/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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 1 0 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 1 2 0 0 , 1 2 0 1 3 ⟶ 0 1 2 0 1 , 1 2 0 1 5 ⟶ 0 1 2 0 4 , 3 2 0 1 2 ⟶ 2 1 2 0 0 , 3 2 0 1 3 ⟶ 2 1 2 0 1 , 3 2 0 1 5 ⟶ 2 1 2 0 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 1 2 0 0 , 1 2 0 1 3 ⟶ 0 1 2 0 1 , 1 2 0 1 5 ⟶ 0 1 2 0 4 , 3 2 0 1 2 ⟶ 2 1 2 0 0 , 3 2 0 1 3 ⟶ 2 1 2 0 1 , 3 2 0 1 5 ⟶ 2 1 2 0 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 0 1 2 0 , 3 2 0 1 2 ⟶ 2 0 1 2 0 , 5 2 0 1 2 ⟶ 4 0 1 2 0 , 1 2 0 1 3 ⟶ 0 0 1 2 1 , 3 2 0 1 3 ⟶ 2 0 1 2 1 , 5 2 0 1 3 ⟶ 4 0 1 2 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 1 8 3 1 , 2 3 1 8 3 ⟶ 0 8 3 1 , 2 3 1 8 3 ⟶ 2 3 1 , 2 3 1 8 3 ⟶ 4 1 , 2 3 1 8 3 ⟶ 0 , 5 3 1 8 3 ⟶ 4 1 8 3 1 , 5 3 1 8 3 ⟶ 0 8 3 1 , 5 3 1 8 3 ⟶ 2 3 1 , 5 3 1 8 3 ⟶ 4 1 , 5 3 1 8 3 ⟶ 0 , 7 3 1 8 3 ⟶ 6 1 8 3 1 , 7 3 1 8 3 ⟶ 0 8 3 1 , 7 3 1 8 3 ⟶ 2 3 1 , 7 3 1 8 3 ⟶ 4 1 , 7 3 1 8 3 ⟶ 0 , 2 3 1 8 10 ⟶ 0 1 8 3 8 , 2 3 1 8 10 ⟶ 0 8 3 8 , 2 3 1 8 10 ⟶ 2 3 8 , 2 3 1 8 10 ⟶ 4 8 , 2 3 1 8 10 ⟶ 2 , 5 3 1 8 10 ⟶ 4 1 8 3 8 , 5 3 1 8 10 ⟶ 0 8 3 8 , 5 3 1 8 10 ⟶ 2 3 8 , 5 3 1 8 10 ⟶ 4 8 , 5 3 1 8 10 ⟶ 2 , 7 3 1 8 10 ⟶ 6 1 8 3 8 , 7 3 1 8 10 ⟶ 0 8 3 8 , 7 3 1 8 10 ⟶ 2 3 8 , 7 3 1 8 10 ⟶ 4 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 1 8 3 1 , 10 3 1 8 3 →= 3 1 8 3 1 , 12 3 1 8 3 →= 11 1 8 3 1 , 8 3 1 8 10 →= 1 1 8 3 8 , 10 3 1 8 10 →= 3 1 8 3 8 , 12 3 1 8 10 →= 11 1 8 3 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 1 8 3 1 , 5 3 1 8 3 ⟶ 4 1 8 3 1 , 7 3 1 8 3 ⟶ 6 1 8 3 1 , 2 3 1 8 10 ⟶ 0 1 8 3 8 , 5 3 1 8 10 ⟶ 4 1 8 3 8 , 7 3 1 8 10 ⟶ 6 1 8 3 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 1 8 3 1 , 10 3 1 8 3 →= 3 1 8 3 1 , 12 3 1 8 3 →= 11 1 8 3 1 , 8 3 1 8 10 →= 1 1 8 3 8 , 10 3 1 8 10 →= 3 1 8 3 8 , 12 3 1 8 10 →= 11 1 8 3 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 1 8 3 1 , 5 3 1 8 3 ⟶ 4 1 8 3 1 , 7 3 1 8 3 ⟶ 6 1 8 3 1 , 2 3 1 8 10 ⟶ 0 1 8 3 8 , 5 3 1 8 10 ⟶ 4 1 8 3 8 , 7 3 1 8 10 ⟶ 6 1 8 3 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 1 8 3 1 , 10 3 1 8 3 →= 3 1 8 3 1 , 12 3 1 8 3 →= 11 1 8 3 1 , 8 3 1 8 10 →= 1 1 8 3 8 , 10 3 1 8 10 →= 3 1 8 3 8 , 12 3 1 8 10 →= 11 1 8 3 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 1 8 3 1 , 5 3 1 8 3 ⟶ 4 1 8 3 1 , 7 3 1 8 3 ⟶ 6 1 8 3 1 , 2 3 1 8 9 ⟶ 0 1 8 3 8 , 5 3 1 8 9 ⟶ 4 1 8 3 8 , 7 3 1 8 9 ⟶ 6 1 8 3 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 1 8 3 1 , 9 3 1 8 3 →= 3 1 8 3 1 , 11 3 1 8 3 →= 10 1 8 3 1 , 8 3 1 8 9 →= 1 1 8 3 8 , 9 3 1 8 9 →= 3 1 8 3 8 , 11 3 1 8 9 →= 10 1 8 3 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, (3,8) ↦ 20, (9,3) ↦ 21, (9,9) ↦ 22, (0,8) ↦ 23, (4,8) ↦ 24, (6,8) ↦ 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 1 6 17 5 2 , 3 4 5 6 17 20 ⟶ 0 1 6 17 5 6 , 11 12 5 6 17 5 ⟶ 9 10 6 17 5 2 , 11 12 5 6 17 20 ⟶ 9 10 6 17 5 6 , 15 16 5 6 17 5 ⟶ 13 14 6 17 5 2 , 15 16 5 6 17 20 ⟶ 13 14 6 17 5 6 , 3 4 5 6 18 21 ⟶ 0 1 6 17 20 17 , 3 4 5 6 18 22 ⟶ 0 1 6 17 20 18 , 11 12 5 6 18 21 ⟶ 9 10 6 17 20 17 , 11 12 5 6 18 22 ⟶ 9 10 6 17 20 18 , 15 16 5 6 18 21 ⟶ 13 14 6 17 20 17 , 15 16 5 6 18 22 ⟶ 13 14 6 17 20 18 , 1 2 2 2 2 2 →= 23 17 5 2 2 2 , 1 2 2 2 2 6 →= 23 17 5 2 2 6 , 1 2 2 2 2 7 →= 23 17 5 2 2 7 , 1 2 2 2 2 8 →= 23 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 →= 20 17 5 2 2 2 , 5 2 2 2 2 6 →= 20 17 5 2 2 6 , 5 2 2 2 2 7 →= 20 17 5 2 2 7 , 5 2 2 2 2 8 →= 20 17 5 2 2 8 , 10 2 2 2 2 2 →= 24 17 5 2 2 2 , 10 2 2 2 2 6 →= 24 17 5 2 2 6 , 10 2 2 2 2 7 →= 24 17 5 2 2 7 , 10 2 2 2 2 8 →= 24 17 5 2 2 8 , 14 2 2 2 2 2 →= 25 17 5 2 2 2 , 14 2 2 2 2 6 →= 25 17 5 2 2 6 , 14 2 2 2 2 7 →= 25 17 5 2 2 7 , 14 2 2 2 2 8 →= 25 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 21 5 2 2 2 , 4 5 2 2 2 6 →= 30 21 5 2 2 6 , 4 5 2 2 2 7 →= 30 21 5 2 2 7 , 4 5 2 2 2 8 →= 30 21 5 2 2 8 , 12 5 2 2 2 2 →= 31 21 5 2 2 2 , 12 5 2 2 2 6 →= 31 21 5 2 2 6 , 12 5 2 2 2 7 →= 31 21 5 2 2 7 , 12 5 2 2 2 8 →= 31 21 5 2 2 8 , 16 5 2 2 2 2 →= 32 21 5 2 2 2 , 16 5 2 2 2 6 →= 32 21 5 2 2 6 , 16 5 2 2 2 7 →= 32 21 5 2 2 7 , 16 5 2 2 2 8 →= 32 21 5 2 2 8 , 17 5 2 2 2 2 →= 18 21 5 2 2 2 , 17 5 2 2 2 6 →= 18 21 5 2 2 6 , 17 5 2 2 2 7 →= 18 21 5 2 2 7 , 17 5 2 2 2 8 →= 18 21 5 2 2 8 , 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 7 →= 22 21 5 2 2 7 , 21 5 2 2 2 8 →= 22 21 5 2 2 8 , 33 5 2 2 2 2 →= 34 21 5 2 2 2 , 33 5 2 2 2 6 →= 34 21 5 2 2 6 , 33 5 2 2 2 7 →= 34 21 5 2 2 7 , 33 5 2 2 2 8 →= 34 21 5 2 2 8 , 35 5 2 2 2 2 →= 36 21 5 2 2 2 , 35 5 2 2 2 6 →= 36 21 5 2 2 6 , 35 5 2 2 2 7 →= 36 21 5 2 2 7 , 35 5 2 2 2 8 →= 36 21 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 →= 23 17 5 2 6 17 , 1 2 2 2 6 18 →= 23 17 5 2 6 18 , 1 2 2 2 6 19 →= 23 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 →= 20 17 5 2 6 17 , 5 2 2 2 6 18 →= 20 17 5 2 6 18 , 5 2 2 2 6 19 →= 20 17 5 2 6 19 , 10 2 2 2 6 17 →= 24 17 5 2 6 17 , 10 2 2 2 6 18 →= 24 17 5 2 6 18 , 10 2 2 2 6 19 →= 24 17 5 2 6 19 , 14 2 2 2 6 17 →= 25 17 5 2 6 17 , 14 2 2 2 6 18 →= 25 17 5 2 6 18 , 14 2 2 2 6 19 →= 25 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 21 5 2 6 17 , 4 5 2 2 6 18 →= 30 21 5 2 6 18 , 4 5 2 2 6 19 →= 30 21 5 2 6 19 , 12 5 2 2 6 17 →= 31 21 5 2 6 17 , 12 5 2 2 6 18 →= 31 21 5 2 6 18 , 12 5 2 2 6 19 →= 31 21 5 2 6 19 , 16 5 2 2 6 17 →= 32 21 5 2 6 17 , 16 5 2 2 6 18 →= 32 21 5 2 6 18 , 16 5 2 2 6 19 →= 32 21 5 2 6 19 , 17 5 2 2 6 17 →= 18 21 5 2 6 17 , 17 5 2 2 6 18 →= 18 21 5 2 6 18 , 17 5 2 2 6 19 →= 18 21 5 2 6 19 , 21 5 2 2 6 17 →= 22 21 5 2 6 17 , 21 5 2 2 6 18 →= 22 21 5 2 6 18 , 21 5 2 2 6 19 →= 22 21 5 2 6 19 , 33 5 2 2 6 17 →= 34 21 5 2 6 17 , 33 5 2 2 6 18 →= 34 21 5 2 6 18 , 33 5 2 2 6 19 →= 34 21 5 2 6 19 , 35 5 2 2 6 17 →= 36 21 5 2 6 17 , 35 5 2 2 6 18 →= 36 21 5 2 6 18 , 35 5 2 2 6 19 →= 36 21 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 →= 23 17 5 2 7 39 , 2 2 2 2 7 39 →= 6 17 5 2 7 39 , 5 2 2 2 7 39 →= 20 17 5 2 7 39 , 10 2 2 2 7 39 →= 24 17 5 2 7 39 , 14 2 2 2 7 39 →= 25 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 21 5 2 7 39 , 12 5 2 2 7 39 →= 31 21 5 2 7 39 , 16 5 2 2 7 39 →= 32 21 5 2 7 39 , 17 5 2 2 7 39 →= 18 21 5 2 7 39 , 21 5 2 2 7 39 →= 22 21 5 2 7 39 , 33 5 2 2 7 39 →= 34 21 5 2 7 39 , 35 5 2 2 7 39 →= 36 21 5 2 7 39 , 23 17 5 6 17 5 →= 1 2 6 17 5 2 , 23 17 5 6 17 20 →= 1 2 6 17 5 6 , 6 17 5 6 17 5 →= 2 2 6 17 5 2 , 6 17 5 6 17 20 →= 2 2 6 17 5 6 , 20 17 5 6 17 5 →= 5 2 6 17 5 2 , 20 17 5 6 17 20 →= 5 2 6 17 5 6 , 24 17 5 6 17 5 →= 10 2 6 17 5 2 , 24 17 5 6 17 20 →= 10 2 6 17 5 6 , 25 17 5 6 17 5 →= 14 2 6 17 5 2 , 25 17 5 6 17 20 →= 14 2 6 17 5 6 , 27 17 5 6 17 5 →= 26 2 6 17 5 2 , 27 17 5 6 17 20 →= 26 2 6 17 5 6 , 29 17 5 6 17 5 →= 28 2 6 17 5 2 , 29 17 5 6 17 20 →= 28 2 6 17 5 6 , 30 21 5 6 17 5 →= 4 5 6 17 5 2 , 30 21 5 6 17 20 →= 4 5 6 17 5 6 , 31 21 5 6 17 5 →= 12 5 6 17 5 2 , 31 21 5 6 17 20 →= 12 5 6 17 5 6 , 32 21 5 6 17 5 →= 16 5 6 17 5 2 , 32 21 5 6 17 20 →= 16 5 6 17 5 6 , 18 21 5 6 17 5 →= 17 5 6 17 5 2 , 18 21 5 6 17 20 →= 17 5 6 17 5 6 , 22 21 5 6 17 5 →= 21 5 6 17 5 2 , 22 21 5 6 17 20 →= 21 5 6 17 5 6 , 34 21 5 6 17 5 →= 33 5 6 17 5 2 , 34 21 5 6 17 20 →= 33 5 6 17 5 6 , 36 21 5 6 17 5 →= 35 5 6 17 5 2 , 36 21 5 6 17 20 →= 35 5 6 17 5 6 , 38 33 5 6 17 5 →= 37 26 6 17 5 2 , 38 33 5 6 17 20 →= 37 26 6 17 5 6 , 23 17 5 6 18 21 →= 1 2 6 17 20 17 , 23 17 5 6 18 22 →= 1 2 6 17 20 18 , 6 17 5 6 18 21 →= 2 2 6 17 20 17 , 6 17 5 6 18 22 →= 2 2 6 17 20 18 , 20 17 5 6 18 21 →= 5 2 6 17 20 17 , 20 17 5 6 18 22 →= 5 2 6 17 20 18 , 24 17 5 6 18 21 →= 10 2 6 17 20 17 , 24 17 5 6 18 22 →= 10 2 6 17 20 18 , 25 17 5 6 18 21 →= 14 2 6 17 20 17 , 25 17 5 6 18 22 →= 14 2 6 17 20 18 , 27 17 5 6 18 21 →= 26 2 6 17 20 17 , 27 17 5 6 18 22 →= 26 2 6 17 20 18 , 29 17 5 6 18 21 →= 28 2 6 17 20 17 , 29 17 5 6 18 22 →= 28 2 6 17 20 18 , 30 21 5 6 18 21 →= 4 5 6 17 20 17 , 30 21 5 6 18 22 →= 4 5 6 17 20 18 , 31 21 5 6 18 21 →= 12 5 6 17 20 17 , 31 21 5 6 18 22 →= 12 5 6 17 20 18 , 32 21 5 6 18 21 →= 16 5 6 17 20 17 , 32 21 5 6 18 22 →= 16 5 6 17 20 18 , 18 21 5 6 18 21 →= 17 5 6 17 20 17 , 18 21 5 6 18 22 →= 17 5 6 17 20 18 , 22 21 5 6 18 21 →= 21 5 6 17 20 17 , 22 21 5 6 18 22 →= 21 5 6 17 20 18 , 34 21 5 6 18 21 →= 33 5 6 17 20 17 , 34 21 5 6 18 22 →= 33 5 6 17 20 18 , 36 21 5 6 18 21 →= 35 5 6 17 20 17 , 36 21 5 6 18 22 →= 35 5 6 17 20 18 , 38 33 5 6 18 21 →= 37 26 6 17 20 17 , 38 33 5 6 18 22 →= 37 26 6 17 20 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 1 6 17 5 2 , 3 4 5 6 17 20 ⟶ 0 1 6 17 5 6 , 10 11 5 6 17 5 ⟶ 8 9 6 17 5 2 , 10 11 5 6 17 20 ⟶ 8 9 6 17 5 6 , 15 16 5 6 17 5 ⟶ 13 14 6 17 5 2 , 15 16 5 6 17 20 ⟶ 13 14 6 17 5 6 , 3 4 5 6 18 21 ⟶ 0 1 6 17 20 17 , 3 4 5 6 18 22 ⟶ 0 1 6 17 20 18 , 10 11 5 6 18 21 ⟶ 8 9 6 17 20 17 , 10 11 5 6 18 22 ⟶ 8 9 6 17 20 18 , 15 16 5 6 18 21 ⟶ 13 14 6 17 20 17 , 15 16 5 6 18 22 ⟶ 13 14 6 17 20 18 , 1 2 2 2 2 2 →= 23 17 5 2 2 2 , 1 2 2 2 2 6 →= 23 17 5 2 2 6 , 1 2 2 2 2 12 →= 23 17 5 2 2 12 , 1 2 2 2 2 7 →= 23 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 →= 20 17 5 2 2 2 , 5 2 2 2 2 6 →= 20 17 5 2 2 6 , 5 2 2 2 2 12 →= 20 17 5 2 2 12 , 5 2 2 2 2 7 →= 20 17 5 2 2 7 , 9 2 2 2 2 2 →= 24 17 5 2 2 2 , 9 2 2 2 2 6 →= 24 17 5 2 2 6 , 9 2 2 2 2 12 →= 24 17 5 2 2 12 , 9 2 2 2 2 7 →= 24 17 5 2 2 7 , 14 2 2 2 2 2 →= 25 17 5 2 2 2 , 14 2 2 2 2 6 →= 25 17 5 2 2 6 , 14 2 2 2 2 12 →= 25 17 5 2 2 12 , 14 2 2 2 2 7 →= 25 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 21 5 2 2 2 , 4 5 2 2 2 6 →= 30 21 5 2 2 6 , 4 5 2 2 2 12 →= 30 21 5 2 2 12 , 4 5 2 2 2 7 →= 30 21 5 2 2 7 , 11 5 2 2 2 2 →= 31 21 5 2 2 2 , 11 5 2 2 2 6 →= 31 21 5 2 2 6 , 11 5 2 2 2 12 →= 31 21 5 2 2 12 , 11 5 2 2 2 7 →= 31 21 5 2 2 7 , 16 5 2 2 2 2 →= 32 21 5 2 2 2 , 16 5 2 2 2 6 →= 32 21 5 2 2 6 , 16 5 2 2 2 12 →= 32 21 5 2 2 12 , 16 5 2 2 2 7 →= 32 21 5 2 2 7 , 17 5 2 2 2 2 →= 18 21 5 2 2 2 , 17 5 2 2 2 6 →= 18 21 5 2 2 6 , 17 5 2 2 2 12 →= 18 21 5 2 2 12 , 17 5 2 2 2 7 →= 18 21 5 2 2 7 , 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 12 →= 22 21 5 2 2 12 , 21 5 2 2 2 7 →= 22 21 5 2 2 7 , 33 5 2 2 2 2 →= 34 21 5 2 2 2 , 33 5 2 2 2 6 →= 34 21 5 2 2 6 , 33 5 2 2 2 12 →= 34 21 5 2 2 12 , 33 5 2 2 2 7 →= 34 21 5 2 2 7 , 35 5 2 2 2 2 →= 36 21 5 2 2 2 , 35 5 2 2 2 6 →= 36 21 5 2 2 6 , 35 5 2 2 2 12 →= 36 21 5 2 2 12 , 35 5 2 2 2 7 →= 36 21 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 →= 23 17 5 2 6 17 , 1 2 2 2 6 18 →= 23 17 5 2 6 18 , 1 2 2 2 6 19 →= 23 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 →= 20 17 5 2 6 17 , 5 2 2 2 6 18 →= 20 17 5 2 6 18 , 5 2 2 2 6 19 →= 20 17 5 2 6 19 , 9 2 2 2 6 17 →= 24 17 5 2 6 17 , 9 2 2 2 6 18 →= 24 17 5 2 6 18 , 9 2 2 2 6 19 →= 24 17 5 2 6 19 , 14 2 2 2 6 17 →= 25 17 5 2 6 17 , 14 2 2 2 6 18 →= 25 17 5 2 6 18 , 14 2 2 2 6 19 →= 25 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 21 5 2 6 17 , 4 5 2 2 6 18 →= 30 21 5 2 6 18 , 4 5 2 2 6 19 →= 30 21 5 2 6 19 , 11 5 2 2 6 17 →= 31 21 5 2 6 17 , 11 5 2 2 6 18 →= 31 21 5 2 6 18 , 11 5 2 2 6 19 →= 31 21 5 2 6 19 , 16 5 2 2 6 17 →= 32 21 5 2 6 17 , 16 5 2 2 6 18 →= 32 21 5 2 6 18 , 16 5 2 2 6 19 →= 32 21 5 2 6 19 , 17 5 2 2 6 17 →= 18 21 5 2 6 17 , 17 5 2 2 6 18 →= 18 21 5 2 6 18 , 17 5 2 2 6 19 →= 18 21 5 2 6 19 , 21 5 2 2 6 17 →= 22 21 5 2 6 17 , 21 5 2 2 6 18 →= 22 21 5 2 6 18 , 21 5 2 2 6 19 →= 22 21 5 2 6 19 , 33 5 2 2 6 17 →= 34 21 5 2 6 17 , 33 5 2 2 6 18 →= 34 21 5 2 6 18 , 33 5 2 2 6 19 →= 34 21 5 2 6 19 , 35 5 2 2 6 17 →= 36 21 5 2 6 17 , 35 5 2 2 6 18 →= 36 21 5 2 6 18 , 35 5 2 2 6 19 →= 36 21 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 →= 23 17 5 2 12 39 , 2 2 2 2 12 39 →= 6 17 5 2 12 39 , 5 2 2 2 12 39 →= 20 17 5 2 12 39 , 9 2 2 2 12 39 →= 24 17 5 2 12 39 , 14 2 2 2 12 39 →= 25 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 21 5 2 12 39 , 11 5 2 2 12 39 →= 31 21 5 2 12 39 , 16 5 2 2 12 39 →= 32 21 5 2 12 39 , 17 5 2 2 12 39 →= 18 21 5 2 12 39 , 21 5 2 2 12 39 →= 22 21 5 2 12 39 , 33 5 2 2 12 39 →= 34 21 5 2 12 39 , 35 5 2 2 12 39 →= 36 21 5 2 12 39 , 23 17 5 6 17 5 →= 1 2 6 17 5 2 , 23 17 5 6 17 20 →= 1 2 6 17 5 6 , 6 17 5 6 17 5 →= 2 2 6 17 5 2 , 6 17 5 6 17 20 →= 2 2 6 17 5 6 , 20 17 5 6 17 5 →= 5 2 6 17 5 2 , 20 17 5 6 17 20 →= 5 2 6 17 5 6 , 24 17 5 6 17 5 →= 9 2 6 17 5 2 , 24 17 5 6 17 20 →= 9 2 6 17 5 6 , 25 17 5 6 17 5 →= 14 2 6 17 5 2 , 25 17 5 6 17 20 →= 14 2 6 17 5 6 , 27 17 5 6 17 5 →= 26 2 6 17 5 2 , 27 17 5 6 17 20 →= 26 2 6 17 5 6 , 29 17 5 6 17 5 →= 28 2 6 17 5 2 , 29 17 5 6 17 20 →= 28 2 6 17 5 6 , 30 21 5 6 17 5 →= 4 5 6 17 5 2 , 30 21 5 6 17 20 →= 4 5 6 17 5 6 , 31 21 5 6 17 5 →= 11 5 6 17 5 2 , 31 21 5 6 17 20 →= 11 5 6 17 5 6 , 32 21 5 6 17 5 →= 16 5 6 17 5 2 , 32 21 5 6 17 20 →= 16 5 6 17 5 6 , 18 21 5 6 17 5 →= 17 5 6 17 5 2 , 18 21 5 6 17 20 →= 17 5 6 17 5 6 , 22 21 5 6 17 5 →= 21 5 6 17 5 2 , 22 21 5 6 17 20 →= 21 5 6 17 5 6 , 34 21 5 6 17 5 →= 33 5 6 17 5 2 , 34 21 5 6 17 20 →= 33 5 6 17 5 6 , 36 21 5 6 17 5 →= 35 5 6 17 5 2 , 36 21 5 6 17 20 →= 35 5 6 17 5 6 , 38 33 5 6 17 5 →= 37 26 6 17 5 2 , 38 33 5 6 17 20 →= 37 26 6 17 5 6 , 23 17 5 6 18 21 →= 1 2 6 17 20 17 , 23 17 5 6 18 22 →= 1 2 6 17 20 18 , 6 17 5 6 18 21 →= 2 2 6 17 20 17 , 6 17 5 6 18 22 →= 2 2 6 17 20 18 , 20 17 5 6 18 21 →= 5 2 6 17 20 17 , 20 17 5 6 18 22 →= 5 2 6 17 20 18 , 24 17 5 6 18 21 →= 9 2 6 17 20 17 , 24 17 5 6 18 22 →= 9 2 6 17 20 18 , 25 17 5 6 18 21 →= 14 2 6 17 20 17 , 25 17 5 6 18 22 →= 14 2 6 17 20 18 , 27 17 5 6 18 21 →= 26 2 6 17 20 17 , 27 17 5 6 18 22 →= 26 2 6 17 20 18 , 29 17 5 6 18 21 →= 28 2 6 17 20 17 , 29 17 5 6 18 22 →= 28 2 6 17 20 18 , 30 21 5 6 18 21 →= 4 5 6 17 20 17 , 30 21 5 6 18 22 →= 4 5 6 17 20 18 , 31 21 5 6 18 21 →= 11 5 6 17 20 17 , 31 21 5 6 18 22 →= 11 5 6 17 20 18 , 32 21 5 6 18 21 →= 16 5 6 17 20 17 , 32 21 5 6 18 22 →= 16 5 6 17 20 18 , 18 21 5 6 18 21 →= 17 5 6 17 20 17 , 18 21 5 6 18 22 →= 17 5 6 17 20 18 , 22 21 5 6 18 21 →= 21 5 6 17 20 17 , 22 21 5 6 18 22 →= 21 5 6 17 20 18 , 34 21 5 6 18 21 →= 33 5 6 17 20 17 , 34 21 5 6 18 22 →= 33 5 6 17 20 18 , 36 21 5 6 18 21 →= 35 5 6 17 20 17 , 36 21 5 6 18 22 →= 35 5 6 17 20 18 , 38 33 5 6 18 21 →= 37 26 6 17 20 17 , 38 33 5 6 18 22 →= 37 26 6 17 20 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 1 6 17 5 2 , 3 4 5 6 17 20 ⟶ 0 1 6 17 5 6 , 9 10 5 6 17 5 ⟶ 7 8 6 17 5 2 , 9 10 5 6 17 20 ⟶ 7 8 6 17 5 6 , 15 16 5 6 17 5 ⟶ 13 14 6 17 5 2 , 15 16 5 6 17 20 ⟶ 13 14 6 17 5 6 , 3 4 5 6 18 21 ⟶ 0 1 6 17 20 17 , 3 4 5 6 18 22 ⟶ 0 1 6 17 20 18 , 9 10 5 6 18 21 ⟶ 7 8 6 17 20 17 , 9 10 5 6 18 22 ⟶ 7 8 6 17 20 18 , 15 16 5 6 18 21 ⟶ 13 14 6 17 20 17 , 15 16 5 6 18 22 ⟶ 13 14 6 17 20 18 , 1 2 2 2 2 2 →= 23 17 5 2 2 2 , 1 2 2 2 2 6 →= 23 17 5 2 2 6 , 1 2 2 2 2 11 →= 23 17 5 2 2 11 , 1 2 2 2 2 12 →= 23 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 →= 20 17 5 2 2 2 , 5 2 2 2 2 6 →= 20 17 5 2 2 6 , 5 2 2 2 2 11 →= 20 17 5 2 2 11 , 5 2 2 2 2 12 →= 20 17 5 2 2 12 , 8 2 2 2 2 2 →= 24 17 5 2 2 2 , 8 2 2 2 2 6 →= 24 17 5 2 2 6 , 8 2 2 2 2 11 →= 24 17 5 2 2 11 , 8 2 2 2 2 12 →= 24 17 5 2 2 12 , 14 2 2 2 2 2 →= 25 17 5 2 2 2 , 14 2 2 2 2 6 →= 25 17 5 2 2 6 , 14 2 2 2 2 11 →= 25 17 5 2 2 11 , 14 2 2 2 2 12 →= 25 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 21 5 2 2 2 , 4 5 2 2 2 6 →= 30 21 5 2 2 6 , 4 5 2 2 2 11 →= 30 21 5 2 2 11 , 4 5 2 2 2 12 →= 30 21 5 2 2 12 , 10 5 2 2 2 2 →= 31 21 5 2 2 2 , 10 5 2 2 2 6 →= 31 21 5 2 2 6 , 10 5 2 2 2 11 →= 31 21 5 2 2 11 , 10 5 2 2 2 12 →= 31 21 5 2 2 12 , 16 5 2 2 2 2 →= 32 21 5 2 2 2 , 16 5 2 2 2 6 →= 32 21 5 2 2 6 , 16 5 2 2 2 11 →= 32 21 5 2 2 11 , 16 5 2 2 2 12 →= 32 21 5 2 2 12 , 17 5 2 2 2 2 →= 18 21 5 2 2 2 , 17 5 2 2 2 6 →= 18 21 5 2 2 6 , 17 5 2 2 2 11 →= 18 21 5 2 2 11 , 17 5 2 2 2 12 →= 18 21 5 2 2 12 , 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 11 →= 22 21 5 2 2 11 , 21 5 2 2 2 12 →= 22 21 5 2 2 12 , 33 5 2 2 2 2 →= 34 21 5 2 2 2 , 33 5 2 2 2 6 →= 34 21 5 2 2 6 , 33 5 2 2 2 11 →= 34 21 5 2 2 11 , 33 5 2 2 2 12 →= 34 21 5 2 2 12 , 35 5 2 2 2 2 →= 36 21 5 2 2 2 , 35 5 2 2 2 6 →= 36 21 5 2 2 6 , 35 5 2 2 2 11 →= 36 21 5 2 2 11 , 35 5 2 2 2 12 →= 36 21 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 →= 23 17 5 2 6 17 , 1 2 2 2 6 18 →= 23 17 5 2 6 18 , 1 2 2 2 6 19 →= 23 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 →= 20 17 5 2 6 17 , 5 2 2 2 6 18 →= 20 17 5 2 6 18 , 5 2 2 2 6 19 →= 20 17 5 2 6 19 , 8 2 2 2 6 17 →= 24 17 5 2 6 17 , 8 2 2 2 6 18 →= 24 17 5 2 6 18 , 8 2 2 2 6 19 →= 24 17 5 2 6 19 , 14 2 2 2 6 17 →= 25 17 5 2 6 17 , 14 2 2 2 6 18 →= 25 17 5 2 6 18 , 14 2 2 2 6 19 →= 25 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 21 5 2 6 17 , 4 5 2 2 6 18 →= 30 21 5 2 6 18 , 4 5 2 2 6 19 →= 30 21 5 2 6 19 , 10 5 2 2 6 17 →= 31 21 5 2 6 17 , 10 5 2 2 6 18 →= 31 21 5 2 6 18 , 10 5 2 2 6 19 →= 31 21 5 2 6 19 , 16 5 2 2 6 17 →= 32 21 5 2 6 17 , 16 5 2 2 6 18 →= 32 21 5 2 6 18 , 16 5 2 2 6 19 →= 32 21 5 2 6 19 , 17 5 2 2 6 17 →= 18 21 5 2 6 17 , 17 5 2 2 6 18 →= 18 21 5 2 6 18 , 17 5 2 2 6 19 →= 18 21 5 2 6 19 , 21 5 2 2 6 17 →= 22 21 5 2 6 17 , 21 5 2 2 6 18 →= 22 21 5 2 6 18 , 21 5 2 2 6 19 →= 22 21 5 2 6 19 , 33 5 2 2 6 17 →= 34 21 5 2 6 17 , 33 5 2 2 6 18 →= 34 21 5 2 6 18 , 33 5 2 2 6 19 →= 34 21 5 2 6 19 , 35 5 2 2 6 17 →= 36 21 5 2 6 17 , 35 5 2 2 6 18 →= 36 21 5 2 6 18 , 35 5 2 2 6 19 →= 36 21 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 →= 23 17 5 2 11 39 , 2 2 2 2 11 39 →= 6 17 5 2 11 39 , 5 2 2 2 11 39 →= 20 17 5 2 11 39 , 8 2 2 2 11 39 →= 24 17 5 2 11 39 , 14 2 2 2 11 39 →= 25 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 21 5 2 11 39 , 10 5 2 2 11 39 →= 31 21 5 2 11 39 , 16 5 2 2 11 39 →= 32 21 5 2 11 39 , 17 5 2 2 11 39 →= 18 21 5 2 11 39 , 21 5 2 2 11 39 →= 22 21 5 2 11 39 , 33 5 2 2 11 39 →= 34 21 5 2 11 39 , 35 5 2 2 11 39 →= 36 21 5 2 11 39 , 23 17 5 6 17 5 →= 1 2 6 17 5 2 , 23 17 5 6 17 20 →= 1 2 6 17 5 6 , 6 17 5 6 17 5 →= 2 2 6 17 5 2 , 6 17 5 6 17 20 →= 2 2 6 17 5 6 , 20 17 5 6 17 5 →= 5 2 6 17 5 2 , 20 17 5 6 17 20 →= 5 2 6 17 5 6 , 24 17 5 6 17 5 →= 8 2 6 17 5 2 , 24 17 5 6 17 20 →= 8 2 6 17 5 6 , 25 17 5 6 17 5 →= 14 2 6 17 5 2 , 25 17 5 6 17 20 →= 14 2 6 17 5 6 , 27 17 5 6 17 5 →= 26 2 6 17 5 2 , 27 17 5 6 17 20 →= 26 2 6 17 5 6 , 29 17 5 6 17 5 →= 28 2 6 17 5 2 , 29 17 5 6 17 20 →= 28 2 6 17 5 6 , 30 21 5 6 17 5 →= 4 5 6 17 5 2 , 30 21 5 6 17 20 →= 4 5 6 17 5 6 , 31 21 5 6 17 5 →= 10 5 6 17 5 2 , 31 21 5 6 17 20 →= 10 5 6 17 5 6 , 32 21 5 6 17 5 →= 16 5 6 17 5 2 , 32 21 5 6 17 20 →= 16 5 6 17 5 6 , 18 21 5 6 17 5 →= 17 5 6 17 5 2 , 18 21 5 6 17 20 →= 17 5 6 17 5 6 , 22 21 5 6 17 5 →= 21 5 6 17 5 2 , 22 21 5 6 17 20 →= 21 5 6 17 5 6 , 34 21 5 6 17 5 →= 33 5 6 17 5 2 , 34 21 5 6 17 20 →= 33 5 6 17 5 6 , 36 21 5 6 17 5 →= 35 5 6 17 5 2 , 36 21 5 6 17 20 →= 35 5 6 17 5 6 , 38 33 5 6 17 5 →= 37 26 6 17 5 2 , 38 33 5 6 17 20 →= 37 26 6 17 5 6 , 23 17 5 6 18 21 →= 1 2 6 17 20 17 , 23 17 5 6 18 22 →= 1 2 6 17 20 18 , 6 17 5 6 18 21 →= 2 2 6 17 20 17 , 6 17 5 6 18 22 →= 2 2 6 17 20 18 , 20 17 5 6 18 21 →= 5 2 6 17 20 17 , 20 17 5 6 18 22 →= 5 2 6 17 20 18 , 24 17 5 6 18 21 →= 8 2 6 17 20 17 , 24 17 5 6 18 22 →= 8 2 6 17 20 18 , 25 17 5 6 18 21 →= 14 2 6 17 20 17 , 25 17 5 6 18 22 →= 14 2 6 17 20 18 , 27 17 5 6 18 21 →= 26 2 6 17 20 17 , 27 17 5 6 18 22 →= 26 2 6 17 20 18 , 29 17 5 6 18 21 →= 28 2 6 17 20 17 , 29 17 5 6 18 22 →= 28 2 6 17 20 18 , 30 21 5 6 18 21 →= 4 5 6 17 20 17 , 30 21 5 6 18 22 →= 4 5 6 17 20 18 , 31 21 5 6 18 21 →= 10 5 6 17 20 17 , 31 21 5 6 18 22 →= 10 5 6 17 20 18 , 32 21 5 6 18 21 →= 16 5 6 17 20 17 , 32 21 5 6 18 22 →= 16 5 6 17 20 18 , 18 21 5 6 18 21 →= 17 5 6 17 20 17 , 18 21 5 6 18 22 →= 17 5 6 17 20 18 , 22 21 5 6 18 21 →= 21 5 6 17 20 17 , 22 21 5 6 18 22 →= 21 5 6 17 20 18 , 34 21 5 6 18 21 →= 33 5 6 17 20 17 , 34 21 5 6 18 22 →= 33 5 6 17 20 18 , 36 21 5 6 18 21 →= 35 5 6 17 20 17 , 36 21 5 6 18 22 →= 35 5 6 17 20 18 , 38 33 5 6 18 21 →= 37 26 6 17 20 17 , 38 33 5 6 18 22 →= 37 26 6 17 20 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 1 6 17 5 2 , 3 4 5 6 17 20 ⟶ 0 1 6 17 5 6 , 9 10 5 6 17 5 ⟶ 7 8 6 17 5 2 , 9 10 5 6 17 20 ⟶ 7 8 6 17 5 6 , 14 15 5 6 17 5 ⟶ 12 13 6 17 5 2 , 14 15 5 6 17 20 ⟶ 12 13 6 17 5 6 , 3 4 5 6 18 21 ⟶ 0 1 6 17 20 17 , 3 4 5 6 18 22 ⟶ 0 1 6 17 20 18 , 9 10 5 6 18 21 ⟶ 7 8 6 17 20 17 , 9 10 5 6 18 22 ⟶ 7 8 6 17 20 18 , 14 15 5 6 18 21 ⟶ 12 13 6 17 20 17 , 14 15 5 6 18 22 ⟶ 12 13 6 17 20 18 , 1 2 2 2 2 2 →= 23 17 5 2 2 2 , 1 2 2 2 2 6 →= 23 17 5 2 2 6 , 1 2 2 2 2 16 →= 23 17 5 2 2 16 , 1 2 2 2 2 11 →= 23 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 →= 20 17 5 2 2 2 , 5 2 2 2 2 6 →= 20 17 5 2 2 6 , 5 2 2 2 2 16 →= 20 17 5 2 2 16 , 5 2 2 2 2 11 →= 20 17 5 2 2 11 , 8 2 2 2 2 2 →= 24 17 5 2 2 2 , 8 2 2 2 2 6 →= 24 17 5 2 2 6 , 8 2 2 2 2 16 →= 24 17 5 2 2 16 , 8 2 2 2 2 11 →= 24 17 5 2 2 11 , 13 2 2 2 2 2 →= 25 17 5 2 2 2 , 13 2 2 2 2 6 →= 25 17 5 2 2 6 , 13 2 2 2 2 16 →= 25 17 5 2 2 16 , 13 2 2 2 2 11 →= 25 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 21 5 2 2 2 , 4 5 2 2 2 6 →= 30 21 5 2 2 6 , 4 5 2 2 2 16 →= 30 21 5 2 2 16 , 4 5 2 2 2 11 →= 30 21 5 2 2 11 , 10 5 2 2 2 2 →= 31 21 5 2 2 2 , 10 5 2 2 2 6 →= 31 21 5 2 2 6 , 10 5 2 2 2 16 →= 31 21 5 2 2 16 , 10 5 2 2 2 11 →= 31 21 5 2 2 11 , 15 5 2 2 2 2 →= 32 21 5 2 2 2 , 15 5 2 2 2 6 →= 32 21 5 2 2 6 , 15 5 2 2 2 16 →= 32 21 5 2 2 16 , 15 5 2 2 2 11 →= 32 21 5 2 2 11 , 17 5 2 2 2 2 →= 18 21 5 2 2 2 , 17 5 2 2 2 6 →= 18 21 5 2 2 6 , 17 5 2 2 2 16 →= 18 21 5 2 2 16 , 17 5 2 2 2 11 →= 18 21 5 2 2 11 , 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 16 →= 22 21 5 2 2 16 , 21 5 2 2 2 11 →= 22 21 5 2 2 11 , 33 5 2 2 2 2 →= 34 21 5 2 2 2 , 33 5 2 2 2 6 →= 34 21 5 2 2 6 , 33 5 2 2 2 16 →= 34 21 5 2 2 16 , 33 5 2 2 2 11 →= 34 21 5 2 2 11 , 35 5 2 2 2 2 →= 36 21 5 2 2 2 , 35 5 2 2 2 6 →= 36 21 5 2 2 6 , 35 5 2 2 2 16 →= 36 21 5 2 2 16 , 35 5 2 2 2 11 →= 36 21 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 →= 23 17 5 2 6 17 , 1 2 2 2 6 18 →= 23 17 5 2 6 18 , 1 2 2 2 6 19 →= 23 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 →= 20 17 5 2 6 17 , 5 2 2 2 6 18 →= 20 17 5 2 6 18 , 5 2 2 2 6 19 →= 20 17 5 2 6 19 , 8 2 2 2 6 17 →= 24 17 5 2 6 17 , 8 2 2 2 6 18 →= 24 17 5 2 6 18 , 8 2 2 2 6 19 →= 24 17 5 2 6 19 , 13 2 2 2 6 17 →= 25 17 5 2 6 17 , 13 2 2 2 6 18 →= 25 17 5 2 6 18 , 13 2 2 2 6 19 →= 25 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 21 5 2 6 17 , 4 5 2 2 6 18 →= 30 21 5 2 6 18 , 4 5 2 2 6 19 →= 30 21 5 2 6 19 , 10 5 2 2 6 17 →= 31 21 5 2 6 17 , 10 5 2 2 6 18 →= 31 21 5 2 6 18 , 10 5 2 2 6 19 →= 31 21 5 2 6 19 , 15 5 2 2 6 17 →= 32 21 5 2 6 17 , 15 5 2 2 6 18 →= 32 21 5 2 6 18 , 15 5 2 2 6 19 →= 32 21 5 2 6 19 , 17 5 2 2 6 17 →= 18 21 5 2 6 17 , 17 5 2 2 6 18 →= 18 21 5 2 6 18 , 17 5 2 2 6 19 →= 18 21 5 2 6 19 , 21 5 2 2 6 17 →= 22 21 5 2 6 17 , 21 5 2 2 6 18 →= 22 21 5 2 6 18 , 21 5 2 2 6 19 →= 22 21 5 2 6 19 , 33 5 2 2 6 17 →= 34 21 5 2 6 17 , 33 5 2 2 6 18 →= 34 21 5 2 6 18 , 33 5 2 2 6 19 →= 34 21 5 2 6 19 , 35 5 2 2 6 17 →= 36 21 5 2 6 17 , 35 5 2 2 6 18 →= 36 21 5 2 6 18 , 35 5 2 2 6 19 →= 36 21 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 →= 23 17 5 2 16 39 , 2 2 2 2 16 39 →= 6 17 5 2 16 39 , 5 2 2 2 16 39 →= 20 17 5 2 16 39 , 8 2 2 2 16 39 →= 24 17 5 2 16 39 , 13 2 2 2 16 39 →= 25 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 21 5 2 16 39 , 10 5 2 2 16 39 →= 31 21 5 2 16 39 , 15 5 2 2 16 39 →= 32 21 5 2 16 39 , 17 5 2 2 16 39 →= 18 21 5 2 16 39 , 21 5 2 2 16 39 →= 22 21 5 2 16 39 , 33 5 2 2 16 39 →= 34 21 5 2 16 39 , 35 5 2 2 16 39 →= 36 21 5 2 16 39 , 23 17 5 6 17 5 →= 1 2 6 17 5 2 , 23 17 5 6 17 20 →= 1 2 6 17 5 6 , 6 17 5 6 17 5 →= 2 2 6 17 5 2 , 6 17 5 6 17 20 →= 2 2 6 17 5 6 , 20 17 5 6 17 5 →= 5 2 6 17 5 2 , 20 17 5 6 17 20 →= 5 2 6 17 5 6 , 24 17 5 6 17 5 →= 8 2 6 17 5 2 , 24 17 5 6 17 20 →= 8 2 6 17 5 6 , 25 17 5 6 17 5 →= 13 2 6 17 5 2 , 25 17 5 6 17 20 →= 13 2 6 17 5 6 , 27 17 5 6 17 5 →= 26 2 6 17 5 2 , 27 17 5 6 17 20 →= 26 2 6 17 5 6 , 29 17 5 6 17 5 →= 28 2 6 17 5 2 , 29 17 5 6 17 20 →= 28 2 6 17 5 6 , 30 21 5 6 17 5 →= 4 5 6 17 5 2 , 30 21 5 6 17 20 →= 4 5 6 17 5 6 , 31 21 5 6 17 5 →= 10 5 6 17 5 2 , 31 21 5 6 17 20 →= 10 5 6 17 5 6 , 32 21 5 6 17 5 →= 15 5 6 17 5 2 , 32 21 5 6 17 20 →= 15 5 6 17 5 6 , 18 21 5 6 17 5 →= 17 5 6 17 5 2 , 18 21 5 6 17 20 →= 17 5 6 17 5 6 , 22 21 5 6 17 5 →= 21 5 6 17 5 2 , 22 21 5 6 17 20 →= 21 5 6 17 5 6 , 34 21 5 6 17 5 →= 33 5 6 17 5 2 , 34 21 5 6 17 20 →= 33 5 6 17 5 6 , 36 21 5 6 17 5 →= 35 5 6 17 5 2 , 36 21 5 6 17 20 →= 35 5 6 17 5 6 , 38 33 5 6 17 5 →= 37 26 6 17 5 2 , 38 33 5 6 17 20 →= 37 26 6 17 5 6 , 23 17 5 6 18 21 →= 1 2 6 17 20 17 , 23 17 5 6 18 22 →= 1 2 6 17 20 18 , 6 17 5 6 18 21 →= 2 2 6 17 20 17 , 6 17 5 6 18 22 →= 2 2 6 17 20 18 , 20 17 5 6 18 21 →= 5 2 6 17 20 17 , 20 17 5 6 18 22 →= 5 2 6 17 20 18 , 24 17 5 6 18 21 →= 8 2 6 17 20 17 , 24 17 5 6 18 22 →= 8 2 6 17 20 18 , 25 17 5 6 18 21 →= 13 2 6 17 20 17 , 25 17 5 6 18 22 →= 13 2 6 17 20 18 , 27 17 5 6 18 21 →= 26 2 6 17 20 17 , 27 17 5 6 18 22 →= 26 2 6 17 20 18 , 29 17 5 6 18 21 →= 28 2 6 17 20 17 , 29 17 5 6 18 22 →= 28 2 6 17 20 18 , 30 21 5 6 18 21 →= 4 5 6 17 20 17 , 30 21 5 6 18 22 →= 4 5 6 17 20 18 , 31 21 5 6 18 21 →= 10 5 6 17 20 17 , 31 21 5 6 18 22 →= 10 5 6 17 20 18 , 32 21 5 6 18 21 →= 15 5 6 17 20 17 , 32 21 5 6 18 22 →= 15 5 6 17 20 18 , 18 21 5 6 18 21 →= 17 5 6 17 20 17 , 18 21 5 6 18 22 →= 17 5 6 17 20 18 , 22 21 5 6 18 21 →= 21 5 6 17 20 17 , 22 21 5 6 18 22 →= 21 5 6 17 20 18 , 34 21 5 6 18 21 →= 33 5 6 17 20 17 , 34 21 5 6 18 22 →= 33 5 6 17 20 18 , 36 21 5 6 18 21 →= 35 5 6 17 20 17 , 36 21 5 6 18 22 →= 35 5 6 17 20 18 , 38 33 5 6 18 21 →= 37 26 6 17 20 17 , 38 33 5 6 18 22 →= 37 26 6 17 20 