/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, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5 }, it remains to prove termination of the 30-rule system { 0 1 2 1 ⟶ 3 3 2 , 1 2 3 2 ⟶ 3 4 4 2 , 0 5 1 4 1 ⟶ 4 1 4 3 , 4 3 0 2 2 ⟶ 4 1 1 4 5 , 5 5 1 5 2 ⟶ 4 3 5 2 , 0 4 3 3 4 4 1 ⟶ 4 4 2 5 0 2 2 , 2 0 4 1 2 2 1 3 ⟶ 2 3 0 4 5 5 1 1 , 1 2 2 1 5 2 1 2 1 ⟶ 1 2 2 2 0 2 4 4 3 , 4 5 1 4 3 4 3 5 4 3 ⟶ 4 3 2 0 2 4 3 2 3 , 1 4 1 2 5 3 4 3 3 2 2 ⟶ 0 0 1 4 0 4 5 2 3 0 4 , 4 5 1 3 2 2 5 4 3 5 4 ⟶ 4 0 1 1 5 3 5 4 2 2 4 , 5 1 4 0 1 5 5 3 3 0 3 2 ⟶ 3 0 5 3 2 0 1 0 4 1 2 , 0 4 1 1 3 3 2 5 4 2 2 1 3 ⟶ 1 0 1 4 3 4 4 2 3 4 2 2 1 , 5 1 3 3 5 3 1 3 2 1 2 0 4 ⟶ 2 2 3 2 3 2 3 5 2 5 1 4 , 0 5 3 5 3 3 3 3 4 5 5 5 4 4 ⟶ 0 1 0 3 2 3 4 0 5 5 2 4 0 , 1 5 0 1 0 4 4 2 2 3 4 1 4 1 ⟶ 3 4 5 0 0 4 0 3 5 0 4 1 5 4 , 5 1 0 5 2 2 2 3 3 2 5 1 5 1 ⟶ 5 4 0 1 4 3 2 2 3 3 3 5 5 1 , 5 1 2 2 4 0 2 4 2 5 2 1 4 0 5 ⟶ 0 1 4 3 0 5 3 4 3 3 1 4 1 5 , 0 4 0 3 2 0 2 1 2 0 0 2 4 2 3 4 ⟶ 3 2 1 3 3 4 5 5 4 0 3 2 1 2 3 , 1 5 1 3 3 3 0 4 0 2 3 1 5 1 4 2 ⟶ 3 4 0 5 0 4 4 0 2 1 3 1 4 0 4 2 , 5 1 1 0 0 3 2 5 0 3 4 2 1 2 5 1 ⟶ 5 1 3 2 1 0 1 0 5 5 3 1 1 4 1 0 , 3 2 1 2 4 2 1 1 3 3 3 5 2 2 0 4 4 ⟶ 3 2 3 1 0 2 0 2 4 5 5 4 1 0 0 2 5 0 , 4 1 0 3 0 4 3 2 2 1 3 2 2 4 0 2 4 ⟶ 4 2 5 3 3 3 1 2 4 5 3 5 3 5 1 3 4 , 3 0 0 2 1 1 3 5 1 2 2 2 5 1 0 0 0 1 ⟶ 3 5 1 0 4 0 1 2 2 5 0 3 4 3 5 5 4 3 , 4 5 5 1 5 3 5 3 2 0 4 4 2 1 0 3 5 3 ⟶ 4 4 0 5 1 3 5 5 3 4 4 0 0 4 3 0 0 0 , 4 5 5 2 5 1 0 2 1 0 1 4 4 4 2 1 5 1 ⟶ 4 3 2 3 0 2 5 3 4 1 4 4 5 1 1 4 0 , 0 2 0 2 2 0 1 1 2 4 1 1 0 3 3 2 1 4 1 4 ⟶ 2 2 3 3 0 2 1 3 5 3 4 4 1 2 4 4 4 4 4 0 , 3 4 1 1 0 3 4 0 5 5 5 5 3 5 2 3 2 3 1 3 ⟶ 3 4 3 4 3 1 0 1 1 4 5 5 2 3 2 3 0 2 3 , 4 5 2 3 5 4 5 0 5 1 2 3 0 1 1 0 3 5 0 3 0 ⟶ 4 4 3 1 4 4 0 5 3 5 2 1 4 2 4 1 0 2 4 5 0 , 5 1 4 0 0 3 4 2 3 0 3 5 4 0 4 2 4 0 0 5 0 ⟶ 5 0 3 2 2 0 4 1 1 5 3 0 1 5 0 1 3 2 2 3 } The system was reversed. After renaming modulo the bijection { 1 ↦ 0, 2 ↦ 1, 0 ↦ 2, 3 ↦ 3, 4 ↦ 4, 5 ↦ 5 }, it remains to prove termination of the 30-rule system { 0 1 0 2 ⟶ 1 3 3 , 1 3 1 0 ⟶ 1 4 4 3 , 0 4 0 5 2 ⟶ 3 4 0 4 , 1 1 2 3 4 ⟶ 5 4 0 0 4 , 1 5 0 5 5 ⟶ 1 5 3 4 , 0 4 4 3 3 4 2 ⟶ 1 1 2 5 1 4 4 , 3 0 1 1 0 4 2 1 ⟶ 0 0 5 5 4 2 3 1 , 0 1 0 1 5 0 1 1 0 ⟶ 3 4 4 1 2 1 1 1 0 , 3 4 5 3 4 3 4 0 5 4 ⟶ 3 1 3 4 1 2 1 3 4 , 1 1 3 3 4 3 5 1 0 4 0 ⟶ 4 2 3 1 5 4 2 4 0 2 2 , 4 5 3 4 5 1 1 3 0 5 4 ⟶ 4 1 1 4 5 3 5 0 0 2 4 , 1 3 2 3 3 5 5 0 2 4 0 5 ⟶ 1 0 4 2 0 2 1 3 5 2 3 , 3 0 1 1 4 5 1 3 3 0 0 4 2 ⟶ 0 1 1 4 3 1 4 4 3 4 0 2 0 , 4 2 1 0 1 3 0 3 5 3 3 0 5 ⟶ 4 0 5 1 5 3 1 3 1 3 1 1 , 4 4 5 5 5 4 3 3 3 3 5 3 5 2 ⟶ 2 4 1 5 5 2 4 3 1 3 2 0 2 , 0 4 0 4 3 1 1 4 4 2 0 2 5 0 ⟶ 4 5 0 4 2 5 3 2 4 2 2 5 4 3 , 0 5 0 5 1 3 3 1 1 1 5 2 0 5 ⟶ 0 5 5 3 3 3 1 1 3 4 0 2 4 5 , 5 2 4 0 1 5 1 4 1 2 4 1 1 0 5 ⟶ 5 0 4 0 3 3 4 3 5 2 3 4 0 2 , 4 3 1 4 1 2 2 1 0 1 2 1 3 2 4 2 ⟶ 3 1 0 1 3 2 4 5 5 4 3 3 0 1 3 , 1 4 0 5 0 3 1 2 4 2 3 3 3 0 5 0 ⟶ 1 4 2 4 0 3 0 1 2 4 4 2 5 2 4 3 , 0 5 1 0 1 4 3 2 5 1 3 2 2 0 0 5 ⟶ 2 0 4 0 0 3 5 5 2 0 2 0 1 3 0 5 , 4 4 2 1 1 5 3 3 3 0 0 1 4 1 0 1 3 ⟶ 2 5 1 2 2 0 4 5 5 4 1 2 1 2 0 3 1 3 , 4 1 2 4 1 1 3 0 1 1 3 4 2 3 2 0 4 ⟶ 4 3 0 5 3 5 3 5 4 1 0 3 3 3 5 1 4 , 0 2 2 2 0 5 1 1 1 0 5 3 0 0 1 2 2 3 ⟶ 3 4 5 5 3 4 3 2 5 1 1 0 2 4 2 0 5 3 , 3 5 3 2 0 1 4 4 2 1 3 5 3 5 0 5 5 4 ⟶ 2 2 2 3 4 2 2 4 4 3 5 5 3 0 5 2 4 4 , 0 5 0 1 4 4 4 0 2 0 1 2 0 5 1 5 5 4 ⟶ 2 4 0 0 5 4 4 0 4 3 5 1 2 3 1 3 4 , 4 0 4 0 1 3 3 2 0 0 4 1 0 0 2 1 1 2 1 2 ⟶ 2 4 4 4 4 4 1 0 4 4 3 5 3 0 1 2 3 3 1 1 , 3 0 3 1 3 1 5 3 5 5 5 5 2 4 3 2 0 0 4 3 ⟶ 3 1 2 3 1 3 1 5 5 4 0 0 2 0 3 4 3 4 3 , 2 3 2 5 3 2 0 0 2 3 1 0 5 2 5 4 5 3 1 5 4 ⟶ 2 5 4 1 2 0 4 1 4 0 1 5 3 5 2 4 4 0 3 4 4 , 2 5 2 2 4 1 4 2 4 5 3 2 3 1 4 3 2 2 4 0 5 ⟶ 3 1 1 3 0 2 5 0 2 3 5 0 0 4 2 1 1 3 2 5 } Applying the dependency pairs transformation. Here, ↑ marks so-called defined symbols. After renaming modulo the bijection { (0,↑) ↦ 0, (1,↓) ↦ 1, (0,↓) ↦ 2, (2,↓) ↦ 3, (1,↑) ↦ 4, (3,↓) ↦ 5, (3,↑) ↦ 6, (4,↓) ↦ 7, (4,↑) ↦ 