/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 { a ↦ 0, b ↦ 1, c ↦ 2 }, it remains to prove termination of the 4-rule system { 0 ⟶ , 0 ⟶ 1 , 0 1 2 ⟶ 2 2 0 1 0 , 2 ⟶ } The system was reversed. After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2 }, it remains to prove termination of the 4-rule system { 0 ⟶ , 0 ⟶ 1 , 2 1 0 ⟶ 0 1 0 2 2 , 2 ⟶ } Applying the dependency pairs transformation. Here, ↑ marks so-called defined symbols. After renaming modulo the bijection { (2,↑) ↦ 0, (1,↓) ↦ 1, (0,↓) ↦ 2, (0,↑) ↦ 3, (2,↓) ↦ 4 }, it remains to prove termination of the 8-rule system { 0 1 2 ⟶ 3 1 2 4 4 , 0 1 2 ⟶ 3 4 4 , 0 1 2 ⟶ 0 4 , 0 1 2 ⟶ 0 , 2 →= , 2 →= 1 , 4 1 2 →= 2 1 2 4 4 , 4 →= } 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 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 4 ↦ 3 }, it remains to prove termination of the 6-rule system { 0 1 2 ⟶ 0 3 , 0 1 2 ⟶ 0 , 2 →= , 2 →= 1 , 3 1 2 →= 2 1 2 3 3 , 3 →= } Applying sparse tiling TROC(2) [Geser/Hofbauer/Waldmann, FSCD 2019]. After renaming modulo the bijection { (4,0) ↦ 0, (0,1) ↦ 1, (1,2) ↦ 2, (2,1) ↦ 3, (0,3) ↦ 4, (3,1) ↦ 5, (2,2) ↦ 6, (3,2) ↦ 7, (2,3) ↦ 8, (3,3) ↦ 9, (2,5) ↦ 10, (3,5) ↦ 11, (0,2) ↦ 12, (0,5) ↦ 13, (1,1) ↦ 14, (1,3) ↦ 15, (1,5) ↦ 16, (4,2) ↦ 17, (4,1) ↦ 18, (4,3) ↦ 19, (4,5) ↦ 20 }, it remains to prove termination of the 88-rule system { 0 1 2 3 ⟶ 0 4 5 , 0 1 2 6 ⟶ 0 4 7 , 0 1 2 8 ⟶ 0 4 9 , 0 1 2 10 ⟶ 0 4 11 , 0 1 2 3 ⟶ 0 1 , 0 1 2 6 ⟶ 0 12 , 0 1 2 8 ⟶ 0 4 , 0 1 2 10 ⟶ 0 13 , 12 3 →= 1 , 12 6 →= 12 , 12 8 →= 4 , 12 10 →= 13 , 2 3 →= 14 , 2 6 →= 2 , 2 8 →= 15 , 2 10 →= 16 , 6 3 →= 3 , 6 6 →= 6 , 6 8 →= 8 , 6 10 →= 10 , 7 3 →= 5 , 7 6 →= 7 , 7 8 →= 9 , 7 10 →= 11 , 17 3 →= 18 , 17 6 →= 17 , 17 8 →= 19 , 17 10 →= 20 , 12 3 →= 1 14 , 12 6 →= 1 2 , 12 8 →= 1 15 , 12 10 →= 1 16 , 2 3 →= 14 14 , 2 6 →= 14 2 , 2 8 →= 14 15 , 2 10 →= 14 16 , 6 3 →= 3 14 , 6 6 →= 3 2 , 6 8 →= 3 15 , 6 10 →= 3 16 , 7 3 →= 5 14 , 7 6 →= 5 2 , 7 8 →= 5 15 , 7 10 →= 5 16 , 17 3 →= 18 14 , 17 6 →= 18 2 , 17 8 →= 18 15 , 17 10 →= 18 16 , 4 5 2 3 →= 12 3 2 8 9 5 , 4 5 2 6 →= 12 3 2 8 9 7 , 4 5 2 8 →= 