TORPAcyc is applied to the string rewriting system 0 1 0 2 -> 3 4 4 2 0 0 3 -> 3 4 1 5 3 5 0 1 -> 5 2 3 0 0 0 1 2 2 3 -> 4 0 2 2 3 0 5 3 1 4 3 -> 1 4 0 5 2 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 4 0 2 3 0 0 2 -> 2 4 0 3 4 4 2 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 2 5 5 0 1 1 5 1 4 2 3 3 -> 4 2 3 0 3 0 0 2 3 2 3 3 0 2 4 5 2 1 2 0 2 5 1 -> 3 1 3 0 5 0 2 2 4 0 4 3 3 3 4 3 0 0 4 4 5 0 5 -> 3 1 5 5 0 3 1 0 5 2 5 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 3 2 3 0 2 4 2 1 3 -> 5 1 3 1 4 0 0 1 5 0 4 5 2 0 3 0 2 3 1 0 0 3 0 3 5 3 -> 3 4 0 2 1 4 4 4 0 5 5 5 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 3 5 5 0 2 2 0 0 3 5 1 3 3 5 3 5 -> 3 1 4 2 0 3 4 0 4 1 5 4 2 5 5 5 3 5 0 5 3 5 2 3 1 3 3 4 0 2 -> 5 2 4 2 4 4 0 5 5 1 3 4 0 4 0 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 0 3 0 2 2 2 5 5 2 4 4 3 5 1 0 0 0 3 3 -> 3 3 1 3 4 5 5 2 0 4 2 3 1 1 5 1 2 3 3 3 4 3 3 4 3 0 2 5 3 1 4 5 2 5 2 4 3 5 -> 5 2 5 0 5 0 1 1 1 3 2 4 4 0 3 2 4 1 5 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 1 3 4 0 3 0 2 5 3 0 2 2 0 1 2 3 3 4 1 1 -> 5 0 1 1 4 2 0 1 1 2 1 4 0 4 3 1 2 0 0 2 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 29 continue with: 0 1 0 2 -> 3 4 4 2 0 0 3 -> 3 4 1 5 3 5 0 1 -> 5 2 3 0 0 0 1 2 2 3 -> 4 0 2 2 3 0 5 3 1 4 3 -> 1 4 0 5 2 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 4 0 2 3 0 0 2 -> 2 4 0 3 4 4 2 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 2 5 5 0 1 1 5 1 4 2 3 3 -> 4 2 3 0 3 0 0 2 3 2 3 3 0 2 4 5 2 1 2 0 2 5 1 -> 3 1 3 0 5 0 2 2 4 0 4 3 3 3 4 3 0 0 4 4 5 0 5 -> 3 1 5 5 0 3 1 0 5 2 5 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 3 2 3 0 2 4 2 1 3 -> 5 1 3 1 4 0 0 1 5 0 4 5 2 0 3 0 2 3 1 0 0 3 0 3 5 3 -> 3 4 0 2 1 4 4 4 0 5 5 5 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 3 5 5 0 2 2 0 0 3 5 1 3 3 5 3 5 -> 3 1 4 2 0 3 4 0 4 1 5 4 2 5 5 5 3 5 0 5 3 5 2 3 1 3 3 4 0 2 -> 5 2 4 2 4 4 0 5 5 1 3 4 0 4 0 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 0 3 0 2 2 2 5 5 2 4 4 3 5 1 0 0 0 3 3 -> 3 3 1 3 4 5 5 2 0 4 2 3 1 1 5 1 2 3 3 3 4 3 3 4 3 0 2 5 3 1 4 5 2 5 2 4 3 5 -> 5 2 5 0 5 0 1 1 1 3 2 4 4 0 3 2 4 1 5 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 27 continue with: 0 1 0 2 -> 3 4 4 2 0 0 3 -> 3 4 1 5 3 5 0 1 -> 5 2 3 0 0 0 1 2 2 3 -> 4 0 2 2 3 0 5 3 1 4 3 -> 1 4 0 5 2 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 4 0 2 3 0 0 2 -> 2 4 0 3 4 4 2 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 2 5 5 0 1 1 5 1 4 2 3 3 -> 4 2 3 0 3 0 0 2 3 2 3 3 0 2 4 5 2 1 2 0 2 5 1 -> 3 1 3 0 5 0 2 2 4 0 4 3 3 3 4 3 0 0 4 4 5 0 5 -> 3 1 5 5 0 3 1 0 5 2 5 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 3 2 3 0 2 4 2 1 3 -> 5 1 3 1 4 0 0 1 5 0 4 5 2 0 3 0 2 3 1 0 0 3 0 3 5 3 -> 3 4 0 2 1 4 4 4 0 5 5 5 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 3 5 5 0 2 2 0 0 3 5 1 3 3 5 3 5 -> 3 1 4 2 0 3 4 0 4 1 5 4 2 5 5 5 3 5 0 5 3 5 2 3 1 3 3 4 0 2 -> 5 2 4 2 4 4 0 5 5 1 3 4 0 4 0 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 0 3 0 2 2 2 5 5 2 4 4 3 5 1 0 0 0 3 3 -> 3 3 1 3 4 5 5 2 0 4 2 3 1 1 5 1 2 3 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 26 continue with: 0 1 0 2 -> 3 4 4 2 0 0 3 -> 3 4 1 5 3 5 0 1 -> 5 2 3 0 0 0 1 2 2 3 -> 4 0 2 2 3 0 5 3 1 4 3 -> 1 4 0 5 2 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 