8, (5,↓) ↦ 9, (5,↑) ↦ 10, (2,↑) ↦ 11 }, it remains to prove termination of the 390-rule system { 0 1 2 3 ⟶ 4 5 5 , 0 1 2 3 ⟶ 6 5 , 0 1 2 3 ⟶ 6 , 4 5 1 2 ⟶ 4 7 7 5 , 4 5 1 2 ⟶ 8 7 5 , 4 5 1 2 ⟶ 8 5 , 4 5 1 2 ⟶ 6 , 0 7 2 9 3 ⟶ 6 7 2 7 , 0 7 2 9 3 ⟶ 8 2 7 , 0 7 2 9 3 ⟶ 0 7 , 0 7 2 9 3 ⟶ 8 , 4 1 3 5 7 ⟶ 10 7 2 2 7 , 4 1 3 5 7 ⟶ 8 2 2 7 , 4 1 3 5 7 ⟶ 0 2 7 , 4 1 3 5 7 ⟶ 0 7 , 4 9 2 9 9 ⟶ 4 9 5 7 , 4 9 2 9 9 ⟶ 10 5 7 , 4 9 2 9 9 ⟶ 6 7 , 4 9 2 9 9 ⟶ 8 , 0 7 7 5 5 7 3 ⟶ 4 1 3 9 1 7 7 , 0 7 7 5 5 7 3 ⟶ 4 3 9 1 7 7 , 0 7 7 5 5 7 3 ⟶ 11 9 1 7 7 , 0 7 7 5 5 7 3 ⟶ 10 1 7 7 , 0 7 7 5 5 7 3 ⟶ 4 7 7 , 0 7 7 5 5 7 3 ⟶ 8 7 , 0 7 7 5 5 7 3 ⟶ 8 , 6 2 1 1 2 7 3 1 ⟶ 0 2 9 9 7 3 5 1 , 6 2 1 1 2 7 3 1 ⟶ 0 9 9 7 3 5 1 , 6 2 1 1 2 7 3 1 ⟶ 10 9 7 3 5 1 , 6 2 1 1 2 7 3 1 ⟶ 10 7 3 5 1 , 6 2 1 1 2 7 3 1 ⟶ 8 3 5 1 , 6 2 1 1 2 7 3 1 ⟶ 11 5 1 , 6 2 1 1 2 7 3 1 ⟶ 6 1 , 0 1 2 1 9 2 1 1 2 ⟶ 6 7 7 1 3 1 1 1 2 , 0 1 2 1 9 2 1 1 2 ⟶ 8 7 1 3 1 1 1 2 , 0 1 2 1 9 2 1 1 2 ⟶ 8 1 3 1 1 1 2 , 0 1 2 1 9 2 1 1 2 ⟶ 4 3 1 1 1 2 , 0 1 2 1 9 2 1 1 2 ⟶ 11 1 1 1 2 , 0 1 2 1 9 2 1 1 2 ⟶ 4 1 1 2 , 6 7 9 5 7 5 7 2 9 7 ⟶ 6 1 5 7 1 3 1 5 7 , 6 7 9 5 7 5 7 2 9 7 ⟶ 4 5 7 1 3 1 5 7 , 6 7 9 5 7 5 7 2 9 7 ⟶ 6 7 1 3 1 5 7 , 6 7 9 5 7 5 7 2 9 7 ⟶ 8 1 3 1 5 7 , 6 7 9 5 7 5 7 2 9 7 ⟶ 4 3 1 5 7 , 6 7 9 5 7 5 7 2 9 7 ⟶ 11 1 5 7 , 6 7 9 5 7 5 7 2 9 7 ⟶ 4 5 7 , 6 7 9 5 7 5 7 2 9 7 ⟶ 6 7 , 4 1 5 5 7 5 9 1 2 7 2 ⟶ 8 3 5 1 9 7 3 7 2 3 3 , 4 1 5 5 7 5 9 1 2 7 2 ⟶ 11 5 1 9 7 3 7 2 3 3 , 4 1 5 5 7 5 9 1 2 7 2 ⟶ 6 1 9 7 3 7 2 3 3 , 4 1 5 5 7 5 9 1 2 7 2 ⟶ 4 9 7 3 7 2 3 3 , 4 1 5 5 7 5 9 1 2 7 2 ⟶ 10 7 3 7 2 3 3 , 4 1 5 5 7 5 9 1 2 7 2 ⟶ 8 3 7 2 3 3 , 4 1 5 5 7 5 9 1 2 7 2 ⟶ 11 7 2 3 3 , 4 1 5 5 7 5 9 1 2 7 2 ⟶ 8 2 3 3 , 4 1 5 5 7 5 9 1 2 7 2 ⟶ 0 3 3 , 4 1 5 5 7 5 9 1 2 7 2 ⟶ 11 3 , 4 1 5 5 7 5 9 1 2 7 2 ⟶ 11 , 8 9 5 7 9 1 1 5 2 9 7 ⟶ 8 1 1 7 9 5 9 2 2 3 7 , 8 9 5 7 9 1 1 5 2 9 7 ⟶ 4 1 7 9 5 9 2 2 3 7 , 8 9 5 7 9 1 1 5 2 9 7 ⟶ 4 7 9 5 9 2 2 3 7 , 8 9 5 7 9 1 1 5 2 9 7 ⟶ 8 9 5 9 2 2 3 7 , 8 9 5 7 9 1 1 5 2 9 7 ⟶ 10 5 9 2 2 3 7 , 8 9 5 7 9 1 1 5 2 9 7 ⟶ 6 9 2 2 3 7 , 8 9 5 7 9 1 1 5 2 9 7 ⟶ 10 2 2 3 7 , 8 9 5 7 9 1 1 5 2 9 7 ⟶ 0 2 3 7 , 8 9 5 7 9 1 1 5 2 9 7 ⟶ 0 3 7 , 8 9 5 7 9 1 1 5 2 9 7 ⟶ 11 7 , 4 5 3 5 5 9 9 2 3 7 2 9 ⟶ 4 2 7 3 2 3 1 5 9 3 5 , 4 5 3 5 5 9 9 2 3 7 2 9 ⟶ 0 7 3 2 3 1 5 9 3 5 , 4 5 3 5 5 9 9 2 3 7 2 9 ⟶ 8 3 2 3 1 5 9 3 5 , 4 5 3 5 5 9 9 2 3 7 2 9 ⟶ 11 2 3 1 5 9 3 5 , 4 5 3 5 5 9 9 2 3 7 2 9 ⟶ 0 3 1 5 9 3 5 , 4 5 3 5 5 9 9 2 3 7 2 9 ⟶ 11 1 5 9 3 5 , 4 5 3 5 5 9 9 2 3 7 2 9 ⟶ 4 5 9 3 5 , 4 5 3 5 5 9 9 2 3 7 2 9 ⟶ 6 9 3 5 , 4 5 3 5 5 9 9 2 3 7 2 9 ⟶ 10 3 5 , 4 5 3 5 5 9 9 2 3 7 2 9 ⟶ 11 5 , 4 5 3 5 5 9 9 2 3 7 2 9 ⟶ 6 , 6 2 1 1 7 9 1 5 5 2 2 7 3 ⟶ 0 1 1 7 5 1 7 7 5 7 2 3 2 , 6 2 1 1 7 9 1 5 5 2 2 7 3 ⟶ 4 1 7 5 1 7 7 5 7 2 3 2 , 6 2 1 1 7 9 1 5 5 2 2 7 3 ⟶ 4 7 5 1 7 7 5 7 2 3 2 , 6 2 1 1 7 9 1 5 5 2 2 7 3 ⟶ 8 5 1 7 7 5 7 2 3 2 , 6 2 1 1 7 9 1 5 5 2 2 7 3 ⟶ 6 1 7 7 5 7 2 3 2 , 6 2 1 1 7 9 1 5 5 2 2 7 3 ⟶ 4 7 7 5 7 2 3 2 , 6 2 1 1 7 9 1 5 5 2 2 7 3 ⟶ 8 7 5 7 2 3 2 , 6 2 1 1 7 9 1 5 5 2 2 7 3 ⟶ 8 5 7 2 3 2 , 6 2 1 1 7 9 1 5 5 2 2 7 3 ⟶ 6 7 2 3 2 , 6 2 1 1 7 9 1 5 5 2 2 7 3 ⟶ 8 2 3 2 , 6 2 1 1 7 9 1 5 5 2 2 7 3 ⟶ 0 3 2 , 6 2 1 1 7 9 1 5 5 2 2 7 3 ⟶ 11 2 , 6 2 1 1 7 9 1 5 5 2 2 7 3 ⟶ 0 , 8 3 1 2 1 5 2 5 9 5 5 2 9 ⟶ 8 2 9 1 9 5 1 5 1 5 1 1 , 8 3 1 2 1 5 2 5 9 5 5 2 9 ⟶ 0 9 1 9 5 1 5 1 5 1 1 , 8 3 1 2 1 5 2 5 9 5 5 2 9 ⟶ 10 1 9 5 1 5 1 5 1 1 , 8 3 1 2 1 5 2 5 9 5 5 2 9 ⟶ 4 9 5 1 5 1 5 1 1 , 8 3 1 2 1 5 2 5 9 5 5 2 9 ⟶ 10 5 1 5 1 5 1 1 , 8 3 1 2 1 5 2 5 9 5 5 2 9 ⟶ 6 1 5 1 5 1 1 , 8 3 1 2 1 5 2 5 9 5 5 2 9 ⟶ 4 5 1 5 1 1 , 8 3 1 2 1 5 2 5 9 5 5 2 9 ⟶ 6 1 5 1 1 , 8 3 1 2 1 5 2 5 9 5 5 2 9 ⟶ 4 5 1 1 , 8 3 1 2 1 5 2 5 9 5 5 2 9 ⟶ 6 1 1 , 8 3 1 2 1 5 2 5 9 5 5 2 9 ⟶ 4 1 , 8 3 1 2 1 5 2 5 9 5 5 2 9 ⟶ 4 , 8 7 9 9 9 7 5 5 5 5 9 5 9 3 ⟶ 11 7 1 9 9 3 7 5 1 5 3 2 3 , 8 7 9 9 9 7 5 5 5 5 9 5 9 3 ⟶ 8 1 9 9 3 7 5 1 5 3 2 3 , 8 7 9 9 9 7 5 5 5 5 9 5 9 3 ⟶ 4 9 9 3 7 5 1 5 3 2 3 , 8 7 9 9 9 7 5 5 5 5 9 5 9 3 ⟶ 