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 1 6 17 5 2 , 3 4 5 6 17 20 ⟶ 0 1 6 17 5 6 , 9 10 5 6 17 5 ⟶ 7 8 6 17 5 2 , 9 10 5 6 17 20 ⟶ 7 8 6 17 5 6 , 13 14 5 6 17 5 ⟶ 11 12 6 17 5 2 , 13 14 5 6 17 20 ⟶ 11 12 6 17 5 6 , 3 4 5 6 18 21 ⟶ 0 1 6 17 20 17 , 3 4 5 6 18 22 ⟶ 0 1 6 17 20 18 , 9 10 5 6 18 21 ⟶ 7 8 6 17 20 17 , 9 10 5 6 18 22 ⟶ 7 8 6 17 20 18 , 13 14 5 6 18 21 ⟶ 11 12 6 17 20 17 , 13 14 5 6 18 22 ⟶ 11 12 6 17 20 18 , 1 2 2 2 2 2 →= 23 17 5 2 2 2 , 1 2 2 2 2 6 →= 23 17 5 2 2 6 , 1 2 2 2 2 15 →= 23 17 5 2 2 15 , 1 2 2 2 2 16 →= 23 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 →= 20 17 5 2 2 2 , 5 2 2 2 2 6 →= 20 17 5 2 2 6 , 5 2 2 2 2 15 →= 20 17 5 2 2 15 , 5 2 2 2 2 16 →= 20 17 5 2 2 16 , 8 2 2 2 2 2 →= 24 17 5 2 2 2 , 8 2 2 2 2 6 →= 24 17 5 2 2 6 , 8 2 2 2 2 15 →= 24 17 5 2 2 15 , 8 2 2 2 2 16 →= 24 17 5 2 2 16 , 12 2 2 2 2 2 →= 25 17 5 2 2 2 , 12 2 2 2 2 6 →= 25 17 5 2 2 6 , 12 2 2 2 2 15 →= 25 17 5 2 2 15 , 12 2 2 2 2 16 →= 25 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 21 5 2 2 2 , 4 5 2 2 2 6 →= 30 21 5 2 2 6 , 4 5 2 2 2 15 →= 30 21 5 2 2 15 , 4 5 2 2 2 16 →= 30 21 5 2 2 16 , 10 5 2 2 2 2 →= 31 21 5 2 2 2 , 10 5 2 2 2 6 →= 31 21 5 2 2 6 , 10 5 2 2 2 15 →= 31 21 5 2 2 15 , 10 5 2 2 2 16 →= 31 21 5 2 2 16 , 14 5 2 2 2 2 →= 32 21 5 2 2 2 , 14 5 2 2 2 6 →= 32 21 5 2 2 6 , 14 5 2 2 2 15 →= 32 21 5 2 2 15 , 14 5 2 2 2 16 →= 32 21 5 2 2 16 , 17 5 2 2 2 2 →= 18 21 5 2 2 2 , 17 5 2 2 2 6 →= 18 21 5 2 2 6 , 17 5 2 2 2 15 →= 18 21 5 2 2 15 , 17 5 2 2 2 16 →= 18 21 5 2 2 16 , 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 15 →= 22 21 5 2 2 15 , 21 5 2 2 2 16 →= 22 21 5 2 2 16 , 33 5 2 2 2 2 →= 34 21 5 2 2 2 , 33 5 2 2 2 6 →= 34 21 5 2 2 6 , 33 5 2 2 2 15 →= 34 21 5 2 2 15 , 33 5 2 2 2 16 →= 34 21 5 2 2 16 , 35 5 2 2 2 2 →= 36 21 5 2 2 2 , 35 5 2 2 2 6 →= 36 21 5 2 2 6 , 35 5 2 2 2 15 →= 36 21 5 2 2 15 , 35 5 2 2 2 16 →= 36 21 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 →= 23 17 5 2 6 17 , 1 2 2 2 6 18 →= 23 17 5 2 6 18 , 1 2 2 2 6 19 →= 23 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 →= 20 17 5 2 6 17 , 5 2 2 2 6 18 →= 20 17 5 2 6 18 , 5 2 2 2 6 19 →= 20 17 5 2 6 19 , 8 2 2 2 6 17 →= 24 17 5 2 6 17 , 8 2 2 2 6 18 →= 24 17 5 2 6 18 , 8 2 2 2 6 19 →= 24 17 5 2 6 19 , 12 2 2 2 6 17 →= 25 17 5 2 6 17 , 12 2 2 2 6 18 →= 25 17 5 2 6 18 , 12 2 2 2 6 19 →= 25 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 21 5 2 6 17 , 4 5 2 2 6 18 →= 30 21 5 2 6 18 , 4 5 2 2 6 19 →= 30 21 5 2 6 19 , 10 5 2 2 6 17 →= 31 21 5 2 6 17 , 10 5 2 2 6 18 →= 31 21 5 2 6 18 , 10 5 2 2 6 19 →= 31 21 5 2 6 19 , 14 5 2 2 6 17 →= 32 21 5 2 6 17 , 14 5 2 2 6 18 →= 32 21 5 2 6 18 , 14 5 2 2 6 19 →= 32 21 5 2 6 19 , 17 5 2 2 6 17 →= 18 21 5 2 6 17 , 17 5 2 2 6 18 →= 18 21 5 2 6 18 , 17 5 2 2 6 19 →= 18 21 5 2 6 19 , 21 5 2 2 6 17 →= 22 21 5 2 6 17 , 21 5 2 2 6 18 →= 22 21 5 2 6 18 , 21 5 2 2 6 19 →= 22 21 5 2 6 19 , 33 5 2 2 6 17 →= 34 21 5 2 6 17 , 33 5 2 2 6 18 →= 34 21 5 2 6 18 , 33 5 2 2 6 19 →= 34 21 5 2 6 19 , 35 5 2 2 6 17 →= 36 21 5 2 6 17 , 35 5 2 2 6 18 →= 36 21 5 2 6 18 , 35 5 2 2 6 19 →= 36 21 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 →= 23 17 5 2 15 39 , 2 2 2 2 15 39 →= 6 17 5 2 15 39 , 5 2 2 2 15 39 →= 20 17 5 2 15 39 , 8 2 2 2 15 39 →= 24 17 5 2 15 39 , 12 2 2 2 15 39 →= 25 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 21 5 2 15 39 , 10 5 2 2 15 39 →= 31 21 5 2 15 39 , 14 5 2 2 15 39 →= 32 21 5 2 15 39 , 17 5 2 2 15 39 →= 18 21 5 2 15 39 , 21 5 2 2 15 39 →= 22 21 5 2 15 39 , 33 5 2 2 15 39 →= 34 21 5 2 15 39 , 35 5 2 2 15 39 →= 36 21 5 2 15 39 , 23 17 5 6 17 5 →= 1 2 6 17 5 2 , 23 17 5 6 17 20 →= 1 2 6 17 5 6 , 6 17 5 6 17 5 →= 2 2 6 17 5 2 , 6 17 5 6 17 20 →= 2 2 6 17 5 6 , 20 17 5 6 17 5 →= 5 2 6 17 5 2 , 20 17 5 6 17 20 →= 5 2 6 17 5 6 , 24 17 5 6 17 5 →= 8 2 6 17 5 2 , 24 17 5 6 17 20 →= 8 2 6 17 5 6 , 25 17 5 6 17 5 →= 12 2 6 17 5 2 , 25 17 5 6 17 20 →= 12 2 6 17 5 6 , 27 17 5 6 17 5 →= 26 2 6 17 5 2 , 27 17 5 6 17 20 →= 26 2 6 17 5 6 , 29 17 5 6 17 5 →= 28 2 6 17 5 2 , 29 17 5 6 17 20 →= 28 2 6 17 5 6 , 30 21 5 6 17 5 →= 4 5 6 17 5 2 , 30 21 5 6 17 20 →= 4 5 6 17 5 6 , 31 21 5 6 17 5 →= 10 5 6 17 5 2 , 31 21 5 6 17 20 →= 10 5 6 17 5 6 , 32 21 5 6 17 5 →= 14 5 6 17 5 2 , 32 21 5 6 17 20 →= 14 5 6 17 5 6 , 18 21 5 6 17 5 →= 17 5 6 17 5 2 , 18 21 5 6 17 20 →= 17 5 6 17 5 6 , 22 21 5 6 17 5 →= 21 5 6 17 5 2 , 22 21 5 6 17 20 →= 21 5 6 17 5 6 , 34 21 5 6 17 5 →= 33 5 6 17 5 2 , 34 21 5 6 17 20 →= 33 5 6 17 5 6 , 36 21 5 6 17 5 →= 35 5 6 17 5 2 , 36 21 5 6 17 20 →= 35 5 6 17 5 6 , 38 33 5 6 17 5 →= 37 26 6 17 5 2 , 38 33 5 6 17 20 →= 37 26 6 17 5 6 , 23 17 5 6 18 21 →= 1 2 6 17 20 17 , 23 17 5 6 18 22 →= 1 2 6 17 20 18 , 6 17 5 6 18 21 →= 2 2 6 17 20 17 , 6 17 5 6 18 22 →= 2 2 6 17 20 18 , 20 17 5 6 18 21 →= 5 2 6 17 20 17 , 20 17 5 6 18 22 →= 5 2 6 17 20 18 , 24 17 5 6 18 21 →= 8 2 6 17 20 17 , 24 17 5 6 18 22 →= 8 2 6 17 20 18 , 25 17 5 6 18 21 →= 12 2 6 17 20 17 , 25 17 5 6 18 22 →= 12 2 6 17 20 18 , 27 17 5 6 18 21 →= 26 2 6 17 20 17 , 27 17 5 6 18 22 →= 26 2 6 17 20 18 , 29 17 5 6 18 21 →= 28 2 6 17 20 17 , 29 17 5 6 18 22 →= 28 2 6 17 20 18 , 30 21 5 6 18 21 →= 4 5 6 17 20 17 , 30 21 5 6 18 22 →= 4 5 6 17 20 18 , 31 21 5 6 18 21 →= 10 5 6 17 20 17 , 31 21 5 6 18 22 →= 10 5 6 17 20 18 , 32 21 5 6 18 21 →= 14 5 6 17 20 17 , 32 21 5 6 18 22 →= 14 5 6 17 20 18 , 18 21 5 6 18 21 →= 17 5 6 17 20 17 , 18 21 5 6 18 22 →= 17 5 6 17 20 18 , 22 21 5 6 18 21 →= 21 5 6 17 20 17 , 22 21 5 6 18 22 →= 21 5 6 17 20 18 , 34 21 5 6 18 21 →= 33 5 6 17 20 17 , 34 21 5 6 18 22 →= 33 5 6 17 20 18 , 36 21 5 6 18 21 →= 35 5 6 17 20 17 , 36 21 5 6 18 22 →= 35 5 6 17 20 18 , 38 33 5 6 18 21 →= 37 26 6 17 20 17 , 38 33 5 6 18 22 →= 37 26 6 17 20 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, 15 ↦ 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 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 1 6 16 5 2 , 3 4 5 6 16 19 ⟶ 0 1 6 16 5 6 , 9 10 5 6 16 5 ⟶ 7 8 6 16 5 2 , 9 10 5 6 16 19 ⟶ 7 8 6 16 5 6 , 13 14 5 6 16 5 ⟶ 11 12 6 16 5 2 , 13 14 5 6 16 19 ⟶ 11 12 6 16 5 6 , 3 4 5 6 17 20 ⟶ 0 1 6 16 19 16 , 3 4 5 6 17 21 ⟶ 0 1 6 16 19 17 , 9 10 5 6 17 20 ⟶ 7 8 6 16 19 16 , 9 10 5 6 17 21 ⟶ 7 8 6 16 19 17 , 13 14 5 6 17 20 ⟶ 11 12 6 16 19 16 , 13 14 5 6 17 21 ⟶ 11 12 6 16 19 17 , 1 2 2 2 2 2 →= 22 16 5 2 2 2 , 1 2 2 2 2 6 →= 22 16 5 2 2 6 , 1 2 2 2 2 23 →= 22 16 5 2 2 23 , 1 2 2 2 2 15 →= 22 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 23 →= 6 16 5 2 2 23 , 2 2 2 2 2 15 →= 6 16 5 2 2 15 , 5 2 2 2 2 2 →= 19 16 5 2 2 2 , 5 2 2 2 2 6 →= 19 16 5 2 2 6 , 5 2 2 2 2 23 →= 19 16 5 2 2 23 , 5 2 2 2 2 15 →= 19 16 5 2 2 15 , 8 2 2 2 2 2 →= 24 16 5 2 2 2 , 8 2 2 2 2 6 →= 24 16 5 2 2 6 , 8 2 2 2 2 23 →= 24 16 5 2 2 23 , 8 2 2 2 2 15 →= 24 16 5 2 2 15 , 12 2 2 2 2 2 →= 25 16 5 2 2 2 , 12 2 2 2 2 6 →= 25 16 5 2 2 6 , 12 2 2 2 2 23 →= 25 16 5 2 2 23 , 12 2 2 2 2 15 →= 25 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 23 →= 27 16 5 2 2 23 , 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 23 →= 29 16 5 2 2 23 , 28 2 2 2 2 15 →= 29 16 5 2 2 15 , 4 5 2 2 2 2 →= 30 20 5 2 2 2 , 4 5 2 2 2 6 →= 30 20 5 2 2 6 , 4 5 2 2 2 23 →= 30 20 5 2 2 23 , 4 5 2 2 2 15 →= 30 20 5 2 2 15 , 10 5 2 2 2 2 →= 31 20 5 2 2 2 , 10 5 2 2 2 6 →= 31 20 5 2 2 6 , 10 5 2 2 2 23 →= 31 20 5 2 2 23 , 10 5 2 2 2 15 →= 31 20 5 2 2 15 , 14 5 2 2 2 2 →= 32 20 5 2 2 2 , 14 5 2 2 2 6 →= 32 20 5 2 2 6 , 14 5 2 2 2 23 →= 32 20 5 2 2 23 , 14 5 2 2 2 15 →= 32 20 5 2 2 15 , 16 5 2 2 2 2 →= 17 20 5 2 2 2 , 16 5 2 2 2 6 →= 17 20 5 2 2 6 , 16 5 2 2 2 23 →= 17 20 5 2 2 23 , 16 5 2 2 2 15 →= 17 20 5 2 2 15 , 20 5 2 2 2 2 →= 21 20 5 2 2 2 , 20 5 2 2 2 6 →= 21 20 5 2 2 6 , 20 5 2 2 2 23 →= 21 20 5 2 2 23 , 20 5 2 2 2 15 →= 21 20 5 2 2 15 , 33 5 2 2 2 2 →= 34 20 5 2 2 2 , 33 5 2 2 2 6 →= 34 20 5 2 2 6 , 33 5 2 2 2 23 →= 34 20 5 2 2 23 , 33 5 2 2 2 15 →= 34 20 5 2 2 15 , 35 5 2 2 2 2 →= 36 20 5 2 2 2 , 35 5 2 2 2 6 →= 36 20 5 2 2 6 , 35 5 2 2 2 23 →= 36 20 5 2 2 23 , 35 5 2 2 2 15 →= 36 20 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 23 →= 38 33 5 2 2 23 , 37 26 2 2 2 15 →= 38 33 5 2 2 15 , 1 2 2 2 6 16 →= 22 16 5 2 6 16 , 1 2 2 2 6 17 →= 22 16 5 2 6 17 , 1 2 2 2 6 18 →= 22 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 →= 19 16 5 2 6 16 , 5 2 2 2 6 17 →= 19 16 5 2 6 17 , 5 2 2 2 6 18 →= 19 16 5 2 6 18 , 8 2 2 2 6 16 →= 24 16 5 2 6 16 , 8 2 2 2 6 17 →= 24 16 5 2 6 17 , 8 2 2 2 6 18 →= 24 16 5 2 6 18 , 12 2 2 2 6 16 →= 25 16 5 2 6 16 , 12 2 2 2 6 17 →= 25 16 5 2 6 17 , 12 2 2 2 6 18 →= 25 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 20 5 2 6 16 , 4 5 2 2 6 17 →= 30 20 5 2 6 17 , 4 5 2 2 6 18 →= 30 20 5 2 6 18 , 10 5 2 2 6 16 →= 31 20 5 2 6 16 , 10 5 2 2 6 17 →= 31 20 5 2 6 17 , 10 5 2 2 6 18 →= 31 20 5 2 6 18 , 14 5 2 2 6 16 →= 32 20 5 2 6 16 , 14 5 2 2 6 17 →= 32 20 5 2 6 17 , 14 5 2 2 6 18 →= 32 20 5 2 6 18 , 16 5 2 2 6 16 →= 17 20 5 2 6 16 , 16 5 2 2 6 17 →= 17 20 5 2 6 17 , 16 5 2 2 6 18 →= 17 20 5 2 6 18 , 20 5 2 2 6 16 →= 21 20 5 2 6 16 , 20 5 2 2 6 17 →= 21 20 5 2 6 17 , 20 5 2 2 6 18 →= 21 20 5 2 6 18 , 33 5 2 2 6 16 →= 34 20 5 2 6 16 , 33 5 2 2 6 17 →= 34 20 5 2 6 17 , 33 5 2 2 6 18 →= 34 20 5 2 6 18 , 35 5 2 2 6 16 →= 36 20 5 2 6 16 , 35 5 2 2 6 17 →= 36 20 5 2 6 17 , 35 5 2 2 6 18 →= 36 20 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 23 39 →= 22 16 5 2 23 39 , 2 2 2 2 23 39 →= 6 16 5 2 23 39 , 5 2 2 2 23 39 →= 19 16 5 2 23 39 , 8 2 2 2 23 39 →= 24 16 5 2 23 39 , 12 2 2 2 23 39 →= 25 16 5 2 23 39 , 26 2 2 2 23 39 →= 27 16 5 2 23 39 , 28 2 2 2 23 39 →= 29 16 5 2 23 39 , 4 5 2 2 23 39 →= 30 20 5 2 23 39 , 10 5 2 2 23 39 →= 31 20 5 2 23 39 , 14 5 2 2 23 39 →= 32 20 5 2 23 39 , 16 5 2 2 23 39 →= 17 20 5 2 23 39 , 20 5 2 2 23 39 →= 21 20 5 2 23 39 , 33 5 2 2 23 39 →= 34 20 5 2 23 39 , 35 5 2 2 23 39 →= 36 20 5 2 23 39 , 22 16 5 6 16 5 →= 1 2 6 16 5 2 , 22 16 5 6 16 19 →= 1 2 6 16 5 6 , 6 16 5 6 16 5 →= 2 2 6 16 5 2 , 6 16 5 6 16 19 →= 2 2 6 16 5 6 , 19 16 5 6 16 5 →= 5 2 6 16 5 2 , 19 16 5 6 16 19 →= 5 2 6 16 5 6 , 24 16 5 6 16 5 →= 8 2 6 16 5 2 , 24 16 5 6 16 19 →= 8 2 6 16 5 6 , 25 16 5 6 16 5 →= 12 2 6 16 5 2 , 25 16 5 6 16 19 →= 12 2 6 16 5 6 , 27 16 5 6 16 5 →= 26 2 6 16 5 2 , 27 16 5 6 16 19 →= 26 2 6 16 5 6 , 29 16 5 6 16 5 →= 28 2 6 16 5 2 , 29 16 5 6 16 19 →= 28 2 6 16 5 6 , 30 20 5 6 16 5 →= 4 5 6 16 5 2 , 30 20 5 6 16 19 →= 4 5 6 16 5 6 , 31 20 5 6 16 5 →= 10 5 6 16 5 2 , 31 20 5 6 16 19 →= 10 5 6 16 5 6 , 32 20 5 6 16 5 →= 14 5 6 16 5 2 , 32 20 5 6 16 19 →= 14 5 6 16 5 6 , 17 20 5 6 16 5 →= 16 5 6 16 5 2 , 17 20 5 6 16 19 →= 16 5 6 16 5 6 , 21 20 5 6 16 5 →= 20 5 6 16 5 2 , 21 20 5 6 16 19 →= 20 5 6 16 5 6 , 34 20 5 6 16 5 →= 33 5 6 16 5 2 , 34 20 5 6 16 19 →= 33 5 6 16 5 6 , 36 20 5 6 16 5 →= 35 5 6 16 5 2 , 36 20 5 6 16 19 →= 35 5 6 16 5 6 , 38 33 5 6 16 5 →= 37 26 6 16 5 2 , 38 33 5 6 16 19 →= 37 26 6 16 5 6 , 22 16 5 6 17 20 →= 1 2 6 16 19 16 , 22 16 5 6 17 21 →= 1 2 6 16 19 17 , 6 16 5 6 17 20 →= 2 2 6 16 19 16 , 6 16 5 6 17 21 →= 2 2 6 16 19 17 , 19 16 5 6 17 20 →= 5 2 6 16 19 16 , 19 16 5 6 17 21 →= 5 2 6 16 19 17 , 24 16 5 6 17 20 →= 8 2 6 16 19 16 , 24 16 5 6 17 21 →= 8 2 6 16 19 17 , 25 16 5 6 17 20 →= 12 2 6 16 19 16 , 25 16 5 6 17 21 →= 12 2 6 16 19 17 , 27 16 5 6 17 20 →= 26 2 6 16 19 16 , 27 16 5 6 17 21 →= 26 2 6 16 19 17 , 29 16 5 6 17 20 →= 28 2 6 16 19 16 , 29 16 5 6 17 21 →= 28 2 6 16 19 17 , 30 20 5 6 17 20 →= 4 5 6 16 19 16 , 30 20 5 6 17 21 →= 4 5 6 16 19 17 , 31 20 5 6 17 20 →= 10 5 6 16 19 16 , 31 20 5 6 17 21 →= 10 5 6 16 19 17 , 32 20 5 6 17 20 →= 14 5 6 16 19 16 , 32 20 5 6 17 21 →= 14 5 6 16 19 17 , 17 20 5 6 17 20 →= 16 5 6 16 19 16 , 17 20 5 6 17 21 →= 16 5 6 16 19 17 , 21 20 5 6 17 20 →= 20 5 6 16 19 16 , 21 20 5 6 17 21 →= 20 5 6 16 19 17 , 34 20 5 6 17 20 →= 33 5 6 16 19 16 , 34 20 5 6 17 21 →= 33 5 6 16 19 17 , 36 20 5 6 17 20 →= 35 5 6 16 19 16 , 36 20 5 6 17 21 →= 35 5 6 16 19 17 , 38 33 5 6 17 20 →= 37 26 6 16 19 16 , 38 33 5 6 17 21 →= 37 26 6 16 19 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, 15 ↦ 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 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 1 6 15 5 2 , 3 4 5 6 15 18 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 18 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 18 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 19 ⟶ 0 1 6 15 18 15 , 3 4 5 6 16 20 ⟶ 0 1 6 15 18 16 , 9 10 5 6 16 19 ⟶ 7 8 6 15 18 15 , 9 10 5 6 16 20 ⟶ 7 8 6 15 18 16 , 13 14 5 6 16 19 ⟶ 11 12 6 15 18 15 , 13 14 5 6 16 20 ⟶ 11 12 6 15 18 16 , 1 2 2 2 2 2 →= 21 15 5 2 2 2 , 1 2 2 2 2 6 →= 21 15 5 2 2 6 , 1 2 2 2 2 22 →= 21 15 5 2 2 22 , 1 2 2 2 2 23 →= 21 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 22 →= 6 15 5 2 2 22 , 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 22 →= 18 15 5 2 2 22 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 8 2 2 2 2 2 →= 24 15 5 2 2 2 , 8 2 2 2 2 6 →= 24 15 5 2 2 6 , 8 2 2 2 2 22 →= 24 15 5 2 2 22 , 8 2 2 2 2 23 →= 24 15 5 2 2 23 , 12 2 2 2 2 2 →= 25 15 5 2 2 2 , 12 2 2 2 2 6 →= 25 15 5 2 2 6 , 12 2 2 2 2 22 →= 25 15 5 2 2 22 , 12 2 2 2 2 23 →= 25 15 5 2 2 23 , 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 22 →= 27 15 5 2 2 22 , 26 2 2 2 2 23 →= 27 15 5 2 2 23 , 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 22 →= 29 15 5 2 2 22 , 28 2 2 2 2 23 →= 29 15 5 2 2 23 , 4 5 2 2 2 2 →= 30 19 5 2 2 2 , 4 5 2 2 2 6 →= 30 19 5 2 2 6 , 4 5 2 2 2 22 →= 30 19 5 2 2 22 , 4 5 2 2 2 23 →= 30 19 5 2 2 23 , 10 5 2 2 2 2 →= 31 19 5 2 2 2 , 10 5 2 2 2 6 →= 31 19 5 2 2 6 , 10 5 2 2 2 22 →= 31 19 5 2 2 22 , 10 5 2 2 2 23 →= 31 19 5 2 2 23 , 14 5 2 2 2 2 →= 32 19 5 2 2 2 , 14 5 2 2 2 6 →= 32 19 5 2 2 6 , 14 5 2 2 2 22 →= 32 19 5 2 2 22 , 14 5 2 2 2 23 →= 32 19 5 2 2 23 , 15 5 2 2 2 2 →= 16 19 5 2 2 2 , 15 5 2 2 2 6 →= 16 19 5 2 2 6 , 15 5 2 2 2 22 →= 16 19 5 2 2 22 , 15 5 2 2 2 23 →= 16 19 5 2 2 23 , 19 5 2 2 2 2 →= 20 19 5 2 2 2 , 19 5 2 2 2 6 →= 20 19 5 2 2 6 , 19 5 2 2 2 22 →= 20 19 5 2 2 22 , 19 5 2 2 2 23 →= 20 19 5 2 2 23 , 33 5 2 2 2 2 →= 34 19 5 2 2 2 , 33 5 2 2 2 6 →= 34 19 5 2 2 6 , 33 5 2 2 2 22 →= 34 19 5 2 2 22 , 33 5 2 2 2 23 →= 34 19 5 2 2 23 , 35 5 2 2 2 2 →= 36 19 5 2 2 2 , 35 5 2 2 2 6 →= 36 19 5 2 2 6 , 35 5 2 2 2 22 →= 36 19 5 2 2 22 , 35 5 2 2 2 23 →= 36 19 5 2 2 23 , 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 22 →= 38 33 5 2 2 22 , 37 26 2 2 2 23 →= 38 33 5 2 2 23 , 1 2 2 2 6 15 →= 21 15 5 2 6 15 , 1 2 2 2 6 16 →= 21 15 5 2 6 16 , 1 2 2 2 6 17 →= 21 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 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 17 →= 18 15 5 2 6 17 , 8 2 2 2 6 15 →= 24 15 5 2 6 15 , 8 2 2 2 6 16 →= 24 15 5 2 6 16 , 8 2 2 2 6 17 →= 24 15 5 2 6 17 , 12 2 2 2 6 15 →= 25 15 5 2 6 15 , 12 2 2 2 6 16 →= 25 15 5 2 6 16 , 12 2 2 2 6 17 →= 25 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 19 5 2 6 15 , 4 5 2 2 6 16 →= 30 19 5 2 6 16 , 4 5 2 2 6 17 →= 30 19 5 2 6 17 , 10 5 2 2 6 15 →= 31 19 5 2 6 15 , 10 5 2 2 6 16 →= 31 19 5 2 6 16 , 10 5 2 2 6 17 →= 31 19 5 2 6 17 , 14 5 2 2 6 15 →= 32 19 5 2 6 15 , 14 5 2 2 6 16 →= 32 19 5 2 6 16 , 14 5 2 2 6 17 →= 32 19 5 2 6 17 , 15 5 2 2 6 15 →= 16 19 5 2 6 15 , 15 5 2 2 6 16 →= 16 19 5 2 6 16 , 15 5 2 2 6 17 →= 16 19 5 2 6 17 , 19 5 2 2 6 15 →= 20 19 5 2 6 15 , 19 5 2 2 6 16 →= 20 19 5 2 6 16 , 19 5 2 2 6 17 →= 20 19 5 2 6 17 , 33 5 2 2 6 15 →= 34 19 5 2 6 15 , 33 5 2 2 6 16 →= 34 19 5 2 6 16 , 33 5 2 2 6 17 →= 34 19 5 2 6 17 , 35 5 2 2 6 15 →= 36 19 5 2 6 15 , 35 5 2 2 6 16 →= 36 19 5 2 6 16 , 35 5 2 2 6 17 →= 36 19 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 22 39 →= 21 15 5 2 22 39 , 2 2 2 2 22 39 →= 6 15 5 2 22 39 , 5 2 2 2 22 39 →= 18 15 5 2 22 39 , 8 2 2 2 22 39 →= 24 15 5 2 22 39 , 12 2 2 2 22 39 →= 25 15 5 2 22 39 , 26 2 2 2 22 39 →= 27 15 5 2 22 39 , 28 2 2 2 22 39 →= 29 15 5 2 22 39 , 4 5 2 2 22 39 →= 30 19 5 2 22 39 , 10 5 2 2 22 39 →= 31 19 5 2 22 39 , 14 5 2 2 22 39 →= 32 19 5 2 22 39 , 15 5 2 2 22 39 →= 16 19 5 2 22 39 , 19 5 2 2 22 39 →= 20 19 5 2 22 39 , 33 5 2 2 22 39 →= 34 19 5 2 22 39 , 35 5 2 2 22 39 →= 36 19 5 2 22 39 , 21 15 5 6 15 5 →= 1 2 6 15 5 2 , 21 15 5 6 15 18 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 18 →= 2 2 6 15 5 6 , 18 15 5 6 15 5 →= 5 2 6 15 5 2 , 18 15 5 6 15 18 →= 5 2 6 15 5 6 , 24 15 5 6 15 5 →= 8 2 6 15 5 2 , 24 15 5 6 15 18 →= 8 2 6 15 5 6 , 25 15 5 6 15 5 →= 12 2 6 15 5 2 , 25 15 5 6 15 18 →= 12 2 6 15 5 6 , 27 15 5 6 15 5 →= 26 2 6 15 5 2 , 27 15 5 6 15 18 →= 26 2 6 15 5 6 , 29 15 5 6 15 5 →= 28 2 6 15 5 2 , 29 15 5 6 15 18 →= 28 2 6 15 5 6 , 30 19 5 6 15 5 →= 4 5 6 15 5 2 , 30 19 5 6 15 18 →= 4 5 6 15 5 6 , 31 19 5 6 15 5 →= 10 5 6 15 5 2 , 31 19 5 6 15 18 →= 10 5 6 15 5 6 , 32 19 5 6 15 5 →= 14 5 6 15 5 2 , 32 19 5 6 15 18 →= 14 5 6 15 5 6 , 16 19 5 6 15 5 →= 15 5 6 15 5 2 , 16 19 5 6 15 18 →= 15 5 6 15 5 6 , 20 19 5 6 15 5 →= 19 5 6 15 5 2 , 20 19 5 6 15 18 →= 19 5 6 15 5 6 , 34 19 5 6 15 5 →= 33 5 6 15 5 2 , 34 19 5 6 15 18 →= 33 5 6 15 5 6 , 36 19 5 6 15 5 →= 35 5 6 15 5 2 , 36 19 5 6 15 18 →= 35 5 6 15 5 6 , 38 33 5 6 15 5 →= 37 26 6 15 5 2 , 38 33 5 6 15 18 →= 37 26 6 15 5 6 , 21 15 5 6 16 19 →= 1 2 6 15 18 15 , 21 15 5 6 16 20 →= 1 2 6 15 18 16 , 6 15 5 6 16 19 →= 2 2 6 15 18 15 , 6 15 5 6 16 20 →= 2 2 6 15 18 16 , 18 15 5 6 16 19 →= 5 2 6 15 18 15 , 18 15 5 6 16 20 →= 5 2 6 15 18 16 , 24 15 5 6 16 19 →= 8 2 6 15 18 15 , 24 15 5 6 16 20 →= 8 2 6 15 18 16 , 25 15 5 6 16 19 →= 12 2 6 15 18 15 , 25 15 5 6 16 20 →= 12 2 6 15 18 16 , 27 15 5 6 16 19 →= 26 2 6 15 18 15 , 27 15 5 6 16 20 →= 26 2 6 15 18 16 , 29 15 5 6 16 19 →= 28 2 6 15 18 15 , 29 15 5 6 16 20 →= 28 2 6 15 18 16 , 30 19 5 6 16 19 →= 4 5 6 15 18 15 , 30 19 5 6 16 20 →= 4 5 6 15 18 16 , 31 19 5 6 16 19 →= 10 5 6 15 18 15 , 31 19 5 6 16 20 →= 10 5 6 15 18 16 , 32 19 5 6 16 19 →= 14 5 6 15 18 15 , 32 19 5 6 16 20 →= 14 5 6 15 18 16 , 16 19 5 6 16 19 →= 15 5 6 15 18 15 , 16 19 5 6 16 20 →= 15 5 6 15 18 16 , 20 19 5 6 16 19 →= 19 5 6 15 18 15 , 20 19 5 6 16 20 →= 19 5 6 15 18 16 , 34 19 5 6 16 19 →= 33 5 6 15 18 15 , 34 19 5 6 16 20 →= 33 5 6 15 18 16 , 36 19 5 6 16 19 →= 35 5 6 15 18 15 , 36 19 5 6 16 20 →= 35 5 6 15 18 16 , 38 33 5 6 16 19 →= 37 26 6 15 18 15 , 38 33 5 6 16 20 →= 37 26 6 15 18 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 1 6 15 5 2 , 3 4 5 6 15 18 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 18 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 18 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 19 ⟶ 0 1 6 15 18 15 , 3 4 5 6 16 20 ⟶ 0 1 6 15 18 16 , 9 10 5 6 16 19 ⟶ 7 8 6 15 18 15 , 9 10 5 6 16 20 ⟶ 7 8 6 15 18 16 , 13 14 5 6 16 19 ⟶ 11 12 6 15 18 15 , 13 14 5 6 16 20 ⟶ 11 12 6 15 18 16 , 1 2 2 2 2 2 →= 21 15 5 2 2 2 , 1 2 2 2 2 6 →= 21 15 5 2 2 6 , 1 2 2 2 2 22 →= 21 15 5 2 2 22 , 1 2 2 2 2 23 →= 21 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 22 →= 6 15 5 2 2 22 , 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 22 →= 18 15 5 2 2 22 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 8 2 2 2 2 2 →= 24 15 5 2 2 2 , 8 2 2 2 2 6 →= 24 15 5 2 2 6 , 8 2 2 2 2 22 →= 24 15 5 2 2 22 , 8 2 2 2 2 23 →= 24 15 5 2 2 23 , 12 2 2 2 2 2 →= 25 15 5 2 2 2 , 12 2 2 2 2 6 →= 25 15 5 2 2 6 , 12 2 2 2 2 22 →= 25 15 5 2 2 22 , 12 2 2 2 2 23 →= 25 15 5 2 2 23 , 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 22 →= 27 15 5 2 2 22 , 26 2 2 2 2 23 →= 27 15 5 2 2 23 , 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 22 →= 29 15 5 2 2 22 , 28 2 2 2 2 23 →= 29 15 5 2 2 23 , 4 5 2 2 2 2 →= 30 19 5 2 2 2 , 4 5 2 2 2 6 →= 30 19 5 2 2 6 , 4 5 2 2 2 22 →= 30 19 5 2 2 22 , 4 5 2 2 2 23 →= 30 19 5 2 2 23 , 10 5 2 2 2 2 →= 31 19 5 2 2 2 , 10 5 2 2 2 6 →= 31 19 5 2 2 6 , 10 5 2 2 2 22 →= 31 19 5 2 2 22 , 10 5 2 2 2 23 →= 31 19 5 2 2 23 , 14 5 2 2 2 2 →= 32 19 5 2 2 2 , 14 5 2 2 2 6 →= 32 19 5 2 2 6 , 14 5 2 2 2 22 →= 32 19 5 2 2 22 , 14 5 2 2 2 23 →= 32 19 5 2 2 23 , 15 5 2 2 2 2 →= 16 19 5 2 2 2 , 15 5 2 2 2 6 →= 16 19 5 2 2 6 , 15 5 2 2 2 22 →= 16 19 5 2 2 22 , 15 5 2 2 2 23 →= 16 19 5 2 2 23 , 19 5 2 2 2 2 →= 20 19 5 2 2 2 , 19 5 2 2 2 6 →= 20 19 5 2 2 6 , 19 5 2 2 2 22 →= 20 19 5 2 2 22 , 19 5 2 2 2 23 →= 20 19 5 2 2 23 , 33 5 2 2 2 2 →= 34 19 5 2 2 2 , 33 5 2 2 2 6 →= 34 19 5 2 2 6 , 33 5 2 2 2 22 →= 34 19 5 2 2 22 , 33 5 2 2 2 23 →= 34 19 5 2 2 23 , 35 5 2 2 2 2 →= 36 19 5 2 2 2 , 35 5 2 2 2 6 →= 36 19 5 2 2 6 , 35 5 2 2 2 22 →= 36 19 5 2 2 22 , 35 5 2 2 2 23 →= 36 19 5 2 2 23 , 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 22 →= 38 33 5 2 2 22 , 37 26 2 2 2 23 →= 38 33 5 2 2 23 , 1 2 2 2 6 15 →= 21 15 5 2 6 15 , 1 2 2 2 6 16 →= 21 15 5 2 6 16 , 1 2 2 2 6 17 →= 21 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 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 17 →= 18 15 5 2 6 17 , 8 2 2 2 6 15 →= 24 15 5 2 6 15 , 8 2 2 2 6 16 →= 24 15 5 2 6 16 , 8 2 2 2 6 17 →= 24 15 5 2 6 17 , 12 2 2 2 6 15 →= 25 15 5 2 6 15 , 12 2 2 2 6 16 →= 25 15 5 2 6 16 , 12 2 2 2 6 17 →= 25 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 19 5 2 6 15 , 4 5 2 2 6 16 →= 30 19 5 2 6 16 , 4 5 2 2 6 17 →= 30 19 5 2 6 17 , 10 5 2 2 6 15 →= 31 19 5 2 6 15 , 10 5 2 2 6 16 →= 31 19 5 2 6 16 , 10 5 2 2 6 17 →= 31 19 5 2 6 17 , 14 5 2 2 6 15 →= 32 19 5 2 6 15 , 14 5 2 2 6 16 →= 32 19 5 2 6 16 , 14 5 2 2 6 17 →= 32 19 5 2 6 17 , 15 5 2 2 6 15 →= 16 19 5 2 6 15 , 15 5 2 2 6 16 →= 16 19 5 2 6 16 , 15 5 2 2 6 17 →= 16 19 5 2 6 17 , 19 5 2 2 6 15 →= 20 19 5 2 6 15 , 19 5 2 2 6 16 →= 20 19 5 2 6 16 , 19 5 2 2 6 17 →= 20 19 5 2 6 17 , 33 5 2 2 6 15 →= 34 19 5 2 6 15 , 33 5 2 2 6 16 →= 34 19 5 2 6 16 , 33 5 2 2 6 17 →= 34 19 5 2 6 17 , 35 5 2 2 6 15 →= 36 19 5 2 6 15 , 35 5 2 2 6 16 →= 36 19 5 2 6 16 , 35 5 2 2 6 17 →= 36 19 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 22 39 →= 21 15 5 2 22 39 , 2 2 2 2 22 39 →= 6 15 5 2 22 39 , 5 2 2 2 22 39 →= 18 15 5 2 22 39 , 8 2 2 2 22 39 →= 24 15 5 2 22 39 , 12 2 2 2 22 39 →= 25 15 5 2 22 39 , 26 2 2 2 22 39 →= 27 15 5 2 22 39 , 28 2 2 2 22 39 →= 29 15 5 2 22 39 , 4 5 2 2 22 39 →= 30 19 5 2 22 39 , 10 5 2 2 22 39 →= 31 19 5 2 22 39 , 14 5 2 2 22 39 →= 32 19 5 2 22 39 , 15 5 2 2 22 39 →= 16 19 5 2 22 39 , 19 5 2 2 22 39 →= 20 19 5 2 22 39 , 33 5 2 2 22 39 →= 34 19 5 2 22 39 , 35 5 2 2 22 39 →= 36 19 5 2 22 39 , 21 15 5 6 15 5 →= 1 2 6 15 5 2 , 21 15 5 6 15 18 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 18 →= 2 2 6 15 5 6 , 18 15 5 6 15 5 →= 5 2 6 15 5 2 , 18 15 5 6 15 18 →= 5 2 6 15 5 6 , 24 15 5 6 15 5 →= 8 2 6 15 5 2 , 24 15 5 6 15 18 →= 8 2 6 15 5 6 , 25 15 5 6 15 5 →= 12 2 6 15 5 2 , 25 15 5 6 15 18 →= 12 2 6 15 5 6 , 27 15 5 6 15 5 →= 26 2 6 15 5 2 , 27 15 5 6 15 18 →= 26 2 6 15 5 6 , 29 15 5 6 15 5 →= 28 2 6 15 5 2 , 29 15 5 6 15 18 →= 28 2 6 15 5 6 , 30 19 5 6 15 5 →= 4 5 6 15 5 2 , 30 19 5 6 15 18 →= 4 5 6 15 5 6 , 31 19 5 6 15 5 →= 10 5 6 15 5 2 , 31 19 5 6 15 18 →= 10 5 6 15 5 6 , 32 19 5 6 15 5 →= 14 5 6 15 5 2 , 32 19 5 6 15 18 →= 14 5 6 15 5 6 , 16 19 5 6 15 5 →= 15 5 6 15 5 2 , 16 19 5 6 15 18 →= 15 5 6 15 5 6 , 20 19 5 6 15 5 →= 19 5 6 15 5 2 , 20 19 5 6 15 18 →= 19 5 6 15 5 6 , 34 19 5 6 15 5 →= 33 5 6 15 5 2 , 34 19 5 6 15 18 →= 33 5 6 15 5 6 , 36 19 5 6 15 5 →= 35 5 6 15 5 2 , 36 19 5 6 15 18 →= 35 5 6 15 5 6 , 38 33 5 6 15 5 →= 37 26 6 15 5 2 , 38 33 5 6 15 18 →= 37 26 6 15 5 6 , 21 15 5 6 16 19 →= 1 2 6 15 18 15 , 21 15 5 6 16 20 →= 1 2 6 15 18 16 , 6 15 5 6 16 19 →= 2 2 6 15 18 15 , 6 15 5 6 16 20 →= 2 2 6 15 18 16 , 18 15 5 6 16 19 →= 5 2 6 15 18 15 , 18 15 5 6 16 20 →= 5 2 6 15 18 16 , 24 15 5 6 16 19 →= 8 2 6 15 18 15 , 24 15 5 6 16 20 →= 8 2 6 15 18 16 , 25 15 5 6 16 19 →= 12 2 6 15 18 15 , 25 15 5 6 16 20 →= 12 2 6 15 18 16 , 27 15 5 6 16 19 →= 26 2 6 15 18 15 , 27 15 5 6 16 20 →= 26 2 6 15 18 16 , 29 15 5 6 16 19 →= 28 2 6 15 18 15 , 29 15 5 6 16 20 →= 28 2 6 15 18 16 , 30 19 5 6 16 19 →= 4 5 6 15 18 15 , 30 19 5 6 16 20 →= 4 5 6 15 18 16 , 31 19 5 6 16 19 →= 10 5 6 15 18 15 , 31 19 5 6 16 20 →= 10 5 6 15 18 16 , 32 19 5 6 16 19 →= 14 5 6 15 18 15 , 32 19 5 6 16 20 →= 14 5 6 15 18 16 , 16 19 5 6 16 19 →= 15 5 6 15 18 15 , 16 19 5 6 16 20 →= 15 5 6 15 18 16 , 20 19 5 6 16 19 →= 19 5 6 15 18 15 , 20 19 5 6 16 20 →= 19 5 6 15 18 16 , 34 19 5 6 16 19 →= 33 5 6 15 18 15 , 34 19 5 6 16 20 →= 33 5 6 15 18 16 , 36 19 5 6 16 19 →= 35 5 6 15 18 15 , 36 19 5 6 16 20 →= 35 5 6 15 18 16 , 38 33 5 6 16 19 →= 37 26 6 15 18 15 , 38 33 5 6 16 20 →= 37 26 6 15 18 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 1 6 15 5 2 , 3 4 5 6 15 18 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 18 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 18 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 19 ⟶ 0 1 6 15 18 15 , 3 4 5 6 16 20 ⟶ 0 1 6 15 18 16 , 9 10 5 6 16 19 ⟶ 7 8 6 15 18 15 , 9 10 5 6 16 20 ⟶ 7 8 6 15 18 16 , 13 14 5 6 16 19 ⟶ 11 12 6 15 18 15 , 13 14 5 6 16 20 ⟶ 11 12 6 15 18 16 , 1 2 2 2 2 2 →= 21 15 5 2 2 2 , 1 2 2 2 2 6 →= 21 15 5 2 2 6 , 1 2 2 2 2 22 →= 21 15 5 2 2 22 , 1 2 2 2 2 23 →= 21 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 22 →= 6 15 5 2 2 22 , 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 22 →= 18 15 5 2 2 22 , 5 2 2 2 2 23 →= 18 15 5 2 2 23 , 8 2 2 2 2 2 →= 24 15 5 2 2 2 , 8 2 2 2 2 6 →= 24 15 5 2 2 6 , 8 2 2 2 2 22 →= 24 15 5 2 2 22 , 8 2 2 2 2 23 →= 24 15 5 2 2 23 , 12 2 2 2 2 2 →= 25 15 5 2 2 2 , 12 2 2 2 2 6 →= 25 15 5 2 2 6 , 12 2 2 2 2 22 →= 25 15 5 2 2 22 , 12 2 2 2 2 23 →= 25 15 5 2 2 23 , 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 22 →= 27 15 5 2 2 22 , 26 2 2 2 2 23 →= 27 15 5 2 2 23 , 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 22 →= 29 15 5 2 2 22 , 28 2 2 2 2 23 →= 29 15 5 2 2 23 , 4 5 2 2 2 2 →= 30 19 5 2 2 2 , 4 5 2 2 2 6 →= 30 19 5 2 2 6 , 4 5 2 2 2 22 →= 30 19 5 2 2 22 , 4 5 2 2 2 23 →= 30 19 