12 3 2 8 9 9 , 4 5 2 10 →= 12 3 2 8 9 11 , 15 5 2 3 →= 2 3 2 8 9 5 , 15 5 2 6 →= 2 3 2 8 9 7 , 15 5 2 8 →= 2 3 2 8 9 9 , 15 5 2 10 →= 2 3 2 8 9 11 , 8 5 2 3 →= 6 3 2 8 9 5 , 8 5 2 6 →= 6 3 2 8 9 7 , 8 5 2 8 →= 6 3 2 8 9 9 , 8 5 2 10 →= 6 3 2 8 9 11 , 9 5 2 3 →= 7 3 2 8 9 5 , 9 5 2 6 →= 7 3 2 8 9 7 , 9 5 2 8 →= 7 3 2 8 9 9 , 9 5 2 10 →= 7 3 2 8 9 11 , 19 5 2 3 →= 17 3 2 8 9 5 , 19 5 2 6 →= 17 3 2 8 9 7 , 19 5 2 8 →= 17 3 2 8 9 9 , 19 5 2 10 →= 17 3 2 8 9 11 , 4 5 →= 1 , 4 7 →= 12 , 4 9 →= 4 , 4 11 →= 13 , 15 5 →= 14 , 15 7 →= 2 , 15 9 →= 15 , 15 11 →= 16 , 8 5 →= 3 , 8 7 →= 6 , 8 9 →= 8 , 8 11 →= 10 , 9 5 →= 5 , 9 7 →= 7 , 9 9 →= 9 , 9 11 →= 11 , 19 5 →= 18 , 19 7 →= 17 , 19 9 →= 19 , 19 11 →= 20 } Applying sparse untiling TROCU(2) after reversal [Geser/Hofbauer/Waldmann, FSCD 2019]. After renaming modulo the bijection { 3 ↦ 0, 2 ↦ 1, 1 ↦ 2, 0 ↦ 3, 5 ↦ 4, 4 ↦ 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 }, it remains to prove termination of the 64-rule system { 0 1 2 3 ⟶ 0 4 5 , 0 1 2 6 ⟶ 0 4 7 , 0 1 2 8 ⟶ 0 4 9 , 0 1 2 10 ⟶ 0 4 11 , 0 1 2 3 ⟶ 0 1 , 0 1 2 6 ⟶ 0 12 , 0 1 2 8 ⟶ 0 4 , 0 1 2 10 ⟶ 0 13 , 12 3 →= 1 , 2 3 →= 14 , 2 6 →= 2 , 2 8 →= 15 , 2 10 →= 16 , 6 3 →= 3 , 7 3 →= 5 , 17 3 →= 18 , 12 3 →= 1 14 , 2 3 →= 14 14 , 2 6 →= 14 2 , 2 8 →= 14 15 , 2 10 →= 14 16 , 6 3 →= 3 14 , 7 3 →= 5 14 , 17 3 →= 18 14 , 4 5 2 3 →= 12 3 2 8 9 5 , 4 5 2 6 →= 12 3 2 8 9 7 , 4 5 2 8 →= 12 3 2 8 9 9 , 4 5 2 10 →= 12 3 2 8 9 11 , 15 5 2 3 →= 2 3 2 8 9 5 , 15 5 2 6 →= 2 3 2 8 9 7 , 15 5 2 8 →= 2 3 2 8 9 9 , 15 5 2 10 →= 2 3 2 8 9 11 , 8 5 2 3 →= 6 3 2 8 9 5 , 8 5 2 6 →= 6 3 2 8 9 7 , 8 5 2 8 →= 6 3 2 8 9 9 , 8 5 2 10 →= 6 3 2 8 9 11 , 9 5 2 3 →= 7 3 2 8 9 5 , 9 5 2 6 →= 7 3 2 8 9 7 , 9 5 2 8 →= 7 3 2 8 9 9 , 9 5 2 10 →= 7 3 2 8 9 11 , 19 5 2 3 →= 17 3 2 8 9 5 , 19 5 2 6 →= 17 3 2 8 9 7 , 19 5 2 8 →= 17 3 2 8 9 9 , 19 5 2 10 →= 17 3 2 8 9 11 , 4 5 →= 1 , 4 7 →= 12 , 4 9 →= 4 , 4 11 →= 13 , 15 5 →= 14 , 15 7 →= 2 , 15 9 →= 15 , 15 11 →= 16 , 8 5 →= 3 , 8 7 →= 6 , 8 9 →= 8 , 8 11 →= 10 , 9 5 →= 5 , 9 7 →= 7 , 9 9 →= 9 , 9 11 →= 11 , 19 5 →= 18 , 19 7 →= 17 , 19 9 →= 19 , 