10 9 3 7 5 1 5 3 2 3 , 8 7 9 9 9 7 5 5 5 5 9 5 9 3 ⟶ 10 3 7 5 1 5 3 2 3 , 8 7 9 9 9 7 5 5 5 5 9 5 9 3 ⟶ 11 7 5 1 5 3 2 3 , 8 7 9 9 9 7 5 5 5 5 9 5 9 3 ⟶ 8 5 1 5 3 2 3 , 8 7 9 9 9 7 5 5 5 5 9 5 9 3 ⟶ 6 1 5 3 2 3 , 8 7 9 9 9 7 5 5 5 5 9 5 9 3 ⟶ 4 5 3 2 3 , 8 7 9 9 9 7 5 5 5 5 9 5 9 3 ⟶ 6 3 2 3 , 8 7 9 9 9 7 5 5 5 5 9 5 9 3 ⟶ 11 2 3 , 8 7 9 9 9 7 5 5 5 5 9 5 9 3 ⟶ 0 3 , 0 7 2 7 5 1 1 7 7 3 2 3 9 2 ⟶ 8 9 2 7 3 9 5 3 7 3 3 9 7 5 , 0 7 2 7 5 1 1 7 7 3 2 3 9 2 ⟶ 10 2 7 3 9 5 3 7 3 3 9 7 5 , 0 7 2 7 5 1 1 7 7 3 2 3 9 2 ⟶ 0 7 3 9 5 3 7 3 3 9 7 5 , 0 7 2 7 5 1 1 7 7 3 2 3 9 2 ⟶ 8 3 9 5 3 7 3 3 9 7 5 , 0 7 2 7 5 1 1 7 7 3 2 3 9 2 ⟶ 11 9 5 3 7 3 3 9 7 5 , 0 7 2 7 5 1 1 7 7 3 2 3 9 2 ⟶ 10 5 3 7 3 3 9 7 5 , 0 7 2 7 5 1 1 7 7 3 2 3 9 2 ⟶ 6 3 7 3 3 9 7 5 , 0 7 2 7 5 1 1 7 7 3 2 3 9 2 ⟶ 11 7 3 3 9 7 5 , 0 7 2 7 5 1 1 7 7 3 2 3 9 2 ⟶ 8 3 3 9 7 5 , 0 7 2 7 5 1 1 7 7 3 2 3 9 2 ⟶ 11 3 9 7 5 , 0 7 2 7 5 1 1 7 7 3 2 3 9 2 ⟶ 11 9 7 5 , 0 7 2 7 5 1 1 7 7 3 2 3 9 2 ⟶ 10 7 5 , 0 7 2 7 5 1 1 7 7 3 2 3 9 2 ⟶ 8 5 , 0 7 2 7 5 1 1 7 7 3 2 3 9 2 ⟶ 6 , 0 9 2 9 1 5 5 1 1 1 9 3 2 9 ⟶ 0 9 9 5 5 5 1 1 5 7 2 3 7 9 , 0 9 2 9 1 5 5 1 1 1 9 3 2 9 ⟶ 10 9 5 5 5 1 1 5 7 2 3 7 9 , 0 9 2 9 1 5 5 1 1 1 9 3 2 9 ⟶ 10 5 5 5 1 1 5 7 2 3 7 9 , 0 9 2 9 1 5 5 1 1 1 9 3 2 9 ⟶ 6 5 5 1 1 5 7 2 3 7 9 , 0 9 2 9 1 5 5 1 1 1 9 3 2 9 ⟶ 6 5 1 1 5 7 2 3 7 9 , 0 9 2 9 1 5 5 1 1 1 9 3 2 9 ⟶ 6 1 1 5 7 2 3 7 9 , 0 9 2 9 1 5 5 1 1 1 9 3 2 9 ⟶ 4 1 5 7 2 3 7 9 , 0 9 2 9 1 5 5 1 1 1 9 3 2 9 ⟶ 4 5 7 2 3 7 9 , 0 9 2 9 1 5 5 1 1 1 9 3 2 9 ⟶ 6 7 2 3 7 9 , 0 9 2 9 1 5 5 1 1 1 9 3 2 9 ⟶ 8 2 3 7 9 , 0 9 2 9 1 5 5 1 1 1 9 3 2 9 ⟶ 0 3 7 9 , 0 9 2 9 1 5 5 1 1 1 9 3 2 9 ⟶ 11 7 9 , 0 9 2 9 1 5 5 1 1 1 9 3 2 9 ⟶ 8 9 , 10 3 7 2 1 9 1 7 1 3 7 1 1 2 9 ⟶ 10 2 7 2 5 5 7 5 9 3 5 7 2 3 , 10 3 7 2 1 9 1 7 1 3 7 1 1 2 9 ⟶ 0 7 2 5 5 7 5 9 3 5 7 2 3 , 10 3 7 2 1 9 1 7 1 3 7 1 1 2 9 ⟶ 8 2 5 5 7 5 9 3 5 7 2 3 , 10 3 7 2 1 9 1 7 1 3 7 1 1 2 9 ⟶ 0 5 5 7 5 9 3 5 7 2 3 , 10 3 7 2 1 9 1 7 1 3 7 1 1 2 9 ⟶ 6 5 7 5 9 3 5 7 2 3 , 10 3 7 2 1 9 1 7 1 3 7 1 1 2 9 ⟶ 6 7 5 9 3 5 7 2 3 , 10 3 7 2 1 9 1 7 1 3 7 1 1 2 9 ⟶ 8 5 9 3 5 7 2 3 , 10 3 7 2 1 9 1 7 1 3 7 1 1 2 9 ⟶ 6 9 3 5 7 2 3 , 10 3 7 2 1 9 1 7 1 3 7 1 1 2 9 ⟶ 10 3 5 7 2 3 , 10 3 7 2 1 9 1 7 1 3 7 1 1 2 9 ⟶ 11 5 7 2 3 , 10 3 7 2 1 9 1 7 1 3 7 1 1 2 9 ⟶ 6 7 2 3 , 10 3 7 2 1 9 1 7 1 3 7 1 1 2 9 ⟶ 8 2 3 , 10 3 7 2 1 9 1 7 1 3 7 1 1 2 9 ⟶ 0 3 , 10 3 7 2 1 9 1 7 1 3 7 1 1 2 9 ⟶ 11 , 8 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 ⟶ 6 1 2 1 5 3 7 9 9 7 5 5 2 1 5 , 8 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 ⟶ 4 2 1 5 3 7 9 9 7 5 5 2 1 5 , 8 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 ⟶ 0 1 5 3 7 9 9 7 5 5 2 1 5 , 8 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 ⟶ 4 5 3 7 9 9 7 5 5 2 1 5 , 8 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 ⟶ 6 3 7 9 9 7 5 5 2 1 5 , 8 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 ⟶ 11 7 9 9 7 5 5 2 1 5 , 8 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 ⟶ 8 9 9 7 5 5 2 1 5 , 8 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 ⟶ 10 9 7 5 5 2 1 5 , 8 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 ⟶ 10 7 5 5 2 1 5 , 8 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 ⟶ 8 5 5 2 1 5 , 8 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 ⟶ 6 5 2 1 5 , 8 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 ⟶ 6 2 1 5 , 8 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 ⟶ 0 1 5 , 8 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 ⟶ 4 5 , 8 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 ⟶ 6 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 4 7 3 7 2 5 2 1 3 7 7 3 9 3 7 5 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 8 3 7 2 5 2 1 3 7 7 3 9 3 7 5 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 11 7 2 5 2 1 3 7 7 3 9 3 7 5 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 8 2 5 2 1 3 7 7 3 9 3 7 5 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 