YES After renaming modulo { 0->0, 1->1 }, it remains to prove termination of the 31-rule system { 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 -> 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 , 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 -> 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 1 0 0 0 0 , 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 -> 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 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1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 0 0 0 , 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 1 0 0 1 1 -> 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 , 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 1 0 -> 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 , 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 -> 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 0 1 0 0 , 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 0 0 -> 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 0 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 0->0, 1->1 }, it remains to prove termination of the 1-rule system { 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 -> 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 1 0 0 0 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 82: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | 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