1 6 12 81 →= 2 3 4 0 6 12 81 , 15 0 1 1 6 12 81 →= 16 17 4 0 6 12 81 , 18 0 1 1 6 12 81 →= 19 17 4 0 6 12 81 , 20 0 1 1 6 12 81 →= 21 17 4 0 6 12 81 , 22 0 1 1 6 12 81 →= 23 17 4 0 6 12 81 , 24 0 1 1 6 12 81 →= 25 17 4 0 6 12 81 , 26 0 1 1 6 12 81 →= 27 17 4 0 6 12 81 , 28 0 1 1 6 12 81 →= 29 17 4 0 6 12 81 , 4 0 1 1 6 12 81 →= 30 17 4 0 6 12 81 , 46 4 0 1 6 12 81 →= 47 48 22 0 6 12 81 , 17 4 0 1 6 12 81 →= 49 48 22 0 6 12 81 , 50 4 0 1 6 12 81 →= 51 48 22 0 6 12 81 , 52 4 0 1 6 12 81 →= 53 48 22 0 6 12 81 , 3 4 0 1 6 12 81 →= 9 48 22 0 6 12 81 , 54 4 0 1 6 12 81 →= 55 48 22 0 6 12 81 , 56 4 0 1 6 12 81 →= 57 48 22 0 6 12 81 , 58 4 0 1 6 12 81 →= 59 48 22 0 6 12 81 , 48 22 0 1 6 12 81 →= 60 61 22 0 6 12 81 , 62 22 0 1 6 12 81 →= 63 61 22 0 6 12 81 , 64 22 0 1 6 12 81 →= 65 61 22 0 6 12 81 , 61 22 0 1 6 12 81 →= 66 61 22 0 6 12 81 , 67 22 0 1 6 12 81 →= 68 61 22 0 6 12 81 , 33 22 0 1 6 12 81 →= 69 61 22 0 6 12 81 , 38 22 0 1 6 12 81 →= 70 61 22 0 6 12 81 , 43 22 0 1 6 12 81 →= 71 61 22 0 6 12 81 , 5 3 4 2 3 4 0 →= 1 5 3 4 0 1 1 , 16 17 4 2 3 4 0 →= 15 2 3 4 0 1 1 , 19 17 4 2 3 4 0 →= 18 2 3 4 0 1 1 , 21 17 4 2 3 4 0 →= 20 2 3 4 0 1 1 , 23 17 4 2 3 4 0 →= 22 2 3 4 0 1 1 , 25 17 4 2 3 4 0 →= 24 2 3 4 0 1 1 , 27 17 4 2 3 4 0 →= 26 2 3 4 0 1 1 , 29 17 4 2 3 4 0 →= 28 2 3 4 0 1 1 , 30 17 4 2 3 4 0 →= 4 2 3 4 0 1 1 , 32 33 22 2 3 4 0 →= 31 21 17 4 0 1 1 , 35 33 22 2 3 4 0 →= 34 21 17 4 0 1 1 , 37 38 22 2 3 4 0 →= 36 27 17 4 0 1 1 , 40 38 22 2 3 4 0 →= 39 27 17 4 0 1 1 , 42 43 22 2 3 4 0 →= 41 29 17 4 0 1 1 , 45 43 22 2 3 4 0 →= 44 29 17 4 0 1 1 , 47 48 22 2 3 4 0 →= 46 30 17 4 0 1 1 , 49 48 22 2 3 4 0 →= 17 30 17 4 0 1 1 , 51 48 22 2 3 4 0 →= 50 30 17 4 0 1 1 , 53 48 22 2 3 4 0 →= 52 30 17 4 0 1 1 , 9 48 22 2 3 4 0 →= 3 30 17 4 0 1 1 , 55 48 22 2 3 4 0 →= 54 30 17 4 0 1 1 , 57 48 22 2 3 4 0 →= 56 30 17 4 0 1 1 , 59 48 22 2 3 4 0 →= 58 30 17 4 0 1 1 , 60 61 22 2 3 4 0 →= 48 23 17 4 0 1 1 , 63 61 22 2 3 4 0 →= 62 23 17 4 0 1 1 , 65 61 22 2 3 4 0 →= 64 23 17 4 0 1 1 , 66 61 22 2 3 4 0 →= 61 23 17 4 0 1 1 , 68 61 22 2 3 4 0 →= 67 23 17 4 0 1 1 , 69 61 22 2 3 4 0 →= 33 23 17 4 0 1 1 , 70 61 22 2 3 4 0 →= 38 23 17 4 0 1 1 , 71 61 22 2 3 4 0 →= 43 23 17 4 0 1 1 , 73 62 22 2 3 4 0 →= 72 16 17 4 0 1 1 , 75 62 22 2 3 4 0 →= 74 16 17 4 0 1 1 , 77 64 22 2 3 4 0 →= 76 19 17 4 0 1 1 , 5 3 4 2 9 48 23 →= 1 5 3 4 2 3 30 , 5 3 4 2 9 48 22 →= 1 5 3 4 2 3 4 , 5 3 4 2 9 60 61 →= 1 5 3 4 2 9 48 , 5 3 4 2 9 60 66 →= 1 5 3 4 2 9 60 , 16 17 4 2 9 48 23 →= 15 2 3 4 2 3 30 , 16 17 4 2 9 48 22 →= 15 2 3 4 2 3 4 , 19 17 4 2 9 48 23 →= 18 2 3 4 2 3 30 , 19 17 4 2 9 48 22 →= 18 2 3 4 2 3 4 , 21 17 4 2 9 48 23 →= 20 2 3 4 2 3 30 , 21 17 4 2 9 48 22 →= 20 2 3 4 2 3 4 , 23 17 4 2 9 48 23 →= 22 2 3 4 2 3 30 , 23 17 4 2 9 48 22 →= 22 2 3 4 2 3 4 , 25 17 4 2 9 48 23 →= 24 2 3 4 2 3 30 , 25 17 4 2 9 48 22 →= 24 2 3 4 2 3 4 , 27 17 4 2 9 48 23 →= 26 2 3 4 2 3 30 , 27 17 4 2 9 48 22 →= 26 2 3 4 2 3 4 , 29 17 4 2 9 48 23 →= 28 2 3 4 2 3 30 , 29 17 4 2 9 48 22 →= 28 2 3 4 2 3 4 , 30 17 4 2 9 48 23 →= 4 2 3 4 2 3 30 , 30 17 4 2 9 48 22 →= 4 2 3 4 2 3 4 , 16 17 4 2 9 60 61 →= 15 2 3 4 2 9 48 , 16 17 4 2 9 60 66 →= 15 2 3 4 2 9 60 , 19 17 4 2 9 60 61 →= 18 2 3 4 2 9 48 , 19 17 4 2 9 60 66 →= 18 2 3 4 2 9 60 , 21 17 4 2 9 60 61 →= 20 2 3 4 2 9 48 , 21 17 4 2 9 60 66 →= 20 2 3 4 2 9 60 , 23 17 4 2 9 60 61 →= 22 2 3 4 2 9 48 , 23 17 4 2 9 60 66 →= 22 2 3 4 2 9 60 , 25 17 4 2 9 60 61 →= 24 2 3 4 2 9 48 , 25 17 4 2 9 60 66 →= 24 2 3 4 2 9 60 , 27 17 4 2 9 60 61 →= 26 2 3 4 2 9 48 , 27 17 4 2 9 60 66 →= 26 2 3 4 2 9 60 , 29 17 4 2 9 60 61 →= 28 2 3 4 2 9 48 , 29 17 4 2 9 60 66 →= 28 2 3 4 2 9 60 , 30 17 4 2 9 60 61 →= 4 2 3 4 2 9 48 , 30 17 4 2 9 60 66 →= 4 2 3 4 2 9 60 , 32 33 22 2 9 48 23 →= 31 21 17 4 2 3 30 , 32 33 22 2 9 48 22 →= 31 21 17 4 2 3 4 , 35 33 22 2 9 48 23 →= 34 21 17 4 2 3 30 , 35 33 22 2 9 48 22 →= 34 21 17 4 2 3 4 , 32 33 22 2 9 60 61 →= 31 21 17 4 2 9 48 , 32 33 22 2 9 60 66 →= 31 21 17 4 2 9 60 , 35 33 22 