19 11 →= 20 } 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 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 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 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 20 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 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, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 17 ↦ 17, 18 ↦ 18, 19 ↦ 19 }, it remains to prove termination of the 57-rule system { 0 1 2 3 ⟶ 0 4 5 , 0 1 2 6 ⟶ 0 4 7 , 0 1 2 8 ⟶ 0 4 9 , 0 1 2 10 ⟶ 0 4 11 , 0 1 2 3 ⟶ 0 1 , 0 1 2 6 ⟶ 0 12 , 0 1 2 8 ⟶ 0 4 , 0 1 2 10 ⟶ 0 13 , 12 3 →= 1 , 2 3 →= 14 , 2 6 →= 2 , 2 8 →= 15 , 2 10 →= 16 , 6 3 →= 3 , 7 3 →= 5 , 17 3 →= 18 , 12 3 →= 1 14 , 2 3 →= 14 14 , 2 6 →= 14 2 , 2 8 →= 14 15 , 2 10 →= 14 16 , 6 3 →= 3 14 , 7 3 →= 5 14 , 17 3 →= 18 14 , 4 5 2 3 →= 12 3 2 8 9 5 , 4 5 2 6 →= 12 3 2 8 9 7 , 4 5 2 8 →= 12 3 2 8 9 9 , 4 5 2 10 →= 12 3 2 8 9 11 , 15 5 2 3 →= 2 3 2 8 9 5 , 15 5 2 6 →= 2 3 2 8 9 7 , 15 5 2 8 →= 2 3 2 8 9 9 , 15 5 2 10 →= 2 3 2 8 9 11 , 8 5 2 3 →= 6 3 2 8 9 5 , 8 5 2 6 →= 6 3 2 8 9 7 , 8 5 2 8 →= 6 3 2 8 9 9 , 8 5 2 10 →= 6 3 2 8 9 11 , 9 5 2 3 →= 7 3 2 8 9 5 , 9 5 2 6 →= 7 3 2 8 9 7 , 9 5 2 8 →= 7 3 2 8 9 9 , 9 5 2 10 →= 7 3 2 8 9 11 , 4 5 →= 1 , 4 7 →= 12 , 4 9 →= 4 , 4 11 →= 13 , 15 5 →= 14 , 15 7 →= 2 , 15 9 →= 15 , 15 11 →= 16 , 8 5 →= 3 , 8 7 →= 6 , 8 9 →= 8 , 8 11 →= 10 , 9 5 →= 5 , 9 7 →= 7 , 9 9 →= 9 , 9 11 →= 11 , 19 9 →= 19 } 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 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 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 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 18 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 19 ↦ ⎛ ⎞ ⎜ 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, 13 ↦ 13, 14 ↦ 14, 15 ↦ 15, 16 ↦ 16, 19 ↦ 17 }, it remains to prove termination of the 55-rule system { 0 1 2 3 ⟶ 0 4 5 , 0 1 2 6 ⟶ 0 4 7 , 0 1 2 8 ⟶ 0 4 9 , 0 1 2 10 ⟶ 0 4 11 , 0 1 2 3 ⟶ 0 1 , 0 1 2 6 ⟶ 0 12 , 0 1 2 8 ⟶ 0 4 , 0 1 2 10 ⟶ 0 13 , 12 3 →= 1 , 2 3 →= 14 , 2 6 →= 2 , 2 8 →= 15 , 2 10 →= 