0 5 2 1 3 7 7 3 9 3 7 5 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 6 2 1 3 7 7 3 9 3 7 5 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 0 1 3 7 7 3 9 3 7 5 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 4 3 7 7 3 9 3 7 5 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 11 7 7 3 9 3 7 5 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 8 7 3 9 3 7 5 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 8 3 9 3 7 5 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 11 9 3 7 5 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 10 3 7 5 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 11 7 5 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 8 5 , 4 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 ⟶ 6 , 0 9 1 2 1 7 5 3 9 1 5 3 3 2 2 9 ⟶ 11 2 7 2 2 5 9 9 3 2 3 2 1 5 2 9 , 0 9 1 2 1 7 5 3 9 1 5 3 3 2 2 9 ⟶ 0 7 2 2 5 9 9 3 2 3 2 1 5 2 9 , 0 9 1 2 1 7 5 3 9 1 5 3 3 2 2 9 ⟶ 8 2 2 5 9 9 3 2 3 2 1 5 2 9 , 0 9 1 2 1 7 5 3 9 1 5 3 3 2 2 9 ⟶ 0 2 5 9 9 3 2 3 2 1 5 2 9 , 0 9 1 2 1 7 5 3 9 1 5 3 3 2 2 9 ⟶ 0 5 9 9 3 2 3 2 1 5 2 9 , 0 9 1 2 1 7 5 3 9 1 5 3 3 2 2 9 ⟶ 6 9 9 3 2 3 2 1 5 2 9 , 0 9 1 2 1 7 5 3 9 1 5 3 3 2 2 9 ⟶ 10 9 3 2 3 2 1 5 2 9 , 0 9 1 2 1 7 5 3 9 1 5 3 3 2 2 9 ⟶ 10 3 2 3 2 1 5 2 9 , 0 9 1 2 1 7 5 3 9 1 5 3 3 2 2 9 ⟶ 11 2 3 2 1 5 2 9 , 0 9 1 2 1 7 5 3 9 1 5 3 3 2 2 9 ⟶ 0 3 2 1 5 2 9 , 0 9 1 2 1 7 5 3 9 1 5 3 3 2 2 9 ⟶ 11 2 1 5 2 9 , 0 9 1 2 1 7 5 3 9 1 5 3 3 2 2 9 ⟶ 0 1 5 2 9 , 0 9 1 2 1 7 5 3 9 1 5 3 3 2 2 9 ⟶ 4 5 2 9 , 0 9 1 2 1 7 5 3 9 1 5 3 3 2 2 9 ⟶ 6 2 9 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 11 9 1 3 3 2 7 9 9 7 1 3 1 3 2 5 1 5 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 10 1 3 3 2 7 9 9 7 1 3 1 3 2 5 1 5 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 4 3 3 2 7 9 9 7 1 3 1 3 2 5 1 5 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 11 3 2 7 9 9 7 1 3 1 3 2 5 1 5 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 11 2 7 9 9 7 1 3 1 3 2 5 1 5 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 0 7 9 9 7 1 3 1 3 2 5 1 5 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 8 9 9 7 1 3 1 3 2 5 1 5 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 10 9 7 1 3 1 3 2 5 1 5 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 10 7 1 3 1 3 2 5 1 5 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 8 1 3 1 3 2 5 1 5 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 4 3 1 3 2 5 1 5 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 11 1 3 2 5 1 5 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 4 3 2 5 1 5 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 11 2 5 1 5 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 0 5 1 5 , 8 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 ⟶ 6 1 5 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 8 5 2 9 5 9 5 9 7 1 2 5 5 5 9 1 7 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 6 2 9 5 9 5 9 7 1 2 5 5 5 9 1 7 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 0 9 5 9 5 9 7 1 2 5 5 5 9 1 7 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 10 5 9 5 9 7 1 2 5 5 5 9 1 7 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 6 9 5 9 7 1 2 5 5 5 9 1 7 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 10 5 9 7 1 2 5 5 5 9 1 7 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 6 9 7 1 2 5 5 5 9 1 7 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 10 7 1 2 5 5 5 9 1 7 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 8 1 2 5 5 5 9 1 7 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 4 2 5 5 5 9 1 7 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 0 5 5 5 9 1 7 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 6 5 5 9 1 7 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 6 5 9 1 7 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 6 9 1 7 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 10 1 7 , 8 