5 2 2 23 , 10 5 2 2 2 2 →= 31 19 5 2 2 2 , 10 5 2 2 2 6 →= 31 19 5 2 2 6 , 10 5 2 2 2 22 →= 31 19 5 2 2 22 , 10 5 2 2 2 23 →= 31 19 5 2 2 23 , 14 5 2 2 2 2 →= 32 19 5 2 2 2 , 14 5 2 2 2 6 →= 32 19 5 2 2 6 , 14 5 2 2 2 22 →= 32 19 5 2 2 22 , 14 5 2 2 2 23 →= 32 19 5 2 2 23 , 15 5 2 2 2 2 →= 16 19 5 2 2 2 , 15 5 2 2 2 6 →= 16 19 5 2 2 6 , 15 5 2 2 2 22 →= 16 19 5 2 2 22 , 15 5 2 2 2 23 →= 16 19 5 2 2 23 , 19 5 2 2 2 2 →= 20 19 5 2 2 2 , 19 5 2 2 2 6 →= 20 19 5 2 2 6 , 19 5 2 2 2 22 →= 20 19 5 2 2 22 , 19 5 2 2 2 23 →= 20 19 5 2 2 23 , 33 5 2 2 2 2 →= 34 19 5 2 2 2 , 33 5 2 2 2 6 →= 34 19 5 2 2 6 , 33 5 2 2 2 22 →= 34 19 5 2 2 22 , 33 5 2 2 2 23 →= 34 19 5 2 2 23 , 35 5 2 2 2 2 →= 36 19 5 2 2 2 , 35 5 2 2 2 6 →= 36 19 5 2 2 6 , 35 5 2 2 2 22 →= 36 19 5 2 2 22 , 35 5 2 2 2 23 →= 36 19 5 2 2 23 , 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 22 →= 38 33 5 2 2 22 , 37 26 2 2 2 23 →= 38 33 5 2 2 23 , 1 2 2 2 6 15 →= 21 15 5 2 6 15 , 1 2 2 2 6 16 →= 21 15 5 2 6 16 , 1 2 2 2 6 17 →= 21 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 →= 18 15 5 2 6 15 , 5 2 2 2 6 16 →= 18 15 5 2 6 16 , 5 2 2 2 6 17 →= 18 15 5 2 6 17 , 8 2 2 2 6 15 →= 24 15 5 2 6 15 , 8 2 2 2 6 16 →= 24 15 5 2 6 16 , 8 2 2 2 6 17 →= 24 15 5 2 6 17 , 12 2 2 2 6 15 →= 25 15 5 2 6 15 , 12 2 2 2 6 16 →= 25 15 5 2 6 16 , 12 2 2 2 6 17 →= 25 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 19 5 2 6 15 , 4 5 2 2 6 16 →= 30 19 5 2 6 16 , 4 5 2 2 6 17 →= 30 19 5 2 6 17 , 10 5 2 2 6 15 →= 31 19 5 2 6 15 , 10 5 2 2 6 16 →= 31 19 5 2 6 16 , 10 5 2 2 6 17 →= 31 19 5 2 6 17 , 14 5 2 2 6 15 →= 32 19 5 2 6 15 , 14 5 2 2 6 16 →= 32 19 5 2 6 16 , 14 5 2 2 6 17 →= 32 19 5 2 6 17 , 15 5 2 2 6 15 →= 16 19 5 2 6 15 , 15 5 2 2 6 16 →= 16 19 5 2 6 16 , 15 5 2 2 6 17 →= 16 19 5 2 6 17 , 19 5 2 2 6 15 →= 20 19 5 2 6 15 , 19 5 2 2 6 16 →= 20 19 5 2 6 16 , 19 5 2 2 6 17 →= 20 19 5 2 6 17 , 33 5 2 2 6 15 →= 34 19 5 2 6 15 , 33 5 2 2 6 16 →= 34 19 5 2 6 16 , 33 5 2 2 6 17 →= 34 19 5 2 6 17 , 35 5 2 2 6 15 →= 36 19 5 2 6 15 , 35 5 2 2 6 16 →= 36 19 5 2 6 16 , 35 5 2 2 6 17 →= 36 19 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 22 39 →= 21 15 5 2 22 39 , 2 2 2 2 22 39 →= 6 15 5 2 22 39 , 5 2 2 2 22 39 →= 18 15 5 2 22 39 , 8 2 2 2 22 39 →= 24 15 5 2 22 39 , 12 2 2 2 22 39 →= 25 15 5 2 22 39 , 26 2 2 2 22 39 →= 27 15 5 2 22 39 , 28 2 2 2 22 39 →= 29 15 5 2 22 39 , 4 5 2 2 22 39 →= 30 19 5 2 22 39 , 10 5 2 2 22 39 →= 31 19 5 2 22 39 , 14 5 2 2 22 39 →= 32 19 5 2 22 39 , 15 5 2 2 22 39 →= 16 19 5 2 22 39 , 19 5 2 2 22 39 →= 20 19 5 2 22 39 , 33 5 2 2 22 39 →= 34 19 5 2 22 39 , 35 5 2 2 22 39 →= 36 19 5 2 22 39 , 21 15 5 6 15 5 →= 1 2 6 15 5 2 , 21 15 5 6 15 18 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 18 →= 2 2 6 15 5 6 , 18 15 5 6 15 5 →= 5 2 6 15 5 2 , 18 15 5 6 15 18 →= 5 2 6 15 5 6 , 24 15 5 6 15 5 →= 8 2 6 15 5 2 , 24 15 5 6 15 18 →= 8 2 6 15 5 6 , 25 15 5 6 15 5 →= 12 2 6 15 5 2 , 25 15 5 6 15 18 →= 12 2 6 15 5 6 , 27 15 5 6 15 5 →= 26 2 6 15 5 2 , 27 15 5 6 15 18 →= 26 2 6 15 5 6 , 29 15 5 6 15 5 →= 28 2 6 15 5 2 , 29 15 5 6 15 18 →= 28 2 6 15 5 6 , 30 19 5 6 15 5 →= 4 5 6 15 5 2 , 30 19 5 6 15 18 →= 4 5 6 15 5 6 , 31 19 5 6 15 5 →= 10 5 6 15 5 2 , 31 19 5 6 15 18 →= 10 5 6 15 5 6 , 32 19 5 6 15 5 →= 14 5 6 15 5 2 , 32 19 5 6 15 18 →= 14 5 6 15 5 6 , 16 19 5 6 15 5 →= 15 5 6 15 5 2 , 16 19 5 6 15 18 →= 15 5 6 15 5 6 , 20 19 5 6 15 5 →= 19 5 6 15 5 2 , 20 19 5 6 15 18 →= 19 5 6 15 5 6 , 34 19 5 6 15 5 →= 33 5 6 15 5 2 , 34 19 5 6 15 18 →= 33 5 6 15 5 6 , 36 19 5 6 15 5 →= 35 5 6 15 5 2 , 36 19 5 6 15 18 →= 35 5 6 15 5 6 , 38 33 5 6 15 5 →= 37 26 6 15 5 2 , 38 33 5 6 15 18 →= 37 26 6 15 5 6 , 21 15 5 6 16 19 →= 1 2 6 15 18 15 , 21 15 5 6 16 20 →= 1 2 6 15 18 16 , 6 15 5 6 16 19 →= 2 2 6 15 18 15 , 6 15 5 6 16 20 →= 2 2 6 15 18 16 , 18 15 5 6 16 19 →= 5 2 6 15 18 15 , 18 15 5 6 16 20 →= 5 2 6 15 18 16 , 24 15 5 6 16 19 →= 8 2 6 15 18 15 , 24 15 5 6 16 20 →= 8 2 6 15 18 16 , 25 15 5 6 16 19 →= 12 2 6 15 18 15 , 25 15 5 6 16 20 →= 12 2 6 15 18 16 , 27 15 5 6 16 19 →= 26 2 6 15 18 15 , 27 15 5 6 16 20 →= 26 2 6 15 18 16 , 29 15 5 6 16 19 →= 28 2 6 15 18 15 , 29 15 5 6 16 20 →= 28 2 6 15 18 16 , 30 19 5 6 16 19 →= 4 5 6 15 18 15 , 30 19 5 6 16 20 →= 4 5 6 15 18 16 , 31 19 5 6 16 19 →= 10 5 6 15 18 15 , 31 19 5 6 16 20 →= 10 5 6 15 18 16 , 32 19 5 6 16 19 →= 14 5 6 15 18 15 , 32 19 5 6 16 20 →= 14 5 6 15 18 16 , 16 19 5 6 16 19 →= 15 5 6 15 18 15 , 16 19 5 6 16 20 →= 15 5 6 15 18 16 , 20 19 5 6 16 19 →= 19 5 6 15 18 15 , 20 19 5 6 16 20 →= 19 5 6 15 18 16 , 34 19 5 6 16 19 →= 33 5 6 15 18 15 , 34 19 5 6 16 20 →= 33 5 6 15 18 16 , 36 19 5 6 16 19 →= 35 5 6 15 18 15 , 36 19 5 6 16 20 →= 35 5 6 15 18 16 , 38 33 5 6 16 19 →= 37 26 6 15 18 15 , 38 33 5 6 16 20 →= 37 26 6 15 18 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 15 5 2 2 6 , 1 2 2 2 2 21 →= 20 15 5 2 2 21 , 1 2 2 2 2 22 →= 20 15 5 2 2 22 , 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 8 2 2 2 2 21 →= 23 15 5 2 2 21 , 8 2 2 2 2 22 →= 23 15 5 2 2 22 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 15 5 2 2 6 , 12 2 2 2 2 21 →= 24 15 5 2 2 21 , 12 2 2 2 2 22 →= 24 15 5 2 2 22 , 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 21 →= 26 15 5 2 2 21 , 25 2 2 2 2 22 →= 26 15 5 2 2 22 , 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 21 →= 28 15 5 2 2 21 , 27 2 2 2 2 22 →= 28 15 5 2 2 22 , 4 5 2 2 2 2 →= 29 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 5 2 2 6 , 34 5 2 2 2 21 →= 35 18 5 2 2 21 , 34 5 2 2 2 22 →= 35 18 5 2 2 22 , 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 21 →= 37 32 5 2 2 21 , 36 25 2 2 2 22 →= 37 32 5 2 2 22 , 1 2 2 2 6 15 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 15 5 2 6 16 , 1 2 2 2 6 38 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 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, 22 ↦ 21, 21 ↦ 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 15 5 2 2 6 , 1 2 2 2 2 21 →= 20 15 5 2 2 21 , 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 22 →= 6 15 5 2 2 22 , 2 2 2 2 2 21 →= 6 15 5 2 2 21 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 8 2 2 2 2 22 →= 23 15 5 2 2 22 , 8 2 2 2 2 21 →= 23 15 5 2 2 21 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 15 5 2 2 6 , 12 2 2 2 2 22 →= 24 15 5 2 2 22 , 12 2 2 2 2 21 →= 24 15 5 2 2 21 , 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 22 →= 26 15 5 2 2 22 , 25 2 2 2 2 21 →= 26 15 5 2 2 21 , 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 22 →= 28 15 5 2 2 22 , 27 2 2 2 2 21 →= 28 15 5 2 2 21 , 4 5 2 2 2 2 →= 29 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 5 2 2 6 , 34 5 2 2 2 22 →= 35 18 5 2 2 22 , 34 5 2 2 2 21 →= 35 18 5 2 2 21 , 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 22 →= 37 32 5 2 2 22 , 36 25 2 2 2 21 →= 37 32 5 2 2 21 , 1 2 2 2 6 15 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 15 5 2 6 16 , 1 2 2 2 6 38 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 22 39 →= 20 15 5 2 22 39 , 2 2 2 2 22 39 →= 6 15 5 2 22 39 , 5 2 2 2 22 39 →= 17 15 5 2 22 39 , 8 2 2 2 22 39 →= 23 15 5 2 22 39 , 12 2 2 2 22 39 →= 24 15 5 2 22 39 , 25 2 2 2 22 39 →= 26 15 5 2 22 39 , 27 2 2 2 22 39 →= 28 15 5 2 22 39 , 4 5 2 2 22 39 →= 29 18 5 2 22 39 , 10 5 2 2 22 39 →= 30 18 5 2 22 39 , 14 5 2 2 22 39 →= 31 18 5 2 22 39 , 15 5 2 2 22 39 →= 16 18 5 2 22 39 , 18 5 2 2 22 39 →= 19 18 5 2 22 39 , 32 5 2 2 22 39 →= 33 18 5 2 22 39 , 34 5 2 2 22 39 →= 35 18 5 2 22 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 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, 22 ↦ 21, 21 ↦ 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 8 2 2 2 2 21 →= 23 15 5 2 2 21 , 8 2 2 2 2 22 →= 23 15 5 2 2 22 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 15 5 2 2 6 , 12 2 2 2 2 21 →= 24 15 5 2 2 21 , 12 2 2 2 2 22 →= 24 15 5 2 2 22 , 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 21 →= 26 15 5 2 2 21 , 25 2 2 2 2 22 →= 26 15 5 2 2 22 , 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 21 →= 28 15 5 2 2 21 , 27 2 2 2 2 22 →= 28 15 5 2 2 22 , 4 5 2 2 2 2 →= 29 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 5 2 2 6 , 34 5 2 2 2 21 →= 35 18 5 2 2 21 , 34 5 2 2 2 22 →= 35 18 5 2 2 22 , 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 21 →= 37 32 5 2 2 21 , 36 25 2 2 2 22 →= 37 32 5 2 2 22 , 1 2 2 2 6 15 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 15 5 2 6 16 , 1 2 2 2 6 38 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 8 2 2 2 2 22 →= 23 15 5 2 2 22 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 15 5 2 2 6 , 12 2 2 2 2 21 →= 24 15 5 2 2 21 , 12 2 2 2 2 22 →= 24 15 5 2 2 22 , 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 21 →= 26 15 5 2 2 21 , 25 2 2 2 2 22 →= 26 15 5 2 2 22 , 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 21 →= 28 15 5 2 2 21 , 27 2 2 2 2 22 →= 28 15 5 2 2 22 , 4 5 2 2 2 2 →= 29 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 5 2 2 6 , 34 5 2 2 2 21 →= 35 18 5 2 2 21 , 34 5 2 2 2 22 →= 35 18 5 2 2 22 , 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 21 →= 37 32 5 2 2 21 , 36 25 2 2 2 22 →= 37 32 5 2 2 22 , 1 2 2 2 6 15 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 15 5 2 6 16 , 1 2 2 2 6 38 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 15 5 2 2 6 , 12 2 2 2 2 21 →= 24 15 5 2 2 21 , 12 2 2 2 2 22 →= 24 15 5 2 2 22 , 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 21 →= 26 15 5 2 2 21 , 25 2 2 2 2 22 →= 26 15 5 2 2 22 , 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 21 →= 28 15 5 2 2 21 , 27 2 2 2 2 22 →= 28 15 5 2 2 22 , 4 5 2 2 2 2 →= 29 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 5 2 2 6 , 34 5 2 2 2 21 →= 35 18 5 2 2 21 , 34 5 2 2 2 22 →= 35 18 5 2 2 22 , 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 21 →= 37 32 5 2 2 21 , 36 25 2 2 2 22 →= 37 32 5 2 2 22 , 1 2 2 2 6 15 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 15 5 2 6 16 , 1 2 2 2 6 38 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 15 5 2 2 6 , 12 2 2 2 2 22 →= 24 15 5 2 2 22 , 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 21 →= 26 15 5 2 2 21 , 25 2 2 2 2 22 →= 26 15 5 2 2 22 , 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 21 →= 28 15 5 2 2 21 , 27 2 2 2 2 22 →= 28 15 5 2 2 22 , 4 5 2 2 2 2 →= 29 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 5 2 2 6 , 34 5 2 2 2 21 →= 35 18 5 2 2 21 , 34 5 2 2 2 22 →= 35 18 5 2 2 22 , 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 21 →= 37 32 5 2 2 21 , 36 25 2 2 2 22 →= 37 32 5 2 2 22 , 1 2 2 2 6 15 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 15 5 2 6 16 , 1 2 2 2 6 38 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 21 →= 26 15 5 2 2 21 , 25 2 2 2 2 22 →= 26 15 5 2 2 22 , 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 21 →= 28 15 5 2 2 21 , 27 2 2 2 2 22 →= 28 15 5 2 2 22 , 4 5 2 2 2 2 →= 29 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 5 2 2 6 , 34 5 2 2 2 21 →= 35 18 5 2 2 21 , 34 5 2 2 2 22 →= 35 18 5 2 2 22 , 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 21 →= 37 32 5 2 2 21 , 36 25 2 2 2 22 →= 37 32 5 2 2 22 , 1 2 2 2 6 15 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 15 5 2 6 16 , 1 2 2 2 6 38 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 22 →= 26 15 5 2 2 22 , 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 21 →= 28 15 5 2 2 21 , 27 2 2 2 2 22 →= 28 15 5 2 2 22 , 4 5 2 2 2 2 →= 29 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 5 2 2 6 , 34 5 2 2 2 21 →= 35 18 5 2 2 21 , 34 5 2 2 2 22 →= 35 18 5 2 2 22 , 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 21 →= 37 32 5 2 2 21 , 36 25 2 2 2 22 →= 37 32 5 2 2 22 , 1 2 2 2 6 15 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 15 5 2 6 16 , 1 2 2 2 6 38 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 21 →= 28 15 5 2 2 21 , 27 2 2 2 2 22 →= 28 15 5 2 2 22 , 4 5 2 2 2 2 →= 29 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 5 2 2 6 , 34 5 2 2 2 21 →= 35 18 5 2 2 21 , 34 5 2 2 2 22 →= 35 18 5 2 2 22 , 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 21 →= 37 32 5 2 2 21 , 36 25 2 2 2 22 →= 37 32 5 2 2 22 , 1 2 2 2 6 15 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 15 5 2 6 16 , 1 2 2 2 6 38 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 22 →= 28 15 5 2 2 22 , 4 5 2 2 2 2 →= 29 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 5 2 2 6 , 34 5 2 2 2 21 →= 35 18 5 2 2 21 , 34 5 2 2 2 22 →= 35 18 5 2 2 22 , 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 21 →= 37 32 5 2 2 21 , 36 25 2 2 2 22 →= 37 32 5 2 2 22 , 1 2 2 2 6 15 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 15 5 2 6 16 , 1 2 2 2 6 38 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 5 2 2 6 , 34 5 2 2 2 21 →= 35 18 5 2 2 21 , 34 5 2 2 2 22 →= 35 18 5 2 2 22 , 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 21 →= 37 32 5 2 2 21 , 36 25 2 2 2 22 →= 37 32 5 2 2 22 , 1 2 2 2 6 15 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 15 5 2 6 16 , 1 2 2 2 6 38 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 5 2 2 6 , 34 5 2 2 2 22 →= 35 18 5 2 2 22 , 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 21 →= 37 32 5 2 2 21 , 36 25 2 2 2 22 →= 37 32 5 2 2 22 , 1 2 2 2 6 15 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 15 5 2 6 16 , 1 2 2 2 6 38 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 21 →= 37 32 5 2 2 21 , 36 25 2 2 2 22 →= 37 32 5 2 2 22 , 1 2 2 2 6 15 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 15 5 2 6 16 , 1 2 2 2 6 38 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 22 →= 37 32 5 2 2 22 , 1 2 2 2 6 15 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 15 5 2 6 16 , 1 2 2 2 6 38 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 15 5 2 6 16 , 1 2 2 2 6 38 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 8 2 2 2 6 38 →= 23 15 5 2 6 38 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 15 5 2 6 16 , 12 2 2 2 6 38 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 5 2 6 16 , 34 5 2 2 6 38 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 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 21 39 →= 20 15 5 2 21 39 , 2 2 2 2 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 ⎟ ⎜ 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 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 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 8 2 2 2 21 39 →= 23 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 ⎟ ⎜ 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 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 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 12 2 2 2 21 39 →= 24 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 ⎟ ⎜ 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 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 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 25 2 2 2 21 39 →= 26 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 ⎟ ⎜ 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 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 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 27 2 2 2 21 39 →= 28 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 ⎟ ⎜ 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 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 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 4 5 2 2 21 39 →= 29 18 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 ⎟ ⎜ 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 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 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 10 5 2 2 21 39 →= 30 18 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 ⎟ ⎜ 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 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 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 14 5 2 2 21 39 →= 31 18 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 ⎟ ⎜ 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 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 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 32 5 2 2 21 39 →= 33 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 ⎟ ⎜ 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 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 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 34 5 2 2 21 39 →= 35 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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 1 ⎟ ⎜ 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 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 1 6 15 5 2 , 3 4 5 6 15 17 ⟶ 0 1 6 15 5 6 , 9 10 5 6 15 5 ⟶ 7 8 6 15 5 2 , 9 10 5 6 15 17 ⟶ 7 8 6 15 5 6 , 13 14 5 6 15 5 ⟶ 11 12 6 15 5 2 , 13 14 5 6 15 17 ⟶ 11 12 6 15 5 6 , 3 4 5 6 16 18 ⟶ 0 1 6 15 17 15 , 3 4 5 6 16 19 ⟶ 0 1 6 15 17 16 , 9 10 5 6 16 18 ⟶ 7 8 6 15 17 15 , 9 10 5 6 16 19 ⟶ 7 8 6 15 17 16 , 13 14 5 6 16 18 ⟶ 11 12 6 15 17 15 , 13 14 5 6 16 19 ⟶ 11 12 6 15 17 16 , 1 2 2 2 2 2 →= 20 15 5 2 2 2 , 1 2 2 2 2 6 →= 20 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 21 →= 6 15 5 2 2 21 , 2 2 2 2 2 22 →= 6 15 5 2 2 22 , 5 2 2 2 2 2 →= 17 15 5 2 2 2 , 5 2 2 2 2 6 →= 17 15 5 2 2 6 , 5 2 2 2 2 21 →= 17 15 5 2 2 21 , 5 2 2 2 2 22 →= 17 15 5 2 2 22 , 8 2 2 2 2 2 →= 23 15 5 2 2 2 , 8 2 2 2 2 6 →= 23 15 5 2 2 6 , 12 2 2 2 2 2 →= 24 15 5 2 2 2 , 12 2 2 2 2 6 →= 24 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 18 5 2 2 2 , 4 5 2 2 2 6 →= 29 18 5 2 2 6 , 4 5 2 2 2 21 →= 29 18 5 2 2 21 , 4 5 2 2 2 22 →= 29 18 5 2 2 22 , 10 5 2 2 2 2 →= 30 18 5 2 2 2 , 10 5 2 2 2 6 →= 30 18 5 2 2 6 , 10 5 2 2 2 21 →= 30 18 5 2 2 21 , 10 5 2 2 2 22 →= 30 18 5 2 2 22 , 14 5 2 2 2 2 →= 31 18 5 2 2 2 , 14 5 2 2 2 6 →= 31 18 5 2 2 6 , 14 5 2 2 2 21 →= 31 18 5 2 2 21 , 14 5 2 2 2 22 →= 31 18 5 2 2 22 , 15 5 2 2 2 2 →= 16 18 5 2 2 2 , 15 5 2 2 2 6 →= 16 18 5 2 2 6 , 15 5 2 2 2 21 →= 16 18 5 2 2 21 , 15 5 2 2 2 22 →= 16 18 5 2 2 22 , 18 5 2 2 2 2 →= 19 18 5 2 2 2 , 18 5 2 2 2 6 →= 19 18 5 2 2 6 , 18 5 2 2 2 21 →= 19 18 5 2 2 21 , 18 5 2 2 2 22 →= 19 18 5 2 2 22 , 32 5 2 2 2 2 →= 33 18 5 2 2 2 , 32 5 2 2 2 6 →= 33 18 5 2 2 6 , 32 5 2 2 2 21 →= 33 18 5 2 2 21 , 32 5 2 2 2 22 →= 33 18 5 2 2 22 , 34 5 2 2 2 2 →= 35 18 5 2 2 2 , 34 5 2 2 2 6 →= 35 18 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 →= 20 15 5 2 6 15 , 1 2 2 2 6 16 →= 20 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 →= 17 15 5 2 6 15 , 5 2 2 2 6 16 →= 17 15 5 2 6 16 , 5 2 2 2 6 38 →= 17 15 5 2 6 38 , 8 2 2 2 6 15 →= 23 15 5 2 6 15 , 8 2 2 2 6 16 →= 23 15 5 2 6 16 , 12 2 2 2 6 15 →= 24 15 5 2 6 15 , 12 2 2 2 6 16 →= 24 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 18 5 2 6 15 , 4 5 2 2 6 16 →= 29 18 5 2 6 16 , 4 5 2 2 6 38 →= 29 18 5 2 6 38 , 10 5 2 2 6 15 →= 30 18 5 2 6 15 , 10 5 2 2 6 16 →= 30 18 5 2 6 16 , 10 5 2 2 6 38 →= 30 18 5 2 6 38 , 14 5 2 2 6 15 →= 31 18 5 2 6 15 , 14 5 2 2 6 16 →= 31 18 5 2 6 16 , 14 5 2 2 6 38 →= 31 18 5 2 6 38 , 15 5 2 2 6 15 →= 16 18 5 2 6 15 , 15 5 2 2 6 16 →= 16 18 5 2 6 16 , 15 5 2 2 6 38 →= 16 18 5 2 6 38 , 18 5 2 2 6 15 →= 19 18 5 2 6 15 , 18 5 2 2 6 16 →= 19 18 5 2 6 16 , 18 5 2 2 6 38 →= 19 18 5 2 6 38 , 32 5 2 2 6 15 →= 33 18 5 2 6 15 , 32 5 2 2 6 16 →= 33 18 5 2 6 16 , 32 5 2 2 6 38 →= 33 18 5 2 6 38 , 34 5 2 2 6 15 →= 35 18 5 2 6 15 , 34 5 2 2 6 16 →= 35 18 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 21 39 →= 6 15 5 2 21 39 , 5 2 2 2 21 39 →= 17 15 5 2 21 39 , 15 5 2 2 21 39 →= 16 18 5 2 21 39 , 18 5 2 2 21 39 →= 19 18 5 2 21 39 , 20 15 5 6 15 5 →= 1 2 6 15 5 2 , 20 15 5 6 15 17 →= 1 2 6 15 5 6 , 6 15 5 6 15 5 →= 2 2 6 15 5 2 , 6 15 5 6 15 17 →= 2 2 6 15 5 6 , 17 15 5 6 15 5 →= 5 2 6 15 5 2 , 17 15 5 6 15 17 →= 5 2 6 15 5 6 , 23 15 5 6 15 5 →= 8 2 6 15 5 2 , 23 15 5 6 15 17 →= 8 2 6 15 5 6 , 24 15 5 6 15 5 →= 12 2 6 15 5 2 , 24 15 5 6 15 17 →= 12 2 6 15 5 6 , 26 15 5 6 15 5 →= 25 2 6 15 5 2 , 26 15 5 6 15 17 →= 25 2 6 15 5 6 , 28 15 5 6 15 5 →= 27 2 6 15 5 2 , 28 15 5 6 15 17 →= 27 2 6 15 5 6 , 29 18 5 6 15 5 →= 4 5 6 15 5 2 , 29 18 5 6 15 17 →= 4 5 6 15 5 6 , 30 18 5 6 15 5 →= 10 5 6 15 5 2 , 30 18 5 6 15 17 →= 10 5 6 15 5 6 , 31 18 5 6 15 5 →= 14 5 6 15 5 2 , 31 18 5 6 15 17 →= 14 5 6 15 5 6 , 16 18 5 6 15 5 →= 15 5 6 15 5 2 , 16 18 5 6 15 17 →= 15 5 6 15 5 6 , 19 18 5 6 15 5 →= 18 5 6 15 5 2 , 19 18 5 6 15 17 →= 18 5 6 15 5 6 , 33 18 5 6 15 5 →= 32 5 6 15 5 2 , 33 18 5 6 15 17 →= 32 5 6 15 5 6 , 35 18 5 6 15 5 →= 34 5 6 15 5 2 , 35 18 5 6 15 17 →= 34 5 6 15 5 6 , 37 32 5 6 15 5 →= 36 25 6 15 5 2 , 37 32 5 6 15 17 →= 36 25 6 15 5 6 , 20 15 5 6 16 18 →= 1 2 6 15 17 15 , 20 15 5 6 16 19 →= 1 2 6 15 17 16 , 6 15 5 6 16 18 →= 2 2 6 15 17 15 , 6 15 5 6 16 19 →= 2 2 6 15 17 16 , 17 15 5 6 16 18 →= 5 2 6 15 17 15 , 17 15 5 6 16 19 →= 5 2 6 15 17 16 , 23 15 5 6 16 18 →= 8 2 6 15 17 15 , 23 15 5 6 16 19 →= 8 2 6 15 17 16 , 24 15 5 6 16 18 →= 12 2 6 15 17 15 , 24 15 5 6 16 19 →= 12 2 6 15 17 16 , 26 15 5 6 16 18 →= 25 2 6 15 17 15 , 26 15 5 6 16 19 →= 25 2 6 15 17 16 , 28 15 5 6 16 18 →= 27 2 6 15 17 15 , 28 15 5 6 16 19 →= 27 2 6 15 17 16 , 29 18 5 6 16 18 →= 4 5 6 15 17 15 , 29 18 5 6 16 19 →= 4 5 6 15 17 16 , 30 18 5 6 16 18 →= 10 5 6 15 17 15 , 30 18 5 6 16 19 →= 10 5 6 15 17 16 , 31 18 5 6 16 18 →= 14 5 6 15 17 15 , 31 18 5 6 16 19 →= 14 5 6 15 17 16 , 16 18 5 6 16 18 →= 15 5 6 15 17 15 , 16 18 5 6 16 19 →= 15 5 6 15 17 16 , 19 18 5 6 16 18 →= 18 5 6 15 17 15 , 19 18 5 6 16 19 →= 18 5 6 15 17 16 , 33 18 5 6 16 18 →= 32 5 6 15 17 15 , 33 18 5 6 16 19 →= 32 5 6 15 17 16 , 35 18 5 6 16 18 →= 34 5 6 15 17 15 , 35 18 5 6 16 19 →= 34 5 6 15 17 16 , 37 32 5 6 16 18 →= 36 25 6 15 17 15 , 37 32 5 6 16 19 →= 36 25 6 15 17 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, (2,21) ↦ 8, (2,6) ↦ 9, (2,22) ↦ 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, (15,17) ↦ 28, (15,5) ↦ 29, (15,41) ↦ 30, (16,18) ↦ 31, (16,19) ↦ 32, (16,41) ↦ 33, (5,6) ↦ 34, (1,6) ↦ 35, (17,16) ↦ 36, (17,15) ↦ 37, (8,6) ↦ 38, (12,6) ↦ 39, (18,17) ↦ 40, (18,5) ↦ 41, (19,18) ↦ 42, (19,19) ↦ 43, (0,20) ↦ 44, (20,15) ↦ 45, (40,1) ↦ 46, (40,20) ↦ 47, (40,2) ↦ 48, (40,6) ↦ 49, (25,2) ↦ 50, (25,6) ↦ 51, (27,2) ↦ 52, (27,6) ↦ 53, (21,39) ↦ 54, (21,41) ↦ 55, (22,41) ↦ 56, (32,5) ↦ 57, (32,17) ↦ 58, (34,5) ↦ 59, (34,17) ↦ 60, (4,17) ↦ 61, (40,5) ↦ 62, (40,17) ↦ 63, (10,17) ↦ 64, (14,17) ↦ 65, (7,23) ↦ 66, (23,15) ↦ 67, (40,8) ↦ 68, (40,23) ↦ 69, (40,12) ↦ 70, (40,24) ↦ 71, (24,15) ↦ 72, (11,24) ↦ 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, (29,18) ↦ 83, (40,4) ↦ 84, (40,29) ↦ 85, (40,10) ↦ 86, (40,30) ↦ 87, (30,18) ↦ 88, (9,30) ↦ 89, (40,14) ↦ 90, (40,31) ↦ 91, (31,18) ↦ 92, (13,31) ↦ 93, (20,16) ↦ 94, (23,16) ↦ 95, (24,16) ↦ 96, (40,15) ↦ 97, (40,16) ↦ 98, (26,16) ↦ 99, (28,16) ↦ 100, (33,18) ↦ 101, (33,19) ↦ 102, (35,18) ↦ 103, (35,19) ↦ 104, (40,18) ↦ 105, (40,19) ↦ 106, (29,19) ↦ 107, (30,19) ↦ 108, (31,19) ↦ 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 9 12 ⟶ 4 5 6 7 3 9 12 , 0 1 2 3 3 9 13 ⟶ 4 5 6 7 3 9 13 , 0 1 2 3 3 9 14 ⟶ 4 5 6 7 3 9 14 , 0 1 2 3 3 9 15 ⟶ 4 5 6 7 3 9 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 9 12 ⟶ 19 20 21 7 3 9 12 , 16 17 18 3 3 9 13 ⟶ 19 20 21 7 3 9 13 , 16 17 18 3 3 9 14 ⟶ 19 20 21 7 3 9 14 , 16 17 18 3 3 9 15 ⟶ 19 20 21 7 3 9 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 9 12 ⟶ 25 26 27 7 3 9 12 , 22 23 24 3 3 9 13 ⟶ 25 26 27 7 3 9 13 , 22 23 24 3 3 9 14 ⟶ 25 26 27 7 3 9 14 , 22 23 24 3 3 9 15 ⟶ 25 26 27 7 3 9 15 , 0 1 2 3 9 15 28 ⟶ 4 5 6 7 9 15 28 , 0 1 2 3 9 15 29 ⟶ 4 5 6 7 9 15 29 , 0 1 2 3 9 15 30 ⟶ 4 5 6 7 9 15 30 , 0 1 2 3 9 12 31 ⟶ 4 5 6 7 9 12 31 , 0 1 2 3 9 12 32 ⟶ 4 5 6 7 9 12 32 , 0 1 2 3 9 12 33 ⟶ 4 5 6 7 9 12 33 , 16 17 18 3 9 15 28 ⟶ 19 20 21 7 9 15 28 , 16 17 18 3 9 15 29 ⟶ 19 20 21 7 9 15 29 , 16 17 18 3 9 15 30 ⟶ 19 20 21 7 9 15 30 , 16 17 18 3 9 12 31 ⟶ 19 20 21 7 9 12 31 , 16 17 18 3 9 12 32 ⟶ 19 20 21 7 9 12 32 , 16 17 18 3 9 12 33 ⟶ 19 20 21 7 9 12 33 , 22 23 24 3 9 15 28 ⟶ 25 26 27 7 9 15 28 , 22 23 24 3 9 15 29 ⟶ 25 26 27 7 9 15 29 , 22 23 24 3 9 15 30 ⟶ 25 26 27 7 9 15 30 , 22 23 24 3 9 12 31 ⟶ 25 26 27 7 9 12 31 , 22 23 24 3 9 12 32 ⟶ 25 26 27 7 9 12 32 , 22 23 24 3 9 12 33 ⟶ 25 26 27 7 9 12 33 , 4 5 6 34 15 29 7 ⟶ 0 1 35 15 29 7 3 , 4 5 6 34 15 29 34 ⟶ 0 1 35 15 29 7 9 , 4 5 6 34 15 28 36 ⟶ 0 1 35 15 29 34 12 , 4 5 6 34 15 28 37 ⟶ 0 1 35 15 29 34 15 , 19 20 21 34 15 29 7 ⟶ 16 17 38 15 29 7 3 , 19 20 21 34 15 29 34 ⟶ 16 17 38 15 29 7 9 , 19 20 21 34 15 28 36 ⟶ 16 17 38 15 29 34 12 , 19 20 21 34 15 28 37 ⟶ 16 17 38 15 29 34 15 , 25 26 27 34 15 29 7 ⟶ 22 23 39 15 29 7 3 , 25 26 27 34 15 29 34 ⟶ 22 23 39 15 29 7 9 , 25 26 27 34 15 28 36 ⟶ 22 23 39 15 29 34 12 , 25 26 27 34 15 28 37 ⟶ 22 23 39 15 29 34 15 , 4 5 6 34 12 31 40 ⟶ 0 1 35 15 28 37 28 , 4 5 6 34 12 31 41 ⟶ 0 1 35 15 28 37 29 , 4 5 6 34 12 32 42 ⟶ 0 1 35 15 28 36 31 , 4 5 6 34 12 32 43 ⟶ 0 1 35 15 28 36 32 , 19 20 21 34 12 31 40 ⟶ 16 17 38 15 28 37 28 , 19 20 21 34 12 31 41 ⟶ 16 17 38 15 28 37 29 , 19 20 21 34 12 32 42 ⟶ 16 17 38 15 28 36 31 , 19 20 21 34 12 32 43 ⟶ 16 17 38 15 28 36 32 , 25 26 27 34 12 31 40 ⟶ 22 23 39 15 28 37 28 , 25 26 27 34 12 31 41 ⟶ 22 23 39 15 28 37 29 , 25 26 27 34 12 32 42 ⟶ 22 23 39 15 28 36 31 , 25 26 27 34 12 32 43 ⟶ 22 23 39 15 28 36 32 , 1 2 3 3 3 3 3 →= 44 45 29 7 3 3 3 , 1 2 3 3 3 3 8 →= 44 45 29 7 3 3 8 , 1 2 3 3 3 3 9 →= 44 45 29 7 3 3 9 , 1 2 3 3 3 3 10 →= 44 45 29 7 3 3 10 , 1 2 3 3 3 3 11 →= 44 45 29 7 3 3 11 , 46 2 3 3 3 3 3 →= 47 45 29 7 3 3 3 , 46 2 3 3 3 3 8 →= 47 45 29 7 3 3 8 , 46 2 3 3 3 3 9 →= 47 45 29 7 3 3 9 , 46 2 3 3 3 3 10 →= 47 45 29 7 3 3 10 , 46 2 3 3 3 3 11 →= 47 45 29 7 3 3 11 , 1 2 3 3 3 9 12 →= 44 45 29 7 3 9 12 , 1 2 3 3 3 9 13 →= 44 45 29 7 3 9 