2 9 60 61 →= 34 21 17 4 2 9 48 , 35 33 22 2 9 60 66 →= 34 21 17 4 2 9 60 , 37 38 22 2 9 48 23 →= 36 27 17 4 2 3 30 , 37 38 22 2 9 48 22 →= 36 27 17 4 2 3 4 , 40 38 22 2 9 48 23 →= 39 27 17 4 2 3 30 , 40 38 22 2 9 48 22 →= 39 27 17 4 2 3 4 , 37 38 22 2 9 60 61 →= 36 27 17 4 2 9 48 , 37 38 22 2 9 60 66 →= 36 27 17 4 2 9 60 , 40 38 22 2 9 60 61 →= 39 27 17 4 2 9 48 , 40 38 22 2 9 60 66 →= 39 27 17 4 2 9 60 , 42 43 22 2 9 48 23 →= 41 29 17 4 2 3 30 , 42 43 22 2 9 48 22 →= 41 29 17 4 2 3 4 , 45 43 22 2 9 48 23 →= 44 29 17 4 2 3 30 , 45 43 22 2 9 48 22 →= 44 29 17 4 2 3 4 , 42 43 22 2 9 60 61 →= 41 29 17 4 2 9 48 , 42 43 22 2 9 60 66 →= 41 29 17 4 2 9 60 , 45 43 22 2 9 60 61 →= 44 29 17 4 2 9 48 , 45 43 22 2 9 60 66 →= 44 29 17 4 2 9 60 , 47 48 22 2 9 48 23 →= 46 30 17 4 2 3 30 , 47 48 22 2 9 48 22 →= 46 30 17 4 2 3 4 , 49 48 22 2 9 48 23 →= 17 30 17 4 2 3 30 , 49 48 22 2 9 48 22 →= 17 30 17 4 2 3 4 , 51 48 22 2 9 48 23 →= 50 30 17 4 2 3 30 , 51 48 22 2 9 48 22 →= 50 30 17 4 2 3 4 , 53 48 22 2 9 48 23 →= 52 30 17 4 2 3 30 , 53 48 22 2 9 48 22 →= 52 30 17 4 2 3 4 , 9 48 22 2 9 48 23 →= 3 30 17 4 2 3 30 , 9 48 22 2 9 48 22 →= 3 30 17 4 2 3 4 , 55 48 22 2 9 48 23 →= 54 30 17 4 2 3 30 , 55 48 22 2 9 48 22 →= 54 30 17 4 2 3 4 , 57 48 22 2 9 48 23 →= 56 30 17 4 2 3 30 , 57 48 22 2 9 48 22 →= 56 30 17 4 2 3 4 , 59 48 22 2 9 48 23 →= 58 30 17 4 2 3 30 , 59 48 22 2 9 48 22 →= 58 30 17 4 2 3 4 , 47 48 22 2 9 60 61 →= 46 30 17 4 2 9 48 , 47 48 22 2 9 60 66 →= 46 30 17 4 2 9 60 , 49 48 22 2 9 60 61 →= 17 30 17 4 2 9 48 , 49 48 22 2 9 60 66 →= 17 30 17 4 2 9 60 , 51 48 22 2 9 60 61 →= 50 30 17 4 2 9 48 , 51 48 22 2 9 60 66 →= 50 30 17 4 2 9 60 , 53 48 22 2 9 60 61 →= 52 30 17 4 2 9 48 , 53 48 22 2 9 60 66 →= 52 30 17 4 2 9 60 , 9 48 22 2 9 60 61 →= 3 30 17 4 2 9 48 , 9 48 22 2 9 60 66 →= 3 30 17 4 2 9 60 , 55 48 22 2 9 60 61 →= 54 30 17 4 2 9 48 , 55 48 22 2 9 60 66 →= 54 30 17 4 2 9 60 , 57 48 22 2 9 60 61 →= 56 30 17 4 2 9 48 , 57 48 22 2 9 60 66 →= 56 30 