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 ⟶ 4 7 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 6 7 9 9 5 7 5 3 9 1 1 2 3 7 3 2 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 8 9 9 5 7 5 3 9 1 1 2 3 7 3 2 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 10 9 5 7 5 3 9 1 1 2 3 7 3 2 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 10 5 7 5 3 9 1 1 2 3 7 3 2 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 6 7 5 3 9 1 1 2 3 7 3 2 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 8 5 3 9 1 1 2 3 7 3 2 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 6 3 9 1 1 2 3 7 3 2 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 11 9 1 1 2 3 7 3 2 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 10 1 1 2 3 7 3 2 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 4 1 2 3 7 3 2 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 4 2 3 7 3 2 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 0 3 7 3 2 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 11 7 3 2 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 8 3 2 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 11 2 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 0 9 5 , 0 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 ⟶ 10 5 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 11 3 3 5 7 3 3 7 7 5 9 9 5 2 9 3 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 11 3 5 7 3 3 7 7 5 9 9 5 2 9 3 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 11 5 7 3 3 7 7 5 9 9 5 2 9 3 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 6 7 3 3 7 7 5 9 9 5 2 9 3 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 8 3 3 7 7 5 9 9 5 2 9 3 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 11 3 7 7 5 9 9 5 2 9 3 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 11 7 7 5 9 9 5 2 9 3 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 8 7 5 9 9 5 2 9 3 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 8 5 9 9 5 2 9 3 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 6 9 9 5 2 9 3 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 10 9 5 2 9 3 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 10 5 2 9 3 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 6 2 9 3 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 0 9 3 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 10 3 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 11 7 7 , 6 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 ⟶ 8 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 11 7 2 2 9 7 7 2 7 5 9 1 3 5 1 5 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 8 2 2 9 7 7 2 7 5 9 1 3 5 1 5 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 0 2 9 7 7 2 7 5 9 1 3 5 1 5 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 0 9 7 7 2 7 5 9 1 3 5 1 5 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 10 7 7 2 7 5 9 1 3 5 1 5 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 8 7 2 7 5 9 1 3 5 1 5 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 8 2 7 5 9 1 3 5 1 5 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 0 7 5 9 1 3 5 1 5 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 8 5 9 1 3 5 1 5 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 6 9 1 3 5 1 5 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 10 1 3 5 1 5 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 4 3 5 1 5 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 11 5 1 5 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 6 1 5 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 4 5 7 , 0 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 ⟶ 6 7 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 11 7 7 7 7 7 1 2 7 7 5 9 5 2 1 3 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 8 7 7 7 7 1 2 7 7 5 9 5 2 1 3 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 8 7 7 7 1 2 7 7 5 9 5 2 1 3 