13 , 1 2 3 3 3 9 14 →= 44 45 29 7 3 9 14 , 1 2 3 3 3 9 15 →= 44 45 29 7 3 9 15 , 46 2 3 3 3 9 12 →= 47 45 29 7 3 9 12 , 46 2 3 3 3 9 13 →= 47 45 29 7 3 9 13 , 46 2 3 3 3 9 14 →= 47 45 29 7 3 9 14 , 46 2 3 3 3 9 15 →= 47 45 29 7 3 9 15 , 2 3 3 3 3 3 3 →= 35 15 29 7 3 3 3 , 2 3 3 3 3 3 8 →= 35 15 29 7 3 3 8 , 2 3 3 3 3 3 9 →= 35 15 29 7 3 3 9 , 2 3 3 3 3 3 10 →= 35 15 29 7 3 3 10 , 2 3 3 3 3 3 11 →= 35 15 29 7 3 3 11 , 3 3 3 3 3 3 3 →= 9 15 29 7 3 3 3 , 3 3 3 3 3 3 8 →= 9 15 29 7 3 3 8 , 3 3 3 3 3 3 9 →= 9 15 29 7 3 3 9 , 3 3 3 3 3 3 10 →= 9 15 29 7 3 3 10 , 3 3 3 3 3 3 11 →= 9 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 →= 38 15 29 7 3 3 3 , 18 3 3 3 3 3 8 →= 38 15 29 7 3 3 8 , 18 3 3 3 3 3 9 →= 38 15 29 7 3 3 9 , 18 3 3 3 3 3 10 →= 38 15 29 7 3 3 10 , 18 3 3 3 3 3 11 →= 38 15 29 7 3 3 11 , 48 3 3 3 3 3 3 →= 49 15 29 7 3 3 3 , 48 3 3 3 3 3 8 →= 49 15 29 7 3 3 8 , 48 3 3 3 3 3 9 →= 49 15 29 7 3 3 9 , 48 3 3 3 3 3 10 →= 49 15 29 7 3 3 10 , 48 3 3 3 3 3 11 →= 49 15 29 7 3 3 11 , 50 3 3 3 3 3 3 →= 51 15 29 7 3 3 3 , 50 3 3 3 3 3 8 →= 51 15 29 7 3 3 8 , 50 3 3 3 3 3 9 →= 51 15 29 7 3 3 9 , 50 3 3 3 3 3 10 →= 51 15 29 7 3 3 10 , 50 3 3 3 3 3 11 →= 51 15 29 7 3 3 11 , 52 3 3 3 3 3 3 →= 53 15 29 7 3 3 3 , 52 3 3 3 3 3 8 →= 53 15 29 7 3 3 8 , 52 3 3 3 3 3 9 →= 53 15 29 7 3 3 9 , 52 3 3 3 3 3 10 →= 53 15 29 7 3 3 10 , 52 3 3 3 3 3 11 →= 53 15 29 7 3 3 11 , 24 3 3 3 3 3 3 →= 39 15 29 7 3 3 3 , 24 3 3 3 3 3 8 →= 39 15 29 7 3 3 8 , 24 3 3 3 3 3 9 →= 39 15 29 7 3 3 9 , 24 3 3 3 3 3 10 →= 39 15 29 7 3 3 10 , 24 3 3 3 3 3 11 →= 39 15 29 7 3 3 11 , 2 3 3 3 3 9 12 →= 35 15 29 7 3 9 12 , 2 3 3 3 3 9 13 →= 35 15 29 7 3 9 13 , 2 3 3 3 3 9 14 →= 35 15 29 7 3 9 14 , 2 3 3 3 3 9 15 →= 35 15 29 7 3 9 15 , 3 3 3 3 3 9 12 →= 9 15 29 7 3 9 12 , 3 3 3 3 3 9 13 →= 9 15 29 7 3 9 13 , 3 3 3 3 3 9 14 →= 9 15 29 7 3 9 14 , 3 3 3 3 3 9 15 →= 9 15 29 7 3 9 15 , 7 3 3 3 3 9 12 →= 34 15 29 7 3 9 12 , 7 3 3 3 3 9 13 →= 34 15 29 7 3 9 13 , 7 3 3 3 3 9 14 →= 34 15 29 7 3 9 14 , 7 3 3 3 3 9 15 →= 34 15 29 7 3 9 15 , 18 3 3 3 3 9 12 →= 38 15 29 7 3 9 12 , 18 3 3 3 3 9 13 →= 38 15 29 7 3 9 13 , 18 3 3 3 3 9 14 →= 38 15 29 7 3 9 14 , 18 3 3 3 3 9 15 →= 38 15 29 7 3 9 15 , 48 3 3 3 3 9 12 →= 49 15 29 7 3 9 12 , 48 3 3 3 3 9 13 →= 49 15 29 7 3 9 13 , 48 3 3 3 3 9 14 →= 49 15 29 7 3 9 14 , 48 3 3 3 3 9 15 →= 49 15 29 7 3 9 15 , 50 3 3 3 3 9 12 →= 51 15 29 7 3 9 12 , 50 3 3 3 3 9 13 →= 51 15 29 7 3 9 13 , 50 3 3 3 3 9 14 →= 51 15 29 7 3 9 14 , 50 3 3 3 3 9 15 →= 51 15 29 7 3 9 15 , 52 3 3 3 3 9 12 →= 53 15 29 7 3 9 12 , 52 3 3 3 3 9 13 →= 53 15 29 7 3 9 13 , 52 3 3 3 3 9 14 →= 53 15 29 7 3 9 14 , 52 3 3 3 3 9 15 →= 53 15 29 7 3 9 15 , 24 3 3 3 3 9 12 →= 39 15 29 7 3 9 12 , 24 3 3 3 3 9 13 →= 39 15 29 7 3 9 13 , 24 3 3 3 3 9 14 →= 39 15 29 7 3 9 14 , 24 3 3 3 3 9 15 →= 39 15 29 7 3 9 15 , 2 3 3 3 3 8 54 →= 35 15 29 7 3 8 54 , 2 3 3 3 3 8 55 →= 35 15 29 7 3 8 55 , 3 3 3 3 3 8 54 →= 9 15 29 7 3 8 54 , 3 3 3 3 3 8 55 →= 9 15 29 7 3 8 55 , 7 3 3 3 3 8 54 →= 34 15 29 7 3 8 54 , 7 3 3 3 3 8 55 →= 34 15 29 7 3 8 55 , 18 3 3 3 3 8 54 →= 38 15 29 7 3 8 54 , 18 3 3 3 3 8 55 →= 38 15 29 7 3 8 55 , 48 3 3 3 3 8 54 →= 49 15 29 7 3 8 54 , 48 3 3 3 3 8 55 →= 49 15 29 7 3 8 55 , 50 3 3 3 3 8 54 →= 51 15 29 7 3 8 54 , 50 3 3 3 3 8 55 →= 51 15 29 7 3 8 55 , 52 3 3 3 3 8 54 →= 53 15 29 7 3 8 54 , 52 3 3 3 3 8 55 →= 53 15 29 7 3 8 55 , 24 3 3 3 3 8 54 →= 39 15 29 7 3 8 54 , 24 3 3 3 3 8 55 →= 39 15 29 7 3 8 55 , 2 3 3 3 3 10 56 →= 35 15 29 7 3 10 56 , 3 3 3 3 3 10 56 →= 9 15 29 7 3 10 56 , 7 3 3 3 3 10 56 →= 34 15 29 7 3 10 56 , 18 3 3 3 3 10 56 →= 38 15 29 7 3 10 56 , 48 3 3 3 3 10 56 →= 49 15 29 7 3 10 56 , 50 3 3 3 3 10 56 →= 51 15 29 7 3 10 56 , 52 3 3 3 3 10 56 →= 53 15 29 7 3 10 56 , 24 3 3 3 3 10 56 →= 39 15 29 7 3 10 56 , 57 7 3 3 3 3 3 →= 58 37 29 7 3 3 3 , 57 7 3 3 3 3 8 →= 58 37 29 7 3 3 8 , 57 7 3 3 3 3 9 →= 58 37 29 7 3 3 9 , 57 7 3 3 3 3 10 →= 58 37 29 7 3 3 10 , 57 7 3 3 3 3 11 →= 58 37 29 7 3 3 11 , 41 7 3 3 3 3 3 →= 40 37 29 7 3 3 3 , 41 7 3 3 3 3 8 →= 40 37 29 7 3 3 8 , 41 7 3 3 3 3 9 →= 40 37 29 7 3 3 9 , 41 7 3 3 3 3 10 →= 40 37 29 7 3 3 10 , 41 7 3 3 3 3 11 →= 40 37 29 7 3 3 11 , 59 7 3 3 3 3 3 →= 60 37 29 7 3 3 3 , 59 7 3 3 3 3 8 →= 60 37 29 7 3 3 8 , 59 7 3 3 3 3 9 →= 60 37 29 7 3 3 9 , 59 7 3 3 3 3 10 →= 60 37 29 7 3 3 10 , 59 7 3 3 3 3 11 →= 60 37 29 7 3 3 11 , 6 7 3 3 3 3 3 →= 61 37 29 7 3 3 3 , 6 7 3 3 3 3 8 →= 61 37 29 7 3 3 8 , 6 7 3 3 3 3 9 →= 61 37 29 7 3 3 9 , 6 7 3 3 3 3 10 →= 61 37 29 7 3 3 10 , 6 7 3 3 3 3 11 →= 61 37 29 7 3 3 11 , 62 7 3 3 3 3 3 →= 63 37 29 7 3 3 3 , 62 7 3 3 3 3 8 →= 63 37 29 7 3 3 8 , 62 7 3 3 3 3 9 →= 63 37 29 7 3 3 9 , 62 7 3 3 3 3 10 →= 63 37 29 7 3 3 10 , 62 7 3 3 3 3 11 →= 63 37 29 7 3 3 11 , 21 7 3 3 3 3 3 →= 64 37 29 7 3 3 3 , 21 7 3 3 3 3 8 →= 64 37 29 7 3 3 8 , 21 7 3 3 3 3 9 →= 64 37 29 7 3 3 9 , 21 7 3 3 3 3 10 →= 64 37 29 7 3 3 10 , 21 7 3 3 3 3 11 →= 64 37 29 7 3 3 11 , 27 7 3 3 3 3 3 →= 65 37 29 7 3 3 3 , 27 7 3 3 3 3 8 →= 65 37 29 7 3 3 8 , 27 7 3 3 3 3 9 →= 65 37 29 7 3 3 9 , 27 7 3 3 3 3 10 →= 65 37 29 7 3 3 10 , 27 7 3 3 3 3 11 →= 65 37 29 7 3 3 11 , 29 7 3 3 3 3 3 →= 28 37 29 7 3 3 3 , 29 7 3 3 3 3 8 →= 28 37 29 7 3 3 8 , 29 7 3 3 3 3 9 →= 28 37 29 7 3 3 9 , 29 7 3 3 3 3 10 →= 28 37 29 7 3 3 10 , 29 7 3 3 3 3 11 →= 28 37 29 7 3 3 11 , 57 7 3 3 3 9 12 →= 58 37 29 7 3 9 12 , 57 7 3 3 3 9 13 →= 58 37 29 7 3 9 13 , 57 7 3 3 3 9 14 →= 58 37 29 7 3 9 14 , 57 7 3 3 3 9 15 →= 58 37 29 7 3 9 15 , 41 7 3 3 3 9 12 →= 40 37 29 7 3 9 12 , 41 7 3 3 3 9 13 →= 40 37 29 7 3 9 13 , 41 7 3 3 3 9 14 →= 40 37 29 7 3 9 14 , 41 7 3 3 3 9 15 →= 40 37 29 7 3 9 15 , 59 7 3 3 3 9 12 →= 60 37 29 7 3 9 12 , 59 7 3 3 3 9 13 →= 60 37 29 7 3 9 13 , 59 7 3 3 3 9 14 →= 60 37 29 7 3 9 14 , 59 7 3 3 3 9 15 →= 60 37 29 7 3 9 15 , 6 7 3 3 3 9 12 →= 61 37 29 7 3 9 12 , 6 7 3 3 3 9 13 →= 61 37 29 7 3 9 13 , 6 7 3 3 3 9 14 →= 61 37 29 7 3 9 14 , 6 7 3 3 3 9 15 →= 61 37 29 7 3 9 15 , 62 7 3 3 3 9 12 →= 63 37 29 7 3 9 12 , 62 7 3 3 3 9 13 →= 63 37 29 7 3 9 13 , 62 7 3 3 3 9 14 →= 63 37 29 7 3 9 14 , 62 7 3 3 3 9 15 →= 63 37 29 7 3 9 15 , 21 7 3 3 3 9 12 →= 64 37 29 7 3 9 12 , 21 7 3 3 3 9 13 →= 64 37 29 7 3 9 13 , 21 7 3 3 3 9 14 →= 64 37 29 7 3 9 14 , 21 7 3 3 3 9 15 →= 64 37 29 7 3 9 15 , 27 7 3 3 3 9 12 →= 65 37 29 7 3 9 12 , 27 7 3 3 3 9 13 →= 65 37 29 7 3 9 13 , 27 7 3 3 3 9 14 →= 65 37 29 7 3 9 14 , 27 7 3 3 3 9 15 →= 65 37 29 7 3 9 15 , 29 7 3 3 3 9 12 →= 28 37 29 7 3 9 12 , 29 7 3 3 3 9 13 →= 28 37 29 7 3 9 13 , 29 7 3 3 3 9 14 →= 28 37 29 7 3 9 14 , 29 7 3 3 3 9 15 →= 28 37 29 7 3 9 15 , 57 7 3 3 3 8 54 →= 58 37 29 7 3 8 54 , 57 7 3 3 3 8 55 →= 58 37 29 7 3 8 55 , 41 7 3 3 3 8 54 →= 40 37 29 7 3 8 54 , 41 7 3 3 3 8 55 →= 40 37 29 7 3 8 55 , 59 7 3 3 3 8 54 →= 60 37 29 7 3 8 54 , 59 7 3 3 3 8 55 →= 60 37 29 7 3 8 55 , 6 7 3 3 3 8 54 →= 61 37 29 7 3 8 54 , 6 7 3 3 3 8 55 →= 61 37 29 7 3 8 55 , 62 7 3 3 3 8 54 →= 63 37 29 7 3 8 54 , 62 7 3 3 3 8 55 →= 63 37 29 7 3 8 55 , 21 7 3 3 3 8 54 →= 64 37 29 7 3 8 54 , 21 7 3 3 3 8 55 →= 64 37 29 7 3 8 55 , 27 7 3 3 3 8 54 →= 65 37 29 7 3 8 54 , 27 7 3 3 3 8 55 →= 65 37 29 7 3 8 55 , 29 7 3 3 3 8 54 →= 28 37 29 7 3 8 54 , 29 7 3 3 3 8 55 →= 28 37 29 7 3 8 55 , 57 7 3 3 3 10 56 →= 58 37 29 7 3 10 56 , 41 7 3 3 3 10 56 →= 40 37 29 7 3 10 56 , 59 7 3 3 3 10 56 →= 60 37 29 7 3 10 56 , 6 7 3 3 3 10 56 →= 61 37 29 7 3 10 56 , 62 7 3 3 3 10 56 →= 63 37 29 7 3 10 56 , 21 7 3 3 3 10 56 →= 64 37 29 7 3 10 56 , 27 7 3 3 3 10 56 →= 65 37 29 7 3 10 56 , 29 7 3 3 3 10 56 →= 28 37 29 7 3 10 56 , 17 18 3 3 3 3 3 →= 66 67 29 7 3 3 3 , 17 18 3 3 3 3 8 →= 66 67 29 7 3 3 8 , 17 18 3 3 3 3 9 →= 66 67 29 7 3 3 9 , 17 18 3 3 3 3 10 →= 66 67 29 7 3 3 10 , 17 18 3 3 3 3 11 →= 66 67 29 7 3 3 11 , 68 18 3 3 3 3 3 →= 69 67 29 7 3 3 3 , 68 18 3 3 3 3 8 →= 69 67 29 7 3 3 8 , 68 18 3 3 3 3 9 →= 69 67 29 7 3 3 9 , 68 18 3 3 3 3 10 →= 69 67 29 7 3 3 10 , 68 18 3 3 3 3 11 →= 69 67 29 7 3 3 11 , 17 18 3 3 3 9 12 →= 66 67 29 7 3 9 12 , 17 18 3 3 3 9 13 →= 66 67 29 7 3 9 13 , 17 18 3 3 3 9 14 →= 66 67 29 7 3 9 14 , 17 18 3 3 3 9 15 →= 66 67 29 7 3 9 15 , 68 18 3 3 3 9 12 →= 69 67 29 7 3 9 12 , 68 18 3 3 3 9 13 →= 69 67 29 7 3 9 13 , 68 18 3 3 3 9 14 →= 69 67 29 7 3 9 14 , 68 18 3 3 3 9 15 →= 69 67 29 7 3 9 15 , 70 24 3 3 3 3 3 →= 71 72 29 7 3 3 3 , 70 24 3 3 3 3 8 →= 71 72 29 7 3 3 8 , 70 24 3 3 3 3 9 →= 71 72 29 7 3 3 9 , 70 24 3 3 3 3 10 →= 71 72 29 7 3 3 10 , 70 24 3 3 3 3 11 →= 71 72 29 7 3 3 11 , 23 24 3 3 3 3 3 →= 73 72 29 7 3 3 3 , 23 24 3 3 3 3 8 →= 73 72 29 7 3 3 8 , 23 24 3 3 3 3 9 →= 73 72 29 7 3 3 9 , 23 24 3 3 3 3 10 →= 73 72 29 7 3 3 10 , 23 24 3 3 3 3 11 →= 73 72 29 7 3 3 11 , 70 24 3 3 3 9 12 →= 71 72 29 7 3 9 12 , 70 24 3 3 3 9 13 →= 71 72 29 7 3 9 13 , 70 24 3 3 3 9 14 →= 71 72 29 7 3 9 14 , 70 24 3 3 3 9 15 →= 71 72 29 7 3 9 15 , 23 24 3 3 3 9 12 →= 73 72 29 7 3 9 12 , 23 24 3 3 3 9 13 →= 73 72 29 7 3 9 13 , 23 24 3 3 3 9 14 →= 73 72 29 7 3 9 14 , 23 24 3 3 3 9 15 →= 73 72 29 7 3 9 15 , 74 50 3 3 3 3 3 →= 75 76 29 7 3 3 3 , 74 50 3 3 3 3 8 →= 75 76 29 7 3 3 8 , 74 50 3 3 3 3 9 →= 75 76 29 7 3 3 9 , 74 50 3 3 3 3 10 →= 75 76 29 7 3 3 10 , 74 50 3 3 3 3 11 →= 75 76 29 7 3 3 11 , 77 50 3 3 3 3 3 →= 78 76 29 7 3 3 3 , 77 50 3 3 3 3 8 →= 78 76 29 7 3 3 8 , 77 50 3 3 3 3 9 →= 78 76 29 7 3 3 9 , 77 50 3 3 3 3 10 →= 78 76 29 7 3 3 10 , 77 50 3 3 3 3 11 →= 78 76 29 7 3 3 11 , 74 50 3 3 3 9 12 →= 75 76 29 7 3 9 12 , 74 50 3 3 3 9 13 →= 75 76 29 7 3 9 13 , 74 50 3 3 3 9 14 →= 75 76 29 7 3 9 14 , 74 50 3 3 3 9 15 →= 75 76 29 7 3 9 15 , 77 50 3 3 3 9 12 →= 78 76 29 7 3 9 12 , 77 50 3 3 3 9 13 →= 78 76 29 7 3 9 13 , 77 50 3 3 3 9 14 →= 78 76 29 7 3 9 14 , 77 50 3 3 3 9 15 →= 78 76 29 7 3 9 15 , 79 52 3 3 3 3 3 →= 80 81 29 7 3 3 3 , 79 52 3 3 3 3 8 →= 80 81 29 7 3 3 8 , 79 52 3 3 3 3 9 →= 80 81 29 7 3 3 9 , 79 52 3 3 3 3 10 →= 80 81 29 7 3 3 10 , 79 52 3 3 3 3 11 →= 80 81 29 7 3 3 11 , 79 52 3 3 3 9 12 →= 80 81 29 7 3 9 12 , 79 52 3 3 3 9 13 →= 80 81 29 7 3 9 13 , 79 52 3 3 3 9 14 →= 80 81 29 7 3 9 14 , 79 52 3 3 3 9 15 →= 80 81 29 7 3 9 15 , 5 6 7 3 3 3 3 →= 82 83 41 7 3 3 3 , 5 6 7 3 3 3 8 →= 82 83 41 7 3 3 8 , 5 6 7 3 3 3 9 →= 82 83 41 7 3 3 9 , 5 6 7 3 3 3 10 →= 82 83 41 7 3 3 10 , 5 6 7 3 3 3 11 →= 82 83 41 7 3 3 11 , 84 6 7 3 3 3 3 →= 85 83 41 7 3 3 3 , 84 6 7 3 3 3 8 →= 85 83 41 7 3 3 8 , 84 6 7 3 3 3 9 →= 85 83 41 7 3 3 9 , 84 6 7 3 3 3 10 →= 85 83 41 7 3 3 10 , 84 6 7 3 3 3 11 →= 85 83 41 7 3 3 11 , 5 6 7 3 3 9 12 →= 82 83 41 7 3 9 12 , 5 6 7 3 3 9 13 →= 82 83 41 7 3 9 13 , 5 6 7 3 3 9 14 →= 82 83 41 7 3 9 14 , 5 6 7 3 3 9 15 →= 82 83 41 7 3 9 15 , 84 6 7 3 3 9 12 →= 85 83 41 7 3 9 12 , 84 6 7 3 3 9 13 →= 85 83 41 7 3 9 13 , 84 6 7 3 3 9 14 →= 85 83 41 7 3 9 14 , 84 6 7 3 3 9 15 →= 85 83 41 7 3 9 15 , 5 6 7 3 3 8 54 →= 82 83 41 7 3 8 54 , 5 6 7 3 3 8 55 →= 82 83 41 7 3 8 55 , 84 6 7 3 3 8 54 →= 85 83 41 7 3 8 54 , 84 6 7 3 3 8 55 →= 85 83 41 7 3 8 55 , 5 6 7 3 3 10 56 →= 82 83 41 7 3 10 56 , 84 6 7 3 3 10 56 →= 85 83 41 7 3 10 56 , 86 21 7 3 3 3 3 →= 87 88 41 7 3 3 3 , 86 21 7 3 3 3 8 →= 87 88 41 7 3 3 8 , 86 21 7 3 3 3 9 →= 87 88 41 7 3 3 9 , 86 21 7 3 3 3 10 →= 87 88 41 7 3 3 10 , 86 21 7 3 3 3 11 →= 87 88 41 7 3 3 11 , 20 21 7 3 3 3 3 →= 89 88 41 7 3 3 3 , 20 21 7 3 3 3 8 →= 89 88 41 7 3 3 8 , 20 21 7 3 3 3 9 →= 89 88 41 7 3 3 9 , 20 21 7 3 3 3 10 →= 89 88 41 7 3 3 10 , 20 21 7 3 3 3 11 →= 89 88 41 7 3 3 11 , 86 21 7 3 3 9 12 →= 87 88 41 7 3 9 12 , 86 21 7 3 3 9 13 →= 87 88 41 7 3 9 13 , 86 21 7 3 3 9 14 →= 87 88 41 7 3 9 14 , 86 21 7 3 3 9 15 →= 87 88 41 7 3 9 15 , 20 21 7 3 3 9 12 →= 89 88 41 7 3 9 12 , 20 21 7 3 3 9 13 →= 89 88 41 7 3 9 13 , 20 21 7 3 3 9 14 →= 89 88 41 7 3 9 14 , 20 21 7 3 3 9 15 →= 89 88 41 7 3 9 15 , 86 21 7 3 3 8 54 →= 87 88 41 7 3 8 54 , 86 21 7 3 3 8 55 →= 87 88 41 7 3 8 55 , 20 21 7 3 3 8 54 →= 89 88 41 7 3 8 54 , 20 21 7 3 3 8 55 →= 89 88 41 7 3 8 55 , 86 21 7 3 3 10 56 →= 87 88 41 7 3 10 56 , 20 21 7 3 3 10 56 →= 89 88 41 7 3 10 56 , 90 27 7 3 3 3 3 →= 91 92 41 7 3 3 3 , 90 27 7 3 3 3 8 →= 91 92 41 7 3 3 8 , 90 27 7 3 3 3 9 →= 91 92 41 7 3 3 9 , 90 27 7 3 3 3 10 →= 91 92 41 7 3 3 10 , 90 27 7 3 3 3 11 →= 91 92 41 7 3 3 11 , 26 27 7 3 3 3 3 →= 93 92 41 7 3 3 3 , 26 27 7 3 3 3 8 →= 93 92 41 7 3 3 8 , 26 27 7 3 3 3 9 →= 93 92 41 7 3 3 9 , 26 27 7 3 3 3 10 →= 93 92 41 7 3 3 10 , 26 27 7 3 3 3 11 →= 93 92 41 7 3 3 11 , 90 27 7 3 3 9 12 →= 91 92 41 7 3 9 12 , 90 27 7 3 3 9 13 →= 91 92 41 7 3 9 13 , 90 27 7 3 3 9 14 →= 91 92 41 7 3 9 14 , 90 27 7 3 3 9 15 →= 91 92 41 7 3 9 15 , 26 27 7 3 3 9 12 →= 93 92 41 7 3 9 12 , 26 27 7 3 3 9 13 →= 93 92 41 7 3 9 13 , 26 27 7 3 3 9 14 →= 93 92 41 7 3 9 14 , 26 27 7 3 3 9 15 →= 93 92 41 7 3 9 15 , 90 27 7 3 3 8 54 →= 91 92 41 7 3 8 54 , 90 27 7 3 3 8 55 →= 91 92 41 7 3 8 55 , 26 27 7 3 3 8 54 →= 93 92 41 7 3 8 54 , 26 27 7 3 3 8 55 →= 93 92 41 7 3 8 55 , 90 27 7 3 3 10 56 →= 91 92 41 7 3 10 56 , 26 27 7 3 3 10 56 →= 93 92 41 7 3 10 56 , 37 29 7 3 3 3 3 →= 36 31 41 7 3 3 3 , 37 29 7 3 3 3 8 →= 36 31 41 7 3 3 8 , 37 29 7 3 3 3 9 →= 36 31 41 7 3 3 9 , 37 29 7 3 3 3 10 →= 36 31 41 7 3 3 10 , 37 29 7 3 3 3 11 →= 36 31 41 7 3 3 11 , 45 29 7 3 3 3 3 →= 94 31 41 7 3 3 3 , 45 29 7 3 3 3 8 →= 94 31 41 7 3 3 8 , 45 29 7 3 3 3 9 →= 94 31 41 7 3 3 9 , 45 29 7 3 3 3 10 →= 94 31 41 7 3 3 10 , 45 29 7 3 3 3 11 →= 94 31 41 7 3 3 11 , 15 29 7 3 3 3 3 →= 12 31 41 7 3 3 3 , 15 29 7 3 3 3 8 →= 12 31 41 7 3 3 8 , 15 29 7 3 3 3 9 →= 12 31 41 7 3 3 9 , 15 29 7 3 3 3 10 →= 12 31 41 7 3 3 10 , 15 29 7 3 3 3 11 →= 12 31 41 7 3 3 11 , 67 29 7 3 3 3 3 →= 95 31 41 7 3 3 3 , 67 29 7 3 3 3 8 →= 95 31 41 7 3 3 8 , 67 29 7 3 3 3 9 →= 95 31 41 7 3 3 9 , 67 29 7 3 3 3 10 →= 95 31 41 7 3 3 10 , 67 29 7 3 3 3 11 →= 95 31 41 7 3 3 11 , 72 29 7 3 3 3 3 →= 96 31 41 7 3 3 3 , 72 29 7 3 3 3 8 →= 96 31 41 7 3 3 8 , 72 29 7 3 3 3 9 →= 96 31 41 7 3 3 9 , 72 29 7 3 3 3 10 →= 96 31 41 7 3 3 10 , 72 29 7 3 3 3 11 →= 96 31 41 7 3 3 11 , 97 29 7 3 3 3 3 →= 98 31 41 7 3 3 3 , 97 29 7 3 3 3 8 →= 98 31 41 7 3 3 8 , 97 29 7 3 3 3 9 →= 98 31 41 7 3 3 9 , 97 29 7 3 3 3 10 →= 98 31 41 7 3 3 10 , 97 29 7 3 3 3 11 →= 98 31 41 7 3 3 11 , 76 29 7 3 3 3 3 →= 99 31 41 7 3 3 3 , 76 29 7 3 3 3 8 →= 99 31 41 7 3 3 8 , 76 29 7 3 3 3 9 →= 99 31 41 7 3 3 9 , 76 29 7 3 3 3 10 →= 99 31 41 7 3 3 10 , 76 29 7 3 3 3 11 →= 99 31 41 7 3 3 11 , 81 29 7 3 3 3 3 →= 100 31 41 7 3 3 3 , 81 29 7 3 3 3 8 →= 100 31 41 7 3 3 8 , 81 29 7 3 3 3 9 →= 100 31 41 7 3 3 9 , 81 29 7 3 3 3 10 →= 100 31 41 7 3 3 10 , 81 29 7 3 3 3 11 →= 100 31 41 7 3 3 11 , 37 29 7 3 3 9 12 →= 36 31 41 7 3 9 12 , 37 29 7 3 3 9 13 →= 36 31 41 7 3 9 13 , 37 29 7 3 3 9 14 →= 36 31 41 7 3 9 14 , 37 29 7 3 3 9 15 →= 36 31 41 7 3 9 15 , 45 29 7 3 3 9 12 →= 94 31 41 7 3 9 12 , 45 29 7 3 3 9 13 →= 94 31 41 7 3 9 13 , 45 29 7 3 3 9 14 →= 94 31 41 7 3 9 14 , 45 29 7 3 3 9 15 →= 94 31 41 7 3 9 15 , 15 29 7 3 3 9 12 →= 12 31 41 7 3 9 12 , 15 29 7 3 3 9 13 →= 12 31 41 7 3 9 13 , 15 29 7 3 3 9 14 →= 12 31 41 7 3 9 14 , 15 29 7 3 3 9 15 →= 12 31 41 7 3 9 15 , 67 29 7 3 3 9 12 →= 95 31 41 7 3 9 12 , 67 29 7 3 3 9 13 →= 95 31 41 7 3 9 13 , 67 29 7 3 3 9 14 →= 95 31 41 7 3 9 14 , 67 29 7 3 3 9 15 →= 95 31 41 7 3 9 15 , 72 29 7 3 3 9 12 →= 96 31 41 7 3 9 12 , 72 29 7 3 3 9 13 →= 96 31 41 7 3 9 13 , 72 29 7 3 3 9 14 →= 96 31 41 7 3 9 14 , 72 29 7 3 3 9 15 →= 96 31 41 7 3 9 15 , 97 29 7 3 3 9 12 →= 98 31 41 7 3 9 12 , 97 29 7 3 3 9 13 →= 98 31 41 7 3 9 13 , 97 29 7 3 3 9 14 →= 98 31 41 7 3 9 14 , 97 29 7 3 3 9 15 →= 98 31 41 7 3 9 15 , 76 29 7 3 3 9 12 →= 99 31 41 7 3 9 12 , 76 29 7 3 3 9 13 →= 99 31 41 7 3 9 13 , 76 29 7 3 3 9 14 →= 99 31 41 7 3 9 14 , 76 29 7 3 3 9 15 →= 99 31 41 7 3 9 15 , 81 29 7 3 3 9 12 →= 100 31 41 7 3 9 12 , 81 29 7 3 3 9 13 →= 100 31 41 7 3 9 13 , 81 29 7 3 3 9 14 →= 100 31 41 7 3 9 14 , 81 29 7 3 3 9 15 →= 100 31 41 7 3 9 15 , 37 29 7 3 3 8 54 →= 36 31 41 7 3 8 54 , 37 29 7 3 3 8 55 →= 36 31 41 7 3 8 55 , 45 29 7 3 3 8 54 →= 94 31 41 7 3 8 54 , 45 29 7 3 3 8 55 →= 94 31 41 7 3 8 55 , 15 29 7 3 3 8 54 →= 12 31 41 7 3 8 54 , 15 29 7 3 3 8 55 →= 12 31 41 7 3 8 55 , 67 29 7 3 3 8 54 →= 95 31 41 7 3 8 54 , 67 29 7 3 3 8 55 →= 95 31 41 7 3 8 55 , 72 29 7 3 3 8 54 →= 96 31 41 7 3 8 54 , 72 29 7 3 3 8 55 →= 96 31 41 7 3 8 55 , 97 29 7 3 3 8 54 →= 98 31 41 7 3 8 54 , 97 29 7 3 3 8 55 →= 98 31 41 7 3 8 55 , 76 29 7 3 3 8 54 →= 99 31 41 7 3 8 54 , 76 29 7 3 3 8 55 →= 99 31 41 7 3 8 55 , 81 29 7 3 3 8 54 →= 100 31 41 7 3 8 54 , 81 29 7 3 3 8 55 →= 100 31 41 7 3 8 55 , 37 29 7 3 3 10 56 →= 36 31 41 7 3 10 56 , 45 29 7 3 3 10 56 →= 94 31 41 7 3 10 56 , 15 29 7 3 3 10 56 →= 12 31 41 7 3 10 56 , 67 29 7 3 3 10 56 →= 95 31 41 7 3 10 56 , 72 29 7 3 3 10 56 →= 96 31 41 7 3 10 56 , 97 29 7 3 3 10 56 →= 98 31 41 7 3 10 56 , 76 29 7 3 3 10 56 →= 99 31 41 7 3 10 56 , 81 29 7 3 3 10 56 →= 100 31 41 7 3 10 56 , 31 41 7 3 3 3 3 →= 32 42 41 7 3 3 3 , 31 41 7 3 3 3 8 →= 32 42 41 7 3 3 8 , 31 41 7 3 3 3 9 →= 32 42 41 7 3 3 9 , 31 41 7 3 3 3 10 →= 32 42 41 7 3 3 10 , 31 41 7 3 3 3 11 →= 32 42 41 7 3 3 11 , 101 41 7 3 3 3 3 →= 102 42 41 7 3 3 3 , 101 41 7 3 3 3 8 →= 102 42 41 7 3 3 8 , 101 41 7 3 3 3 9 →= 102 42 41 7 3 3 9 , 101 41 7 3 3 3 10 →= 102 42 41 7 3 3 10 , 101 41 7 3 3 3 11 →= 102 42 41 7 3 3 11 , 42 41 7 3 3 3 3 →= 43 42 41 7 3 3 3 , 42 41 7 3 3 3 8 →= 43 42 41 7 3 3 8 , 42 41 7 3 3 3 9 →= 43 42 41 7 3 3 9 , 42 41 7 3 3 3 10 →= 43 42 41 7 3 3 10 , 42 41 7 3 3 3 11 →= 43 42 41 7 3 3 11 , 103 41 7 3 3 3 3 →= 104 42 41 7 3 3 3 , 103 41 7 3 3 3 8 →= 104 42 41 7 3 3 8 , 103 41 7 3 3 3 9 →= 104 42 41 7 3 3 9 , 103 41 7 3 3 3 10 →= 104 42 41 7 3 3 10 , 103 41 7 3 3 3 11 →= 104 42 41 7 3 3 11 , 105 41 7 3 3 3 3 →= 106 42 41 7 3 3 3 , 105 41 7 3 3 3 8 →= 106 42 41 7 3 3 8 , 105 41 7 3 3 3 9 →= 106 42 41 7 3 3 9 , 105 41 7 3 3 3 10 →= 106 42 41 7 3 3 10 , 105 41 7 3 3 3 11 →= 106 42 41 7 3 3 11 , 83 41 7 3 3 3 3 →= 107 42 41 7 3 3 3 , 83 41 7 3 3 3 8 →= 107 42 41 7 3 3 8 , 83 41 7 3 3 3 9 →= 107 42 41 7 3 3 9 , 83 41 7 3 3 3 10 →= 107 42 41 7 3 3 10 , 83 41 7 3 3 3 11 →= 107 42 41 7 3 3 11 , 88 41 7 3 3 3 3 →= 108 42 41 7 3 3 3 , 88 41 7 3 3 3 8 →= 108 42 41 7 3 3 8 , 88 41 7 3 3 3 9 →= 108 42 41 7 3 3 9 , 88 41 7 3 3 3 10 →= 108 42 41 7 3 3 10 , 88 41 7 3 3 3 11 →= 108 42 41 7 3 3 11 , 92 41 7 3 3 3 3 →= 109 42 41 7 3 3 3 , 92 41 7 3 3 3 8 →= 109 42 41 7 3 3 8 , 92 41 7 3 3 3 9 →= 109 42 41 7 3 3 9 , 92 41 7 3 3 3 10 →= 109 42 41 7 3 3 10 , 92 41 7 3 3 3 11 →= 109 42 41 7 3 3 11 , 31 41 7 3 3 9 12 →= 32 42 41 7 3 9 12 , 31 41 7 3 3 9 13 →= 32 42 41 7 3 9 13 , 31 41 7 3 3 9 14 →= 32 42 41 7 3 9 14 , 31 41 7 3 3 9 15 →= 32 42 41 7 3 9 15 , 101 41 7 3 3 9 12 →= 102 42 41 7 3 9 12 , 101 41 7 3 3 9 13 →= 102 42 41 7 3 9 13 , 101 41 7 3 3 9 14 →= 102 42 41 7 3 9 14 , 101 41 7 3 3 9 15 →= 102 42 41 7 3 9 15 , 42 41 7 3 3 9 12 →= 43 42 41 7 3 9 12 , 42 41 7 3 3 9 13 →= 43 42 41 7 3 9 13 , 42 41 7 3 3 9 14 →= 43 42 41 7 3 9 14 , 42 41 7 3 3 9 15 →= 43 42 41 7 3 9 15 , 103 41 7 3 3 9 12 →= 104 42 41 7 3 9 12 , 103 41 7 3 3 9 13 →= 104 42 41 7 3 9 13 , 103 41 7 3 3 9 14 →= 104 42 41 7 3 9 14 , 103 41 7 3 3 9 15 →= 104 42 41 7 3 9 15 , 105 41 7 3 3 9 12 →= 106 42 41 7 3 9 12 , 105 41 7 3 3 9 13 →= 106 42 41 7 3 9 13 , 105 41 7 3 3 9 14 →= 106 42 41 7 3 9 14 , 105 41 7 3 3 9 15 →= 106 42 41 7 3 9 15 , 83 41 7 3 3 9 12 →= 107 42 41 7 3 9 12 , 83 41 7 3 3 9 13 →= 107 42 41 7 3 9 13 , 83 41 7 3 3 9 14 →= 107 42 41 7 3 9 14 , 83 41 7 3 3 9 15 →= 107 42 41 7 3 9 15 , 88 41 7 3 3 9 12 →= 108 42 41 7 3 9 12 , 88 41 7 3 3 9 13 →= 108 42 41 7 3 9 13 , 88 41 7 3 3 9 14 →= 108 42 41 7 3 9 14 , 88 41 7 3 3 9 15 →= 108 42 41 7 3 9 15 , 92 41 7 3 3 9 12 →= 109 42 41 7 3 9 12 , 92 41 7 3 3 9 13 →= 109 42 41 7 3 9 13 , 92 41 7 3 3 9 14 →= 109 42 41 7 3 9 14 , 92 41 7 3 3 9 15 →= 109 42 41 7 3 9 15 , 31 41 7 3 3 8 54 →= 32 42 41 7 3 8 54 , 31 41 7 3 3 8 55 →= 32 42 41 7 3 8 55 , 101 41 7 3 3 8 54 →= 102 42 41 7 3 8 54 , 101 41 7 3 3 8 55 →= 102 42 41 7 3 8 55 , 42 41 7 3 3 8 54 →= 43 42 41 7 3 8 54 , 42 41 7 3 3 8 55 →= 43 42 41 7 3 8 55 , 103 41 7 3 3 8 54 →= 104 42 41 7 3 8 54 , 103 41 7 3 3 8 55 →= 104 42 41 7 3 8 55 , 105 41 7 3 3 8 54 →= 106 42 41 7 3 8 54 , 105 41 7 3 3 8 55 →= 106 42 41 7 3 8 55 , 83 41 7 3 3 8 54 →= 107 42 41 7 3 8 54 , 83 41 7 3 3 8 55 →= 107 42 41 7 3 8 55 , 88 41 7 3 3 8 54 →= 108 42 41 7 3 8 54 , 88 41 7 3 3 8 55 →= 108 42 41 7 3 8 55 , 92 41 7 3 3 8 54 →= 109 42 41 7 3 8 54 , 92 41 7 3 3 8 55 →= 109 42 41 7 3 8 55 , 31 41 7 3 3 10 56 →= 32 42 41 7 3 10 56 , 101 41 7 3 3 10 56 →= 102 42 41 7 3 10 56 , 42 41 7 3 3 10 56 →= 43 42 41 7 3 10 56 , 103 41 7 3 3 10 56 →= 104 42 41 7 3 10 56 , 105 41 7 3 3 10 56 →= 106 42 41 7 3 10 56 , 83 41 7 3 3 10 56 →= 107 42 41 7 3 10 56 , 88 41 7 3 3 10 56 →= 108 42 41 7 3 10 56 , 92 41 7 3 3 10 56 →= 109 42 41 7 3 10 56 , 110 57 7 3 3 3 3 →= 111 101 41 7 3 3 3 , 110 57 7 3 3 3 8 →= 111 101 41 7 3 3 8 , 110 57 7 3 3 3 9 →= 111 101 41 7 3 3 9 , 110 57 7 3 3 3 10 →= 111 101 41 7 3 3 10 , 110 57 7 3 3 3 11 →= 111 101 41 7 3 3 11 , 112 57 7 3 3 3 3 →= 113 101 41 7 3 3 3 , 112 57 7 3 3 3 8 →= 113 101 41 7 3 3 8 , 112 57 7 3 3 3 9 →= 113 101 41 7 3 3 9 , 112 57 7 3 3 3 10 →= 113 101 41 7 3 3 10 , 112 57 7 3 3 3 11 →= 113 101 41 7 3 3 11 , 110 57 7 3 3 9 12 →= 111 101 41 7 3 9 12 , 110 57 7 3 3 9 13 →= 111 101 41 7 3 9 13 , 110 57 7 3 3 9 14 →= 111 101 41 7 3 9 14 , 110 57 7 3 3 9 15 →= 111 101 41 7 3 9 15 , 112 57 7 3 3 9 12 →= 113 101 41 7 3 9 12 , 112 57 7 3 3 9 13 →= 113 101 41 7 3 9 13 , 112 57 7 3 3 9 14 →= 113 101 41 7 3 9 14 , 112 57 7 3 3 9 15 →= 113 101 41 7 3 9 15 , 110 57 7 3 3 8 54 →= 111 101 41 7 3 8 54 , 110 57 7 3 3 8 55 →= 111 101 41 7 3 8 55 , 112 57 7 3 3 8 54 →= 113 101 41 7 3 8 54 , 112 57 7 3 3 8 55 →= 113 101 41 7 3 8 55 , 110 57 7 3 3 10 56 →= 111 101 41 7 3 10 56 , 112 57 7 3 3 10 56 →= 113 101 41 7 3 10 56 , 114 59 7 3 3 3 3 →= 115 103 41 7 3 3 3 , 114 59 7 3 3 3 8 →= 115 103 41 7 3 3 8 , 114 59 7 3 3 3 9 →= 115 103 41 7 3 3 9 , 114 59 7 3 3 3 10 →= 115 103 41 7 3 3 10 , 114 59 7 3 3 3 11 →= 115 103 41 7 3 3 11 , 114 59 7 3 3 9 12 →= 115 103 41 7 3 9 12 , 114 59 7 3 3 9 13 →= 115 103 41 7 3 9 13 , 114 59 7 3 3 9 14 →= 115 103 41 7 3 9 14 , 114 59 7 3 3 9 15 →= 115 103 41 7 3 9 15 , 116 74 50 3 3 3 3 →= 117 110 57 7 3 3 3 , 116 74 50 3 3 3 8 →= 117 110 57 7 3 3 8 , 116 74 50 3 3 3 9 →= 117 110 57 7 3 3 9 , 116 74 50 3 3 3 10 →= 117 110 57 7 3 3 10 , 116 74 50 3 3 3 11 →= 117 110 57 7 3 3 11 , 116 74 50 3 3 9 12 →= 117 110 57 7 3 9 12 , 116 74 50 3 3 9 13 →= 117 110 57 7 3 9 13 , 116 74 50 3 3 9 14 →= 117 110 57 7 3 9 14 , 116 74 50 3 3 9 15 →= 117 110 57 7 3 9 15 , 1 2 3 3 9 15 28 →= 44 45 29 7 9 15 28 , 1 2 3 3 9 15 29 →= 44 45 29 7 9 15 29 , 1 2 3 3 9 15 30 →= 44 45 29 7 9 15 30 , 46 2 3 3 9 15 28 →= 47 45 29 7 9 15 28 , 46 2 3 3 9 15 29 →= 47 45 29 7 9 15 29 , 46 2 3 3 9 15 30 →= 47 45 29 7 9 15 30 , 1 2 3 3 9 12 31 →= 44 45 29 7 9 12 31 , 1 2 3 3 9 12 32 →= 44 45 29 7 9 12 32 , 1 2 3 3 9 12 33 →= 44 45 29 7 9 12 33 , 46 2 3 3 9 12 31 →= 47 45 29 7 9 12 31 , 46 2 3 3 9 12 32 →= 47 45 29 7 9 12 32 , 46 2 3 3 9 12 33 →= 47 45 29 7 9 12 33 , 2 3 3 3 9 15 28 →= 35 15 29 7 9 15 28 , 2 3 3 3 9 15 29 →= 35 15 29 7 9 15 29 , 2 3 3 3 9 15 30 →= 35 15 29 7 9 15 30 , 3 3 3 3 9 15 28 →= 9 15 29 7 9 15 28 , 3 3 3 3 9 15 29 →= 9 15 29 7 9 15 29 , 3 3 3 3 9 15 30 →= 9 15 29 7 9 15 30 , 7 3 3 3 9 15 28 →= 34 15 29 7 9 15 28 , 7 3 3 3 9 15 29 →= 34 15 29 7 9 15 29 , 7 3 3 3 9 15 30 →= 34 15 29 7 9 15 30 , 18 3 3 3 9 15 28 →= 38 15 29 7 9 15 28 , 18 3 3 3 9 15 29 →= 38 15 29 7 9 15 29 , 18 3 3 3 9 15 30 →= 38 15 29 7 9 15 30 , 48 3 3 3 9 15 28 →= 49 15 29 7 9 15 28 , 48 3 3 3 9 15 29 →= 49 15 29 7 9 15 29 , 48 3 3 3 9 15 30 →= 49 15 29 7 9 15 30 , 50 3 3 3 9 15 28 →= 51 15 29 7 9 15 28 , 50 3 3 3 9 15 29 →= 51 15 29 7 9 15 29 , 50 3 3 3 9 15 30 →= 51 15 29 7 9 15 30 , 52 3 3 3 9 15 28 →= 53 15 29 7 9 15 28 , 52 3 3 3 9 15 29 →= 53 15 29 7 9 15 29 , 52 3 3 3 9 15 30 →= 53 15 29 7 9 15 30 , 24 3 3 3 9 15 28 →= 39 15 29 7 9 15 28 , 24 3 3 3 9 15 29 →= 39 15 29 7 9 15 29 , 24 3 3 3 9 15 30 →= 39 15 29 7 9 15 30 , 2 3 3 3 9 12 31 →= 35 15 29 7 9 12 31 , 2 3 3 3 9 12 32 →= 35 15 29 7 9 12 32 , 2 3 3 3 9 12 33 →= 35 15 29 7 9 12 33 , 3 3 3 3 9 12 31 →= 9 15 29 7 9 12 31 , 3 3 3 3 9 12 32 →= 9 15 29 7 9 12 32 , 3 3 3 3 9 12 33 →= 9 15 29 7 9 12 33 , 7 3 3 3 9 12 31 →= 34 15 29 7 9 12 31 , 7 3 3 3 9 12 32 →= 34 15 29 7 9 12 32 , 7 3 3 3 9 12 33 →= 34 15 29 7 9 12 33 , 18 3 3 3 9 12 31 →= 38 15 29 7 9 12 31 , 18 3 3 3 9 12 32 →= 38 15 29 7 9 12 32 , 18 3 3 3 9 12 33 →= 38 15 29 7 9 12 33 , 48 3 3 3 9 12 31 →= 49 15 29 7 9 12 31 , 48 3 3 3 9 12 32 →= 49 15 29 7 9 12 32 , 48 3 3 3 9 12 33 →= 49 15 29 7 9 12 33 , 50 3 3 3 9 12 31 →= 51 15 29 7 9 12 31 , 50 3 3 3 9 12 32 →= 51 15 29 7 9 12 32 , 50 3 3 3 9 12 33 →= 51 15 29 7 9 12 33 , 52 3 3 3 9 12 31 →= 53 15 29 7 9 12 31 , 52 3 3 3 9 12 32 →= 53 15 29 7 9 12 32 , 52 3 3 3 9 12 33 →= 53 15 29 7 9 12 33 , 24 3 3 3 9 12 31 →= 39 15 29 7 9 12 31 , 24 3 3 3 9 12 32 →= 39 15 29 7 9 12 32 , 24 3 3 3 9 12 33 →= 39 15 29 7 9 12 33 , 2 3 3 3 9 13 118 →= 35 15 29 7 9 13 118 , 3 3 3 3 9 13 118 →= 9 15 29 7 9 13 118 , 7 3 3 3 9 13 118 →= 34 15 29 7 9 13 118 , 18 3 3 3 9 13 118 →= 38 15 29 7 9 13 118 , 48 3 3 3 9 13 118 →= 49 15 29 7 9 13 118 , 50 3 3 3 9 13 118 →= 51 15 29 7 9 13 118 , 52 3 3 3 9 13 118 →= 53 15 29 7 9 13 118 , 24 3 3 3 9 13 118 →= 39 15 29 7 9 13 118 , 57 7 3 3 9 15 28 →= 58 37 29 7 9 15 28 , 57 7 3 3 9 15 29 →= 58 37 29 7 9 15 29 , 57 7 3 3 9 15 30 →= 58 37 29 7 9 15 30 , 41 7 3 3 9 15 28 →= 40 37 29 7 9 15 28 , 41 7 3 3 9 15 29 →= 40 37 29 7 9 15 29 , 41 7 3 3 9 15 30 →= 40 37 29 7 9 15 30 , 59 7 3 3 9 15 28 →= 60 37 29 7 9 15 28 , 59 7 3 3 9 15 29 →= 60 37 29 7 9 15 29 , 59 7 3 3 9 15 30 →= 60 37 29 7 9 15 30 , 6 7 3 3 9 15 28 →= 61 37 