16 , 6 3 →= 3 , 7 3 →= 5 , 12 3 →= 1 14 , 2 3 →= 14 14 , 2 6 →= 14 2 , 2 8 →= 14 15 , 2 10 →= 14 16 , 6 3 →= 3 14 , 7 3 →= 5 14 , 4 5 2 3 →= 12 3 2 8 9 5 , 4 5 2 6 →= 12 3 2 8 9 7 , 4 5 2 8 →= 12 3 2 8 9 9 , 4 5 2 10 →= 12 3 2 8 9 11 , 15 5 2 3 →= 2 3 2 8 9 5 , 15 5 2 6 →= 2 3 2 8 9 7 , 15 5 2 8 →= 2 3 2 8 9 9 , 15 5 2 10 →= 2 3 2 8 9 11 , 8 5 2 3 →= 6 3 2 8 9 5 , 8 5 2 6 →= 6 3 2 8 9 7 , 8 5 2 8 →= 6 3 2 8 9 9 , 8 5 2 10 →= 6 3 2 8 9 11 , 9 5 2 3 →= 7 3 2 8 9 5 , 9 5 2 6 →= 7 3 2 8 9 7 , 9 5 2 8 →= 7 3 2 8 9 9 , 9 5 2 10 →= 7 3 2 8 9 11 , 4 5 →= 1 , 4 7 →= 12 , 4 9 →= 4 , 4 11 →= 13 , 15 5 →= 14 , 15 7 →= 2 , 15 9 →= 15 , 15 11 →= 16 , 8 5 →= 3 , 8 7 →= 6 , 8 9 →= 8 , 8 11 →= 10 , 9 5 →= 5 , 9 7 →= 7 , 9 9 →= 9 , 9 11 →= 11 , 17 9 →= 17 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 1 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 2 ⎟ ⎜ 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 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 12 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 13 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 14 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 15 ↦ ⎛ ⎞ ⎜ 1 2 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 16 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 17 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ After renaming modulo the bijection { 2 ↦ 0, 6 ↦ 1, 8 ↦ 2, 15 ↦ 3, 3 ↦ 4, 7 ↦ 5, 5 ↦ 6, 14 ↦ 7, 9 ↦ 8, 10 ↦ 9, 11 ↦ 10, 4 ↦ 11, 17 ↦ 12 }, it remains to prove termination of the 32-rule system { 0 1 →= 0 , 0 2 →= 3 , 1 4 →= 4 , 5 4 →= 6 , 0 1 →= 7 0 , 0 2 →= 7 3 , 1 4 →= 4 7 , 5 4 →= 6 7 , 3 6 0 4 →= 0 4 0 2 8 6 , 3 6 0 1 →= 0 4 0 2 8 5 , 3 6 0 2 →= 0 4 0 2 8 8 , 3 6 0 9 →= 0 4 0 2 8 10 , 2 6 0 4 →= 1 4 0 2 8 6 , 2 6 0 1 →= 1 4 0 2 8 5 , 2 6 0 2 →= 1 4 0 2 8 8 , 2 6 0 9 →= 1 4 0 2 8 10 , 8 6 0 4 →= 5 4 0 2 8 6 , 8 6 0 1 →= 5 4 0 2 8 5 , 8 6 0 2 →= 5 4 0 2 8 8 , 8 6 0 9 →= 5 4 0 2 8 10 , 11 8 →= 11 , 3 5 →= 0 , 3 8 →= 3 , 2 6 →= 4 , 2 5 →= 1 , 2 8 →= 2 , 2 10 →= 9 , 8 6 →= 6 , 8 5 →= 5 , 8 8 →= 8 , 8 10 →= 10 , 12 8 →= 12 } The system is trivially terminating.