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 8 7 7 1 2 7 7 5 9 5 2 1 3 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 8 7 1 2 7 7 5 9 5 2 1 3 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 8 1 2 7 7 5 9 5 2 1 3 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 4 2 7 7 5 9 5 2 1 3 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 0 7 7 5 9 5 2 1 3 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 8 7 5 9 5 2 1 3 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 8 5 9 5 2 1 3 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 6 9 5 2 1 3 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 10 5 2 1 3 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 6 2 1 3 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 0 1 3 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 4 3 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 11 5 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 6 5 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 6 1 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 4 1 , 8 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 ⟶ 4 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 6 1 3 5 1 5 1 9 9 7 2 2 3 2 5 7 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 4 3 5 1 5 1 9 9 7 2 2 3 2 5 7 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 11 5 1 5 1 9 9 7 2 2 3 2 5 7 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 6 1 5 1 9 9 7 2 2 3 2 5 7 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 4 5 1 9 9 7 2 2 3 2 5 7 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 6 1 9 9 7 2 2 3 2 5 7 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 4 9 9 7 2 2 3 2 5 7 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 10 9 7 2 2 3 2 5 7 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 10 7 2 2 3 2 5 7 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 8 2 2 3 2 5 7 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 0 2 3 2 5 7 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 0 3 2 5 7 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 11 2 5 7 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 0 5 7 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 6 7 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 8 5 7 5 , 6 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 ⟶ 6 7 5 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 11 9 7 1 3 2 7 1 7 2 1 9 5 9 3 7 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 10 7 1 3 2 7 1 7 2 1 9 5 9 3 7 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 8 1 3 2 7 1 7 2 1 9 5 9 3 7 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 4 3 2 7 1 7 2 1 9 5 9 3 7 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 11 2 7 1 7 2 1 9 5 9 3 7 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 0 7 1 7 2 1 9 5 9 3 7 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 8 1 7 2 1 9 5 9 3 7 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 4 7 2 1 9 5 9 3 7 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 8 2 1 9 5 9 3 7 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 0 1 9 5 9 3 7 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 4 9 5 9 3 7 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 10 5 9 3 7 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 6 9 3 7 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 10 3 7 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 11 7 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 8 7 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 8 2 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 0 5 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 6 7 7 , 11 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 ⟶ 8 7 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 6 1 1 5 2 3 9 2 3 5 9 2 2 7 3 1 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 4 1 5 2 3 9 2 3 5 9 2 2 7 3 1 