29 7 9 15 28 , 6 7 3 3 9 15 29 →= 61 37 29 7 9 15 29 , 6 7 3 3 9 15 30 →= 61 37 29 7 9 15 30 , 62 7 3 3 9 15 28 →= 63 37 29 7 9 15 28 , 62 7 3 3 9 15 29 →= 63 37 29 7 9 15 29 , 62 7 3 3 9 15 30 →= 63 37 29 7 9 15 30 , 21 7 3 3 9 15 28 →= 64 37 29 7 9 15 28 , 21 7 3 3 9 15 29 →= 64 37 29 7 9 15 29 , 21 7 3 3 9 15 30 →= 64 37 29 7 9 15 30 , 27 7 3 3 9 15 28 →= 65 37 29 7 9 15 28 , 27 7 3 3 9 15 29 →= 65 37 29 7 9 15 29 , 27 7 3 3 9 15 30 →= 65 37 29 7 9 15 30 , 29 7 3 3 9 15 28 →= 28 37 29 7 9 15 28 , 29 7 3 3 9 15 29 →= 28 37 29 7 9 15 29 , 29 7 3 3 9 15 30 →= 28 37 29 7 9 15 30 , 57 7 3 3 9 12 31 →= 58 37 29 7 9 12 31 , 57 7 3 3 9 12 32 →= 58 37 29 7 9 12 32 , 57 7 3 3 9 12 33 →= 58 37 29 7 9 12 33 , 41 7 3 3 9 12 31 →= 40 37 29 7 9 12 31 , 41 7 3 3 9 12 32 →= 40 37 29 7 9 12 32 , 41 7 3 3 9 12 33 →= 40 37 29 7 9 12 33 , 59 7 3 3 9 12 31 →= 60 37 29 7 9 12 31 , 59 7 3 3 9 12 32 →= 60 37 29 7 9 12 32 , 59 7 3 3 9 12 33 →= 60 37 29 7 9 12 33 , 6 7 3 3 9 12 31 →= 61 37 29 7 9 12 31 , 6 7 3 3 9 12 32 →= 61 37 29 7 9 12 32 , 6 7 3 3 9 12 33 →= 61 37 29 7 9 12 33 , 62 7 3 3 9 12 31 →= 63 37 29 7 9 12 31 , 62 7 3 3 9 12 32 →= 63 37 29 7 9 12 32 , 62 7 3 3 9 12 33 →= 63 37 29 7 9 12 33 , 21 7 3 3 9 12 31 →= 64 37 29 7 9 12 31 , 21 7 3 3 9 12 32 →= 64 37 29 7 9 12 32 , 21 7 3 3 9 12 33 →= 64 37 29 7 9 12 33 , 27 7 3 3 9 12 31 →= 65 37 29 7 9 12 31 , 27 7 3 3 9 12 32 →= 65 37 29 7 9 12 32 , 27 7 3 3 9 12 33 →= 65 37 29 7 9 12 33 , 29 7 3 3 9 12 31 →= 28 37 29 7 9 12 31 , 29 7 3 3 9 12 32 →= 28 37 29 7 9 12 32 , 29 7 3 3 9 12 33 →= 28 37 29 7 9 12 33 , 57 7 3 3 9 13 118 →= 58 37 29 7 9 13 118 , 41 7 3 3 9 13 118 →= 40 37 29 7 9 13 118 , 59 7 3 3 9 13 118 →= 60 37 29 7 9 13 118 , 6 7 3 3 9 13 118 →= 61 37 29 7 9 13 118 , 62 7 3 3 9 13 118 →= 63 37 29 7 9 13 118 , 21 7 3 3 9 13 118 →= 64 37 29 7 9 13 118 , 27 7 3 3 9 13 118 →= 65 37 29 7 9 13 118 , 29 7 3 3 9 13 118 →= 28 37 29 7 9 13 118 , 17 18 3 3 9 15 28 →= 66 67 29 7 9 15 28 , 17 18 3 3 9 15 29 →= 66 67 29 7 9 15 29 , 17 18 3 3 9 15 30 →= 66 67 29 7 9 15 30 , 68 18 3 3 9 15 28 →= 69 67 29 7 9 15 28 , 68 18 3 3 9 15 29 →= 69 67 29 7 9 15 29 , 68 18 3 3 9 15 30 →= 69 67 29 7 9 15 30 , 17 18 3 3 9 12 31 →= 66 67 29 7 9 12 31 , 17 18 3 3 9 12 32 →= 66 67 29 7 9 12 32 , 17 18 3 3 9 12 33 →= 66 67 29 7 9 12 33 , 68 18 3 3 9 12 31 →= 69 67 29 7 9 12 31 , 68 18 3 3 9 12 32 →= 69 67 29 7 9 12 32 , 68 18 3 3 9 12 33 →= 69 67 29 7 9 12 33 , 70 24 3 3 9 15 28 →= 71 72 29 7 9 15 28 , 70 24 3 3 9 15 29 →= 71 72 29 7 9 15 29 , 70 24 3 3 9 15 30 →= 71 72 29 7 9 15 30 , 23 24 3 3 9 15 28 →= 73 72 29 7 9 15 28 , 23 24 3 3 9 15 29 →= 73 72 29 7 9 15 29 , 23 24 3 3 9 15 30 →= 73 72 29 7 9 15 30 , 70 24 3 3 9 12 31 →= 71 72 29 7 9 12 31 , 70 24 3 3 9 12 32 →= 71 72 29 7 9 12 32 , 70 24 3 3 9 12 33 →= 71 72 29 7 9 12 33 , 23 24 3 3 9 12 31 →= 73 72 29 7 9 12 31 , 23 24 3 3 9 12 32 →= 73 72 29 7 9 12 32 , 23 24 3 3 9 12 33 →= 73 72 29 7 9 12 33 , 74 50 3 3 9 15 28 →= 75 76 29 7 9 15 28 , 74 50 3 3 9 15 29 →= 75 76 29 7 9 15 29 , 74 50 3 3 9 15 30 →= 75 76 29 7 9 15 30 , 77 50 3 3 9 15 28 →= 78 76 29 7 9 15 28 , 77 50 3 3 9 15 29 →= 78 76 29 7 9 15 29 , 77 50 3 3 9 15 30 →= 78 76 29 7 9 15 30 , 74 50 3 3 9 12 31 →= 75 76 29 7 9 12 31 , 74 50 3 3 9 12 32 →= 75 76 29 7 9 12 32 , 74 50 3 3 9 12 33 →= 75 76 29 7 9 12 33 , 77 50 3 3 9 12 31 →= 78 76 29 7 9 12 31 , 77 50 3 3 9 12 32 →= 78 76 29 7 9 12 32 , 77 50 3 3 9 12 33 →= 78 76 29 7 9 12 33 , 79 52 3 3 9 15 28 →= 80 81 29 7 9 15 28 , 79 52 3 3 9 15 29 →= 80 81 29 7 9 15 29 , 79 52 3 3 9 15 30 →= 80 81 29 7 9 15 30 , 79 52 3 3 9 12 31 →= 80 81 29 7 9 12 31 , 79 52 3 3 9 12 32 →= 80 81 29 7 9 12 32 , 79 52 3 3 9 12 33 →= 80 81 29 7 9 12 33 , 5 6 7 3 9 15 28 →= 82 83 41 7 9 15 28 , 5 6 7 3 9 15 29 →= 82 83 41 7 9 15 29 , 5 6 7 3 9 15 30 →= 82 83 41 7 9 15 30 , 84 6 7 3 9 15 28 →= 85 83 41 7 9 15 28 , 84 6 7 3 9 15 29 →= 85 83 41 7 9 15 29 , 84 6 7 3 9 15 30 →= 85 83 41 7 9 15 30 , 5 6 7 3 9 12 31 →= 82 83 41 7 9 12 31 , 5 6 7 3 9 12 32 →= 82 83 41 7 9 12 32 , 5 6 7 3 9 12 33 →= 82 83 41 7 9 12 33 , 84 6 7 3 9 12 31 →= 85 83 41 7 9 12 31 , 84 6 7 3 9 12 32 →= 85 83 41 7 9 12 32 , 84 6 7 3 9 12 33 →= 85 83 41 7 9 12 33 , 5 6 7 3 9 13 118 →= 82 83 41 7 9 13 118 , 84 6 7 3 9 13 118 →= 85 83 41 7 9 13 118 , 86 21 7 3 9 15 28 →= 87 88 41 7 9 15 28 , 86 21 7 3 9 15 29 →= 87 88 41 7 9 15 29 , 86 21 7 3 9 15 30 →= 87 88 41 7 9 15 30 , 20 21 7 3 9 15 28 →= 89 88 41 7 9 15 28 , 20 21 7 3 9 15 29 →= 89 88 41 7 9 15 29 , 20 21 7 3 9 15 30 →= 89 88 41 7 9 15 30 , 86 21 7 3 9 12 31 →= 87 88 41 7 9 12 31 , 86 21 7 3 9 12 32 →= 87 88 41 7 9 12 32 , 86 21 7 3 9 12 33 →= 87 88 41 7 9 12 33 , 20 21 7 3 9 12 31 →= 89 88 41 7 9 12 31 , 20 21 7 3 9 12 32 →= 89 88 41 7 9 12 32 , 20 21 7 3 9 12 33 →= 89 88 41 7 9 12 33 , 86 21 7 3 9 13 118 →= 87 88 41 7 9 13 118 , 20 21 7 3 9 13 118 →= 89 88 41 7 9 13 118 , 90 27 7 3 9 15 28 →= 91 92 41 7 9 15 28 , 90 27 7 3 9 15 29 →= 91 92 41 7 9 15 29 , 90 27 7 3 9 15 30 →= 91 92 41 7 9 15 30 , 26 27 7 3 9 15 28 →= 93 92 41 7 9 15 28 , 26 27 7 3 9 15 29 →= 93 92 41 7 9 15 29 , 26 27 7 3 9 15 30 →= 93 92 41 7 9 15 30 , 90 27 7 3 9 12 31 →= 91 92 41 7 9 12 31 , 90 27 7 3 9 12 32 →= 91 92 41 7 9 12 32 , 90 27 7 3 9 12 33 →= 91 92 41 7 9 12 33 , 26 27 7 3 9 12 31 →= 93 92 41 7 9 12 31 , 26 27 7 3 9 12 32 →= 93 92 41 7 9 12 32 , 26 27 7 3 9 12 33 →= 93 92 41 7 9 12 33 , 90 27 7 3 9 13 118 →= 91 92 41 7 9 13 118 , 26 27 7 3 9 13 118 →= 93 92 41 7 9 13 118 , 37 29 7 3 9 15 28 →= 36 31 41 7 9 15 28 , 37 29 7 3 9 15 29 →= 36 31 41 7 9 15 29 , 37 29 7 3 9 15 30 →= 36 31 41 7 9 15 30 , 45 29 7 3 9 15 28 →= 94 31 41 7 9 15 28 , 45 29 7 3 9 15 29 →= 94 31 41 7 9 15 29 , 45 29 7 3 9 15 30 →= 94 31 41 7 9 15 30 , 15 29 7 3 9 15 28 →= 12 31 41 7 9 15 28 , 15 29 7 3 9 15 29 →= 12 31 41 7 9 15 29 , 15 29 7 3 9 15 30 →= 12 31 41 7 9 15 30 , 67 29 7 3 9 15 28 →= 95 31 41 7 9 15 28 , 67 29 7 3 9 15 29 →= 95 31 41 7 9 15 29 , 67 29 7 3 9 15 30 →= 95 31 41 7 9 15 30 , 72 29 7 3 9 15 28 →= 96 31 41 7 9 15 28 , 72 29 7 3 9 15 29 →= 96 31 41 7 9 15 29 , 72 29 7 3 9 15 30 →= 96 31 41 7 9 15 30 , 97 29 7 3 9 15 28 →= 98 31 41 7 9 15 28 , 97 29 7 3 9 15 29 →= 98 31 41 7 9 15 29 , 97 29 7 3 9 15 30 →= 98 31 41 7 9 15 30 , 76 29 7 3 9 15 28 →= 99 31 41 7 9 15 28 , 76 29 7 3 9 15 29 →= 99 31 41 7 9 15 29 , 76 29 7 3 9 15 30 →= 99 31 41 7 9 15 30 , 81 29 7 3 9 15 28 →= 100 31 41 7 9 15 28 , 81 29 7 3 9 15 29 →= 100 31 41 7 9 15 29 , 81 29 7 3 9 15 30 →= 100 31 41 7 9 15 30 , 37 29 7 3 9 12 31 →= 36 31 41 7 9 12 31 , 37 29 7 3 9 12 32 →= 36 31 41 7 9 12 32 , 37 29 7 3 9 12 33 →= 36 31 41 7 9 12 33 , 45 29 7 3 9 12 31 →= 94 31 41 7 9 12 31 , 45 29 7 3 9 12 32 →= 94 31 41 7 9 12 32 , 45 29 7 3 9 12 33 →= 94 31 41 7 9 12 33 , 15 29 7 3 9 12 31 →= 12 31 41 7 9 12 31 , 15 29 7 3 9 12 32 →= 12 31 41 7 9 12 32 , 15 29 7 3 9 12 33 →= 12 31 41 7 9 12 33 , 67 29 7 3 9 12 31 →= 95 31 41 7 9 12 31 , 67 29 7 3 9 12 32 →= 95 31 41 7 9 12 32 , 67 29 7 3 9 12 33 →= 95 31 41 7 9 12 33 , 72 29 7 3 9 12 31 →= 96 31 41 7 9 12 31 , 72 29 7 3 9 12 32 →= 96 31 41 7 9 12 32 , 72 29 7 3 9 12 33 →= 96 31 41 7 9 12 33 , 97 29 7 3 9 12 31 →= 98 31 41 7 9 12 31 , 97 29 7 3 9 12 32 →= 98 31 41 7 9 12 32 , 97 29 7 3 9 12 33 →= 98 31 41 7 9 12 33 , 76 29 7 3 9 12 31 →= 99 31 41 7 9 12 31 , 76 29 7 3 9 12 32 →= 99 31 41 7 9 12 32 , 76 29 7 3 9 12 33 →= 99 31 41 7 9 12 33 , 81 29 7 3 9 12 31 →= 100 31 41 7 9 12 31 , 81 29 7 3 9 12 32 →= 100 31 41 7 9 12 32 , 81 29 7 3 9 12 33 →= 100 31 41 7 9 12 33 , 37 29 7 3 9 13 118 →= 36 31 41 7 9 13 118 , 45 29 7 3 9 13 118 →= 94 31 41 7 9 13 118 , 15 29 7 3 9 13 118 →= 12 31 41 7 9 13 118 , 67 29 7 3 9 13 118 →= 95 31 41 7 9 13 118 , 72 29 7 3 9 13 118 →= 96 31 41 7 9 13 118 , 97 29 7 3 9 13 118 →= 98 31 41 7 9 13 118 , 76 29 7 3 9 13 118 →= 99 31 41 7 9 13 118 , 81 29 7 3 9 13 118 →= 100 31 41 7 9 13 118 , 31 41 7 3 9 15 28 →= 32 42 41 7 9 15 28 , 31 41 7 3 9 15 29 →= 32 42 41 7 9 15 29 , 31 41 7 3 9 15 30 →= 32 42 41 7 9 15 30 , 101 41 7 3 9 15 28 →= 102 42 41 7 9 15 28 , 101 41 7 3 9 15 29 →= 102 42 41 7 9 15 29 , 101 41 7 3 9 15 30 →= 102 42 41 7 9 15 30 , 42 41 7 3 9 15 28 →= 43 42 41 7 9 15 28 , 42 41 7 3 9 15 29 →= 43 42 41 7 9 15 29 , 42 41 7 3 9 15 30 →= 43 42 41 7 9 15 30 , 103 41 7 3 9 15 28 →= 104 42 41 7 9 15 28 , 103 41 7 3 9 15 29 →= 104 42 41 7 9 15 29 , 103 41 7 3 9 15 30 →= 104 42 41 7 9 15 30 , 105 41 7 3 9 15 28 →= 106 42 41 7 9 15 28 , 105 41 7 3 9 15 29 →= 106 42 41 7 9 15 29 , 105 41 7 3 9 15 30 →= 106 42 41 7 9 15 30 , 83 41 7 3 9 15 28 →= 107 42 41 7 9 15 28 , 83 41 7 3 9 15 29 →= 107 42 41 7 9 15 29 , 83 41 7 3 9 15 30 →= 107 42 41 7 9 15 30 , 88 41 7 3 9 15 28 →= 108 42 41 7 9 15 28 , 88 41 7 3 9 15 29 →= 108 42 41 7 9 15 29 , 88 41 7 3 9 15 30 →= 108 42 41 7 9 15 30 , 92 41 7 3 9 15 28 →= 109 42 41 7 9 15 28 , 92 41 7 3 9 15 29 →= 109 42 41 7 9 15 29 , 92 41 7 3 9 15 30 →= 109 42 41 7 9 15 30 , 31 41 7 3 9 12 31 →= 32 42 41 7 9 12 31 , 31 41 7 3 9 12 32 →= 32 42 41 7 9 12 32 , 31 41 7 3 9 12 33 →= 32 42 41 7 9 12 33 , 101 41 7 3 9 12 31 →= 102 42 41 7 9 12 31 , 101 41 7 3 9 12 32 →= 102 42 41 7 9 12 32 , 101 41 7 3 9 12 33 →= 102 42 41 7 9 12 33 , 42 41 7 3 9 12 31 →= 43 42 41 7 9 12 31 , 42 41 7 3 9 12 32 →= 43 42 41 7 9 12 32 , 42 41 7 3 9 12 33 →= 43 42 41 7 9 12 33 , 103 41 7 3 9 12 31 →= 104 42 41 7 9 12 31 , 103 41 7 3 9 12 32 →= 104 42 41 7 9 12 32 , 103 41 7 3 9 12 33 →= 104 42 41 7 9 12 33 , 105 41 7 3 9 12 31 →= 106 42 41 7 9 12 31 , 105 41 7 3 9 12 32 →= 106 42 41 7 9 12 32 , 105 41 7 3 9 12 33 →= 106 42 41 7 9 12 33 , 83 41 7 3 9 12 31 →= 107 42 41 7 9 12 31 , 83 41 7 3 9 12 32 →= 107 42 41 7 9 12 32 , 83 41 7 3 9 12 33 →= 107 42 41 7 9 12 33 , 88 41 7 3 9 12 31 →= 108 42 41 7 9 12 31 , 88 41 7 3 9 12 32 →= 108 42 41 7 9 12 32 , 88 41 7 3 9 12 33 →= 108 42 41 7 9 12 33 , 92 41 7 3 9 12 31 →= 109 42 41 7 9 12 31 , 92 41 7 3 9 12 32 →= 109 42 41 7 9 12 32 , 92 41 7 3 9 12 33 →= 109 42 41 7 9 12 33 , 31 41 7 3 9 13 118 →= 32 42 41 7 9 13 118 , 101 41 7 3 9 13 118 →= 102 42 41 7 9 13 118 , 42 41 7 3 9 13 118 →= 43 42 41 7 9 13 118 , 103 41 7 3 9 13 118 →= 104 42 41 7 9 13 118 , 105 41 7 3 9 13 118 →= 106 42 41 7 9 13 118 , 83 41 7 3 9 13 118 →= 107 42 41 7 9 13 118 , 88 41 7 3 9 13 118 →= 108 42 41 7 9 13 118 , 92 41 7 3 9 13 118 →= 109 42 41 7 9 13 118 , 110 57 7 3 9 15 28 →= 111 101 41 7 9 15 28 , 110 57 7 3 9 15 29 →= 111 101 41 7 9 15 29 , 110 57 7 3 9 15 30 →= 111 101 41 7 9 15 30 , 112 57 7 3 9 15 28 →= 113 101 41 7 9 15 28 , 112 57 7 3 9 15 29 →= 113 101 41 7 9 15 29 , 112 57 7 3 9 15 30 →= 113 101 41 7 9 15 30 , 110 57 7 3 9 12 31 →= 111 101 41 7 9 12 31 , 110 57 7 3 9 12 32 →= 111 101 41 7 9 12 32 , 110 57 7 3 9 12 33 →= 111 101 41 7 9 12 33 , 112 57 7 3 9 12 31 →= 113 101 41 7 9 12 31 , 112 57 7 3 9 12 32 →= 113 101 41 7 9 12 32 , 112 57 7 3 9 12 33 →= 113 101 41 7 9 12 33 , 110 57 7 3 9 13 118 →= 111 101 41 7 9 13 118 , 112 57 7 3 9 13 118 →= 113 101 41 7 9 13 118 , 114 59 7 3 9 15 28 →= 115 103 41 7 9 15 28 , 114 59 7 3 9 15 29 →= 115 103 41 7 9 15 29 , 114 59 7 3 9 15 30 →= 115 103 41 7 9 15 30 , 114 59 7 3 9 12 31 →= 115 103 41 7 9 12 31 , 114 59 7 3 9 12 32 →= 115 103 41 7 9 12 32 , 114 59 7 3 9 12 33 →= 115 103 41 7 9 12 33 , 116 74 50 3 9 15 28 →= 117 110 57 7 9 15 28 , 116 74 50 3 9 15 29 →= 117 110 57 7 9 15 29 , 116 74 50 3 9 15 30 →= 117 110 57 7 9 15 30 , 116 74 50 3 9 12 31 →= 117 110 57 7 9 12 31 , 116 74 50 3 9 12 32 →= 117 110 57 7 9 12 32 , 116 74 50 3 9 12 33 →= 117 110 57 7 9 12 33 , 2 3 3 3 8 54 119 →= 35 15 29 7 8 54 119 , 3 3 3 3 8 54 119 →= 9 15 29 7 8 54 119 , 7 3 3 3 8 54 119 →= 34 15 29 7 8 54 119 , 18 3 3 3 8 54 119 →= 38 15 29 7 8 54 119 , 48 3 3 3 8 54 119 →= 49 15 29 7 8 54 119 , 50 3 3 3 8 54 119 →= 51 15 29 7 8 54 119 , 52 3 3 3 8 54 119 →= 53 15 29 7 8 54 119 , 24 3 3 3 8 54 119 →= 39 15 29 7 8 54 119 , 57 7 3 3 8 54 119 →= 58 37 29 7 8 54 119 , 41 7 3 3 8 54 119 →= 40 37 29 7 8 54 119 , 59 7 3 3 8 54 119 →= 60 37 29 7 8 54 119 , 6 7 3 3 8 54 119 →= 61 37 29 7 8 54 119 , 62 7 3 3 8 54 119 →= 63 37 29 7 8 54 119 , 21 7 3 3 8 54 119 →= 64 37 29 7 8 54 119 , 27 7 3 3 8 54 119 →= 65 37 29 7 8 54 119 , 29 7 3 3 8 54 119 →= 28 37 29 7 8 54 119 , 37 29 7 3 8 54 119 →= 36 31 41 7 8 54 119 , 45 29 7 3 8 54 119 →= 94 31 41 7 8 54 119 , 15 29 7 3 8 54 119 →= 12 31 41 7 8 54 119 , 67 29 7 3 8 54 119 →= 95 31 41 7 8 54 119 , 72 29 7 3 8 54 119 →= 96 31 41 7 8 54 119 , 97 29 7 3 8 54 119 →= 98 31 41 7 8 54 119 , 76 29 7 3 8 54 119 →= 99 31 41 7 8 54 119 , 81 29 7 3 8 54 119 →= 100 31 41 7 8 54 119 , 31 41 7 3 8 54 119 →= 32 42 41 7 8 54 119 , 101 41 7 3 8 54 119 →= 102 42 41 7 8 54 119 , 42 41 7 3 8 54 119 →= 43 42 41 7 8 54 119 , 103 41 7 3 8 54 119 →= 104 42 41 7 8 54 119 , 105 41 7 3 8 54 119 →= 106 42 41 7 8 54 119 , 83 41 7 3 8 54 119 →= 107 42 41 7 8 54 119 , 88 41 7 3 8 54 119 →= 108 42 41 7 8 54 119 , 92 41 7 3 8 54 119 →= 109 42 41 7 8 54 119 , 44 45 29 34 15 29 7 →= 1 2 9 15 29 7 3 , 44 45 29 34 15 29 34 →= 1 2 9 15 29 7 9 , 47 45 29 34 15 29 7 →= 46 2 9 15 29 7 3 , 47 45 29 34 15 29 34 →= 46 2 9 15 29 7 9 , 44 45 29 34 15 28 36 →= 1 2 9 15 29 34 12 , 44 45 29 34 15 28 37 →= 1 2 9 15 29 34 15 , 47 45 29 34 15 28 36 →= 46 2 9 15 29 34 12 , 47 45 29 34 15 28 37 →= 46 2 9 15 29 34 15 , 35 15 29 34 15 29 7 →= 2 3 9 15 29 7 3 , 35 15 29 34 15 29 34 →= 2 3 9 15 29 7 9 , 9 15 29 34 15 29 7 →= 3 3 9 15 29 7 3 , 9 15 29 34 15 29 34 →= 3 3 9 15 29 7 9 , 34 15 29 34 15 29 7 →= 7 3 9 15 29 7 3 , 34 15 29 34 15 29 34 →= 7 3 9 15 29 7 9 , 38 15 29 34 15 29 7 →= 18 3 9 15 29 7 3 , 38 15 29 34 15 29 34 →= 18 3 9 15 29 7 9 , 49 15 29 34 15 29 7 →= 48 3 9 15 29 7 3 , 49 15 29 34 15 29 34 →= 48 3 9 15 29 7 9 , 51 15 29 34 15 29 7 →= 50 3 9 15 29 7 3 , 51 15 29 34 15 29 34 →= 50 3 9 15 29 7 9 , 53 15 29 34 15 29 7 →= 52 3 9 15 29 7 3 , 53 15 29 34 15 29 34 →= 52 3 9 15 29 7 9 , 39 15 29 34 15 29 7 →= 24 3 9 15 29 7 3 , 39 15 29 34 15 29 34 →= 24 3 9 15 29 7 9 , 35 15 29 34 15 28 36 →= 2 3 9 15 29 34 12 , 35 15 29 34 15 28 37 →= 2 3 9 15 29 34 15 , 9 15 29 34 15 28 36 →= 3 3 9 15 29 34 12 , 9 15 29 34 15 28 37 →= 3 3 9 15 29 34 15 , 34 15 29 34 15 28 36 →= 7 3 9 15 29 34 12 , 34 15 29 34 15 28 37 →= 7 3 9 15 29 34 15 , 38 15 29 34 15 28 36 →= 18 3 9 15 29 34 12 , 38 15 29 34 15 28 37 →= 18 3 9 15 29 34 15 , 49 15 29 34 15 28 36 →= 48 3 9 15 29 34 12 , 49 15 29 34 15 28 37 →= 48 3 9 15 29 34 15 , 51 15 29 34 15 28 36 →= 50 3 9 15 29 34 12 , 51 15 29 34 15 28 37 →= 50 3 9 15 29 34 15 , 53 15 29 34 15 28 36 →= 52 3 9 15 29 34 12 , 53 15 29 34 15 28 37 →= 52 3 9 15 29 34 15 , 39 15 29 34 15 28 36 →= 24 3 9 15 29 34 12 , 39 15 29 34 15 28 37 →= 24 3 9 15 29 34 15 , 58 37 29 34 15 29 7 →= 57 7 9 15 29 7 3 , 58 37 29 34 15 29 34 →= 57 7 9 15 29 7 9 , 40 37 29 34 15 29 7 →= 41 7 9 15 29 7 3 , 40 37 29 34 15 29 34 →= 41 7 9 15 29 7 9 , 60 37 29 34 15 29 7 →= 59 7 9 15 29 7 3 , 60 37 29 34 15 29 34 →= 59 7 9 15 29 7 9 , 61 37 29 34 15 29 7 →= 6 7 9 15 29 7 3 , 61 37 29 34 15 29 34 →= 6 7 9 15 29 7 9 , 63 37 29 34 15 29 7 →= 62 7 9 15 29 7 3 , 63 37 29 34 15 29 34 →= 62 7 9 15 29 7 9 , 64 37 29 34 15 29 7 →= 21 7 9 15 29 7 3 , 64 37 29 34 15 29 34 →= 21 7 9 15 29 7 9 , 65 37 29 34 15 29 7 →= 27 7 9 15 29 7 3 , 65 37 29 34 15 29 34 →= 27 7 9 15 29 7 9 , 28 37 29 34 15 29 7 →= 29 7 9 15 29 7 3 , 28 37 29 34 15 29 34 →= 29 7 9 15 29 7 9 , 58 37 29 34 15 28 36 →= 57 7 9 15 29 34 12 , 58 37 29 34 15 28 37 →= 57 7 9 15 29 34 15 , 40 37 29 34 15 28 36 →= 41 7 9 15 29 34 12 , 40 37 29 34 15 28 37 →= 41 7 9 15 29 34 15 , 60 37 29 34 15 28 36 →= 59 7 9 15 29 34 12 , 60 37 29 34 15 28 37 →= 59 7 9 15 29 34 15 , 61 37 29 34 15 28 36 →= 6 7 9 15 29 34 12 , 61 37 29 34 15 28 37 →= 6 7 9 15 29 34 15 , 63 37 29 34 15 28 36 →= 62 7 9 15 29 34 12 , 63 37 29 34 15 28 37 →= 62 7 9 15 29 34 15 , 64 37 29 34 15 28 36 →= 21 7 9 15 29 34 12 , 64 37 29 34 15 28 37 →= 21 7 9 15 29 34 15 , 65 37 29 34 15 28 36 →= 27 7 9 15 29 34 12 , 65 37 29 34 15 28 37 →= 27 7 9 15 29 34 15 , 28 37 29 34 15 28 36 →= 29 7 9 15 29 34 12 , 28 37 29 34 15 28 37 →= 29 7 9 15 29 34 15 , 66 67 29 34 15 29 7 →= 17 18 9 15 29 7 3 , 66 67 29 34 15 29 34 →= 17 18 9 15 29 7 9 , 69 67 29 34 15 29 7 →= 68 18 9 15 29 7 3 , 69 67 29 34 15 29 34 →= 68 18 9 15 29 7 9 , 66 67 29 34 15 28 36 →= 17 18 9 15 29 34 12 , 66 67 29 34 15 28 37 →= 17 18 9 15 29 34 15 , 69 67 29 34 15 28 36 →= 68 18 9 15 29 34 12 , 69 67 29 34 15 28 37 →= 68 18 9 15 29 34 15 , 71 72 29 34 15 29 7 →= 70 24 9 15 29 7 3 , 71 72 29 34 15 29 34 →= 70 24 9 15 29 7 9 , 73 72 29 34 15 29 7 →= 23 24 9 15 29 7 3 , 73 72 29 34 15 29 34 →= 23 24 9 15 29 7 9 , 71 72 29 34 15 28 36 →= 70 24 9 15 29 34 12 , 71 72 29 34 15 28 37 →= 70 24 9 15 29 34 15 , 73 72 29 34 15 28 36 →= 23 24 9 15 29 34 12 , 73 72 29 34 15 28 37 →= 23 24 9 15 29 34 15 , 75 76 29 34 15 29 7 →= 74 50 9 15 29 7 3 , 75 76 29 34 15 29 34 →= 74 50 9 15 29 7 9 , 78 76 29 34 15 29 7 →= 77 50 9 15 29 7 3 , 78 76 29 34 15 29 34 →= 77 50 9 15 29 7 9 , 75 76 29 34 15 28 36 →= 74 50 9 15 29 34 12 , 75 76 29 34 15 28 37 →= 74 50 9 15 29 34 15 , 78 76 29 34 15 28 36 →= 77 50 9 15 29 34 12 , 78 76 29 34 15 28 37 →= 77 50 9 15 29 34 15 , 80 81 29 34 15 29 7 →= 79 52 9 15 29 7 3 , 80 81 29 34 15 29 34 →= 79 52 9 15 29 7 9 , 80 81 29 34 15 28 36 →= 79 52 9 15 29 34 12 , 80 81 29 34 15 28 37 →= 79 52 9 15 29 34 15 , 82 83 41 34 15 29 7 →= 5 6 34 15 29 7 3 , 82 83 41 34 15 29 34 →= 5 6 34 15 29 7 9 , 85 83 41 34 15 29 7 →= 84 6 34 15 29 7 3 , 85 83 41 34 15 29 34 →= 84 6 34 15 29 7 9 , 82 83 41 34 15 28 36 →= 5 6 34 15 29 34 12 , 82 83 41 34 15 28 37 →= 5 6 34 15 29 34 15 , 85 83 41 34 15 28 36 →= 84 6 34 15 29 34 12 , 85 83 41 34 15 28 37 →= 84 6 34 15 29 34 15 , 87 88 41 34 15 29 7 →= 86 21 34 15 29 7 3 , 87 88 41 34 15 29 34 →= 86 21 34 15 29 7 9 , 89 88 41 34 15 29 7 →= 20 21 34 15 29 7 3 , 89 88 41 34 15 29 34 →= 20 21 34 15 29 7 9 , 87 88 41 34 15 28 36 →= 86 21 34 15 29 34 12 , 87 88 41 34 15 28 37 →= 86 21 34 15 29 34 15 , 89 88 41 34 15 28 36 →= 20 21 34 15 29 34 12 , 89 88 41 34 15 28 37 →= 20 21 34 15 29 34 15 , 91 92 41 34 15 29 7 →= 90 27 34 15 29 7 3 , 91 92 41 34 15 29 34 →= 90 27 34 15 29 7 9 , 93 92 41 34 15 29 7 →= 26 27 34 15 29 7 3 , 93 92 41 34 15 29 34 →= 26 27 34 15 29 7 9 , 91 92 41 34 15 28 36 →= 90 27 34 15 29 34 12 , 91 92 41 34 15 28 37 →= 90 27 34 15 29 34 15 , 93 92 41 34 15 28 36 →= 26 27 34 15 29 34 12 , 93 92 41 34 15 28 37 →= 26 27 34 15 29 34 15 , 36 31 41 34 15 29 7 →= 37 29 34 15 29 7 3 , 36 31 41 34 15 29 34 →= 37 29 34 15 29 7 9 , 94 31 41 34 15 29 7 →= 45 29 34 15 29 7 3 , 94 31 41 34 15 29 34 →= 45 29 34 15 29 7 9 , 12 31 41 34 15 29 7 →= 15 29 34 15 29 7 3 , 12 31 41 34 15 29 34 →= 15 29 34 15 29 7 9 , 95 31 41 34 15 29 7 →= 67 29 34 15 29 7 3 , 95 31 41 34 15 29 34 →= 67 29 34 15 29 7 9 , 96 31 41 34 15 29 7 →= 72 29 34 15 29 7 3 , 96 31 41 34 15 29 34 →= 72 29 34 15 29 7 9 , 98 31 41 34 15 29 7 →= 97 29 34 15 29 7 3 , 98 31 41 34 15 29 34 →= 97 29 34 15 29 7 9 , 99 31 41 34 15 29 7 →= 76 29 34 15 29 7 3 , 99 31 41 34 15 29 34 →= 76 29 34 15 29 7 9 , 100 31 41 34 15 29 7 →= 81 29 34 15 29 7 3 , 100 31 41 34 15 29 34 →= 81 29 34 15 29 7 9 , 36 31 41 34 15 28 36 →= 37 29 34 15 29 34 12 , 36 31 41 34 15 28 37 →= 37 29 34 15 29 34 15 , 94 31 41 34 15 28 36 →= 45 29 34 15 29 34 12 , 94 31 41 34 15 28 37 →= 45 29 34 15 29 34 15 , 12 31 41 34 15 28 36 →= 15 29 34 15 29 34 12 , 12 31 41 34 15 28 37 →= 15 29 34 15 29 34 15 , 95 31 41 34 15 28 36 →= 67 29 34 15 29 34 12 , 95 31 41 34 15 28 37 →= 67 29 34 15 29 34 15 , 96 31 41 34 15 28 36 →= 72 29 34 15 29 34 12 , 96 31 41 34 15 28 37 →= 72 29 34 15 29 34 15 , 98 31 41 34 15 28 36 →= 97 29 34 15 29 34 12 , 98 31 41 34 15 28 37 →= 97 29 34 15 29 34 15 , 99 31 41 34 15 28 36 →= 76 29 34 15 29 34 12 , 99 31 41 34 15 28 37 →= 76 29 34 15 29 34 15 , 100 31 41 34 15 28 36 →= 81 29 34 15 29 34 12 , 100 31 41 34 15 28 37 →= 81 29 34 15 29 34 15 , 32 42 41 34 15 29 7 →= 31 41 34 15 29 7 3 , 32 42 41 34 15 29 34 →= 31 41 34 15 29 7 9 , 102 42 41 34 15 29 7 →= 101 41 34 15 29 7 3 , 102 42 41 34 15 29 34 →= 101 41 34 15 29 7 9 , 43 42 41 34 15 29 7 →= 42 41 34 15 29 7 3 , 43 42 41 34 15 29 34 →= 42 41 34 15 29 7 9 , 104 42 41 34 15 29 7 →= 103 41 34 15 29 7 3 , 104 42 41 34 15 29 34 →= 103 41 34 15 29 7 9 , 106 42 41 34 15 29 7 →= 105 41 34 15 29 7 3 , 106 42 41 34 15 29 34 →= 105 41 34 15 29 7 9 , 107 42 41 34 15 29 7 →= 83 41 34 15 29 7 3 , 107 42 41 34 15 29 34 →= 83 41 34 15 29 7 9 , 108 42 41 34 15 29 7 →= 88 41 34 15 29 7 3 , 108 42 41 34 15 29 34 →= 88 41 34 15 29 7 9 , 109 42 41 34 15 29 7 →= 92 41 34 15 29 7 3 , 109 42 41 34 15 29 34 →= 92 41 34 15 29 7 9 , 32 42 41 34 15 28 36 →= 31 41 34 15 29 34 12 , 32 42 41 34 15 28 37 →= 31 41 34 15 29 34 15 , 102 42 41 34 15 28 36 →= 101 41 34 15 29 34 12 , 102 42 41 34 15 28 37 →= 101 41 34 15 29 34 15 , 43 42 41 34 15 28 36 →= 42 41 34 15 29 34 12 , 43 42 41 34 15 28 37 →= 42 41 34 15 29 34 15 , 104 42 41 34 15 28 36 →= 103 41 34 15 29 34 12 , 104 42 41 34 15 28 37 →= 103 41 34 15 29 34 15 , 106 42 41 34 15 28 36 →= 105 41 34 15 29 34 12 , 106 42 41 34 15 28 37 →= 105 41 34 15 29 34 15 , 107 42 41 34 15 28 36 →= 83 41 34 15 29 34 12 , 107 42 41 34 15 28 37 →= 83 41 34 15 29 34 15 , 108 42 41 34 15 28 36 →= 88 41 34 15 29 34 12 , 108 42 41 34 15 28 37 →= 88 41 34 15 29 34 15 , 109 42 41 34 15 28 36 →= 92 41 34 15 29 34 12 , 109 42 41 34 15 28 37 →= 92 41 34 15 29 34 15 , 111 101 41 34 15 29 7 →= 110 57 34 15 29 7 3 , 111 101 41 34 15 29 34 →= 110 57 34 15 29 7 9 , 113 101 41 34 15 29 7 →= 112 57 34 15 29 7 3 , 113 101 41 34 15 29 34 →= 112 57 34 15 29 7 9 , 111 101 41 34 15 28 36 →= 110 57 34 15 29 34 12 , 111 101 41 34 15 28 37 →= 110 57 34 15 29 34 15 , 113 101 41 34 15 28 36 →= 112 57 34 15 29 34 12 , 113 101 41 34 15 28 37 →= 112 57 34 15 29 34 15 , 115 103 41 34 15 29 7 →= 114 59 34 15 29 7 3 , 115 103 41 34 15 29 34 →= 114 59 34 15 29 7 9 , 115 103 41 34 15 28 36 →= 114 59 34 15 29 34 12 , 115 103 41 34 15 28 37 →= 114 59 34 15 29 34 15 , 117 110 57 34 15 29 7 →= 116 74 51 15 29 7 3 , 117 110 57 34 15 29 34 →= 116 74 51 15 29 7 9 , 117 110 57 34 15 28 36 →= 116 74 51 15 29 34 12 , 117 110 57 34 15 28 37 →= 116 74 51 15 29 34 15 , 44 45 29 34 12 31 40 →= 1 2 9 15 28 37 28 , 44 45 29 34 12 31 41 →= 1 2 9 15 28 37 29 , 47 45 29 34 12 31 40 →= 46 2 9 15 28 37 28 , 47 45 29 34 12 31 41 →= 46 2 9 15 28 37 29 , 44 45 29 34 12 32 42 →= 1 2 9 15 28 36 31 , 44 45 29 34 12 32 43 →= 1 2 9 15 28 36 32 , 47 45 29 34 12 32 42 →= 46 2 9 15 28 36 31 , 47 45 29 34 12 32 43 →= 46 2 9 15 28 36 32 , 35 15 29 34 12 31 40 →= 2 3 9 15 28 37 28 , 35 15 29 34 12 31 41 →= 2 3 9 15 28 37 29 , 9 15 29 34 12 31 40 →= 3 3 9 15 28 37 28 , 9 15 29 34 12 31 41 →= 3 3 9 15 28 37 29 , 34 15 29 34 12 31 40 →= 7 3 9 15 28 37 28 , 34 15 29 34 12 31 41 →= 7 3 9 15 28 37 29 , 38 15 29 34 12 31 40 →= 18 3 9 15 28 37 28 , 38 15 29 34 12 31 41 →= 18 3 9 15 28 37 29 , 49 15 29 34 12 31 40 →= 48 3 9 15 28 37 28 , 49 15 29 34 12 31 41 →= 48 3 9 15 28 37 29 , 51 15 29 34 12 31 40 →= 50 3 9 15 28 37 28 , 51 15 29 34 12 31 41 →= 50 3 9 15 28 37 29 , 53 15 29 34 12 31 40 →= 52 3 9 15 28 37 28 , 53 15 29 34 12 31 41 →= 52 3 9 15 28 37 29 , 39 15 29 34 12 31 40 →= 24 3 9 15 28 37 28 , 39 15 29 34 12 31 41 →= 24 3 9 15 28 37 29 , 35 15 29 34 12 32 42 →= 2 3 9 15 28 36 31 , 35 15 29 34 12 32 43 →= 2 3 9 15 28 36 32 , 9 15 29 34 12 32 42 →= 3 3 9 15 28 36 31 , 9 15 29 34 12 32 43 →= 3 3 9 15 28 36 32 , 34 15 29 34 12 32 42 →= 7 3 9 15 28 36 31 , 34 15 29 34 12 32 43 →= 7 3 9 15 28 36 32 , 38 15 29 34 12 32 42 →= 18 3 9 15 28 36 31 , 38 15 29 34 12 32 43 →= 18 3 9 15 28 36 32 , 49 15 29 34 12 32 42 →= 48 3 9 15 28 36 31 , 49 15 29 34 12 32 43 →= 48 3 9 15 28 36 32 , 51 15 29 34 12 32 42 →= 50 3 9 15 28 36 31 , 51 15 29 34 12 32 43 →= 50 3 9 15 28 36 32 , 53 15 29 34 12 32 42 →= 52 3 9 15 28 36 31 , 53 15 29 34 12 32 43 →= 52 3 9 15 28 36 32 , 39 15 29 34 12 32 42 →= 24 3 9 15 28 36 31 , 39 15 29 34 12 32 43 →= 24 3 9 15 28 36 32 , 58 37 29 34 12 31 40 →= 57 7 9 15 28 37 28 , 58 37 29 34 12 31 41 →= 57 7 9 15 28 37 29 , 40 37 29 34 12 31 40 →= 41 7 9 15 28 37 28 , 40 37 29 34 12 31 41 →= 41 7 9 15 28 37 29 , 60 37 29 34 12 31 40 →= 59 7 9 15 28 37 28 , 60 37 29 34 12 31 41 →= 59 7 9 15 28 37 29 , 61 37 29 34 12 31 40 →= 6 7 9 15 28 37 28 , 61 37 29 34 12 31 41 →= 6 7 9 15 28 37 29 , 63 37 29 34 12 31 40 →= 62 7 9 15 28 37 28 , 63 37 29 34 12 31 41 →= 62 7 9 15 28 37 29 , 64 37 29 34 12 31 40 →= 21 7 9 15 28 37 28 , 64 37 29 34 12 31 41 →= 21 7 9 15 28 37 29 , 65 37 29 34 12 31 40 →= 27 7 9 15 28 37 28 , 65 37 29 34 12 31 41 →= 27 7 9 15 28 37 29 , 28 37 29 34 12 31 40 →= 29 7 9 15 28 37 28 , 28 37 29 34 12 31 41 →= 29 7 9 15 28 37 29 , 58 37 29 34 12 32 42 →= 57 7 9 15 28 36 31 , 58 37 29 34 12 32 43 →= 57 7 9 15 28 36 32 , 40 37 29 34 12 32 42 →= 41 7 9 15 28 36 31 , 40 37 29 34 12 32 43 →= 41 7 9 15 28 36 32 , 60 37 29 34 12 32 42 →= 59 7 9 15 28 36 31 , 60 37 29 34 12 32 43 →= 59 7 9 15 28 36 32 , 61 37 29 34 12 32 42 →= 6 7 9 15 28 36 31 , 61 37 29 34 12 32 43 →= 6 7 9 15 28 36 32 , 63 37 29 34 12 32 42 →= 62 7 9 15 28 36 31 , 63 37 29 34 12 32 43 →= 62 7 9 15 28 36 32 , 64 37 29 34 12 32 42 →= 21 7 9 15 28 36 31 , 64 37 29 34 12 32 43 →= 21 7 9 15 28 36 32 , 65 37 29 34 12 32 42 →= 27 7 9 15 28 36 31 , 65 37 29 34 12 32 43 →= 27 7 9 15 28 36 32 , 28 37 29 34 12 32 42 →= 29 7 9 15 28 36 31 , 28 37 29 34 12 32 43 →= 29 7 9 15 28 36 32 , 66 67 29 34 12 31 40 →= 17 18 9 15 28 37 28 , 66 67 29 34 12 31 41 →= 17 18 9 15 28 37 29 , 69 67 29 34 12 31 40 →= 68 18 9 15 28 37 28 , 69 67 29 34 12 31 41 →= 68 18 9 15 28 37 29 , 66 67 29 