/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1 }, it remains to prove termination of the 32-rule system { 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 0 0 1 1 ⟶ 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 , 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 ⟶ 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 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0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 ⟶ 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 1 1 0 0 1 , 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1 0 1 0 1 1 0 ⟶ 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 1 1 0 0 1 , 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1 0 1 0 1 1 0 ⟶ 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 0 } The system was reversed. After renaming modulo the bijection { 1 ↦ 0, 0 ↦ 1 }, it remains to prove termination of the 32-rule system { 0 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 ⟶ 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 , 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 ⟶ 0 1 1 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 , 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 ⟶ 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1 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1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 , 1 1 1 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 ⟶ 1 1 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 , 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 ⟶ 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 , 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 ⟶ 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 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0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 , 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 ⟶ 0 1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 , 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 ⟶ 0 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 , 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 ⟶ 0 1 0 0 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 , 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 ⟶ 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 , 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 ⟶ 1 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 , 0 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 ⟶ 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 , 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 ⟶ 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 , 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 ⟶ 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 , 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 ⟶ 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 , 1 0 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 ⟶ 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 , 1 0 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 ⟶ 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 } Applying sparse tiling TRFC(2) [Geser/Hofbauer/Waldmann, FSCD 2019]. After renaming modulo the bijection { (0,0) ↦ 0, (0,1) ↦ 1, (1,1) ↦ 2, (1,0) ↦ 3, (1,3) ↦ 4, (2,0) ↦ 5, (2,1) ↦ 6 }, it remains to prove termination of the 288-rule system { 0 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 ⟶ 0 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 3 , 0 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 ⟶ 0 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 2 , 0 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 ⟶ 0 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 4 , 3 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 ⟶ 3 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 3 , 3 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 ⟶ 3 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 2 , 3 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 ⟶ 3 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 4 , 5 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 ⟶ 5 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 3 , 5 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 ⟶ 5 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 2 , 5 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 ⟶ 5 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 4 , 1 3 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 ⟶ 0 1 2 3 0 0 1 2 2 3 1 2 2 3 1 2 3 1 2 3 0 0 1 2 2 3 1 2 2 2 2 3 1 2 3 1 3 1 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 , 1 3 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 ⟶ 0 1 2 3 0 0 1 2 2 3 1 2 2 3 1 2 3 1 2 3 0 0 1 2 2 3 1 2 2 2 2 3 1 2 3 1 3 1 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 , 1 3 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 ⟶ 0 1 2 3 0 0 1 2 2 3 1 2 2 3 1 2 3 1 2 3 0 0 1 2 2 3 1 2 2 2 2 3 1 2 3 1 3 1 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 , 2 3 