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 4 5 2 3 9 2 3 5 9 2 2 7 3 1 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 6 2 3 9 2 3 5 9 2 2 7 3 1 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 0 3 9 2 3 5 9 2 2 7 3 1 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 11 9 2 3 5 9 2 2 7 3 1 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 10 2 3 5 9 2 2 7 3 1 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 0 3 5 9 2 2 7 3 1 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 11 5 9 2 2 7 3 1 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 6 9 2 2 7 3 1 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 10 2 2 7 3 1 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 0 2 7 3 1 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 0 7 3 1 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 8 3 1 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 11 1 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 4 1 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 4 5 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 6 3 9 , 11 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 ⟶ 11 9 , 2 1 2 3 →= 1 5 5 , 1 5 1 2 →= 1 7 7 5 , 2 7 2 9 3 →= 5 7 2 7 , 1 1 3 5 7 →= 9 7 2 2 7 , 1 9 2 9 9 →= 1 9 5 7 , 2 7 7 5 5 7 3 →= 1 1 3 9 1 7 7 , 5 2 1 1 2 7 3 1 →= 2 2 9 9 7 3 5 1 , 2 1 2 1 9 2 1 1 2 →= 5 7 7 1 3 1 1 1 2 , 5 7 9 5 7 5 7 2 9 7 →= 5 1 5 7 1 3 1 5 7 , 1 1 5 5 7 5 9 1 2 7 2 →= 7 3 5 1 9 7 3 7 2 3 3 , 7 9 5 7 9 1 1 5 2 9 7 →= 7 1 1 7 9 5 9 2 2 3 7 , 1 5 3 5 5 9 9 2 3 7 2 9 →= 1 2 7 3 2 3 1 5 9 3 5 , 5 2 1 1 7 9 1 5 5 2 2 7 3 →= 2 1 1 7 5 1 7 7 5 7 2 3 2 , 7 3 1 2 1 5 2 5 9 5 5 2 9 →= 7 2 9 1 9 5 1 5 1 5 1 1 , 7 7 9 9 9 7 5 5 5 5 9 5 9 3 →= 3 7 1 9 9 3 7 5 1 5 3 2 3 , 2 7 2 7 5 1 1 7 7 3 2 3 9 2 →= 7 9 2 7 3 9 5 3 7 3 3 9 7 5 , 2 9 2 9 1 5 5 1 1 1 9 3 2 9 →= 2 9 9 5 5 5 1 1 5 7 2 3 7 9 , 9 3 7 2 1 9 1 7 1 3 7 1 1 2 9 →= 9 2 7 2 5 5 7 5 9 3 5 7 2 3 , 7 5 1 7 1 3 3 1 2 1 3 1 5 3 7 3 →= 5 1 2 1 5 3 7 9 9 7 5 5 2 1 5 , 1 7 2 9 2 5 1 3 7 3 5 5 5 2 9 2 →= 1 7 3 7 2 5 2 1 3 7 7 3 9 3 7 5 , 2 9 1 2 1 7 5 3 9 1 5 3 3 2 2 9 →= 3 2 7 2 2 5 9 9 3 2 3 2 1 5 2 9 , 7 7 3 1 1 9 5 5 5 2 2 1 7 1 2 1 5 →= 3 9 1 3 3 2 7 9 9 7 1 3 1 3 2 5 1 5 , 7 1 3 7 1 1 5 2 1 1 5 7 3 5 3 2 7 →= 7 5 2 9 5 9 5 9 7 1 2 5 5 5 9 1 7 , 2 3 3 3 2 9 1 1 1 2 9 5 2 2 1 3 3 5 →= 5 7 9 9 5 7 5 3 9 1 1 2 3 7 3 2 9 5 , 5 9 5 3 2 1 7 7 3 1 5 9 5 9 2 9 9 7 →= 3 3 3 5 7 3 3 7 7 5 9 9 5 2 9 3 7 7 , 2 9 2 1 7 7 7 2 3 2 1 3 2 9 1 9 9 7 →= 3 7 2 2 9 7 7 2 7 5 9 1 3 5 1 5 7 , 7 2 7 2 1 5 5 3 2 2 7 1 2 2 3 1 1 3 1 3 →= 3 7 7 7 7 7 1 2 7 7 5 9 5 2 1 3 5 5 1 1 , 5 2 5 1 5 1 9 5 9 9 9 9 3 7 5 3 2 2 7 5 →= 5 1 3 5 1 5 1 9 9 7 2 2 3 2 5 7 5 7 5 , 3 5 3 9 5 3 2 2 3 5 1 2 9 3 9 7 9 5 1 9 7 →= 3 9 7 1 3 2 7 1 7 2 1 9 5 9 3 7 7 2 5 7 7 , 3 9 3 3 7 1 7 3 7 9 5 3 5 1 7 5 3 3 7 2 9 →= 5 1 1 5 2 3 9 2 3 5 9 2 2 7 3 1 1 5 3 9 } 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 76 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 70 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 61 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 77 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 7 ↦ ⎛ ⎞ ⎜ 1 64 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 8 ↦ ⎛ ⎞ ⎜ 1 4 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 9 ↦ ⎛ ⎞ ⎜ 1 60 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 10 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 11 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ After renaming modulo the bijection { 0 ↦ 0, 9 ↦ 1, 2 ↦ 2, 1 ↦ 3, 5 ↦ 4, 3 ↦ 5, 7 ↦ 6, 11 ↦ 7 }, it remains to prove termination of the 7-rule system { 0 1 2 1 3 4 4 3 3 3 1 5 2 1 ⟶ 0 1 1 4 4 4 3 3 4 6 2 5 6 1 , 7 4 5 1 4 5 2 2 5 4 3 2 1 5 1 6 1 4 3 1 6 ⟶ 7 1 6 3 5 2 6 3 6 2 3 1 4 1 5 6 6 2 4 6 6 , 2 6 6 4 4 6 5 →= 3 3 5 1 3 6 6 , 2 1 2 1 3 4 4 3 3 3 1 5 2 1 →= 2 1 1 4 4 4 3 3 4 6 2 5 6 1 , 6 6 5 3 3 1 4 4 4 2 2 3 6 3 2 3 4 →= 5 1 3 5 5 2 