34 12 32 42 →= 17 18 9 15 28 36 31 , 66 67 29 34 12 32 43 →= 17 18 9 15 28 36 32 , 69 67 29 34 12 32 42 →= 68 18 9 15 28 36 31 , 69 67 29 34 12 32 43 →= 68 18 9 15 28 36 32 , 71 72 29 34 12 31 40 →= 70 24 9 15 28 37 28 , 71 72 29 34 12 31 41 →= 70 24 9 15 28 37 29 , 73 72 29 34 12 31 40 →= 23 24 9 15 28 37 28 , 73 72 29 34 12 31 41 →= 23 24 9 15 28 37 29 , 71 72 29 34 12 32 42 →= 70 24 9 15 28 36 31 , 71 72 29 34 12 32 43 →= 70 24 9 15 28 36 32 , 73 72 29 34 12 32 42 →= 23 24 9 15 28 36 31 , 73 72 29 34 12 32 43 →= 23 24 9 15 28 36 32 , 75 76 29 34 12 31 40 →= 74 50 9 15 28 37 28 , 75 76 29 34 12 31 41 →= 74 50 9 15 28 37 29 , 78 76 29 34 12 31 40 →= 77 50 9 15 28 37 28 , 78 76 29 34 12 31 41 →= 77 50 9 15 28 37 29 , 75 76 29 34 12 32 42 →= 74 50 9 15 28 36 31 , 75 76 29 34 12 32 43 →= 74 50 9 15 28 36 32 , 78 76 29 34 12 32 42 →= 77 50 9 15 28 36 31 , 78 76 29 34 12 32 43 →= 77 50 9 15 28 36 32 , 80 81 29 34 12 31 40 →= 79 52 9 15 28 37 28 , 80 81 29 34 12 31 41 →= 79 52 9 15 28 37 29 , 80 81 29 34 12 32 42 →= 79 52 9 15 28 36 31 , 80 81 29 34 12 32 43 →= 79 52 9 15 28 36 32 , 82 83 41 34 12 31 40 →= 5 6 34 15 28 37 28 , 82 83 41 34 12 31 41 →= 5 6 34 15 28 37 29 , 85 83 41 34 12 31 40 →= 84 6 34 15 28 37 28 , 85 83 41 34 12 31 41 →= 84 6 34 15 28 37 29 , 82 83 41 34 12 32 42 →= 5 6 34 15 28 36 31 , 82 83 41 34 12 32 43 →= 5 6 34 15 28 36 32 , 85 83 41 34 12 32 42 →= 84 6 34 15 28 36 31 , 85 83 41 34 12 32 43 →= 84 6 34 15 28 36 32 , 87 88 41 34 12 31 40 →= 86 21 34 15 28 37 28 , 87 88 41 34 12 31 41 →= 86 21 34 15 28 37 29 , 89 88 41 34 12 31 40 →= 20 21 34 15 28 37 28 , 89 88 41 34 12 31 41 →= 20 21 34 15 28 37 29 , 87 88 41 34 12 32 42 →= 86 21 34 15 28 36 31 , 87 88 41 34 12 32 43 →= 86 21 34 15 28 36 32 , 89 88 41 34 12 32 42 →= 20 21 34 15 28 36 31 , 89 88 41 34 12 32 43 →= 20 21 34 15 28 36 32 , 91 92 41 34 12 31 40 →= 90 27 34 15 28 37 28 , 91 92 41 34 12 31 41 →= 90 27 34 15 28 37 29 , 93 92 41 34 12 31 40 →= 26 27 34 15 28 37 28 , 93 92 41 34 12 31 41 →= 26 27 34 15 28 37 29 , 91 92 41 34 12 32 42 →= 90 27 34 15 28 36 31 , 91 92 41 34 12 32 43 →= 90 27 34 15 28 36 32 , 93 92 41 34 12 32 42 →= 26 27 34 15 28 36 31 , 93 92 41 34 12 32 43 →= 26 27 34 15 28 36 32 , 36 31 41 34 12 31 40 →= 37 29 34 15 28 37 28 , 36 31 41 34 12 31 41 →= 37 29 34 15 28 37 29 , 94 31 41 34 12 31 40 →= 45 29 34 15 28 37 28 , 94 31 41 34 12 31 41 →= 45 29 34 15 28 37 29 , 12 31 41 34 12 31 40 →= 15 29 34 15 28 37 28 , 12 31 41 34 12 31 41 →= 15 29 34 15 28 37 29 , 95 31 41 34 12 31 40 →= 67 29 34 15 28 37 28 , 95 31 41 34 12 31 41 →= 67 29 34 15 28 37 29 , 96 31 41 34 12 31 40 →= 72 29 34 15 28 37 28 , 96 31 41 34 12 31 41 →= 72 29 34 15 28 37 29 , 98 31 41 34 12 31 40 →= 97 29 34 15 28 37 28 , 98 31 41 34 12 31 41 →= 97 29 34 15 28 37 29 , 99 31 41 34 12 31 40 →= 76 29 34 15 28 37 28 , 99 31 41 34 12 31 41 →= 76 29 34 15 28 37 29 , 100 31 41 34 12 31 40 →= 81 29 34 15 28 37 28 , 100 31 41 34 12 31 41 →= 81 29 34 15 28 37 29 , 36 31 41 34 12 32 42 →= 37 29 34 15 28 36 31 , 36 31 41 34 12 32 43 →= 37 29 34 15 28 36 32 , 94 31 41 34 12 32 42 →= 45 29 34 15 28 36 31 , 94 31 41 34 12 32 43 →= 45 29 34 15 28 36 32 , 12 31 41 34 12 32 42 →= 15 29 34 15 28 36 31 , 12 31 41 34 12 32 43 →= 15 29 34 15 28 36 32 , 95 31 41 34 12 32 42 →= 67 29 34 15 28 36 31 , 95 31 41 34 12 32 43 →= 67 29 34 15 28 36 32 , 96 31 41 34 12 32 42 →= 72 29 34 15 28 36 31 , 96 31 41 34 12 32 43 →= 72 29 34 15 28 36 32 , 98 31 41 34 12 32 42 →= 97 29 34 15 28 36 31 , 98 31 41 34 12 32 43 →= 97 29 34 15 28 36 32 , 99 31 41 34 12 32 42 →= 76 29 34 15 28 36 31 , 99 31 41 34 12 32 43 →= 76 29 34 15 28 36 32 , 100 31 41 34 12 32 42 →= 81 29 34 15 28 36 31 , 100 31 41 34 12 32 43 →= 81 29 34 15 28 36 32 , 32 42 41 34 12 31 40 →= 31 41 34 15 28 37 28 , 32 42 41 34 12 31 41 →= 31 41 34 15 28 37 29 , 102 42 41 34 12 31 40 →= 101 41 34 15 28 37 28 , 102 42 41 34 12 31 41 →= 101 41 34 15 28 37 29 , 43 42 41 34 12 31 40 →= 42 41 34 15 28 37 28 , 43 42 41 34 12 31 41 →= 42 41 34 15 28 37 29 , 104 42 41 34 12 31 40 →= 103 41 34 15 28 37 28 , 104 42 41 34 12 31 41 →= 103 41 34 15 28 37 29 , 106 42 41 34 12 31 40 →= 105 41 34 15 28 37 28 , 106 42 41 34 12 31 41 →= 105 41 34 15 28 37 29 , 107 42 41 34 12 31 40 →= 83 41 34 15 28 37 28 , 107 42 41 34 12 31 41 →= 83 41 34 15 28 37 29 , 108 42 41 34 12 31 40 →= 88 41 34 15 28 37 28 , 108 42 41 34 12 31 41 →= 88 41 34 15 28 37 29 , 109 42 41 34 12 31 40 →= 92 41 34 15 28 37 28 , 109 42 41 34 12 31 41 →= 92 41 34 15 28 37 29 , 32 42 41 34 12 32 42 →= 31 41 34 15 28 36 31 , 32 42 41 34 12 32 43 →= 31 41 34 15 28 36 32 , 102 42 41 34 12 32 42 →= 101 41 34 15 28 36 31 , 102 42 41 34 12 32 43 →= 101 41 34 15 28 36 32 , 43 42 41 34 12 32 42 →= 42 41 34 15 28 36 31 , 43 42 41 34 12 32 43 →= 42 41 34 15 28 36 32 , 104 42 41 34 12 32 42 →= 103 41 34 15 28 36 31 , 104 42 41 34 12 32 43 →= 103 41 34 15 28 36 32 , 106 42 41 34 12 32 42 →= 105 41 34 15 28 36 31 , 106 42 41 34 12 32 43 →= 105 41 34 15 28 36 32 , 107 42 41 34 12 32 42 →= 83 41 34 15 28 36 31 , 107 42 41 34 12 32 43 →= 83 41 34 15 28 36 32 , 108 42 41 34 12 32 42 →= 88 41 34 15 28 36 31 , 108 42 41 34 12 32 43 →= 88 41 34 15 28 36 32 , 109 42 41 34 12 32 42 →= 92 41 34 15 28 36 31 , 109 42 41 34 12 32 43 →= 92 41 34 15 28 36 32 , 111 101 41 34 12 31 40 →= 110 57 34 15 28 37 28 , 111 101 41 34 12 31 41 →= 110 57 34 15 28 37 29 , 113 101 41 34 12 31 40 →= 112 57 34 15 28 37 28 , 113 101 41 34 12 31 41 →= 112 57 34 15 28 37 29 , 111 101 41 34 12 32 42 →= 110 57 34 15 28 36 31 , 111 101 41 34 12 32 43 →= 110 57 34 15 28 36 32 , 113 101 41 34 12 32 42 →= 112 57 34 15 28 36 31 , 113 101 41 34 12 32 43 →= 112 57 34 15 28 36 32 , 115 103 41 34 12 31 40 →= 114 59 34 15 28 37 28 , 115 103 41 34 12 31 41 →= 114 59 34 15 28 37 29 , 115 103 41 34 12 32 42 →= 114 59 34 15 28 36 31 , 115 103 41 34 12 32 43 →= 114 59 34 15 28 36 32 , 117 110 57 34 12 31 40 →= 116 74 51 15 28 37 28 , 117 110 57 34 12 31 41 →= 116 74 51 15 28 37 29 , 117 110 57 34 12 32 42 →= 116 74 51 15 28 36 31 , 117 110 57 34 12 32 43 →= 116 74 51 15 28 36 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 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 55 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 56 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 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 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, 1 ↦ 8, 35 ↦ 9, 3 ↦ 10, 28 ↦ 11, 36 ↦ 12, 12 ↦ 13, 37 ↦ 14, 19 ↦ 15, 20 ↦ 16, 21 ↦ 17, 16 ↦ 18, 17 ↦ 19, 38 ↦ 20, 25 ↦ 21, 26 ↦ 22, 27 ↦ 23, 22 ↦ 24, 23 ↦ 25, 39 ↦ 26, 31 ↦ 27, 40 ↦ 28, 41 ↦ 29, 32 ↦ 30, 42 ↦ 31, 43 ↦ 32, 8 ↦ 33, 9 ↦ 34, 10 ↦ 35, 11 ↦ 36, 13 ↦ 37, 14 ↦ 38, 54 ↦ 39, 55 ↦ 40, 56 ↦ 41, 57 ↦ 42, 58 ↦ 43, 59 ↦ 44, 60 ↦ 45, 61 ↦ 46, 62 ↦ 47, 63 ↦ 48, 64 ↦ 49, 65 ↦ 50, 82 ↦ 51, 83 ↦ 52, 84 ↦ 53, 85 ↦ 54, 86 ↦ 55, 87 ↦ 56, 88 ↦ 57, 89 ↦ 58, 90 ↦ 59, 91 ↦ 60, 92 ↦ 61, 93 ↦ 62, 45 ↦ 63, 94 ↦ 64, 67 ↦ 65, 95 ↦ 66, 72 ↦ 67, 96 ↦ 68, 97 ↦ 69, 98 ↦ 70, 76 ↦ 71, 99 ↦ 72, 81 ↦ 73, 100 ↦ 74, 101 ↦ 75, 102 ↦ 76, 103 ↦ 77, 104 ↦ 78, 105 ↦ 79, 106 ↦ 80, 107 ↦ 81, 108 ↦ 82, 109 ↦ 83, 110 ↦ 84, 111 ↦ 85, 112 ↦ 86, 113 ↦ 87, 114 ↦ 88, 115 ↦ 89, 30 ↦ 90, 33 ↦ 91, 118 ↦ 92, 119 ↦ 93, 117 ↦ 94, 116 ↦ 95, 74 ↦ 96, 51 ↦ 97 }, it remains to prove termination of the 877-rule system { 0 1 2 3 4 5 6 ⟶ 7 8 9 4 5 6 10 , 0 1 2 3 4 11 12 ⟶ 7 8 9 4 5 3 13 , 0 1 2 3 4 11 14 ⟶ 7 8 9 4 5 3 4 , 15 16 17 3 4 5 6 ⟶ 18 19 20 4 5 6 10 , 15 16 17 3 4 11 12 ⟶ 18 19 20 4 5 3 13 , 15 16 17 3 4 11 14 ⟶ 18 19 20 4 5 3 4 , 21 22 23 3 4 5 6 ⟶ 24 25 26 4 5 6 10 , 21 22 23 3 4 11 12 ⟶ 24 25 26 4 5 3 13 , 21 22 23 3 4 11 14 ⟶ 24 25 26 4 5 3 4 , 0 1 2 3 13 27 28 ⟶ 7 8 9 4 11 14 11 , 0 1 2 3 13 27 29 ⟶ 7 8 9 4 11 14 5 , 0 1 2 3 13 30 31 ⟶ 7 8 9 4 11 12 27 , 0 1 2 3 13 30 32 ⟶ 7 8 9 4 11 12 30 , 15 16 17 3 13 27 28 ⟶ 18 19 20 4 11 14 11 , 15 16 17 3 13 27 29 ⟶ 18 19 20 4 11 14 5 , 15 16 17 3 13 30 31 ⟶ 18 19 20 4 11 12 27 , 15 16 17 3 13 30 32 ⟶ 18 19 20 4 11 12 30 , 21 22 23 3 13 27 28 ⟶ 24 25 26 4 11 14 11 , 21 22 23 3 13 27 29 ⟶ 24 25 26 4 11 14 5 , 21 22 23 3 13 30 31 ⟶ 24 25 26 4 11 12 27 , 21 22 23 3 13 30 32 ⟶ 24 25 26 4 11 12 30 , 6 10 10 10 10 10 10 →= 3 4 5 6 10 10 10 , 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 10 35 →= 3 4 5 6 10 10 35 , 6 10 10 10 10 10 36 →= 3 4 5 6 10 10 36 , 6 10 10 10 10 34 13 →= 3 4 5 6 10 34 13 , 6 10 10 10 10 34 37 →= 3 4 5 6 10 34 37 , 6 10 10 10 10 34 38 →= 3 4 5 6 10 34 38 , 6 10 10 10 10 34 4 →= 3 4 5 6 10 34 4 , 6 10 10 10 10 33 39 →= 3 4 5 6 10 33 39 , 6 10 10 10 10 33 40 →= 3 4 5 6 10 33 40 , 6 10 10 10 10 35 41 →= 3 4 5 6 10 35 41 , 42 6 10 10 10 10 10 →= 43 14 5 6 10 10 10 , 42 6 10 10 10 10 33 →= 43 14 5 6 10 10 33 , 42 6 10 10 10 10 34 →= 43 14 5 6 10 10 34 , 42 6 10 10 10 10 35 →= 43 14 5 6 10 10 35 , 42 6 10 10 10 10 36 →= 43 14 5 6 10 10 36 , 29 6 10 10 10 10 10 →= 28 14 5 6 10 10 10 , 29 6 10 10 10 10 33 →= 28 14 5 6 10 10 33 , 29 6 10 10 10 10 34 →= 28 14 5 6 10 10 34 , 29 6 10 10 10 10 35 →= 28 14 5 6 10 10 35 , 29 6 10 10 10 10 36 →= 28 14 5 6 10 10 36 , 44 6 10 10 10 10 10 →= 45 14 5 6 10 10 10 , 44 6 10 10 10 10 33 →= 45 14 5 6 10 10 33 , 44 6 10 10 10 10 34 →= 45 14 5 6 10 10 34 , 44 6 10 10 10 10 35 →= 45 14 5 6 10 10 35 , 44 6 10 10 10 10 36 →= 45 14 5 6 10 10 36 , 2 6 10 10 10 10 10 →= 46 14 5 6 10 10 10 , 2 6 10 10 10 10 33 →= 46 14 5 6 10 10 33 , 2 6 10 10 10 10 34 →= 46 14 5 6 10 10 34 , 2 6 10 10 10 10 35 →= 46 14 5 6 10 10 35 , 2 6 10 10 10 10 36 →= 46 14 5 6 10 10 36 , 47 6 10 10 10 10 10 →= 48 14 5 6 10 10 10 , 47 6 10 10 10 10 33 →= 48 14 5 6 10 10 33 , 47 6 10 10 10 10 34 →= 48 14 5 6 10 10 34 , 47 6 10 10 10 10 35 →= 48 14 5 6 10 10 35 , 47 6 10 10 10 10 36 →= 48 14 5 6 10 10 36 , 17 6 10 10 10 10 10 →= 49 14 5 6 10 10 10 , 17 6 10 10 10 10 33 →= 49 14 5 6 10 10 33 , 17 6 10 10 10 10 34 →= 49 14 5 6 10 10 34 , 17 6 10 10 10 10 35 →= 49 14 5 6 10 10 35 , 17 6 10 10 10 10 36 →= 49 14 5 6 10 10 36 , 23 6 10 10 10 10 10 →= 50 14 5 6 10 10 10 , 23 6 10 10 10 10 33 →= 50 14 5 6 10 10 33 , 23 6 10 10 10 10 34 →= 50 14 5 6 10 10 34 , 23 6 10 10 10 10 35 →= 50 14 5 6 10 10 35 , 23 6 10 10 10 10 36 →= 50 14 5 6 10 10 36 , 5 6 10 10 10 10 10 →= 11 14 5 6 10 10 10 , 5 6 10 10 10 10 33 →= 11 14 5 6 10 10 33 , 5 6 10 10 10 10 34 →= 11 14 5 6 10 10 34 , 5 6 10 10 10 10 35 →= 11 14 5 6 10 10 35 , 5 6 10 10 10 10 36 →= 11 14 5 6 10 10 36 , 42 6 10 10 10 34 13 →= 43 14 5 6 10 34 13 , 42 6 10 10 10 34 37 →= 43 14 5 6 10 34 37 , 42 6 10 10 10 34 38 →= 43 14 5 6 10 34 38 , 42 6 10 10 10 34 4 →= 43 14 5 6 10 34 4 , 29 6 10 10 10 34 13 →= 28 14 5 6 10 34 13 , 29 6 10 10 10 34 37 →= 28 14 5 6 10 34 37 , 29 6 10 10 10 34 38 →= 28 14 5 6 10 34 38 , 29 6 10 10 10 34 4 →= 28 14 5 6 10 34 4 , 44 6 10 10 10 34 13 →= 45 14 5 6 10 34 13 , 44 6 10 10 10 34 37 →= 45 14 5 6 10 34 37 , 44 6 10 10 10 34 38 →= 45 14 5 6 10 34 38 , 44 6 10 10 10 34 4 →= 45 14 5 6 10 34 4 , 2 6 10 10 10 34 13 →= 46 14 5 6 10 34 13 , 2 6 10 10 10 34 37 →= 46 14 5 6 10 34 37 , 2 6 10 10 10 34 38 →= 46 14 5 6 10 34 38 , 2 6 10 10 10 34 4 →= 46 14 5 6 10 34 4 , 47 6 10 10 10 34 13 →= 48 14 5 6 10 34 13 , 47 6 10 10 10 34 37 →= 48 14 5 6 10 34 37 , 47 6 10 10 10 34 38 →= 48 14 5 6 10 34 38 , 47 6 10 10 10 34 4 →= 48 14 5 6 10 34 4 , 17 6 10 10 10 34 13 →= 49 14 5 6 10 34 13 , 17 6 10 10 10 34 37 →= 49 14 5 6 10 34 37 , 17 6 10 10 10 34 38 →= 49 14 5 6 10 34 38 , 17 6 10 10 10 34 4 →= 49 14 5 6 10 34 4 , 23 6 10 10 10 34 13 →= 50 14 5 6 10 34 13 , 23 6 10 10 10 34 37 →= 50 14 5 6 10 34 37 , 23 6 10 10 10 34 38 →= 50 14 5 6 10 34 38 , 23 6 10 10 10 34 4 →= 50 14 5 6 10 34 4 , 5 6 10 10 10 34 13 →= 11 14 5 6 10 34 13 , 5 6 10 10 10 34 37 →= 11 14 5 6 10 34 37 , 5 6 10 10 10 34 38 →= 11 14 5 6 10 34 38 , 5 6 10 10 10 34 4 →= 11 14 5 6 10 34 4 , 42 6 10 10 10 33 39 →= 43 14 5 6 10 33 39 , 42 6 10 10 10 33 40 →= 43 14 5 6 10 33 40 , 29 6 10 10 10 33 39 →= 28 14 5 6 10 33 39 , 29 6 10 10 10 33 40 →= 28 14 5 6 10 33 40 , 44 6 10 10 10 33 39 →= 45 14 5 6 10 33 39 , 44 6 10 10 10 33 40 →= 45 14 5 6 10 33 40 , 2 6 10 10 10 33 39 →= 46 14 5 6 10 33 39 , 2 6 10 10 10 33 40 →= 46 14 5 6 10 33 40 , 47 6 10 10 10 33 39 →= 48 14 5 6 10 33 39 , 47 6 10 10 10 33 40 →= 48 14 5 6 10 33 40 , 17 6 10 10 10 33 39 →= 49 14 5 6 10 33 39 , 17 6 10 10 10 33 40 →= 49 14 5 6 10 33 40 , 23 6 10 10 10 33 39 →= 50 14 5 6 10 33 39 , 23 6 10 10 10 33 40 →= 50 14 5 6 10 33 40 , 5 6 10 10 10 33 39 →= 11 14 5 6 10 33 39 , 5 6 10 10 10 33 40 →= 11 14 5 6 10 33 40 , 42 6 10 10 10 35 41 →= 43 14 5 6 10 35 41 , 29 6 10 10 10 35 41 →= 28 14 5 6 10 35 41 , 44 6 10 10 10 35 41 →= 45 14 5 6 10 35 41 , 2 6 10 10 10 35 41 →= 46 14 5 6 10 35 41 , 47 6 10 10 10 35 41 →= 48 14 5 6 10 35 41 , 17 6 10 10 10 35 41 →= 49 14 5 6 10 35 41 , 23 6 10 10 10 35 41 →= 50 14 5 6 10 35 41 , 5 6 10 10 10 35 41 →= 11 14 5 6 10 35 41 , 1 2 6 10 10 10 10 →= 51 52 29 6 10 10 10 , 1 2 6 10 10 10 33 →= 51 52 29 6 10 10 33 , 1 2 6 10 10 10 34 →= 51 52 29 6 10 10 34 , 1 2 6 10 10 10 35 →= 51 52 29 6 10 10 35 , 1 2 6 10 10 10 36 →= 51 52 29 6 10 10 36 , 53 2 6 10 10 10 10 →= 54 52 29 6 10 10 10 , 53 2 6 10 10 10 33 →= 54 52 29 6 10 10 33 , 53 2 6 10 10 10 34 →= 54 52 29 6 10 10 34 , 53 2 6 10 10 10 35 →= 54 52 29 6 10 10 35 , 53 2 6 10 10 10 36 →= 54 52 29 6 10 10 36 , 1 2 6 10 10 34 13 →= 51 52 29 6 10 34 13 , 1 2 6 10 10 34 37 →= 51 52 29 6 10 34 37 , 1 2 6 10 10 34 38 →= 51 52 29 6 10 34 38 , 1 2 6 10 10 34 4 →= 51 52 29 6 10 34 4 , 53 2 6 10 10 34 13 →= 54 52 29 6 10 34 13 , 53 2 6 10 10 34 37 →= 54 52 29 6 10 34 37 , 53 2 6 10 10 34 38 →= 54 52 29 6 10 34 38 , 53 2 6 10 10 34 4 →= 54 52 29 6 10 34 4 , 1 2 6 10 10 33 39 →= 51 52 29 6 10 33 39 , 1 2 6 10 10 33 40 →= 51 52 29 6 10 33 40 , 53 2 6 10 10 33 39 →= 54 52 29 6 10 33 39 , 53 2 6 10 10 33 40 →= 54 52 29 6 10 33 40 , 1 2 6 10 10 35 41 →= 51 52 29 6 10 35 41 , 53 2 6 10 10 35 41 →= 54 52 29 6 10 35 41 , 55 17 6 10 10 10 10 →= 56 57 29 6 10 10 10 , 55 17 6 10 10 10 33 →= 56 57 29 6 10 10 33 , 55 17 6 10 10 10 34 →= 56 57 29 6 10 10 34 , 55 17 6 10 10 10 35 →= 56 57 29 6 10 10 35 , 55 17 6 10 10 10 36 →= 56 57 29 6 10 10 36 , 16 17 6 10 10 10 10 →= 58 57 29 6 10 10 10 , 16 17 6 10 10 10 33 →= 58 57 29 6 10 10 33 , 16 17 6 10 10 10 34 →= 58 57 29 6 10 10 34 , 16 17 6 10 10 10 35 →= 58 57 29 6 10 10 35 , 16 17 6 10 10 10 36 →= 58 57 29 6 10 10 36 , 55 17 6 10 10 34 13 →= 56 57 29 6 10 34 13 , 55 17 6 10 10 34 37 →= 56 57 29 6 10 34 37 , 55 17 6 10 10 34 38 →= 56 57 29 6 10 34 38 , 55 17 6 10 10 34 4 →= 56 57 29 6 10 34 4 , 16 17 6 10 10 34 13 →= 58 57 29 6 10 34 13 , 16 17 6 10 10 34 37 →= 58 57 29 6 10 34 37 , 16 17 6 10 10 34 38 →= 58 57 29 6 10 34 38 , 16 17 6 10 10 34 4 →= 58 57 29 6 10 34 4 , 55 17 6 10 10 33 39 →= 56 57 29 6 10 33 39 , 55 17 6 10 10 33 40 →= 56 57 29 6 10 33 40 , 16 17 6 10 10 33 39 →= 58 57 29 6 10 33 39 , 16 17 6 10 10 33 40 →= 58 57 29 6 10 33 40 , 55 17 6 10 10 35 41 →= 56 57 29 6 10 35 41 , 16 17 6 10 10 35 41 →= 58 57 29 6 10 35 41 , 59 23 6 10 10 10 10 →= 60 61 29 6 10 10 10 , 59 23 6 10 10 10 33 →= 60 61 29 6 10 10 33 , 59 23 6 10 10 10 34 →= 60 61 29 6 10 10 34 , 59 23 6 10 10 10 35 →= 60 61 29 6 10 10 35 , 59 23 6 10 10 10 36 →= 60 61 29 6 10 10 36 , 22 23 6 10 10 10 10 →= 62 61 29 6 10 10 10 , 22 23 6 10 10 10 33 →= 62 61 29 6 10 10 33 , 22 23 6 10 10 10 34 →= 62 61 29 6 10 10 34 , 22 23 6 10 10 10 35 →= 62 61 29 6 10 10 35 , 22 23 6 10 10 10 36 →= 62 61 29 6 10 10 36 , 59 23 6 10 10 34 13 →= 60 61 29 6 10 34 13 , 59 23 6 10 10 34 37 →= 60 61 29 6 10 34 37 , 59 23 6 10 10 34 38 →= 60 61 29 6 10 34 38 , 59 23 6 10 10 34 4 →= 60 61 29 6 10 34 4 , 22 23 6 10 10 34 13 →= 62 61 29 6 10 34 13 , 22 23 6 10 10 34 37 →= 62 61 29 6 10 34 37 , 22 23 6 10 10 34 38 →= 62 61 29 6 10 34 38 , 22 23 6 10 10 34 4 →= 62 61 29 6 10 34 4 , 59 23 6 10 10 33 39 →= 60 61 29 6 10 33 39 , 59 23 6 10 10 33 40 →= 60 61 29 6 10 33 40 , 22 23 6 10 10 33 39 →= 62 61 29 6 10 33 39 , 22 23 6 10 10 33 40 →= 62 61 29 6 10 33 40 , 59 23 6 10 10 35 41 →= 60 61 29 6 10 35 41 , 22 23 6 10 10 35 41 →= 62 61 29 6 10 35 41 , 14 5 6 10 10 10 10 →= 12 27 29 6 10 10 10 , 14 5 6 10 10 10 33 →= 12 27 29 6 10 10 33 , 14 5 6 10 10 10 34 →= 12 27 29 6 10 10 34 , 14 5 6 10 10 10 35 →= 12 27 29 6 10 10 35 , 14 5 6 10 10 10 36 →= 12 27 29 6 10 10 36 , 63 5 6 10 10 10 10 →= 64 27 29 6 10 10 10 , 63 5 6 10 10 10 33 →= 64 27 29 6 10 10 33 , 63 5 6 10 10 10 34 →= 64 27 29 6 10 10 34 , 63 5 6 10 10 10 35 →= 64 27 29 6 10 10 35 , 63 5 6 10 10 10 36 →= 64 27 29 6 10 10 36 , 4 5 6 10 10 10 10 →= 13 27 29 6 10 10 10 , 4 5 6 10 10 10 33 →= 13 27 29 6 10 10 33 , 4 5 6 10 10 10 34 →= 13 27 29 6 10 10 34 , 4 5 6 10 10 10 35 →= 13 27 29 6 10 10 35 , 4 5 6 10 10 10 36 →= 13 27 29 6 10 10 36 , 65 5 6 10 10 10 10 →= 66 27 29 6 10 10 10 , 65 5 6 10 10 10 33 →= 66 27 29 6 10 10 33 , 65 5 6 10 10 10 34 →= 66 27 29 6 10 10 34 , 65 5 6 10 10 10 35 →= 66 27 29 6 10 10 35 , 65 5 6 10 10 10 36 →= 66 27 29 6 10 10 36 , 67 5 6 10 10 10 10 →= 68 27 29 6 10 10 10 , 67 5 6 10 10 10 33 →= 68 27 29 6 10 10 33 , 67 5 6 10 10 10 34 →= 68 27 29 6 10 10 34 , 67 5 6 10 10 10 35 →= 68 27 29 6 10 10 35 , 67 5 6 10 10 10 36 →= 68 27 29 6 10 10 36 , 69 5 6 10 10 10 10 →= 70 27 29 6 10 10 10 , 69 5 6 10 10 10 33 →= 70 27 29 6 10 10 33 , 69 5 6 10 10 10 34 →= 70 27 29 6 10 10 34 , 69 5 6 10 10 10 35 →= 70 27 29 6 10 10 35 , 69 5 6 10 10 10 36 →= 70 27 29 6 10 10 36 , 71 5 6 10 10 10 10 →= 72 27 29 6 10 10 10 , 71 5 6 10 10 10 33 →= 72 27 29 6 10 10 33 , 71 5 6 10 10 10 34 →= 72 27 29 6 10 10 34 , 71 5 6 10 10 10 35 →= 72 27 29 6 10 10 35 , 71 5 6 10 10 10 36 →= 72 27 29 6 10 10 36 , 73 5 6 10 10 10 10 →= 74 27 29 6 10 10 10 , 73 5 6 10 10 10 33 →= 74 27 29 6 10 10 33 , 73 5 6 10 10 10 34 →= 74 27 29 6 10 10 34 , 73 5 6 10 10 10 35 →= 74 27 29 6 10 10 35 , 73 5 6 10 10 10 36 →= 74 27 29 6 10 10 36 , 14 5 6 10 10 34 13 →= 12 27 29 6 10 34 13 , 14 5 6 10 10 34 37 →= 12 27 29 6 10 34 37 , 14 5 6 10 10 34 38 →= 12 27 29 6 10 34 38 , 14 5 6 10 10 34 4 →= 12 27 29 6 10 34 4 , 63 5 6 10 10 34 13 →= 64 27 29 6 10 34 13 , 63 5 6 10 10 34 37 →= 64 27 29 6 10 34 37 , 63 5 6 10 10 34 38 →= 64 27 29 6 10 34 38 , 63 5 6 10 10 34 4 →= 64 27 29 6 10 34 4 , 4 5 6 10 10 34 13 →= 13 27 29 6 10 34 13 , 4 5 6 10 10 34 37 →= 13 27 29 6 10 34 37 , 4 5 6 10 10 34 38 →= 13 27 29 6 10 34 38 , 4 5 6 10 10 34 4 →= 13 27 29 6 10 34 4 , 65 5 6 10 10 34 13 →= 66 27 29 6 10 34 13 , 65 5 6 10 10 34 37 →= 66 27 29 6 10 34 37 , 65 5 6 10 10 34 38 →= 66 27 29 6 10 34 38 , 65 5 6 10 10 34 4 →= 66 27 29 6 10 34 4 , 67 5 6 10 10 34 13 →= 68 27 29 6 10 34 13 , 67 5 6 10 10 34 37 →= 68 27 29 6 10 34 37 , 67 5 6 10 10 34 38 →= 68 27 29 6 10 34 38 , 67 5 6 10 10 34 4 →= 68 27 29 6 10 34 4 , 69 5 6 10 10 34 13 →= 70 27 29 6 10 34 13 , 69 5 6 10 10 34 37 →= 70 27 29 6 10 34 37 , 69 5 6 10 10 34 38 →= 70 27 29 6 10 34 38 , 69 5 6 10 10 34 4 →= 70 27 29 6 10 34 4 , 71 5 6 10 10 34 13 →= 72 27 29 6 10 34 13 , 71 5 6 10 10 34 37 →= 72 27 29 6 10 34 37 , 71 5 6 10 10 34 38 →= 72 27 29 6 10 34 38 , 71 5 6 10 10 34 4 →= 72 27 29 6 10 34 4 , 73 5 6 10 10 34 13 →= 74 27 29 6 10 34 13 , 73 5 6 10 10 34 37 →= 74 27 29 6 10 34 37 , 73 5 6 10 10 34 38 →= 74 27 29 6 10 34 38 , 73 5 6 10 10 34 4 →= 74 27 29 6 10 34 4 , 14 5 6 10 10 33 39 →= 12 27 29 6 10 33 39 , 14 5 6 10 10 33 40 →= 12 27 29 6 10 33 40 , 63 5 6 10 10 33 39 →= 64 27 29 6 10 33 39 , 63 5 6 10 10 33 40 →= 64 27 29 6 10 33 40 , 4 5 6 10 10 33 39 →= 13 27 29 6 10 33 39 , 4 5 6 10 10 33 40 →= 13 27 29 6 10 33 40 , 65 5 6 10 10 33 39 →= 66 27 29 6 10 33 39 , 65 5 6 10 10 33 40 →= 66 27 29 6 10 33 40 , 67 5 6 10 10 33 39 →= 68 27 29 6 10 33 39 , 67 5 6 10 10 33 40 →= 68 27 29 6 10 33 40 , 69 5 6 10 10 33 39 →= 70 27 29 6 10 33 39 , 69 5 6 10 10 33 40 →= 70 27 29 6 10 33 40 , 71 5 6 10 10 33 39 →= 72 27 29 6 10 33 39 , 71 5 6 10 10 33 40 →= 72 27 29 6 10 33 40 , 73 5 6 10 10 33 39 →= 74 27 29 6 10 33 39 , 73 5 6 10 10 33 40 →= 74 27 29 6 10 33 40 , 14 5 6 10 10 35 41 →= 12 27 29 6 10 35 41 , 63 5 6 10 10 35 41 →= 64 27 29 6 10 35 41 , 4 5 6 10 10 35 41 →= 13 27 29 6 10 35 41 , 65 5 6 10 10 35 41 →= 66 27 29 6 10 35 41 , 67 5 6 10 10 35 41 →= 68 27 29 6 10 35 41 , 69 5 6 10 10 35 41 →= 70 27 29 6 10 35 41 , 71 5 6 10 10 35 41 →= 72 27 29 6 10 35 41 , 73 5 6 10 10 35 41 →= 74 27 29 6 10 35 41 , 27 29 6 10 10 10 10 →= 30 31 29 6 10 10 10 , 27 29 6 10 10 10 33 →= 30 31 29 6 10 10 33 , 27 29 6 10 10 10 34 →= 30 31 29 6 10 10 34 , 27 29 6 10 10 10 35 →= 30 31 29 6 10 10 35 , 27 29 6 10 10 10 36 →= 30 31 29 6 10 10 36 , 75 29 6 10 10 10 10 →= 76 31 29 6 10 10 10 , 75 29 6 10 10 10 33 →= 76 31 29 6 10 10 33 , 75 29 6 10 10 10 34 →= 76 31 29 6 10 10 34 , 75 29 6 10 10 10 35 →= 76 31 29 6 10 10 35 , 75 29 6 10 10 10 36 →= 76 31 29 6 10 10 36 , 31 29 6 10 10 10 10 →= 32 31 29 6 10 10 10 , 31 29 6 10 10 10 33 →= 32 31 29 6 10 10 33 , 31 29 6 10 10 10 34 →= 32 31 29 6 10 10 34 , 31 29 6 10 10 10 35 →= 32 31 29 6 10 10 35 , 31 29 6 10 10 10 36 →= 32 31 29 6 10 10 36 , 77 29 6 10 10 10 10 →= 78 31 29 6 10 10 10 , 77 29 6 10 10 10 33 →= 78 31 29 6 10 10 33 , 77 29 6 10 10 10 34 →= 78 31 29 6 10 10 34 , 77 29 6 10 10 10 35 →= 78 31 29 6 10 10 35 , 77 29 6 10 10 10 36 →= 78 31 29 6 10 10 36 , 79 29 6 10 10 10 10 →= 80 31 29 6 10 10 10 , 79 29 6 10 10 10 33 →= 80 31 29 6 10 10 33 , 79 29 6 10 10 10 34 →= 80 31 29 6 10 10 34 , 79 29 6 10 10 10 35 →= 80 31 29 6 10 10 35 , 79 29 6 10 10 10 36 →= 80 31 29 6 10 10 36 , 52 29 6 10 10 10 10 →= 81 31 29 6 10 10 10 , 52 29 6 10 10 10 33 →= 81 31 29 6 10 10 33 , 52 29 6 10 10 10 34 →= 81 31 29 6 10 10 34 , 52 29 6 10 10 10 35 →= 81 31 29 6 10 10 35 , 52 29 6 10 10 10 36 →= 81 31 29 6 10 10 36 , 57 29 6 10 10 10 10 →= 82 31 29 6 10 10 10 , 57 29 6 10 10 10 33 →= 82 31 29 6 10 10 33 , 57 29 6 10 10 10 34 →= 82 31 29 6 10 10 34 , 57 29 6 10 10 10 35 →= 82 31 29 6 10 10 35 , 57 29 6 10 10 10 36 →= 82 31 29 6 10 10 36 , 61 29 6 10 10 10 10 →= 83 31 29 6 10 10 10 , 61 29 6 10 10 10 33 →= 83 31 29 6 10 10 33 , 61 29 6 10 10 10 34 →= 83 31 29 6 10 10 34 , 61 29 6 10 10 10 35 →= 83 31 29 6 10 10 35 , 61 29 6 10 10 10 36 →= 83 31 29 6 10 10 36 , 27 29 6 10 10 34 13 →= 30 31 29 6 10 34 13 , 27 29 6 10 10 34 37 →= 30 31 29 6 10 34 37 , 27 29 6 10 10 34 38 →= 30 31 29 6 10 34 38 , 27 29 6 10 10 34 4 →= 30 31 29 6 10 34 4 , 75 29 6 10 10 34 13 →= 76 31 29 6 10 34 13 , 75 29 6 10 10 34 37 →= 76 31 29 6 10 34 37 , 75 29 6 10 10 34 38 →= 76 31 29 6 10 34 38 , 75 29 6 10 10 34 4 →= 76 31 29 6 10 34 4 , 31 29 6 10 10 34 13 →= 32 31 29 6 10 34 13 , 31 29 6 10 10 34 37 →= 32 31 29 6 10 34 37 , 31 29 6 10 10 34 38 →= 32 31 29 6 10 34 38 , 31 29 6 10 10 34 4 →= 32 31 29 6 10 34 4 , 77 29 6 10 10 34 13 →= 78 31 29 6 10 34 13 , 77 29 6 10 10 34 37 →= 78 31 29 6 10 34 37 , 77 29 6 10 10 34 38 →= 78 31 29 6 10 34 38 , 77 29 6 10 10 34 4 →= 78 31 29 6 10 34 4 , 79 29 6 10 10 34 13 →= 80 31 29 6 10 34 13 , 79 29 6 10 10 34 37 →= 80 31 29 6 10 34 37 , 79 29 6 10 10 34 38 →= 80 31 29 6 10 34 38 , 79 29 6 10 10 34 4 →= 80 31 29 6 10 34 4 , 52 29 6 10 10 34 13 →= 81 31 29 6 10 34 13 , 52 29 6 10 10 34 37 →= 81 31 29 6 10 34 37 , 52 29 6 10 10 34 38 →= 81 31 29 6 10 34 38 , 52 29 6 10 10 34 4 →= 81 31 29 6 10 34 4 , 57 29 6 10 10 34 13 →= 82 31 29 6 10 34 13 , 57 29 6 10 10 34 37 →= 82 31 29 6 10 34 37 , 57 29 6 10 10 34 38 →= 82 31 29 6 10 34 38 , 57 29 6 10 10 34 4 →= 82 31 29 6 10 34 4 , 61 29 6 10 10 34 13 →= 83 31 29 6 10 34 13 , 61 29 6 10 10 34 37 →= 83 31 29 6 10 34 37 , 61 29 6 10 10 34 38 →= 83 31 29 6 10 34 38 , 61 29 6 10 10 34 4 →= 83 31 29 6 10 34 4 , 27 29 6 10 10 33 39 →= 30 31 29 6 10 33 39 , 27 29 6 10 10 33 40 →= 30 31 29 6 10 33 40 , 75 29 6 10 10 33 39 →= 76 31 29 6 10 33 39 , 75 29 6 10 10 33 40 →= 76 31 29 6 10 33 40 , 31 29 6 10 10 33 39 →= 32 31 29 6 10 33 39 , 31 29 6 10 10 33 40 →= 32 31 29 6 10 33 40 , 77 29 6 10 10 33 39 →= 78 31 29 6 10 33 39 , 77 29 6 10 10 33 40 →= 78 31 29 6 10 33 40 , 79 29 6 10 10 33 39 →= 80 31 29 6 10 33 39 , 79 29 6 10 10 33 40 →= 80 31 29 6 10 33 40 , 52 29 6 10 10 33 39 →= 81 31 29 6 10 33 39 , 52 29 6 10 10 33 40 →= 81 31 29 6 10 33 40 , 57 29 6 10 10 33 39 →= 82 31 29 6 10 33 39 , 57 29 6 10 10 33 40 →= 82 31 29 6 10 33 40 , 61 29 6 10 10 33 39 →= 83 31 29 6 10 33 39 , 61 29 6 10 10 33 40 →= 83 31 29 6 10 33 40 , 27 29 6 10 10 35 41 →= 30 31 29 6 10 35 41 , 75 29 6 10 10 35 41 →= 76 31 29 6 10 35 41 , 31 29 6 10 10 35 41 →= 32 31 29 6 10 35 41 , 77 29 6 10 10 35 41 →= 78 31 29 6 10 35 41 , 79 29 6 10 10 35 41 →= 80 31 29 6 10 35 41 , 52 29 6 10 10 35 41 →= 81 31 29 6 10 35 41 , 57 29 6 10 10 35 41 →= 82 31 29 6 10 35 41 , 61 29 6 10 10 35 41 →= 83 31 29 6 10 35 41 , 84 42 6 10 10 10 10 →= 85 75 29 6 10 10 10 , 84 42 6 10 10 10 33 →= 85 75 29 6 10 10 33 , 84 42 6 10 10 10 34 →= 85 75 29 6 10 10 34 , 84 42 6 10 10 10 35 →= 85 75 29 6 10 10 35 , 84 42 6 10 10 10 36 →= 85 75 29 6 10 10 36 , 86 42 6 10 10 10 10 →= 87 75 29 6 10 10 10 , 86 42 6 10 10 10 33 →= 87 75 29 6 10 10 33 , 86 42 6 10 10 10 34 →= 87 75 29 6 10 10 34 , 86 42 6 10 10 10 35 →= 87 75 29 6 10 10 35 , 86 42 6 10 10 10 36 →= 87 75 29 6 10 10 36 , 84 42 6 10 10 34 13 →= 85 75 29 6 10 34 13 , 84 42 6 10 10 34 37 →= 85 75 29 6 10 34 37 , 84 42 6 10 10 34 38 →= 85 75 29 6 10 34 38 , 84 42 6 10 10 34 4 →= 85 75 29 6 10 34 4 , 86 42 6 10 10 34 13 →= 87 75 29 6 10 34 13 , 86 42 6 10 10 34 37 →= 87 75 29 6 10 34 37 , 86 42 6 10 10 34 38 →= 87 75 29 6 10 34 38 , 86 42 6 10 10 34 4 →= 87 75 29 6 10 34 4 , 84 42 6 10 10 33 39 →= 85 75 29 6 10 33 39 , 84 42 6 10 10 33 40 →= 85 75 29 6 10 33 40 , 86 42 6 10 10 33 39 →= 87 75 29 6 10 33 39 , 86 42 6 10 10 33 40 →= 87 75 29 6 10 33 40 , 84 