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 ⟶ 3 1 2 3 0 0 1 2 2 3 1 2 2 3 1 2 3 1 2 3 0 0 1 2 2 3 1 2 2 2 2 3 1 2 3 1 3 1 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 , 2 3 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 ⟶ 3 1 2 3 0 0 1 2 2 3 1 2 2 3 1 2 3 1 2 3 0 0 1 2 2 3 1 2 2 2 2 3 1 2 3 1 3 1 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 , 2 3 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 ⟶ 3 1 2 3 0 0 1 2 2 3 1 2 2 3 1 2 3 1 2 3 0 0 1 2 2 3 1 2 2 2 2 3 1 2 3 1 3 1 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 , 6 3 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 ⟶ 5 1 2 3 0 0 1 2 2 3 1 2 2 3 1 2 3 1 2 3 0 0 1 2 2 3 1 2 2 2 2 3 1 2 3 1 3 1 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 , 6 3 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 ⟶ 5 1 2 3 0 0 1 2 2 3 1 2 2 3 1 2 3 1 2 3 0 0 1 2 2 3 1 2 2 2 2 3 1 2 3 1 3 1 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 , 6 3 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 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1 3 0 0 0 1 2 2 ⟶ 3 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 2 , 2 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 4 ⟶ 3 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 4 , 6 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 3 ⟶ 5 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 3 , 6 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 2 ⟶ 5 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 2 , 6 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 4 ⟶ 5 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 4 , 1 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 3 ⟶ 1 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 , 1 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 2 ⟶ 1 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 , 1 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 4 ⟶ 1 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 , 2 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 3 ⟶ 2 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 , 2 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 2 ⟶ 2 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 , 2 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 4 ⟶ 2 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 , 6 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 3 ⟶ 6 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 , 6 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 2 ⟶ 6 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 , 6 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 4 ⟶ 6 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 } 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 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 3 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 4 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 5 ↦ ⎛ ⎞ ⎜ 1 0 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 6 ↦ ⎛ ⎞ ⎜ 1 1 ⎟ ⎜ 0 1 ⎟ ⎝ ⎠ 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 255-rule system { 0 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 ⟶ 0 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 3 , 0 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 ⟶ 0 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 2 , 0 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 ⟶ 0 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 4 , 3 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 ⟶ 3 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 3 , 3 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 ⟶ 3 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 2 , 3 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 ⟶ 3 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 4 , 5 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 ⟶ 5 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 3 , 5 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 ⟶ 5 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 2 , 5 0 1 2 3 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 ⟶ 5 0 0 1 3 0 1 3 0 1 2 2 3 0 1 2 2 3 0 1 3 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 4 , 1 3 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 ⟶ 0 1 2 3 0 0 1 2 2 3 1 2 2 3 1 2 3 1 2 3 0 0 1 2 2 3 1 2 2 2 2 3 1 2 3 1 3 1 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 , 1 3 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 ⟶ 0 1 2 3 0 0 1 2 2 3 1 2 2 3 1 2 3 1 2 3 0 0 1 2 2 3 1 2 2 2 2 3 1 2 3 1 3 1 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 , 1 3 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 ⟶ 0 1 2 3 0 0 1 2 2 3 1 2 2 3 1 2 3 1 2 3 0 0 1 2 2 3 1 2 2 2 2 3 1 2 3 1 3 1 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 , 2 3 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 ⟶ 3 1 2 3 0 0 1 2 2 3 1 2 2 3 1 2 3 1 2 3 0 0 1 2 2 3 1 2 2 2 2 3 1 2 3 1 3 1 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 , 2 3 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 ⟶ 