17 4 2 9 60 , 59 48 22 2 9 60 61 →= 58 30 17 4 2 9 48 , 59 48 22 2 9 60 66 →= 58 30 17 4 2 9 60 , 60 61 22 2 9 48 23 →= 48 23 17 4 2 3 30 , 60 61 22 2 9 48 22 →= 48 23 17 4 2 3 4 , 63 61 22 2 9 48 23 →= 62 23 17 4 2 3 30 , 63 61 22 2 9 48 22 →= 62 23 17 4 2 3 4 , 65 61 22 2 9 48 23 →= 64 23 17 4 2 3 30 , 65 61 22 2 9 48 22 →= 64 23 17 4 2 3 4 , 66 61 22 2 9 48 23 →= 61 23 17 4 2 3 30 , 66 61 22 2 9 48 22 →= 61 23 17 4 2 3 4 , 68 61 22 2 9 48 23 →= 67 23 17 4 2 3 30 , 68 61 22 2 9 48 22 →= 67 23 17 4 2 3 4 , 69 61 22 2 9 48 23 →= 33 23 17 4 2 3 30 , 69 61 22 2 9 48 22 →= 33 23 17 4 2 3 4 , 70 61 22 2 9 48 23 →= 38 23 17 4 2 3 30 , 70 61 22 2 9 48 22 →= 38 23 17 4 2 3 4 , 71 61 22 2 9 48 23 →= 43 23 17 4 2 3 30 , 71 61 22 2 9 48 22 →= 43 23 17 4 2 3 4 , 60 61 22 2 9 60 61 →= 48 23 17 4 2 9 48 , 60 61 22 2 9 60 66 →= 48 23 17 4 2 9 60 , 63 61 22 2 9 60 61 →= 62 23 17 4 2 9 48 , 63 61 22 2 9 60 66 →= 62 23 17 4 2 9 60 , 65 61 22 2 9 60 61 →= 64 23 17 4 2 9 48 , 65 61 22 2 9 60 66 →= 64 23 17 4 2 9 60 , 66 61 22 2 9 60 61 →= 61 23 17 4 2 9 48 , 66 61 22 2 9 60 66 →= 61 23 17 4 2 9 60 , 68 61 22 2 9 60 61 →= 67 23 17 4 2 9 48 , 68 61 22 2 9 60 66 →= 67 23 17 4 2 9 60 , 69 61 22 2 9 60 61 →= 33 23 17 4 2 9 48 , 69 61 22 2 9 60 66 →= 33 23 17 4 2 9 60 , 70 61 22 2 9 60 61 →= 38 23 17 4 2 9 48 , 70 61 22 2 9 60 66 →= 38 23 17 4 2 9 60 , 71 61 22 2 9 60 61 →= 43 23 17 4 2 9 48 , 71 61 22 2 9 60 66 →= 43 23 17 4 2 9 60 , 73 62 22 2 9 48 23 →= 72 16 17 4 2 3 30 , 73 62 22 2 9 48 22 →= 72 16 17 4 2 3 4 , 75 62 22 2 9 48 23 →= 74 16 17 4 2 3 30 , 75 62 22 2 9 48 22 →= 74 16 17 4 2 3 4 , 73 62 22 2 9 60 61 →= 72 16 17 4 2 9 48 , 73 62 22 2 9 60 66 →= 72 16 17 4 2 9 60 , 75 62 22 2 9 60 61 →= 74 16 17 4 2 9 48 , 75 62 22 2 9 60 66 →= 74 16 17 4 2 9 60 , 77 64 22 2 9 48 23 →= 76 19 17 4 2 3 30 , 77 64 22 2 9 48 22 →= 76 19 17 4 2 3 4 , 77 64 22 2 9 60 61 →= 76 19 17 4 2 9 48 , 77 64 22 2 9 60 66 →= 76 19 17 4 2 9 60 } The system is trivially terminating.