42 6 10 10 35 41 →= 85 75 29 6 10 35 41 , 86 42 6 10 10 35 41 →= 87 75 29 6 10 35 41 , 88 44 6 10 10 10 10 →= 89 77 29 6 10 10 10 , 88 44 6 10 10 10 33 →= 89 77 29 6 10 10 33 , 88 44 6 10 10 10 34 →= 89 77 29 6 10 10 34 , 88 44 6 10 10 10 35 →= 89 77 29 6 10 10 35 , 88 44 6 10 10 10 36 →= 89 77 29 6 10 10 36 , 88 44 6 10 10 34 13 →= 89 77 29 6 10 34 13 , 88 44 6 10 10 34 37 →= 89 77 29 6 10 34 37 , 88 44 6 10 10 34 38 →= 89 77 29 6 10 34 38 , 88 44 6 10 10 34 4 →= 89 77 29 6 10 34 4 , 6 10 10 10 34 4 11 →= 3 4 5 6 34 4 11 , 6 10 10 10 34 4 5 →= 3 4 5 6 34 4 5 , 6 10 10 10 34 4 90 →= 3 4 5 6 34 4 90 , 6 10 10 10 34 13 27 →= 3 4 5 6 34 13 27 , 6 10 10 10 34 13 30 →= 3 4 5 6 34 13 30 , 6 10 10 10 34 13 91 →= 3 4 5 6 34 13 91 , 6 10 10 10 34 37 92 →= 3 4 5 6 34 37 92 , 42 6 10 10 34 4 11 →= 43 14 5 6 34 4 11 , 42 6 10 10 34 4 5 →= 43 14 5 6 34 4 5 , 42 6 10 10 34 4 90 →= 43 14 5 6 34 4 90 , 29 6 10 10 34 4 11 →= 28 14 5 6 34 4 11 , 29 6 10 10 34 4 5 →= 28 14 5 6 34 4 5 , 29 6 10 10 34 4 90 →= 28 14 5 6 34 4 90 , 44 6 10 10 34 4 11 →= 45 14 5 6 34 4 11 , 44 6 10 10 34 4 5 →= 45 14 5 6 34 4 5 , 44 6 10 10 34 4 90 →= 45 14 5 6 34 4 90 , 2 6 10 10 34 4 11 →= 46 14 5 6 34 4 11 , 2 6 10 10 34 4 5 →= 46 14 5 6 34 4 5 , 2 6 10 10 34 4 90 →= 46 14 5 6 34 4 90 , 47 6 10 10 34 4 11 →= 48 14 5 6 34 4 11 , 47 6 10 10 34 4 5 →= 48 14 5 6 34 4 5 , 47 6 10 10 34 4 90 →= 48 14 5 6 34 4 90 , 17 6 10 10 34 4 11 →= 49 14 5 6 34 4 11 , 17 6 10 10 34 4 5 →= 49 14 5 6 34 4 5 , 17 6 10 10 34 4 90 →= 49 14 5 6 34 4 90 , 23 6 10 10 34 4 11 →= 50 14 5 6 34 4 11 , 23 6 10 10 34 4 5 →= 50 14 5 6 34 4 5 , 23 6 10 10 34 4 90 →= 50 14 5 6 34 4 90 , 5 6 10 10 34 4 11 →= 11 14 5 6 34 4 11 , 5 6 10 10 34 4 5 →= 11 14 5 6 34 4 5 , 5 6 10 10 34 4 90 →= 11 14 5 6 34 4 90 , 42 6 10 10 34 13 27 →= 43 14 5 6 34 13 27 , 42 6 10 10 34 13 30 →= 43 14 5 6 34 13 30 , 42 6 10 10 34 13 91 →= 43 14 5 6 34 13 91 , 29 6 10 10 34 13 27 →= 28 14 5 6 34 13 27 , 29 6 10 10 34 13 30 →= 28 14 5 6 34 13 30 , 29 6 10 10 34 13 91 →= 28 14 5 6 34 13 91 , 44 6 10 10 34 13 27 →= 45 14 5 6 34 13 27 , 44 6 10 10 34 13 30 →= 45 14 5 6 34 13 30 , 44 6 10 10 34 13 91 →= 45 14 5 6 34 13 91 , 2 6 10 10 34 13 27 →= 46 14 5 6 34 13 27 , 2 6 10 10 34 13 30 →= 46 14 5 6 34 13 30 , 2 6 10 10 34 13 91 →= 46 14 5 6 34 13 91 , 47 6 10 10 34 13 27 →= 48 14 5 6 34 13 27 , 47 6 10 10 34 13 30 →= 48 14 5 6 34 13 30 , 47 6 10 10 34 13 91 →= 48 14 5 6 34 13 91 , 17 6 10 10 34 13 27 →= 49 14 5 6 34 13 27 , 17 6 10 10 34 13 30 →= 49 14 5 6 34 13 30 , 17 6 10 10 34 13 91 →= 49 14 5 6 34 13 91 , 23 6 10 10 34 13 27 →= 50 14 5 6 34 13 27 , 23 6 10 10 34 13 30 →= 50 14 5 6 34 13 30 , 23 6 10 10 34 13 91 →= 50 14 5 6 34 13 91 , 5 6 10 10 34 13 27 →= 11 14 5 6 34 13 27 , 5 6 10 10 34 13 30 →= 11 14 5 6 34 13 30 , 5 6 10 10 34 13 91 →= 11 14 5 6 34 13 91 , 42 6 10 10 34 37 92 →= 43 14 5 6 34 37 92 , 29 6 10 10 34 37 92 →= 28 14 5 6 34 37 92 , 44 6 10 10 34 37 92 →= 45 14 5 6 34 37 92 , 2 6 10 10 34 37 92 →= 46 14 5 6 34 37 92 , 47 6 10 10 34 37 92 →= 48 14 5 6 34 37 92 , 17 6 10 10 34 37 92 →= 49 14 5 6 34 37 92 , 23 6 10 10 34 37 92 →= 50 14 5 6 34 37 92 , 5 6 10 10 34 37 92 →= 11 14 5 6 34 37 92 , 1 2 6 10 34 4 11 →= 51 52 29 6 34 4 11 , 1 2 6 10 34 4 5 →= 51 52 29 6 34 4 5 , 1 2 6 10 34 4 90 →= 51 52 29 6 34 4 90 , 53 2 6 10 34 4 11 →= 54 52 29 6 34 4 11 , 53 2 6 10 34 4 5 →= 54 52 29 6 34 4 5 , 53 2 6 10 34 4 90 →= 54 52 29 6 34 4 90 , 1 2 6 10 34 13 27 →= 51 52 29 6 34 13 27 , 1 2 6 10 34 13 30 →= 51 52 29 6 34 13 30 , 1 2 6 10 34 13 91 →= 51 52 29 6 34 13 91 , 53 2 6 10 34 13 27 →= 54 52 29 6 34 13 27 , 53 2 6 10 34 13 30 →= 54 52 29 6 34 13 30 , 53 2 6 10 34 13 91 →= 54 52 29 6 34 13 91 , 1 2 6 10 34 37 92 →= 51 52 29 6 34 37 92 , 53 2 6 10 34 37 92 →= 54 52 29 6 34 37 92 , 55 17 6 10 34 4 11 →= 56 57 29 6 34 4 11 , 55 17 6 10 34 4 5 →= 56 57 29 6 34 4 5 , 55 17 6 10 34 4 90 →= 56 57 29 6 34 4 90 , 16 17 6 10 34 4 11 →= 58 57 29 6 34 4 11 , 16 17 6 10 34 4 5 →= 58 57 29 6 34 4 5 , 16 17 6 10 34 4 90 →= 58 57 29 6 34 4 90 , 55 17 6 10 34 13 27 →= 56 57 29 6 34 13 27 , 55 17 6 10 34 13 30 →= 56 57 29 6 34 13 30 , 55 17 6 10 34 13 91 →= 56 57 29 6 34 13 91 , 16 17 6 10 34 13 27 →= 58 57 29 6 34 13 27 , 16 17 6 10 34 13 30 →= 58 57 29 6 34 13 30 , 16 17 6 10 34 13 91 →= 58 57 29 6 34 13 91 , 55 17 6 10 34 37 92 →= 56 57 29 6 34 37 92 , 16 17 6 10 34 37 92 →= 58 57 29 6 34 37 92 , 59 23 6 10 34 4 11 →= 60 61 29 6 34 4 11 , 59 23 6 10 34 4 5 →= 60 61 29 6 34 4 5 , 59 23 6 10 34 4 90 →= 60 61 29 6 34 4 90 , 22 23 6 10 34 4 11 →= 62 61 29 6 34 4 11 , 22 23 6 10 34 4 5 →= 62 61 29 6 34 4 5 , 22 23 6 10 34 4 90 →= 62 61 29 6 34 4 90 , 59 23 6 10 34 13 27 →= 60 61 29 6 34 13 27 , 59 23 6 10 34 13 30 →= 60 61 29 6 34 13 30 , 59 23 6 10 34 13 91 →= 60 61 29 6 34 13 91 , 22 23 6 10 34 13 27 →= 62 61 29 6 34 13 27 , 22 23 6 10 34 13 30 →= 62 61 29 6 34 13 30 , 22 23 6 10 34 13 91 →= 62 61 29 6 34 13 91 , 59 23 6 10 34 37 92 →= 60 61 29 6 34 37 92 , 22 23 6 10 34 37 92 →= 62 61 29 6 34 37 92 , 14 5 6 10 34 4 11 →= 12 27 29 6 34 4 11 , 14 5 6 10 34 4 5 →= 12 27 29 6 34 4 5 , 14 5 6 10 34 4 90 →= 12 27 29 6 34 4 90 , 63 5 6 10 34 4 11 →= 64 27 29 6 34 4 11 , 63 5 6 10 34 4 5 →= 64 27 29 6 34 4 5 , 63 5 6 10 34 4 90 →= 64 27 29 6 34 4 90 , 4 5 6 10 34 4 11 →= 13 27 29 6 34 4 11 , 4 5 6 10 34 4 5 →= 13 27 29 6 34 4 5 , 4 5 6 10 34 4 90 →= 13 27 29 6 34 4 90 , 65 5 6 10 34 4 11 →= 66 27 29 6 34 4 11 , 65 5 6 10 34 4 5 →= 66 27 29 6 34 4 5 , 65 5 6 10 34 4 90 →= 66 27 29 6 34 4 90 , 67 5 6 10 34 4 11 →= 68 27 29 6 34 4 11 , 67 5 6 10 34 4 5 →= 68 27 29 6 34 4 5 , 67 5 6 10 34 4 90 →= 68 27 29 6 34 4 90 , 69 5 6 10 34 4 11 →= 70 27 29 6 34 4 11 , 69 5 6 10 34 4 5 →= 70 27 29 6 34 4 5 , 69 5 6 10 34 4 90 →= 70 27 29 6 34 4 90 , 71 5 6 10 34 4 11 →= 72 27 29 6 34 4 11 , 71 5 6 10 34 4 5 →= 72 27 29 6 34 4 5 , 71 5 6 10 34 4 90 →= 72 27 29 6 34 4 90 , 73 5 6 10 34 4 11 →= 74 27 29 6 34 4 11 , 73 5 6 10 34 4 5 →= 74 27 29 6 34 4 5 , 73 5 6 10 34 4 90 →= 74 27 29 6 34 4 90 , 14 5 6 10 34 13 27 →= 12 27 29 6 34 13 27 , 14 5 6 10 34 13 30 →= 12 27 29 6 34 13 30 , 14 5 6 10 34 13 91 →= 12 27 29 6 34 13 91 , 63 5 6 10 34 13 27 →= 64 27 29 6 34 13 27 , 63 5 6 10 34 13 30 →= 64 27 29 6 34 13 30 , 63 5 6 10 34 13 91 →= 64 27 29 6 34 13 91 , 4 5 6 10 34 13 27 →= 13 27 29 6 34 13 27 , 4 5 6 10 34 13 30 →= 13 27 29 6 34 13 30 , 4 5 6 10 34 13 91 →= 13 27 29 6 34 13 91 , 65 5 6 10 34 13 27 →= 66 27 29 6 34 13 27 , 65 5 6 10 34 13 30 →= 66 27 29 6 34 13 30 , 65 5 6 10 34 13 91 →= 66 27 29 6 34 13 91 , 67 5 6 10 34 13 27 →= 68 27 29 6 34 13 27 , 67 5 6 10 34 13 30 →= 68 27 29 6 34 13 30 , 67 5 6 10 34 13 91 →= 68 27 29 6 34 13 91 , 69 5 6 10 34 13 27 →= 70 27 29 6 34 13 27 , 69 5 6 10 34 13 30 →= 70 27 29 6 34 13 30 , 69 5 6 10 34 13 91 →= 70 27 29 6 34 13 91 , 71 5 6 10 34 13 27 →= 72 27 29 6 34 13 27 , 71 5 6 10 34 13 30 →= 72 27 29 6 34 13 30 , 71 5 6 10 34 13 91 →= 72 27 29 6 34 13 91 , 73 5 6 10 34 13 27 →= 74 27 29 6 34 13 27 , 73 5 6 10 34 13 30 →= 74 27 29 6 34 13 30 , 73 5 6 10 34 13 91 →= 74 27 29 6 34 13 91 , 14 5 6 10 34 37 92 →= 12 27 29 6 34 37 92 , 63 5 6 10 34 37 92 →= 64 27 29 6 34 37 92 , 4 5 6 10 34 37 92 →= 13 27 29 6 34 37 92 , 65 5 6 10 34 37 92 →= 66 27 29 6 34 37 92 , 67 5 6 10 34 37 92 →= 68 27 29 6 34 37 92 , 69 5 6 10 34 37 92 →= 70 27 29 6 34 37 92 , 71 5 6 10 34 37 92 →= 72 27 29 6 34 37 92 , 73 5 6 10 34 37 92 →= 74 27 29 6 34 37 92 , 27 29 6 10 34 4 11 →= 30 31 29 6 34 4 11 , 27 29 6 10 34 4 5 →= 30 31 29 6 34 4 5 , 27 29 6 10 34 4 90 →= 30 31 29 6 34 4 90 , 75 29 6 10 34 4 11 →= 76 31 29 6 34 4 11 , 75 29 6 10 34 4 5 →= 76 31 29 6 34 4 5 , 75 29 6 10 34 4 90 →= 76 31 29 6 34 4 90 , 31 29 6 10 34 4 11 →= 32 31 29 6 34 4 11 , 31 29 6 10 34 4 5 →= 32 31 29 6 34 4 5 , 31 29 6 10 34 4 90 →= 32 31 29 6 34 4 90 , 77 29 6 10 34 4 11 →= 78 31 29 6 34 4 11 , 77 29 6 10 34 4 5 →= 78 31 29 6 34 4 5 , 77 29 6 10 34 4 90 →= 78 31 29 6 34 4 90 , 79 29 6 10 34 4 11 →= 80 31 29 6 34 4 11 , 79 29 6 10 34 4 5 →= 80 31 29 6 34 4 5 , 79 29 6 10 34 4 90 →= 80 31 29 6 34 4 90 , 52 29 6 10 34 4 11 →= 81 31 29 6 34 4 11 , 52 29 6 10 34 4 5 →= 81 31 29 6 34 4 5 , 52 29 6 10 34 4 90 →= 81 31 29 6 34 4 90 , 57 29 6 10 34 4 11 →= 82 31 29 6 34 4 11 , 57 29 6 10 34 4 5 →= 82 31 29 6 34 4 5 , 57 29 6 10 34 4 90 →= 82 31 29 6 34 4 90 , 61 29 6 10 34 4 11 →= 83 31 29 6 34 4 11 , 61 29 6 10 34 4 5 →= 83 31 29 6 34 4 5 , 61 29 6 10 34 4 90 →= 83 31 29 6 34 4 90 , 27 29 6 10 34 13 27 →= 30 31 29 6 34 13 27 , 27 29 6 10 34 13 30 →= 30 31 29 6 34 13 30 , 27 29 6 10 34 13 91 →= 30 31 29 6 34 13 91 , 75 29 6 10 34 13 27 →= 76 31 29 6 34 13 27 , 75 29 6 10 34 13 30 →= 76 31 29 6 34 13 30 , 75 29 6 10 34 13 91 →= 76 31 29 6 34 13 91 , 31 29 6 10 34 13 27 →= 32 31 29 6 34 13 27 , 31 29 6 10 34 13 30 →= 32 31 29 6 34 13 30 , 31 29 6 10 34 13 91 →= 32 31 29 6 34 13 91 , 77 29 6 10 34 13 27 →= 78 31 29 6 34 13 27 , 77 29 6 10 34 13 30 →= 78 31 29 6 34 13 30 , 77 29 6 10 34 13 91 →= 78 31 29 6 34 13 91 , 79 29 6 10 34 13 27 →= 80 31 29 6 34 13 27 , 79 29 6 10 34 13 30 →= 80 31 29 6 34 13 30 , 79 29 6 10 34 13 91 →= 80 31 29 6 34 13 91 , 52 29 6 10 34 13 27 →= 81 31 29 6 34 13 27 , 52 29 6 10 34 13 30 →= 81 31 29 6 34 13 30 , 52 29 6 10 34 13 91 →= 81 31 29 6 34 13 91 , 57 29 6 10 34 13 27 →= 82 31 29 6 34 13 27 , 57 29 6 10 34 13 30 →= 82 31 29 6 34 13 30 , 57 29 6 10 34 13 91 →= 82 31 29 6 34 13 91 , 61 29 6 10 34 13 27 →= 83 31 29 6 34 13 27 , 61 29 6 10 34 13 30 →= 83 31 29 6 34 13 30 , 61 29 6 10 34 13 91 →= 83 31 29 6 34 13 91 , 27 29 6 10 34 37 92 →= 30 31 29 6 34 37 92 , 75 29 6 10 34 37 92 →= 76 31 29 6 34 37 92 , 31 29 6 10 34 37 92 →= 32 31 29 6 34 37 92 , 77 29 6 10 34 37 92 →= 78 31 29 6 34 37 92 , 79 29 6 10 34 37 92 →= 80 31 29 6 34 37 92 , 52 29 6 10 34 37 92 →= 81 31 29 6 34 37 92 , 57 29 6 10 34 37 92 →= 82 31 29 6 34 37 92 , 61 29 6 10 34 37 92 →= 83 31 29 6 34 37 92 , 84 42 6 10 34 4 11 →= 85 75 29 6 34 4 11 , 84 42 6 10 34 4 5 →= 85 75 29 6 34 4 5 , 84 42 6 10 34 4 90 →= 85 75 29 6 34 4 90 , 86 42 6 10 34 4 11 →= 87 75 29 6 34 4 11 , 86 42 6 10 34 4 5 →= 87 75 29 6 34 4 5 , 86 42 6 10 34 4 90 →= 87 75 29 6 34 4 90 , 84 42 6 10 34 13 27 →= 85 75 29 6 34 13 27 , 84 42 6 10 34 13 30 →= 85 75 29 6 34 13 30 , 84 42 6 10 34 13 91 →= 85 75 29 6 34 13 91 , 86 42 6 10 34 13 27 →= 87 75 29 6 34 13 27 , 86 42 6 10 34 13 30 →= 87 75 29 6 34 13 30 , 86 42 6 10 34 13 91 →= 87 75 29 6 34 13 91 , 84 42 6 10 34 37 92 →= 85 75 29 6 34 37 92 , 86 42 6 10 34 37 92 →= 87 75 29 6 34 37 92 , 88 44 6 10 34 4 11 →= 89 77 29 6 34 4 11 , 88 44 6 10 34 4 5 →= 89 77 29 6 34 4 5 , 88 44 6 10 34 4 90 →= 89 77 29 6 34 4 90 , 88 44 6 10 34 13 27 →= 89 77 29 6 34 13 27 , 88 44 6 10 34 13 30 →= 89 77 29 6 34 13 30 , 88 44 6 10 34 13 91 →= 89 77 29 6 34 13 91 , 6 10 10 10 33 39 93 →= 3 4 5 6 33 39 93 , 42 6 10 10 33 39 93 →= 43 14 5 6 33 39 93 , 29 6 10 10 33 39 93 →= 28 14 5 6 33 39 93 , 44 6 10 10 33 39 93 →= 45 14 5 6 33 39 93 , 2 6 10 10 33 39 93 →= 46 14 5 6 33 39 93 , 47 6 10 10 33 39 93 →= 48 14 5 6 33 39 93 , 17 6 10 10 33 39 93 →= 49 14 5 6 33 39 93 , 23 6 10 10 33 39 93 →= 50 14 5 6 33 39 93 , 5 6 10 10 33 39 93 →= 11 14 5 6 33 39 93 , 14 5 6 10 33 39 93 →= 12 27 29 6 33 39 93 , 63 5 6 10 33 39 93 →= 64 27 29 6 33 39 93 , 4 5 6 10 33 39 93 →= 13 27 29 6 33 39 93 , 65 5 6 10 33 39 93 →= 66 27 29 6 33 39 93 , 67 5 6 10 33 39 93 →= 68 27 29 6 33 39 93 , 69 5 6 10 33 39 93 →= 70 27 29 6 33 39 93 , 71 5 6 10 33 39 93 →= 72 27 29 6 33 39 93 , 73 5 6 10 33 39 93 →= 74 27 29 6 33 39 93 , 27 29 6 10 33 39 93 →= 30 31 29 6 33 39 93 , 75 29 6 10 33 39 93 →= 76 31 29 6 33 39 93 , 31 29 6 10 33 39 93 →= 32 31 29 6 33 39 93 , 77 29 6 10 33 39 93 →= 78 31 29 6 33 39 93 , 79 29 6 10 33 39 93 →= 80 31 29 6 33 39 93 , 52 29 6 10 33 39 93 →= 81 31 29 6 33 39 93 , 57 29 6 10 33 39 93 →= 82 31 29 6 33 39 93 , 61 29 6 10 33 39 93 →= 83 31 29 6 33 39 93 , 34 4 5 3 4 5 6 →= 10 10 34 4 5 6 10 , 34 4 5 3 4 11 12 →= 10 10 34 4 5 3 13 , 34 4 5 3 4 11 14 →= 10 10 34 4 5 3 4 , 51 52 29 3 4 5 6 →= 1 2 3 4 5 6 10 , 54 52 29 3 4 5 6 →= 53 2 3 4 5 6 10 , 51 52 29 3 4 11 12 →= 1 2 3 4 5 3 13 , 51 52 29 3 4 11 14 →= 1 2 3 4 5 3 4 , 54 52 29 3 4 11 12 →= 53 2 3 4 5 3 13 , 54 52 29 3 4 11 14 →= 53 2 3 4 5 3 4 , 56 57 29 3 4 5 6 →= 55 17 3 4 5 6 10 , 58 57 29 3 4 5 6 →= 16 17 3 4 5 6 10 , 56 57 29 3 4 11 12 →= 55 17 3 4 5 3 13 , 56 57 29 3 4 11 14 →= 55 17 3 4 5 3 4 , 58 57 29 3 4 11 12 →= 16 17 3 4 5 3 13 , 58 57 29 3 4 11 14 →= 16 17 3 4 5 3 4 , 60 61 29 3 4 5 6 →= 59 23 3 4 5 6 10 , 62 61 29 3 4 5 6 →= 22 23 3 4 5 6 10 , 60 61 29 3 4 11 12 →= 59 23 3 4 5 3 13 , 60 61 29 3 4 11 14 →= 59 23 3 4 5 3 4 , 62 61 29 3 4 11 12 →= 22 23 3 4 5 3 13 , 62 61 29 3 4 11 14 →= 22 23 3 4 5 3 4 , 12 27 29 3 4 5 6 →= 14 5 3 4 5 6 10 , 64 27 29 3 4 5 6 →= 63 5 3 4 5 6 10 , 13 27 29 3 4 5 6 →= 4 5 3 4 5 6 10 , 66 27 29 3 4 5 6 →= 65 5 3 4 5 6 10 , 68 27 29 3 4 5 6 →= 67 5 3 4 5 6 10 , 70 27 29 3 4 5 6 →= 69 5 3 4 5 6 10 , 72 27 29 3 4 5 6 →= 71 5 3 4 5 6 10 , 74 27 29 3 4 5 6 →= 73 5 3 4 5 6 10 , 12 27 29 3 4 11 12 →= 14 5 3 4 5 3 13 , 12 27 29 3 4 11 14 →= 14 5 3 4 5 3 4 , 64 27 29 3 4 11 12 →= 63 5 3 4 5 3 13 , 64 27 29 3 4 11 14 →= 63 5 3 4 5 3 4 , 13 27 29 3 4 11 12 →= 4 5 3 4 5 3 13 , 13 27 29 3 4 11 14 →= 4 5 3 4 5 3 4 , 66 27 29 3 4 11 12 →= 65 5 3 4 5 3 13 , 66 27 29 3 4 11 14 →= 65 5 3 4 5 3 4 , 68 27 29 3 4 11 12 →= 67 5 3 4 5 3 13 , 68 27 29 3 4 11 14 →= 67 5 3 4 5 3 4 , 70 27 29 3 4 11 12 →= 69 5 3 4 5 3 13 , 70 27 29 3 4 11 14 →= 69 5 3 4 5 3 4 , 72 27 29 3 4 11 12 →= 71 5 3 4 5 3 13 , 72 27 29 3 4 11 14 →= 71 5 3 4 5 3 4 , 74 27 29 3 4 11 12 →= 73 5 3 4 5 3 13 , 74 27 29 3 4 11 14 →= 73 5 3 4 5 3 4 , 30 31 29 3 4 5 6 →= 27 29 3 4 5 6 10 , 76 31 29 3 4 5 6 →= 75 29 3 4 5 6 10 , 32 31 29 3 4 5 6 →= 31 29 3 4 5 6 10 , 78 31 29 3 4 5 6 →= 77 29 3 4 5 6 10 , 80 31 29 3 4 5 6 →= 79 29 3 4 5 6 10 , 81 31 29 3 4 5 6 →= 52 29 3 4 5 6 10 , 82 31 29 3 4 5 6 →= 57 29 3 4 5 6 10 , 83 31 29 3 4 5 6 →= 61 29 3 4 5 6 10 , 30 31 29 3 4 11 12 →= 27 29 3 4 5 3 13 , 30 31 29 3 4 11 14 →= 27 29 3 4 5 3 4 , 76 31 29 3 4 11 12 →= 75 29 3 4 5 3 13 , 76 31 29 3 4 11 14 →= 75 29 3 4 5 3 4 , 32 31 29 3 4 11 12 →= 31 29 3 4 5 3 13 , 32 31 29 3 4 11 14 →= 31 29 3 4 5 3 4 , 78 31 29 3 4 11 12 →= 77 29 3 4 5 3 13 , 78 31 29 3 4 11 14 →= 77 29 3 4 5 3 4 , 80 31 29 3 4 11 12 →= 79 29 3 4 5 3 13 , 80 31 29 3 4 11 14 →= 79 29 3 4 5 3 4 , 81 31 29 3 4 11 12 →= 52 29 3 4 5 3 13 , 81 31 29 3 4 11 14 →= 52 29 3 4 5 3 4 , 82 31 29 3 4 11 12 →= 57 29 3 4 5 3 13 , 82 31 29 3 4 11 14 →= 57 29 3 4 5 3 4 , 83 31 29 3 4 11 12 →= 61 29 3 4 5 3 13 , 83 31 29 3 4 11 14 →= 61 29 3 4 5 3 4 , 85 75 29 3 4 5 6 →= 84 42 3 4 5 6 10 , 87 75 29 3 4 5 6 →= 86 42 3 4 5 6 10 , 85 75 29 3 4 11 12 →= 84 42 3 4 5 3 13 , 85 75 29 3 4 11 14 →= 84 42 3 4 5 3 4 , 87 75 29 3 4 11 12 →= 86 42 3 4 5 3 13 , 87 75 29 3 4 11 14 →= 86 42 3 4 5 3 4 , 89 77 29 3 4 5 6 →= 88 44 3 4 5 6 10 , 89 77 29 3 4 11 12 →= 88 44 3 4 5 3 13 , 89 77 29 3 4 11 14 →= 88 44 3 4 5 3 4 , 94 84 42 3 4 5 6 →= 95 96 97 4 5 6 10 , 94 84 42 3 4 11 12 →= 95 96 97 4 5 3 13 , 94 84 42 3 4 11 14 →= 95 96 97 4 5 3 4 , 34 4 5 3 13 27 28 →= 10 10 34 4 11 14 11 , 34 4 5 3 13 27 29 →= 10 10 34 4 11 14 5 , 34 4 5 3 13 30 31 →= 10 10 34 4 11 12 27 , 34 4 5 3 13 30 32 →= 10 10 34 4 11 12 30 , 51 52 29 3 13 27 28 →= 1 2 3 4 11 14 11 , 51 52 29 3 13 27 29 →= 1 2 3 4 11 14 5 , 54 52 29 3 13 27 28 →= 53 2 3 4 11 14 11 , 54 52 29 3 13 27 29 →= 53 2 3 4 11 14 5 , 51 52 29 3 13 30 31 →= 1 2 3 4 11 12 27 , 51 52 29 3 13 30 32 →= 1 2 3 4 11 12 30 , 54 52 29 3 13 30 31 →= 53 2 3 4 11 12 27 , 54 52 29 3 13 30 32 →= 53 2 3 4 11 12 30 , 56 57 29 3 13 27 28 →= 55 17 3 4 11 14 11 , 56 57 29 3 13 27 29 →= 55 17 3 4 11 14 5 , 58 57 29 3 13 27 28 →= 16 17 3 4 11 14 11 , 58 57 29 3 13 27 29 →= 16 17 3 4 11 14 5 , 56 57 29 3 13 30 31 →= 55 17 3 4 11 12 27 , 56 57 29 3 13 30 32 →= 55 17 3 4 11 12 30 , 58 57 29 3 13 30 31 →= 16 17 3 4 11 12 27 , 58 57 29 3 13 30 32 →= 16 17 3 4 11 12 30 , 60 61 29 3 13 27 28 →= 59 23 3 4 11 14 11 , 60 61 29 3 13 27 29 →= 59 23 3 4 11 14 5 , 62 61 29 3 13 27 28 →= 22 23 3 4 11 14 11 , 62 61 29 3 13 27 29 →= 22 23 3 4 11 14 5 , 60 61 29 3 13 30 31 →= 59 23 3 4 11 12 27 , 60 61 29 3 13 30 32 →= 59 23 3 4 11 12 30 , 62 61 29 3 13 30 31 →= 22 23 3 4 11 12 27 , 62 61 29 3 13 30 32 →= 22 23 3 4 11 12 30 , 12 27 29 3 13 27 28 →= 14 5 3 4 11 14 11 , 12 27 29 3 13 27 29 →= 14 5 3 4 11 14 5 , 64 27 29 3 13 27 28 →= 63 5 3 4 11 14 11 , 64 27 29 3 13 27 29 →= 63 5 3 4 11 14 5 , 13 27 29 3 13 27 28 →= 4 5 3 4 11 14 11 , 13 27 29 3 13 27 29 →= 4 5 3 4 11 14 5 , 66 27 29 3 13 27 28 →= 65 5 3 4 11 14 11 , 66 27 29 3 13 27 29 →= 65 5 3 4 11 14 5 , 68 27 29 3 13 27 28 →= 67 5 3 4 11 14 11 , 68 27 29 3 13 27 29 →= 67 5 3 4 11 14 5 , 70 27 29 3 13 27 28 →= 69 5 3 4 11 14 11 , 70 27 29 3 13 27 29 →= 69 5 3 4 11 14 5 , 72 27 29 3 13 27 28 →= 71 5 3 4 11 14 11 , 72 27 29 3 13 27 29 →= 71 5 3 4 11 14 5 , 74 27 29 3 13 27 28 →= 73 5 3 4 11 14 11 , 74 27 29 3 13 27 29 →= 73 5 3 4 11 14 5 , 12 27 29 3 13 30 31 →= 14 5 3 4 11 12 27 , 12 27 29 3 13 30 32 →= 14 5 3 4 11 12 30 , 64 27 29 3 13 30 31 →= 63 5 3 4 11 12 27 , 64 27 29 3 13 30 32 →= 63 5 3 4 11 12 30 , 13 27 29 3 13 30 31 →= 4 5 3 4 11 12 27 , 13 27 29 3 13 30 32 →= 4 5 3 4 11 12 30 , 66 27 29 3 13 30 31 →= 65 5 3 4 11 12 27 , 66 27 29 3 13 30 32 →= 65 5 3 4 11 12 30 , 68 27 29 3 13 30 31 →= 67 5 3 4 11 12 27 , 68 27 29 3 13 30 32 →= 67 5 3 4 11 12 30 , 70 27 29 3 13 30 31 →= 69 5 3 4 11 12 27 , 70 27 29 3 13 30 32 →= 69 5 3 4 11 12 30 , 72 27 29 3 13 30 31 →= 71 5 3 4 11 12 27 , 72 27 29 3 13 30 32 →= 71 5 3 4 11 12 30 , 74 27 29 3 13 30 31 →= 73 5 3 4 11 12 27 , 74 27 29 3 13 30 32 →= 73 5 3 4 11 12 30 , 30 31 29 3 13 27 28 →= 27 29 3 4 11 14 11 , 30 31 29 3 13 27 29 →= 27 29 3 4 11 14 5 , 76 31 29 3 13 27 28 →= 75 29 3 4 11 14 11 , 76 31 29 3 13 27 29 →= 75 29 3 4 11 14 5 , 32 31 29 3 13 27 28 →= 31 29 3 4 11 14 11 , 32 31 29 3 13 27 29 →= 31 29 3 4 11 14 5 , 78 31 29 3 13 27 28 →= 77 29 3 4 11 14 11 , 78 31 29 3 13 27 29 →= 77 29 3 4 11 14 5 , 80 31 29 3 13 27 28 →= 79 29 3 4 11 14 11 , 80 31 29 3 13 27 29 →= 79 29 3 4 11 14 5 , 81 31 29 3 13 27 28 →= 52 29 3 4 11 14 11 , 81 31 29 3 13 27 29 →= 52 29 3 4 11 14 5 , 82 31 29 3 13 27 28 →= 57 29 3 4 11 14 11 , 82 31 29 3 13 27 29 →= 57 29 3 4 11 14 5 , 83 31 29 3 13 27 28 →= 61 29 3 4 11 14 11 , 83 31 29 3 13 27 29 →= 61 29 3 4 11 14 5 , 30 31 29 3 13 30 31 →= 27 29 3 4 11 12 27 , 30 31 29 3 13 30 32 →= 27 29 3 4 11 12 30 , 76 31 29 3 13 30 31 →= 75 29 3 4 11 12 27 , 76 31 29 3 13 30 32 →= 75 29 3 4 11 12 30 , 32 31 29 3 13 30 31 →= 31 29 3 4 11 12 27 , 32 31 29 3 13 30 32 →= 31 29 3 4 11 12 30 , 78 31 29 3 13 30 31 →= 77 29 3 4 11 12 27 , 78 31 29 3 13 30 32 →= 77 29 3 4 11 12 30 , 80 31 29 3 13 30 31 →= 79 29 3 4 11 12 27 , 80 31 29 3 13 30 32 →= 79 29 3 4 11 12 30 , 81 31 29 3 13 30 31 →= 52 29 3 4 11 12 27 , 81 31 29 3 13 30 32 →= 52 29 3 4 11 12 30 , 82 31 29 3 13 30 31 →= 57 29 3 4 11 12 27 , 82 31 29 3 13 30 32 →= 57 29 3 4 11 12 30 , 83 31 29 3 13 30 31 →= 61 29 3 4 11 12 27 , 83 31 29 3 13 30 32 →= 61 29 3 4 11 12 30 , 85 75 29 3 13 27 28 →= 84 42 3 4 11 14 11 , 85 75 29 3 13 27 29 →= 84 42 3 4 11 14 5 , 87 75 29 3 13 27 28 →= 86 42 3 4 11 14 11 , 87 75 29 3 13 27 29 →= 86 42 3 4 11 14 5 , 85 75 29 3 13 30 31 →= 84 42 3 4 11 12 27 , 85 75 29 3 13 30 32 →= 84 42 3 4 11 12 30 , 87 75 29 3 13 30 31 →= 86 42 3 4 11 12 27 , 87 75 29 3 13 30 32 →= 86 42 3 4 11 12 30 , 89 77 29 3 13 27 28 →= 88 44 3 4 11 14 11 , 89 77 29 3 13 27 29 →= 88 44 3 4 11 14 5 , 89 77 29 3 13 30 31 →= 88 44 3 4 11 12 27 , 89 77 29 3 13 30 32 →= 88 44 3 4 11 12 30 , 94 84 42 3 13 27 28 →= 95 96 97 4 11 14 11 , 94 84 42 3 13 27 29 →= 95 96 97 4 11 14 5 , 94 84 42 3 13 30 31 →= 95 96 97 4 11 12 27 , 94 84 42 3 13 30 32 →= 95 96 97 4 11 12 30 } 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 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 21 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 22 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 23 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 24 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 25 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 26 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 27 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 28 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 29 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 30 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 31 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 32 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 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 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 41 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 42 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 43 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 44 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 45 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 46 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 47 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 48 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 49 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 50 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 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 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 88 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 89 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 90 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 91 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 92 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 93 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 94 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 95 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 96 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 97 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ After renaming modulo the bijection { 6 ↦ 0, 10 ↦ 1, 3 ↦ 2, 4 ↦ 3, 5 ↦ 4, 33 ↦ 5, 34 ↦ 6, 35 ↦ 7, 36 ↦ 8, 13 ↦ 9, 37 ↦ 10, 38 ↦ 11, 39 ↦ 12, 40 ↦ 13, 41 ↦ 14, 29 ↦ 15, 28 ↦ 16, 14 ↦ 17, 11 ↦ 18, 1 ↦ 19, 2 ↦ 20, 51 ↦ 21, 52 ↦ 22, 53 ↦ 23, 54 ↦ 24, 55 ↦ 25, 17 ↦ 26, 56 ↦ 27, 57 ↦ 28, 16 ↦ 29, 58 ↦ 30, 59 ↦ 31, 23 ↦ 32, 60 ↦ 33, 61 ↦ 34, 22 ↦ 35, 62 ↦ 36, 12 ↦ 37, 27 ↦ 38, 63 ↦ 39, 64 ↦ 40, 65 ↦ 41, 66 ↦ 42, 67 ↦ 43, 68 ↦ 44, 69 ↦ 45, 70 ↦ 46, 71 ↦ 47, 72 ↦ 48, 73 ↦ 49, 74 ↦ 50, 30 ↦ 51, 31 ↦ 52, 75 ↦ 53, 76 ↦ 54, 32 ↦ 55, 77 ↦ 56, 78 ↦ 57, 79 ↦ 58, 80 ↦ 59, 81 ↦ 60, 82 ↦ 61, 83 ↦ 62, 84 ↦ 63, 42 ↦ 64, 85 ↦ 65, 86 ↦ 66, 87 ↦ 67, 88 ↦ 68, 44 ↦ 69, 89 ↦ 70, 90 ↦ 71, 91 ↦ 72, 92 ↦ 73, 93 ↦ 74 }, it remains to prove termination of the 729-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 6 9 →= 2 3 4 0 1 6 9 , 0 1 1 1 1 6 10 →= 2 3 4 0 1 6 10 , 0 1 1 1 1 6 11 →= 2 3 4 0 1 6 11 , 0 1 1 1 1 6 3 →= 2 3 4 0 1 6 3 , 0 1 1 1 1 5 12 →= 2 3 4 0 1 5 12 , 0 1 1 1 1 5 13 →= 2 3 4 0 1 5 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 , 4 0 1 1 1 1 1 →= 18 17 4 0 1 1 1 , 4 0 1 1 1 1 5 →= 18 17 4 0 1 1 5 , 4 0 1 1 1 1 6 →= 18 17 4 0 1 1 6 , 4 0 1 1 1 1 7 →= 18 17 4 0 1 1 7 , 4 0 1 1 1 1 8 →= 18 17 4 0 1 1 8 , 15 0 1 1 1 6 9 →= 16 17 4 0 1 6 9 , 15 0 1 1 1 6 10 →= 16 17 4 0 1 6 10 , 15 0 1 1 1 6 11 →= 16 17 4 0 1 6 11 , 15 0 1 1 1 6 3 →= 16 17 4 0 1 6 3 , 4 0 1 1 1 6 9 →= 18 17 4 0 1 6 9 , 4 0 1 1 1 6 10 →= 18 17 4 0 1 6 10 , 4 0 1 1 1 6 11 →= 18 17 4 0 1 6 11 , 4 0 1 1 1 6 3 →= 18 17 4 0 1 6 3 , 15 0 1 1 1 5 12 →= 16 17 4 0 1 5 12 , 15 0 1 1 1 5 13 →= 16 17 4 0 1 5 13 , 4 0 1 1 1 5 12 →= 18 17 4 0 1 5 12 , 4 0 1 1 1 5 13 →= 18 17 4 0 1 5 13 , 15 0 1 1 1 7 14 →= 16 17 4 0 1 7 14 , 4 0 1 1 1 7 14 →= 18 17 4 0 1 7 14 , 19 20 0 1 1 1 1 →= 21 22 15 0 1 1 1 , 19 20 0 1 1 1 5 →= 21 22 15 0 1 1 5 , 19 20 0 1 1 1 6 →= 21 22 15 0 1 1 6 , 19 20 0 1 1 1 7 →= 21 22 15 0 1 1 7 , 19 20 0 1 1 1 8 →= 21 22 15 0 1 1 8 , 23 20 0 1 1 1 1 →= 24 22 15 0 1 1 1 , 23 20 0 1 1 1 5 →= 24 22 15 0 1 1 5 , 23 20 0 1 1 1 6 →= 24 22 15 0 1 1 6 , 23 20 0 1 1 1 7 →= 24 22 15 0 1 1 7 , 23 20 0 1 1 1 8 →= 24 22 15 0 1 1 8 , 19 20 0 1 1 6 9 →= 21 22 15 0 1 6 9 , 19 20 0 1 1 6 10 →= 21 22 15 0 1 6 10 , 19 20 0 1 1 6 11 →= 21 22 15 0 1 6 11 , 19 20 0 1 1 6 3 →= 21 22 15 0 1 6 3 , 23 20 0 1 1 6 9 →= 24 22 15 0 1 6 9 , 23 20 0 1 1 6 10 →= 24 22 15 0 1 6 10 , 23 20 0 1 1 6 11 →= 24 22 15 0 1 6 11 , 23 20 0 1 1 6 3 →= 24 22 15 0 1 6 3 , 19 20 0 1 1 5 12 →= 21 22 15 0 1 5 12 , 19 20 0 1 1 5 13 →= 21 22 15 0 1 5 13 , 23 20 0 1 1 5 12 →= 24 22 15 0 1 5 12 , 23 20 0 1 1 5 13 →= 24 22 15 0 1 5 13 , 19 20 0 1 1 7 14 →= 21 22 15 0 1 7 14 , 23 20 0 1 1 7 14 →= 24 22 15 0 1 7 14 , 25 26 0 1 1 1 1 →= 27 28 15 0 1 1 1 , 25 26 0 1 1 1 5 →= 27 28 15 0 1 1 5 , 25 26 0 1 1 1 6 →= 27 28 15 0 1 1 6 , 25 26 0 1 1 1 7 →= 27 28 15 0 1 1 7 , 25 26 0 1 1 1 8 →= 27 28 15 0 1 1 8 , 29 26 0 1 1 1 1 →= 30 28 15 0 1 1 1 , 29 26 0 1 1 1 5 →= 30 28 15 0 1 1 5 , 29 26 0 1 1 1 6 →= 30 28 15 0 1 1 6 , 29 26 0 1 1 1 7 →= 30 28 15 0 1 1 7 , 29 26 0 1 1 1 8 →= 30 28 15 0 1 1 8 , 25 26 0 1 1 6 9 →= 27 28 15 0 1 6 9 , 25 26 0 1 1 6 10 →= 27 28 15 0 1 6 10 , 25 26 0 1 1 6 11 →= 27 28 15 0 1 6 11 , 25 26 0 1 1 6 3 →= 27 28 15 0 1 6 3 , 29 26 0 1 1 6 9 →= 30 28 15 0 1 6 9 , 29 26 0 1 1 6 10 →= 30 28 15 0 1 6 10 , 29 26 0 1 1 6 11 →= 30 28 15 0 1 6 11 , 29 26 0 1 1 6 3 →= 30 28 15 0 1 6 3 , 25 26 0 1 1 5 12 →= 27 28 15 0 1 5 12 , 25 26 0 1 1 5 13 →= 27 28 15 0 1 5 13 , 29 26 0 1 1 5 12 →= 30 28 15 0 1 5 12 , 29 26 0 1 1 5 13 →= 30 28 15 0 1 5 13 , 25 26 0 1 1 7 14 →= 27 28 15 0 1 7 14 , 29 26 0 1 1 7 14 →= 30 28 15 0 1 