3 1 2 3 0 0 1 2 2 3 1 2 2 3 1 2 3 1 2 3 0 0 1 2 2 3 1 2 2 2 2 3 1 2 3 1 3 1 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 , 2 3 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 ⟶ 3 1 2 3 0 0 1 2 2 3 1 2 2 3 1 2 3 1 2 3 0 0 1 2 2 3 1 2 2 2 2 3 1 2 3 1 3 1 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 , 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 ⟶ 0 0 0 0 1 3 0 0 0 1 3 1 2 2 2 3 0 1 2 3 1 2 2 2 3 1 2 2 2 3 1 3 1 3 1 3 0 0 0 0 1 2 2 3 1 3 1 2 2 2 3 1 2 2 2 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 3 , 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 ⟶ 0 0 0 0 1 3 0 0 0 1 3 1 2 2 2 3 0 1 2 3 1 2 2 2 3 1 2 2 2 3 1 3 1 3 1 3 0 0 0 0 1 2 2 3 1 3 1 2 2 2 3 1 2 2 2 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 2 , 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 ⟶ 0 0 0 0 1 3 0 0 0 1 3 1 2 2 2 3 0 1 2 3 1 2 2 2 3 1 2 2 2 3 1 3 1 3 1 3 0 0 0 0 1 2 2 3 1 3 1 2 2 2 3 1 2 2 2 2 2 2 2 3 0 1 2 2 3 0 1 2 3 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, 0 1 3 0 1 3 1 2 3 1 3 0 1 2 3 1 3 0 1 3 1 2 2 2 2 3 1 2 3 0 0 1 3 0 1 3 0 1 3 0 1 3 0 1 3 1 2 2 2 3 1 2 2 2 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 4 ⟶ 0 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 4 , 3 1 3 0 1 3 1 2 3 1 3 0 1 2 3 1 3 0 1 3 1 2 2 2 2 3 1 2 3 0 0 1 3 0 1 3 0 1 3 0 1 3 0 1 3 1 2 2 2 3 1 2 2 2 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 3 ⟶ 3 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 3 , 3 1 3 0 1 3 1 2 3 1 3 0 1 2 3 1 3 0 1 3 1 2 2 2 2 3 1 2 3 0 0 1 3 0 1 3 0 1 3 0 1 3 0 1 3 1 2 2 2 3 1 2 2 2 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 2 ⟶ 3 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 2 , 3 1 3 0 1 3 1 2 3 1 3 0 1 2 3 1 3 0 1 3 1 2 2 2 2 3 1 2 3 0 0 1 3 0 1 3 0 1 3 0 1 3 0 1 3 1 2 2 2 3 1 2 2 2 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 4 ⟶ 3 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 4 , 5 1 3 0 1 3 1 2 3 1 3 0 1 2 3 1 3 0 1 3 1 2 2 2 2 3 1 2 3 0 0 1 3 0 1 3 0 1 3 0 1 3 0 1 3 1 2 2 2 3 1 2 2 2 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 3 ⟶ 5 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 3 , 5 1 3 0 1 3 1 2 3 1 3 0 1 2 3 1 3 0 1 3 1 2 2 2 2 3 1 2 3 0 0 1 3 0 1 3 0 1 3 0 1 3 0 1 3 1 2 2 2 3 1 2 2 2 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 2 ⟶ 5 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 2 , 5 1 3 0 1 3 1 2 3 1 3 0 1 2 3 1 3 0 1 3 1 2 2 2 2 3 1 2 3 0 0 1 3 0 1 3 0 1 3 0 1 3 0 1 3 1 2 2 2 3 1 2 2 2 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 4 ⟶ 5 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 4 , 1 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 3 ⟶ 0 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 3 , 1 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 2 ⟶ 0 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 2 , 1 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 4 ⟶ 0 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 4 , 2 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 3 ⟶ 3 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 3 , 2 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 2 ⟶ 3 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 2 , 2 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 4 ⟶ 3 1 2 3 0 0 1 2 2 3 1 2 3 1 3 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 3 0 1 2 3 0 1 2 2 2 3 1 3 1 3 0 0 1 2 3 1 2 3 1 3 0 0 0 1 3 0 1 2 2 3 1 2 3 0 0 0 1 2 2 2 2 2 2 3 1 4 , 1 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 3 ⟶ 1 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 , 1 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 2 ⟶ 1 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 , 1 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 4 ⟶ 1 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 , 2 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 3 ⟶ 2 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 , 2 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 2 ⟶ 2 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 , 2 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 4 ⟶ 2 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 4 , 6 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 3 ⟶ 6 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 3 , 6 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 2 ⟶ 6 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 2 , 6 3 0 1 3 1 3 0 1 3 1 2 2 3 1 2 2 3 0 1 2 3 1 3 0 0 0 1 3 1 3 0 1 3 1 3 0 0 0 1 2 3 1 2 3 1 2 3 1 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 2 3 0 0 1 3 0 0 1 3 0 0 0 1 2 4 ⟶ 6 2 3 0 0 0 0 0 1 2 3 1 2 3 0 0 1 2 3 1 2 2 3 0 1 2 2 3 0 1 3 1 3 1 2 3 0 0 1 2 3 0 0 0 1 2 2 2 2 2 3 0 0 0 1 2 2 2 3 1 3 1 2 2 3 1 3 0 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 2 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 3 ⎟ ⎜ 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 ⎟ ⎝ ⎠ After renaming modulo the bijection { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.