6 1 1 6 3 5 3 5 2 4 3 4 , 5 4 5 1 4 5 2 2 5 4 3 2 1 5 1 6 1 4 3 1 6 →= 5 1 6 3 5 2 6 3 6 2 3 1 4 1 5 6 6 2 4 6 6 , 5 1 5 5 6 3 6 5 6 1 4 5 4 3 6 4 5 5 6 2 1 →= 4 3 3 4 2 5 1 2 5 4 1 2 2 6 5 3 3 4 5 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 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 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 1 0 0 0 0 0 0 0 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 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 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 0 0 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 0 0 0 0 0 0 ⎟ ⎝ ⎠ 2 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 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 0 1 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 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 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 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 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 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 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟ ⎜ 0 0 0 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 0 0 ⎟ ⎜ 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 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 ⎟ ⎜ 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 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 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 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 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 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 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 { 7 ↦ 0, 4 ↦ 1, 5 ↦ 2, 1 ↦ 3, 2 ↦ 4, 3 ↦ 5, 6 ↦ 6 }, it remains to prove termination of the 6-rule system { 0 1 2 3 1 2 4 4 2 1 5 4 3 2 3 6 3 1 5 3 6 ⟶ 0 3 6 5 2 4 6 5 6 4 5 3 1 3 2 6 6 4 1 6 6 , 4 6 6 1 1 6 2 →= 5 5 2 3 5 6 6 , 4 3 4 3 5 1 1 5 5 5 3 2 4 3 →= 4 3 3 1 1 1 5 5 1 6 4 2 6 3 , 6 6 2 5 5 3 1 1 1 4 4 5 6 5 4 5 1 →= 2 3 5 2 2 4 6 3 3 6 5 2 5 2 4 1 5 1 , 2 1 2 3 1 2 4 4 2 1 5 4 3 2 3 6 3 1 5 3 6 →= 2 3 6 5 2 4 6 5 6 4 5 3 1 3 2 6 6 4 1 6 6 , 2 3 2 2 6 5 6 2 6 3 1 2 1 5 6 1 2 2 6 4 3 →= 1 5 5 1 4 2 3 4 2 1 3 4 4 6 2 5 5 1 2 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 ↦ ⎛ ⎞ ⎜ 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 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 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 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 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 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 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 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 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 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 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 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 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 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 0 0 0 0 0 0 ⎟ ⎜ 0 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 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 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 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 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 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟ ⎝ ⎠ After renaming modulo the bijection { 4 ↦ 0, 6 ↦ 1, 1 ↦ 2, 2 ↦ 3, 5 ↦ 4, 3 ↦ 5 }, it remains to prove termination of the 5-rule system { 0 1 1 2 2 1 3 →= 4 4 3 5 4 1 1 , 0 5 0 5 4 2 2 4 4 4 5 3 0 5 →= 0 5 5 2 2 2 4 4 2 1 0 3 1 5 , 1 1 3 4 4 5 2 2 2 0 0 4 1 4 0 4 2 →= 3 5 4 3 3 0 1 5 5 1 4 3 4 3 0 2 4 2 , 3 2 3 5 2 3 0 0 3 2 4 0 5 3 5 1 5 2 4 5 1 →= 3 5 1 4 3 0 1 4 1 0 4 5 2 5 3 1 1 0 2 1 1 , 3 5 3 3 1 4 1 3 1 5 2 3 2 4 1 2 3 3 1 0 5 →= 2 4 4 2 0 3 5 0 3 2 5 0 0 1 3 4 4 2 3 5 } The system is trivially terminating.