7 14 , 31 32 0 1 1 1 1 →= 33 34 15 0 1 1 1 , 31 32 0 1 1 1 5 →= 33 34 15 0 1 1 5 , 31 32 0 1 1 1 6 →= 33 34 15 0 1 1 6 , 31 32 0 1 1 1 7 →= 33 34 15 0 1 1 7 , 31 32 0 1 1 1 8 →= 33 34 15 0 1 1 8 , 35 32 0 1 1 1 1 →= 36 34 15 0 1 1 1 , 35 32 0 1 1 1 5 →= 36 34 15 0 1 1 5 , 35 32 0 1 1 1 6 →= 36 34 15 0 1 1 6 , 35 32 0 1 1 1 7 →= 36 34 15 0 1 1 7 , 35 32 0 1 1 1 8 →= 36 34 15 0 1 1 8 , 31 32 0 1 1 6 9 →= 33 34 15 0 1 6 9 , 31 32 0 1 1 6 10 →= 33 34 15 0 1 6 10 , 31 32 0 1 1 6 11 →= 33 34 15 0 1 6 11 , 31 32 0 1 1 6 3 →= 33 34 15 0 1 6 3 , 35 32 0 1 1 6 9 →= 36 34 15 0 1 6 9 , 35 32 0 1 1 6 10 →= 36 34 15 0 1 6 10 , 35 32 0 1 1 6 11 →= 36 34 15 0 1 6 11 , 35 32 0 1 1 6 3 →= 36 34 15 0 1 6 3 , 31 32 0 1 1 5 12 →= 33 34 15 0 1 5 12 , 31 32 0 1 1 5 13 →= 33 34 15 0 1 5 13 , 35 32 0 1 1 5 12 →= 36 34 15 0 1 5 12 , 35 32 0 1 1 5 13 →= 36 34 15 0 1 5 13 , 31 32 0 1 1 7 14 →= 33 34 15 0 1 7 14 , 35 32 0 1 1 7 14 →= 36 34 15 0 1 7 14 , 17 4 0 1 1 1 1 →= 37 38 15 0 1 1 1 , 17 4 0 1 1 1 5 →= 37 38 15 0 1 1 5 , 17 4 0 1 1 1 6 →= 37 38 15 0 1 1 6 , 17 4 0 1 1 1 7 →= 37 38 15 0 1 1 7 , 17 4 0 1 1 1 8 →= 37 38 15 0 1 1 8 , 39 4 0 1 1 1 1 →= 40 38 15 0 1 1 1 , 39 4 0 1 1 1 5 →= 40 38 15 0 1 1 5 , 39 4 0 1 1 1 6 →= 40 38 15 0 1 1 6 , 39 4 0 1 1 1 7 →= 40 38 15 0 1 1 7 , 39 4 0 1 1 1 8 →= 40 38 15 0 1 1 8 , 3 4 0 1 1 1 1 →= 9 38 15 0 1 1 1 , 3 4 0 1 1 1 5 →= 9 38 15 0 1 1 5 , 3 4 0 1 1 1 6 →= 9 38 15 0 1 1 6 , 3 4 0 1 1 1 7 →= 9 38 15 0 1 1 7 , 3 4 0 1 1 1 8 →= 9 38 15 0 1 1 8 , 41 4 0 1 1 1 1 →= 42 38 15 0 1 1 1 , 41 4 0 1 1 1 5 →= 42 38 15 0 1 1 5 , 41 4 0 1 1 1 6 →= 42 38 15 0 1 1 6 , 41 4 0 1 1 1 7 →= 42 38 15 0 1 1 7 , 41 4 0 1 1 1 8 →= 42 38 15 0 1 1 8 , 43 4 0 1 1 1 1 →= 44 38 15 0 1 1 1 , 43 4 0 1 1 1 5 →= 44 38 15 0 1 1 5 , 43 4 0 1 1 1 6 →= 44 38 15 0 1 1 6 , 43 4 0 1 1 1 7 →= 44 38 15 0 1 1 7 , 43 4 0 1 1 1 8 →= 44 38 15 0 1 1 8 , 45 4 0 1 1 1 1 →= 46 38 15 0 1 1 1 , 45 4 0 1 1 1 5 →= 46 38 15 0 1 1 5 , 45 4 0 1 1 1 6 →= 46 38 15 0 1 1 6 , 45 4 0 1 1 1 7 →= 46 38 15 0 1 1 7 , 45 4 0 1 1 1 8 →= 46 38 15 0 1 1 8 , 47 4 0 1 1 1 1 →= 48 38 15 0 1 1 1 , 47 4 0 1 1 1 5 →= 48 38 15 0 1 1 5 , 47 4 0 1 1 1 6 →= 48 38 15 0 1 1 6 , 47 4 0 1 1 1 7 →= 48 38 15 0 1 1 7 , 47 4 0 1 1 1 8 →= 48 38 15 0 1 1 8 , 49 4 0 1 1 1 1 →= 50 38 15 0 1 1 1 , 49 4 0 1 1 1 5 →= 50 38 15 0 1 1 5 , 49 4 0 1 1 1 6 →= 50 38 15 0 1 1 6 , 49 4 0 1 1 1 7 →= 50 38 15 0 1 1 7 , 49 4 0 1 1 1 8 →= 50 38 15 0 1 1 8 , 17 4 0 1 1 6 9 →= 37 38 15 0 1 6 9 , 17 4 0 1 1 6 10 →= 37 38 15 0 1 6 10 , 17 4 0 1 1 6 11 →= 37 38 15 0 1 6 11 , 17 4 0 1 1 6 3 →= 37 38 15 0 1 6 3 , 39 4 0 1 1 6 9 →= 40 38 15 0 1 6 9 , 39 4 0 1 1 6 10 →= 40 38 15 0 1 6 10 , 39 4 0 1 1 6 11 →= 40 38 15 0 1 6 11 , 39 4 0 1 1 6 3 →= 40 38 15 0 1 6 3 , 3 4 0 1 1 6 9 →= 9 38 15 0 1 6 9 , 3 4 0 1 1 6 10 →= 9 38 15 0 1 6 10 , 3 4 0 1 1 6 11 →= 9 38 15 0 1 6 11 , 3 4 0 1 1 6 3 →= 9 38 15 0 1 6 3 , 41 4 0 1 1 6 9 →= 42 38 15 0 1 6 9 , 41 4 0 1 1 6 10 →= 42 38 15 0 1 6 10 , 41 4 0 1 1 6 11 →= 42 38 15 0 1 6 11 , 41 4 0 1 1 6 3 →= 42 38 15 0 1 6 3 , 43 4 0 1 1 6 9 →= 44 38 15 0 1 6 9 , 43 4 0 1 1 6 10 →= 44 38 15 0 1 6 10 , 43 4 0 1 1 6 11 →= 44 38 15 0 1 6 11 , 43 4 0 1 1 6 3 →= 44 38 15 0 1 6 3 , 45 4 0 1 1 6 9 →= 46 38 15 0 1 6 9 , 45 4 0 1 1 6 10 →= 46 38 15 0 1 6 10 , 45 4 0 1 1 6 11 →= 46 38 15 0 1 6 11 , 45 4 0 1 1 6 3 →= 46 38 15 0 1 6 3 , 47 4 0 1 1 6 9 →= 48 38 15 0 1 6 9 , 47 4 0 1 1 6 10 →= 48 38 15 0 1 6 10 , 47 4 0 1 1 6 11 →= 48 38 15 0 1 6 11 , 47 4 0 1 1 6 3 →= 48 38 15 0 1 6 3 , 49 4 0 1 1 6 9 →= 50 38 15 0 1 6 9 , 49 4 0 1 1 6 10 →= 50 38 15 0 1 6 10 , 49 4 0 1 1 6 11 →= 50 38 15 0 1 6 11 , 49 4 0 1 1 6 3 →= 50 38 15 0 1 6 3 , 17 4 0 1 1 5 12 →= 37 38 15 0 1 5 12 , 17 4 0 1 1 5 13 →= 37 38 15 0 1 5 13 , 39 4 0 1 1 5 12 →= 40 38 15 0 1 5 12 , 39 4 0 1 1 5 13 →= 40 38 15 0 1 5 13 , 3 4 0 1 1 5 12 →= 9 38 15 0 1 5 12 , 3 4 0 1 1 5 13 →= 9 38 15 0 1 5 13 , 41 4 0 1 1 5 12 →= 42 38 15 0 1 5 12 , 41 4 0 1 1 5 13 →= 42 38 15 0 1 5 13 , 43 4 0 1 1 5 12 →= 44 38 15 0 1 5 12 , 43 4 0 1 1 5 13 →= 44 38 15 0 1 5 13 , 45 4 0 1 1 5 12 →= 46 38 15 0 1 5 12 , 45 4 0 1 1 5 13 →= 46 38 15 0 1 5 13 , 47 4 0 1 1 5 12 →= 48 38 15 0 1 5 12 , 47 4 0 1 1 5 13 →= 48 38 15 0 1 5 13 , 49 4 0 1 1 5 12 →= 50 38 15 0 1 5 12 , 49 4 0 1 1 5 13 →= 50 38 15 0 1 5 13 , 17 4 0 1 1 7 14 →= 37 38 15 0 1 7 14 , 39 4 0 1 1 7 14 →= 40 38 15 0 1 7 14 , 3 4 0 1 1 7 14 →= 9 38 15 0 1 7 14 , 41 4 0 1 1 7 14 →= 42 38 15 0 1 7 14 , 43 4 0 1 1 7 14 →= 44 38 15 0 1 7 14 , 45 4 0 1 1 7 14 →= 46 38 15 0 1 7 14 , 47 4 0 1 1 7 14 →= 48 38 15 0 1 7 14 , 49 4 0 1 1 7 14 →= 50 38 15 0 1 7 14 , 38 15 0 1 1 1 1 →= 51 52 15 0 1 1 1 , 38 15 0 1 1 1 5 →= 51 52 15 0 1 1 5 , 38 15 0 1 1 1 6 →= 51 52 15 0 1 1 6 , 38 15 0 1 1 1 7 →= 51 52 15 0 1 1 7 , 38 15 0 1 1 1 8 →= 51 52 15 0 1 1 8 , 53 15 0 1 1 1 1 →= 54 52 15 0 1 1 1 , 53 15 0 1 1 1 5 →= 54 52 15 0 1 1 5 , 53 15 0 1 1 1 6 →= 54 52 15 0 1 1 6 , 53 15 0 1 1 1 7 →= 54 52 15 0 1 1 7 , 53 15 0 1 1 1 8 →= 54 52 15 0 1 1 8 , 52 15 0 1 1 1 1 →= 55 52 15 0 1 1 1 , 52 15 0 1 1 1 5 →= 55 52 15 0 1 1 5 , 52 15 0 1 1 1 6 →= 55 52 15 0 1 1 6 , 52 15 0 1 1 1 7 →= 55 52 15 0 1 1 7 , 52 15 0 1 1 1 8 →= 55 52 15 0 1 1 8 , 56 15 0 1 1 1 1 →= 57 52 15 0 1 1 1 , 56 15 0 1 1 1 5 →= 57 52 15 0 1 1 5 , 56 15 0 1 1 1 6 →= 57 52 15 0 1 1 6 , 56 15 0 1 1 1 7 →= 57 52 15 0 1 1 7 , 56 15 0 1 1 1 8 →= 57 52 15 0 1 1 8 , 58 15 0 1 1 1 1 →= 59 52 15 0 1 1 1 , 58 15 0 1 1 1 5 →= 59 52 15 0 1 1 5 , 58 15 0 1 1 1 6 →= 59 52 15 0 1 1 6 , 58 15 0 1 1 1 7 →= 59 52 15 0 1 1 7 , 58 15 0 1 1 1 8 →= 59 52 15 0 1 1 8 , 22 15 0 1 1 1 1 →= 60 52 15 0 1 1 1 , 22 15 0 1 1 1 5 →= 60 52 15 0 1 1 5 , 22 15 0 1 1 1 6 →= 60 52 15 0 1 1 6 , 22 15 0 1 1 1 7 →= 60 52 15 0 1 1 7 , 22 15 0 1 1 1 8 →= 60 52 15 0 1 1 8 , 28 15 0 1 1 1 1 →= 61 52 15 0 1 1 1 , 28 15 0 1 1 1 5 →= 61 52 15 0 1 1 5 , 28 15 0 1 1 1 6 →= 61 52 15 0 1 1 6 , 28 15 0 1 1 1 7 →= 61 52 15 0 1 1 7 , 28 15 0 1 1 1 8 →= 61 52 15 0 1 1 8 , 34 15 0 1 1 1 1 →= 62 52 15 0 1 1 1 , 34 15 0 1 1 1 5 →= 62 52 15 0 1 1 5 , 34 15 0 1 1 1 6 →= 62 52 15 0 1 1 6 , 34 15 0 1 1 1 7 →= 62 52 15 0 1 1 7 , 34 15 0 1 1 1 8 →= 62 52 15 0 1 1 8 , 38 15 0 1 1 6 9 →= 51 52 15 0 1 6 9 , 38 15 0 1 1 6 10 →= 51 52 15 0 1 6 10 , 38 15 0 1 1 6 11 →= 51 52 15 0 1 6 11 , 38 15 0 1 1 6 3 →= 51 52 15 0 1 6 3 , 53 15 0 1 1 6 9 →= 54 52 15 0 1 6 9 , 53 15 0 1 1 6 10 →= 54 52 15 0 1 6 10 , 53 15 0 1 1 6 11 →= 54 52 15 0 1 6 11 , 53 15 0 1 1 6 3 →= 54 52 15 0 1 6 3 , 52 15 0 1 1 6 9 →= 55 52 15 0 1 6 9 , 52 15 0 1 1 6 10 →= 55 52 15 0 1 6 10 , 52 15 0 1 1 6 11 →= 55 52 15 0 1 6 11 , 52 15 0 1 1 6 3 →= 55 52 15 0 1 6 3 , 56 15 0 1 1 6 9 →= 57 52 15 0 1 6 9 , 56 15 0 1 1 6 10 →= 57 52 15 0 1 6 10 , 56 15 0 1 1 6 11 →= 57 52 15 0 1 6 11 , 56 15 0 1 1 6 3 →= 57 52 15 0 1 6 3 , 58 15 0 1 1 6 9 →= 59 52 15 0 1 6 9 , 58 15 0 1 1 6 10 →= 59 52 15 0 1 6 10 , 58 15 0 1 1 6 11 →= 59 52 15 0 1 6 11 , 58 15 0 1 1 6 3 →= 59 52 15 0 1 6 3 , 22 15 0 1 1 6 9 →= 60 52 15 0 1 6 9 , 22 15 0 1 1 6 10 →= 60 52 15 0 1 6 10 , 22 15 0 1 1 6 11 →= 60 52 15 0 1 6 11 , 22 15 0 1 1 6 3 →= 60 52 15 0 1 6 3 , 28 15 0 1 1 6 9 →= 61 52 15 0 1 6 9 , 28 15 0 1 1 6 10 →= 61 52 15 0 1 6 10 , 28 15 0 1 1 6 11 →= 61 52 15 0 1 6 11 , 28 15 0 1 1 6 3 →= 61 52 15 0 1 6 3 , 34 15 0 1 1 6 9 →= 62 52 15 0 1 6 9 , 34 15 0 1 1 6 10 →= 62 52 15 0 1 6 10 , 34 15 0 1 1 6 11 →= 62 52 15 0 1 6 11 , 34 15 0 1 1 6 3 →= 62 52 15 0 1 6 3 , 38 15 0 1 1 5 12 →= 51 52 15 0 1 5 12 , 38 15 0 1 1 5 13 →= 51 52 15 0 1 5 13 , 53 15 0 1 1 5 12 →= 54 52 15 0 1 5 12 , 53 15 0 1 1 5 13 →= 54 52 15 0 1 5 13 , 52 15 0 1 1 5 12 →= 55 52 15 0 1 5 12 , 52 15 0 1 1 5 13 →= 55 52 15 0 1 5 13 , 56 15 0 1 1 5 12 →= 57 52 15 0 1 5 12 , 56 15 0 1 1 5 13 →= 57 52 15 0 1 5 13 , 58 15 0 1 1 5 12 →= 59 52 15 0 1 5 12 , 58 15 0 1 1 5 13 →= 59 52 15 0 1 5 13 , 22 15 0 1 1 5 12 →= 60 52 15 0 1 5 12 , 22 15 0 1 1 5 13 →= 60 52 15 0 1 5 13 , 28 15 0 1 1 5 12 →= 61 52 15 0 1 5 12 , 28 15 0 1 1 5 13 →= 61 52 15 0 1 5 13 , 34 15 0 1 1 5 12 →= 62 52 15 0 1 5 12 , 34 15 0 1 1 5 13 →= 62 52 15 0 1 5 13 , 38 15 0 1 1 7 14 →= 51 52 15 0 1 7 14 , 53 15 0 1 1 7 14 →= 54 52 15 0 1 7 14 , 52 15 0 1 1 7 14 →= 55 52 15 0 1 7 14 , 56 15 0 1 1 7 14 →= 57 52 15 0 1 7 14 , 58 15 0 1 1 7 14 →= 59 52 15 0 1 7 14 , 22 15 0 1 1 7 14 →= 60 52 15 0 1 7 14 , 28 15 0 1 1 7 14 →= 61 52 15 0 1 7 14 , 34 15 0 1 1 7 14 →= 62 52 15 0 1 7 14 , 63 64 0 1 1 1 1 →= 65 53 15 0 1 1 1 , 63 64 0 1 1 1 5 →= 65 53 15 0 1 1 5 , 63 64 0 1 1 1 6 →= 65 53 15 0 1 1 6 , 63 64 0 1 1 1 7 →= 65 53 15 0 1 1 7 , 63 64 0 1 1 1 8 →= 65 53 15 0 1 1 8 , 66 64 0 1 1 1 1 →= 67 53 15 0 1 1 1 , 66 64 0 1 1 1 5 →= 67 53 15 0 1 1 5 , 66 64 0 1 1 1 6 →= 67 53 15 0 1 1 6 , 66 64 0 1 1 1 7 →= 67 53 15 0 1 1 7 , 66 64 0 1 1 1 8 →= 67 53 15 0 1 1 8 , 63 64 0 1 1 6 9 →= 65 53 15 0 1 6 9 , 63 64 0 1 1 6 10 →= 65 53 15 0 1 6 10 , 63 64 0 1 1 6 11 →= 65 53 15 0 1 6 11 , 63 64 0 1 1 6 3 →= 65 53 15 0 1 6 3 , 66 64 0 1 1 6 9 →= 67 53 15 0 1 6 9 , 66 64 0 1 1 6 10 →= 67 53 15 0 1 6 10 , 66 64 0 1 1 6 11 →= 67 53 15 0 1 6 11 , 66 64 0 1 1 6 3 →= 67 53 15 0 1 6 3 , 63 64 0 1 1 5 12 →= 65 53 15 0 1 5 12 , 63 64 0 1 1 5 13 →= 65 53 15 0 1 5 13 , 66 64 0 1 1 5 12 →= 67 53 15 0 1 5 12 , 66 64 0 1 1 5 13 →= 67 53 15 0 1 5 13 , 63 64 0 1 1 7 14 →= 65 53 15 0 1 7 14 , 66 64 0 1 1 7 14 →= 67 53 15 0 1 7 14 , 68 69 0 1 1 1 1 →= 70 56 15 0 1 1 1 , 68 69 0 1 1 1 5 →= 70 56 15 0 1 1 5 , 68 69 0 1 1 1 6 →= 70 56 15 0 1 1 6 , 68 69 0 1 1 1 7 →= 70 56 15 0 1 1 7 , 68 69 0 1 1 1 8 →= 70 56 15 0 1 1 8 , 68 69 0 1 1 6 9 →= 70 56 15 0 1 6 9 , 68 69 0 1 1 6 10 →= 70 56 15 0 1 6 10 , 68 69 0 1 1 6 11 →= 70 56 15 0 1 6 11 , 68 69 0 1 1 6 3 →= 70 56 15 0 1 6 3 , 0 1 1 1 6 3 18 →= 2 3 4 0 6 3 18 , 0 1 1 1 6 3 4 →= 2 3 4 0 6 3 4 , 0 1 1 1 6 3 71 →= 2 3 4 0 6 3 71 , 0 1 1 1 6 9 38 →= 2 3 4 0 6 9 38 , 0 1 1 1 6 9 51 →= 2 3 4 0 6 9 51 , 0 1 1 1 6 9 72 →= 2 3 4 0 6 9 72 , 0 1 1 1 6 10 73 →= 2 3 4 0 6 10 73 , 15 0 1 1 6 3 18 →= 16 17 4 0 6 3 18 , 15 0 1 1 6 3 4 →= 16 17 4 0 6 3 4 , 15 0 1 1 6 3 71 →= 16 17 4 0 6 3 71 , 4 0 1 1 6 3 18 →= 18 17 4 0 6 3 18 , 4 0 1 1 6 3 4 →= 18 17 4 0 6 3 4 , 4 0 1 1 6 3 71 →= 18 17 4 0 6 3 71 , 15 0 1 1 6 9 38 →= 16 17 4 0 6 9 38 , 15 0 1 1 6 9 51 →= 16 17 4 0 6 9 51 , 15 0 1 1 6 9 72 →= 16 17 4 0 6 9 72 , 4 0 1 1 6 9 38 →= 18 17 4 0 6 9 38 , 4 0 1 1 6 9 51 →= 18 17 4 0 6 9 51 , 4 0 1 1 6 9 72 →= 18 17 4 0 6 9 72 , 15 0 1 1 6 10 73 →= 16 17 4 0 6 10 73 , 4 0 1 1 6 10 73 →= 18 17 4 0 6 10 73 , 19 20 0 1 6 3 18 →= 21 22 15 0 6 3 18 , 19 20 0 1 6 3 4 →= 21 22 15 0 6 3 4 , 19 20 0 1 6 3 71 →= 21 22 15 0 6 3 71 , 23 20 0 1 6 3 18 →= 24 22 15 0 6 3 18 , 23 20 0 1 6 3 4 →= 24 22 15 0 6 3 4 , 23 20 0 1 6 3 71 →= 24 22 15 0 6 3 71 , 19 20 0 1 6 9 38 →= 21 22 15 0 6 9 38 , 19 20 0 1 6 9 51 →= 21 22 15 0 6 9 51 , 19 20 0 1 6 9 72 →= 21 22 15 0 6 9 72 , 23 20 0 1 6 9 38 →= 24 22 15 0 6 9 38 , 23 20 0 1 6 9 51 →= 24 22 15 0 6 9 51 , 23 20 0 1 6 9 72 →= 24 22 15 0 6 9 72 , 19 20 0 1 6 10 73 →= 21 22 15 0 6 10 73 , 23 20 0 1 6 10 73 →= 24 22 15 0 6 10 73 , 25 26 0 1 6 3 18 →= 27 28 15 0 6 3 18 , 25 26 0 1 6 3 4 →= 27 28 15 0 6 3 4 , 25 26 0 1 6 3 71 →= 27 28 15 0 6 3 71 , 29 26 0 1 6 3 18 →= 30 28 15 0 6 3 18 , 29 26 0 1 6 3 4 →= 30 28 15 0 6 3 4 , 29 26 0 1 6 3 71 →= 30 28 15 0 6 3 71 , 25 26 0 1 6 9 38 →= 27 28 15 0 6 9 38 , 25 26 0 1 6 9 51 →= 27 28 15 0 6 9 51 , 25 26 0 1 6 9 72 →= 27 28 15 0 6 9 72 , 29 26 0 1 6 9 38 →= 30 28 15 0 6 9 38 , 29 26 0 1 6 9 51 →= 30 28 15 0 6 9 51 , 29 26 0 1 6 9 72 →= 30 28 15 0 6 9 72 , 25 26 0 1 6 10 73 →= 27 28 15 0 6 10 73 , 29 26 0 1 6 10 73 →= 30 28 15 0 6 10 73 , 31 32 0 1 6 3 18 →= 33 34 15 0 6 3 18 , 31 32 0 1 6 3 4 →= 33 34 15 0 6 3 4 , 31 32 0 1 6 3 71 →= 33 34 15 0 6 3 71 , 35 32 0 1 6 3 18 →= 36 34 15 0 6 3 18 , 35 32 0 1 6 3 4 →= 36 34 15 0 6 3 4 , 35 32 0 1 6 3 71 →= 36 34 15 0 6 3 71 , 31 32 0 1 6 9 38 →= 33 34 15 0 6 9 38 , 31 32 0 1 6 9 51 →= 33 34 15 0 6 9 51 , 31 32 0 1 6 9 72 →= 33 34 15 0 6 9 72 , 35 32 0 1 6 9 38 →= 36 34 15 0 6 9 38 , 35 32 0 1 6 9 51 →= 36 34 15 0 6 9 51 , 35 32 0 1 6 9 72 →= 36 34 15 0 6 9 72 , 31 32 0 1 6 10 73 →= 33 34 15 0 6 10 73 , 35 32 0 1 6 10 73 →= 36 34 15 0 6 10 73 , 17 4 0 1 6 3 18 →= 37 38 15 0 6 3 18 , 17 4 0 1 6 3 4 →= 37 38 15 0 6 3 4 , 17 4 0 1 6 3 71 →= 37 38 15 0 6 3 71 , 39 4 0 1 6 3 18 →= 40 38 15 0 6 3 18 , 39 4 0 1 6 3 4 →= 40 38 15 0 6 3 4 , 39 4 0 1 6 3 71 →= 40 38 15 0 6 3 71 , 3 4 0 1 6 3 18 →= 9 38 15 0 6 3 18 , 3 4 0 1 6 3 4 →= 9 38 15 0 6 3 4 , 3 4 0 1 6 3 71 →= 9 38 15 0 6 3 71 , 41 4 0 1 6 3 18 →= 42 38 15 0 6 3 18 , 41 4 0 1 6 3 4 →= 42 38 15 0 6 3 4 , 41 4 0 1 6 3 71 →= 42 38 15 0 6 3 71 , 43 4 0 1 6 3 18 →= 44 38 15 0 6 3 18 , 43 4 0 1 6 3 4 →= 44 38 15 0 6 3 4 , 43 4 0 1 6 3 71 →= 44 38 15 0 6 3 71 , 45 4 0 1 6 3 18 →= 46 38 15 0 6 3 18 , 45 4 0 1 6 3 4 →= 46 38 15 0 6 3 4 , 45 4 0 1 6 3 71 →= 46 38 15 0 6 3 71 , 47 4 0 1 6 3 18 →= 48 38 15 0 6 3 18 , 47 4 0 1 6 3 4 →= 48 38 15 0 6 3 4 , 47 4 0 1 6 3 71 →= 48 38 15 0 6 3 71 , 49 4 0 1 6 3 18 →= 50 38 15 0 6 3 18 , 49 4 0 1 6 3 4 →= 50 38 15 0 6 3 4 , 49 4 0 1 6 3 71 →= 50 38 15 0 6 3 71 , 17 4 0 1 6 9 38 →= 37 38 15 0 6 9 38 , 17 4 0 1 6 9 51 →= 37 38 15 0 6 9 51 , 17 4 0 1 6 9 72 →= 37 38 15 0 6 9 72 , 39 4 0 1 6 9 38 →= 40 38 15 0 6 9 38 , 39 4 0 1 6 9 51 →= 40 38 15 0 6 9 51 , 39 4 0 1 6 9 72 →= 40 38 15 0 6 9 72 , 3 4 0 1 6 9 38 →= 9 38 15 0 6 9 38 , 3 4 0 1 6 9 51 →= 9 38 15 0 6 9 51 , 3 4 0 1 6 9 72 →= 9 38 15 0 6 9 72 , 41 4 0 1 6 9 38 →= 42 38 15 0 6 9 38 , 41 4 0 1 6 9 51 →= 42 38 15 0 6 9 51 , 41 4 0 1 6 9 72 →= 42 38 15 0 6 9 72 , 43 4 0 1 6 9 38 →= 44 38 15 0 6 9 38 , 43 4 0 1 6 9 51 →= 44 38 15 0 6 9 51 , 43 4 0 1 6 9 72 →= 44 38 15 0 6 9 72 , 45 4 0 1 6 9 38 →= 46 38 15 0 6 9 38 , 45 4 0 1 6 9 51 →= 46 38 15 0 6 9 51 , 45 4 0 1 6 9 72 →= 46 38 15 0 6 9 72 , 47 4 0 1 6 9 38 →= 48 38 15 0 6 9 38 , 47 4 0 1 6 9 51 →= 48 38 15 0 6 9 51 , 47 4 0 1 6 9 72 →= 48 38 15 0 6 9 72 , 49 4 0 1 6 9 38 →= 50 38 15 0 6 9 38 , 49 4 0 1 6 9 51 →= 50 38 15 0 6 9 51 , 49 4 0 1 6 9 72 →= 50 38 15 0 6 9 72 , 17 4 0 1 6 10 73 →= 37 38 15 0 6 10 73 , 39 4 0 1 6 10 73 →= 40 38 15 0 6 10 73 , 3 4 0 1 6 10 73 →= 9 38 15 0 6 10 73 , 41 4 0 1 6 10 73 →= 42 38 15 0 6 10 73 , 43 4 0 1 6 10 73 →= 44 38 15 0 6 10 73 , 45 4 0 1 6 10 73 →= 46 38 15 0 6 10 73 , 47 4 0 1 6 10 73 →= 48 38 15 0 6 10 73 , 49 4 0 1 6 10 73 →= 50 38 15 0 6 10 73 , 38 15 0 1 6 3 18 →= 51 52 15 0 6 3 18 , 38 15 0 1 6 3 4 →= 51 52 15 0 6 3 4 , 38 15 0 1 6 3 71 →= 51 52 15 0 6 3 71 , 53 15 0 1 6 3 18 →= 54 52 15 0 6 3 18 , 53 15 0 1 6 3 4 →= 54 52 15 0 6 3 4 , 53 15 0 1 6 3 71 →= 54 52 15 0 6 3 71 , 52 15 0 1 6 3 18 →= 55 52 15 0 6 3 18 , 52 15 0 1 6 3 4 →= 55 52 15 0 6 3 4 , 52 15 0 1 6 3 71 →= 55 52 15 0 6 3 71 , 56 15 0 1 6 3 18 →= 57 52 15 0 6 3 18 , 56 15 0 1 6 3 4 →= 57 52 15 0 6 3 4 , 56 15 0 1 6 3 71 →= 57 52 15 0 6 3 71 , 58 15 0 1 6 3 18 →= 59 52 15 0 6 3 18 , 58 15 0 1 6 3 4 →= 59 52 15 0 6 3 4 , 58 15 0 1 6 3 71 →= 59 52 15 0 6 3 71 , 22 15 0 1 6 3 18 →= 60 52 15 0 6 3 18 , 22 15 0 1 6 3 4 →= 60 52 15 0 6 3 4 , 22 15 0 1 6 3 71 →= 60 52 15 0 6 3 71 , 28 15 0 1 6 3 18 →= 61 52 15 0 6 3 18 , 28 15 0 1 6 3 4 →= 61 52 15 0 6 3 4 , 28 15 0 1 6 3 71 →= 61 52 15 0 6 3 71 , 34 15 0 1 6 3 18 →= 62 52 15 0 6 3 18 , 34 15 0 1 6 3 4 →= 62 52 15 0 6 3 4 , 34 15 0 1 6 3 71 →= 62 52 15 0 6 3 71 , 38 15 0 1 6 9 38 →= 51 52 15 0 6 9 38 , 38 15 0 1 6 9 51 →= 51 52 15 0 6 9 51 , 38 15 0 1 6 9 72 →= 51 52 15 0 6 9 72 , 53 15 0 1 6 9 38 →= 54 52 15 0 6 9 38 , 53 15 0 1 6 9 51 →= 54 52 15 0 6 9 51 , 53 15 0 1 6 9 72 →= 54 52 15 0 6 9 72 , 52 15 0 1 6 9 38 →= 55 52 15 0 6 9 38 , 52 15 0 1 6 9 51 →= 55 52 15 0 6 9 51 , 52 15 0 1 6 9 72 →= 55 52 15 0 6 9 72 , 56 15 0 1 6 9 38 →= 57 52 15 0 6 9 38 , 56 15 0 1 6 9 51 →= 57 52 15 0 6 9 51 , 56 15 0 1 6 9 72 →= 57 52 15 0 6 9 72 , 58 15 0 1 6 9 38 →= 59 52 15 0 6 9 38 , 58 15 0 1 6 9 51 →= 59 52 15 0 6 9 51 , 58 15 0 1 6 9 72 →= 59 52 15 0 6 9 72 , 22 15 0 1 6 9 38 →= 60 52 15 0 6 9 38 , 22 15 0 1 6 9 51 →= 60 52 15 0 6 9 51 , 22 15 0 1 6 9 72 →= 60 52 15 0 6 9 72 , 28 15 0 1 6 9 38 →= 61 52 15 0 6 9 38 , 28 15 0 1 6 9 51 →= 61 52 15 0 6 9 51 , 28 15 0 1 6 9 72 →= 61 52 15 0 6 9 72 , 34 15 0 1 6 9 38 →= 62 52 15 0 6 9 38 , 34 15 0 1 6 9 51 →= 62 52 15 0 6 9 51 , 34 15 0 1 6 9 72 →= 62 52 15 0 6 9 72 , 38 15 0 1 6 10 73 →= 51 52 15 0 6 10 73 , 53 15 0 1 6 10 73 →= 54 52 15 0 6 10 73 , 52 15 0 1 6 10 73 →= 55 52 15 0 6 10 73 , 56 15 0 1 6 10 73 →= 57 52 15 0 6 10 73 , 58 15 0 1 6 10 73 →= 59 52 15 0 6 10 73 , 22 15 0 1 6 10 73 →= 60 52 15 0 6 10 73 , 28 15 0 1 6 10 73 →= 61 52 15 0 6 10 73 , 34 15 0 1 6 10 73 →= 62 52 15 0 6 10 73 , 63 64 0 1 6 3 18 →= 65 53 15 0 6 3 18 , 63 64 0 1 6 3 4 →= 65 53 15 0 6 3 4 , 63 64 0 1 6 3 71 →= 65 53 15 0 6 3 71 , 66 64 0 1 6 3 18 →= 67 53 15 0 6 3 18 , 66 64 0 1 6 3 4 →= 67 53 15 0 6 3 4 , 66 64 0 1 6 3 71 →= 67 53 15 0 6 3 71 , 63 64 0 1 6 9 38 →= 65 53 15 0 6 9 38 , 63 64 0 1 6 9 51 →= 65 53 15 0 6 9 51 , 63 64 0 1 6 9 72 →= 65 53 15 0 6 9 72 , 66 64 0 1 6 9 38 →= 67 53 15 0 6 9 38 , 66 64 0 1 6 9 51 →= 67 53 15 0 6 9 51 , 66 64 0 1 6 9 72 →= 67 53 15 0 6 9 72 , 63 64 0 1 6 10 73 →= 65 53 15 0 6 10 73 , 66 64 0 1 6 10 73 →= 67 53 15 0 6 10 73 , 68 69 0 1 6 3 18 →= 70 56 15 0 6 3 18 , 68 69 0 1 6 3 4 →= 70 56 15 0 6 3 4 , 68 69 0 1 6 3 71 →= 70 56 15 0 6 3 71 , 68 69 0 1 6 9 38 →= 70 56 15 0 6 9 38 , 68 69 0 1 6 9 51 →= 70 56 15 0 6 9 51 , 68 69 0 1 6 9 72 →= 70 56 15 0 6 9 72 , 0 1 1 1 5 12 74 →= 2 3 4 0 5 12 74 , 15 0 1 1 5 12 74 →= 16 17 4 0 5 12 74 , 4 0 1 1 5 12 74 →= 18 17 4 0 5 12 74 , 17 4 0 1 5 12 74 →= 37 38 15 0 5 12 74 , 39 4 0 1 5 12 74 →= 40 38 15 0 5 12 74 , 3 4 0 1 5 12 74 →= 9 38 15 0 5 12 74 , 41 4 0 1 5 12 74 →= 42 38 15 0 5 12 74 , 43 4 0 1 5 12 74 →= 44 38 15 0 5 12 74 , 45 4 0 1 5 12 74 →= 46 38 15 0 5 12 74 , 47 4 0 1 5 12 74 →= 48 38 15 0 5 12 74 , 49 4 0 1 5 12 74 →= 50 38 15 0 5 12 74 , 38 15 0 1 5 12 74 →= 51 52 15 0 5 12 74 , 53 15 0 1 5 12 74 →= 54 52 15 0 5 12 74 , 52 15 0 1 5 12 74 →= 55 52 15 0 5 12 74 , 56 15 0 1 5 12 74 →= 57 52 15 0 5 12 74 , 58 15 0 1 5 12 74 →= 59 52 15 0 5 12 74 , 22 15 0 1 5 12 74 →= 60 52 15 0 5 12 74 , 28 15 0 1 5 12 74 →= 61 52 15 0 5 12 74 , 34 15 0 1 5 12 74 →= 62 52 15 0 5 12 74 , 6 3 4 2 3 4 0 →= 1 1 6 3 4 0 1 , 6 3 4 2 3 18 37 →= 1 1 6 3 4 2 9 , 6 3 4 2 3 18 17 →= 1 1 6 3 4 2 3 , 21 22 15 2 3 4 0 →= 19 20 2 3 4 0 1 , 24 22 15 2 3 4 0 →= 23 20 2 3 4 0 1 , 21 22 15 2 3 18 37 →= 19 20 2 3 4 2 9 , 21 22 15 2 3 18 17 →= 19 20 2 3 4 2 3 , 24 22 15 2 3 18 37 →= 23 20 2 3 4 2 9 , 24 22 15 2 3 18 17 →= 23 20 2 3 4 2 3 , 27 28 15 2 3 4 0 →= 25 26 2 3 4 0 1 , 30 28 15 2 3 4 0 →= 29 26 2 3 4 0 1 , 27 28 15 2 3 18 37 →= 25 26 2 3 4 2 9 , 27 28 15 2 3 18 17 →= 25 26 2 3 4 2 3 , 30 28 15 2 3 18 37 →= 29 26 2 3 4 2 9 , 30 28 15 2 3 18 17 →= 29 26 2 3 4 2 3 , 33 34 15 2 3 4 0 →= 31 32 2 3 4 0 1 , 36 34 15 2 3 4 0 →= 35 32 2 3 4 0 1 , 33 34 15 2 3 18 37 →= 31 32 2 3 4 2 9 , 33 34 15 2 3 18 17 →= 31 32 2 3 4 2 3 , 36 34 15 2 3 18 37 →= 35 32 2 3 4 2 9 , 36 34 15 2 3 18 17 →= 35 32 2 3 4 2 3 , 37 38 15 2 3 4 0 →= 17 4 2 3 4 0 1 , 40 38 15 2 3 4 0 →= 39 4 2 3 4 0 1 , 9 38 15 2 3 4 0 →= 3 4 2 3 4 0 1 , 42 38 15 2 3 4 0 →= 41 4 2 3 4 0 1 , 44 38 15 2 3 4 0 →= 43 4 2 3 4 0 1 , 46 38 15 2 3 4 0 →= 45 4 2 3 4 0 1 , 48 38 15 2 3 4 0 →= 47 4 2 3 4 0 1 , 50 38 15 2 3 4 0 →= 49 4 2 3 4 0 1 , 37 38 15 2 3 18 37 →= 17 4 2 3 4 2 9 , 37 38 15 2 3 18 17 →= 17 4 2 3 4 2 3 , 40 38 15 2 3 18 37 →= 39 4 2 3 4 2 9 , 40 38 15 2 3 18 17 →= 39 4 2 3 4 2 3 , 9 38 15 2 3 18 37 →= 3 4 2 3 4 2 9 , 9 38 15 2 3 18 17 →= 3 4 2 3 4 2 3 , 42 38 15 2 3 18 37 →= 41 4 2 3 4 2 9 , 42 38 15 2 3 18 17 →= 41 4 2 3 4 2 3 , 44 38 15 2 3 18 37 →= 43 4 2 3 4 2 9 , 44 38 15 2 3 18 17 →= 43 4 2 3 4 2 3 , 46 38 15 2 3 18 37 →= 45 4 2 3 4 2 9 , 46 38 15 2 3 18 17 →= 45 4 2 3 4 2 3 , 48 38 15 2 3 18 37 →= 47 4 2 3 4 2 9 , 48 38 15 2 3 18 17 →= 47 4 2 3 4 2 3 , 50 38 15 2 3 18 37 →= 49 4 2 3 4 2 9 , 50 38 15 2 3 18 17 →= 49 4 2 3 4 2 3 , 51 52 15 2 3 4 0 →= 38 15 2 3 4 0 1 , 54 52 15 2 3 4 0 →= 53 15 2 3 4 0 1 , 55 52 15 2 3 4 0 →= 52 15 2 3 4 0 1 , 57 52 15 2 3 4 0 →= 56 15 2 3 4 0 1 , 59 52 15 2 3 4 0 →= 58 15 2 3 4 0 1 , 60 52 15 2 3 4 0 →= 22 15 2 3 4 0 1 , 61 52 15 2 3 4 0 →= 28 15 2 3 4 0 1 , 62 52 15 2 3 4 0 →= 34 15 2 3 4 0 1 , 51 52 15 2 3 18 37 →= 38 15 2 3 4 2 9 , 51 52 15 2 3 18 17 →= 38 15 2 3 4 2 3 , 54 52 15 2 3 18 37 →= 53 15 2 3 4 2 9 , 54 52 15 2 3 18 17 →= 53 15 2 3 4 2 3 , 55 52 15 2 3 18 37 →= 52 15 2 3 4 2 9 , 55 52 15 2 3 18 17 →= 52 15 2 3 4 2 3 , 57 52 15 2 3 18 37 →= 56 15 2 3 4 2 9 , 57 52 15 2 3 18 17 →= 56 15 2 3 4 2 3 , 59 52 15 2 3 18 37 →= 58 15 2 3 4 2 9 , 59 52 15 2 3 18 17 →= 58 15 2 3 4 2 3 , 60 52 15 2 3 18 37 →= 22 15 2 3 4 2 9 , 60 52 15 2 3 18 17 →= 22 15 2 3 4 2 3 , 61 52 15 2 3 18 37 →= 28 15 2 3 4 2 9 , 61 52 15 2 3 18 17 →= 28 15 2 3 4 2 3 , 62 52 15 2 3 18 37 →= 34 15 2 3 4 2 9 , 62 52 15 2 3 18 17 →= 34 15 2 3 4 2 3 , 65 53 15 2 3 4 0 →= 63 64 2 3 4 0 1 , 67 53 15 2 3 4 0 →= 66 64 2 3 4 0 1 , 65 53 15 2 3 18 37 →= 63 64 2 3 4 2 9 , 65 53 15 2 3 18 17 →= 63 64 2 3 4 2 3 , 67 53 15 2 3 18 37 →= 66 64 2 3 4 2 9 , 67 53 15 2 3 18 17 →= 66 64 2 3 4 2 3 , 70 56 15 2 3 4 0 →= 68 69 2 3 4 0 1 , 70 56 15 2 3 18 37 →= 68 69 2 3 4 2 9 , 70 56 15 2 3 18 17 →= 68 69 2 3 4 2 3 , 6 3 4 2 9 38 16 →= 1 1 6 3 18 17 18 , 6 3 4 2 9 38 15 →= 1 1 6 3 18 17 4 , 6 3 4 2 9 51 52 →= 1 1 6 3 18 37 38 , 6 3 4 2 9 51 55 →= 1 1 6 3 18 37 51 , 21 22 15 2 9 38 16 →= 19 20 2 3 18 17 18 , 21 22 15 2 9 38 15 →= 19 20 2 3 18 17 4 , 24 22 15 2 9 38 16 →= 23 20 2 3 18 17 18 , 24 22 15 2 9 38 15 →= 23 20 2 3 18 17 4 , 21 22 15 2 9 51 52 →= 19 20 2 3 18 37 38 , 21 22 15 2 9 51 55 →= 19 20 2 3 18 37 51 , 24 22 15 2 9 51 52 →= 23 20 2 3 18 37 38 , 24 22 15 2 9 51 55 →= 23 20 2 3 18 37 51 , 27 28 15 2 9 38 16 →= 25 26 2 3 18 17 18 , 27 28 15 2 9 38 15 →= 25 26 2 3 18 17 4 , 30 28 15 2 9 38 16 →= 29 26 2 3 18 17 18 , 30 28 15 2 9 38 15 →= 29 26 2 3 18 17 4 , 27 28 15 2 9 51 52 →= 25 26 2 3 18 37 38 , 27 28 15 2 9 51 55 →= 25 26 2 3 18 37 51 , 30 28 15 2 9 51 52 →= 29 26 2 3 18 37 38 , 30 28 15 2 9 51 55 →= 29 26 2 3 18 37 51 , 33 34 15 2 9 38 16 →= 31 32 2 3 18 17 18 , 33 34 15 2 9 38 15 →= 31 32 2 3 18 17 4 , 36 34 15 2 9 38 16 →= 35 32 2 3 18 17 18 , 36 34 15 2 9 38 15 →= 35 32 2 3 18 17 4 , 33 34 15 2 9 51 52 →= 31 32 2 3 18 37 38 , 33 34 15 2 9 51 55 →= 31 32 2 3 18 37 51 , 36 34 15 2 9 51 52 →= 35 32 2 3 18 37 38 , 36 34 15 2 9 51 55 →= 35 32 2 3 18 37 51 , 37 38 15 2 9 38 16 →= 17 4 2 3 18 17 18 , 37 38 15 2 9 38 15 →= 17 4 2 3 18 17 4 , 40 38 15 2 9 38 16 →= 39 4 2 3 18 17 18 , 40 38 15 2 9 38 15 →= 39 4 2 3 18 17 4 , 9 38 15 2 9 38 16 →= 3 4 2 3 18 17 18 , 9 38 15 2 9 38 15 →= 3 4 2 3 18 17 4 , 42 38 15 2 9 38 16 →= 41 4 2 3 18 17 18 , 42 38 15 2 9 38 15 →= 41 4 2 3 18 17 4 , 44 38 15 2 9 38 16 →= 43 4 2 3 18 17 18 , 44 38 15 2 9 38 15 →= 43 4 2 3 18 17 4 , 46 38 15 2 9 38 16 →= 45 4 2 3 18 17 18 , 46 38 15 2 9 38 15 →= 45 4 2 3 18 17 4 , 48 38 15 2 9 38 16 →= 47 4 2 3 18 17 18 , 48 38 15 2 9 38 15 →= 47 4 2 3 18 17 4 , 50 38 15 2 9 38 16 →= 49 4 2 3 18 17 18 , 50 38 15 2 9 38 15 →= 49 4 2 3 18 17 4 , 37 38 15 2 9 51 52 →= 17 4 2 3 18 37 38 , 37 38 15 2 9 51 55 →= 17 4 2 3 18 37 51 , 40 38 15 2 9 51 52 →= 39 4 2 3 18 37 38 , 40 38 15 2 9 51 55 →= 39 4 2 3 18 37 51 , 9 38 15 2 9 51 52 →= 3 4 2 3 18 37 38 , 9 38 15 2 9 51 55 →= 3 4 2 3 18 37 51 , 42 38 15 2 9 51 52 →= 41 4 2 3 18 37 38 , 42 38 15 2 9 51 55 →= 41 4 2 3 18 37 51 , 44 38 15 2 9 51 52 →= 43 4 2 3 18 37 38 , 44 38 15 2 9 51 55 →= 43 4 2 3 18 37 51 , 46 38 15 2 9 51 52 →= 45 4 2 3 18 37 38 , 46 38 15 2 9 51 55 →= 45 4 2 3 18 37 51 , 48 38 15 2 9 51 52 →= 47 4 2 3 18 37 38 , 48 38 15 2 9 51 55 →= 47 4 2 3 18 37 51 , 50 38 15 2 9 51 52 →= 49 4 2 3 18 37 38 , 50 38 15 2 9 51 55 →= 49 4 2 3 18 37 51 , 51 52 15 2 9 38 16 →= 38 15 2 3 18 17 18 , 51 52 15 2 9 38 15 →= 38 15 2 3 18 17 4 , 54 52 15 2 9 38 16 →= 53 15 2 3 18 17 18 , 54 52 15 2 9 38 15 →= 53 15 2 3 18 17 4 , 55 52 15 2 9 38 16 →= 52 15 2 3 18 17 18 , 55 52 15 2 9 38 15 →= 52 15 2 3 18 17 4 , 57 52 15 2 9 38 16 →= 56 15 2 3 18 17 18 , 57 52 15 2 9 38 15 →= 56 15 2 3 18 17 4 , 59 52 15 2 9 38 16 →= 58 15 2 3 18 17 18 , 59 52 15 2 9 38 15 →= 58 15 2 3 18 17 4 , 60 52 15 2 9 38 16 →= 22 15 2 3 18 17 18 , 60 52 15 2 9 38 15 →= 22 15 2 3 18 17 4 , 61 52 15 2 9 38 16 →= 28 15 2 3 18 17 18 , 61 52 15 2 9 38 15 →= 28 15 2 3 18 17 4 , 62 52 15 2 9 38 16 →= 34 15 2 3 18 17 18 , 62 52 15 2 9 38 15 →= 34 15 2 3 18 17 4 , 51 52 15 2 9 51 52 →= 38 15 2 3 18 37 38 , 51 52 15 2 9 51 55 →= 38 15 2 3 18 37 51 , 54 52 15 2 9 51 52 →= 53 15 2 3 18 37 38 , 54 52 15 2 9 51 55 →= 53 15 2 3 18 37 51 , 55 52 15 2 9 51 52 →= 52 15 2 3 18 37 38 , 55 52 15 2 9 51 55 →= 52 15 2 3 18 37 51 , 57 52 15 2 9 51 52 →= 56 15 2 3 18 37 38 , 57 52 15 2 9 51 55 →= 56 15 2 3 18 37 51 , 59 52 15 2 9 51 52 →= 58 15 2 3 18 37 38 , 59 52 15 2 9 51 55 →= 58 15 2 3 18 37 51 , 60 52 15 2 9 51 52 →= 22 15 2 3 18 37 38 , 60 52 15 2 9 51 55 →= 22 15 2 3 18 37 51 , 61 52 15 2 9 51 52 →= 28 15 2 3 18 37 38 , 61 52 15 2 9 51 55 →= 28 15 2 3 18 37 51 , 62 52 15 2 9 51 52 →= 34 15 2 3 18 37 38 , 62 52 15 2 9 51 55 →= 34 15 2 3 18 37 51 , 65 53 15 2 9 38 16 →= 63 64 2 3 18 17 18 , 65 53 15 2 9 38 15 →= 63 64 2 3 18 17 4 , 67 53 15 2 9 38 16 →= 66 64 2 3 18 17 18 , 67 53 15 2 9 38 15 →= 66 64 2 3 18 17 4 , 65 53 15 2 9 51 52 →= 63 64 2 3 18 37 38 , 65 53 15 2 9 51 55 →= 63 64 2 3 18 37 51 , 67 53 15 2 9 51 52 →= 66 64 2 3 18 37 38 , 67 53 15 2 9 51 55 →= 66 64 2 3 18 37 51 , 70 56 15 2 9 38 16 →= 68 69 2 3 18 17 18 , 70 56 15 2 9 38 15 →= 68 69 2 3 18 17 4 , 70 56 15 2 9 51 52 →= 68 69 2 3 18 37 38 , 70 56 15 2 9 51 55 →= 68 69 2 3 18 37 51 } The system is trivially terminating.