4 0 2 3 0 0 2 -> 2 4 0 3 4 4 2 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 2 5 5 0 1 1 5 1 4 2 3 3 -> 4 2 3 0 3 0 0 2 3 2 3 3 0 2 4 5 2 1 2 0 2 5 1 -> 3 1 3 0 5 0 2 2 4 0 4 3 3 3 4 3 0 0 4 4 5 0 5 -> 3 1 5 5 0 3 1 0 5 2 5 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 3 2 3 0 2 4 2 1 3 -> 5 1 3 1 4 0 0 1 5 0 4 5 2 0 3 0 2 3 1 0 0 3 0 3 5 3 -> 3 4 0 2 1 4 4 4 0 5 5 5 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 3 5 5 0 2 2 0 0 3 5 1 3 3 5 3 5 -> 3 1 4 2 0 3 4 0 4 1 5 4 2 5 5 5 3 5 0 5 3 5 2 3 1 3 3 4 0 2 -> 5 2 4 2 4 4 0 5 5 1 3 4 0 4 0 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 24 continue with: 0 1 0 2 -> 3 4 4 2 0 0 3 -> 3 4 1 5 3 5 0 1 -> 5 2 3 0 0 0 1 2 2 3 -> 4 0 2 2 3 0 5 3 1 4 3 -> 1 4 0 5 2 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 4 0 2 3 0 0 2 -> 2 4 0 3 4 4 2 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 2 5 5 0 1 1 5 1 4 2 3 3 -> 4 2 3 0 3 0 0 2 3 2 3 3 0 2 4 5 2 1 2 0 2 5 1 -> 3 1 3 0 5 0 2 2 4 0 4 3 3 3 4 3 0 0 4 4 5 0 5 -> 3 1 5 5 0 3 1 0 5 2 5 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 3 2 3 0 2 4 2 1 3 -> 5 1 3 1 4 0 0 1 5 0 4 5 2 0 3 0 2 3 1 0 0 3 0 3 5 3 -> 3 4 0 2 1 4 4 4 0 5 5 5 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 3 5 5 0 2 2 0 0 3 5 1 3 3 5 3 5 -> 3 1 4 2 0 3 4 0 4 1 5 4 2 5 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 23 continue with: 0 1 0 2 -> 3 4 4 2 0 0 3 -> 3 4 1 5 3 5 0 1 -> 5 2 3 0 0 0 1 2 2 3 -> 4 0 2 2 3 0 5 3 1 4 3 -> 1 4 0 5 2 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 4 0 2 3 0 0 2 -> 2 4 0 3 4 4 2 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 2 5 5 0 1 1 5 1 4 2 3 3 -> 4 2 3 0 3 0 0 2 3 2 3 3 0 2 4 5 2 1 2 0 2 5 1 -> 3 1 3 0 5 0 2 2 4 0 4 3 3 3 4 3 0 0 4 4 5 0 5 -> 3 1 5 5 0 3 1 0 5 2 5 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 3 2 3 0 2 4 2 1 3 -> 5 1 3 1 4 0 0 1 5 0 4 5 2 0 3 0 2 3 1 0 0 3 0 3 5 3 -> 3 4 0 2 1 4 4 4 0 5 5 5 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 21 continue with: 0 1 0 2 -> 3 4 4 2 0 0 3 -> 3 4 1 5 3 5 0 1 -> 5 2 3 0 0 0 1 2 2 3 -> 4 0 2 2 3 0 5 3 1 4 3 -> 1 4 0 5 2 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 4 0 2 3 0 0 2 -> 2 4 0 3 4 4 2 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 2 5 5 0 1 1 5 1 4 2 3 3 -> 4 2 3 0 3 0 0 2 3 2 3 3 0 2 4 5 2 1 2 0 2 5 1 -> 3 1 3 0 5 0 2 2 4 0 4 3 3 3 4 3 0 0 4 4 5 0 5 -> 3 1 5 5 0 3 1 0 5 2 5 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 3 2 3 0 2 4 2 1 3 -> 5 1 3 1 4 0 0 1 5 0 4 5 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 20 continue with: 0 1 0 2 -> 3 4 4 2 0 0 3 -> 3 4 1 5 3 5 0 1 -> 5 2 3 0 0 0 1 2 2 3 -> 4 0 2 2 3 0 5 3 1 4 3 -> 1 4 0 5 2 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 4 0 2 3 0 0 2 -> 2 4 0 3 4 4 2 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 2 5 5 0 1 1 5 1 4 2 3 3 -> 4 2 3 0 3 0 0 2 3 2 3 3 0 2 4 5 2 1 2 0 2 5 1 -> 3 1 3 0 5 0 2 2 4 0 4 3 3 3 4 3 0 0 4 4 5 0 5 -> 3 1 5 5 0 3 1 0 5 2 5 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 16 continue with: 0 1 0 2 -> 3 4 4 2 0 0 3 -> 3 4 1 5 3 5 0 1 -> 5 2 3 0 0 0 1 2 2 3 -> 4 0 2 2 3 0 5 3 1 4 3 -> 1 4 0 5 2 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 4 0 2 3 0 0 2 -> 2 4 0 3 4 4 2 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 2 5 5 0 1 1 5 1 4 2 3 3 -> 4 2 3 0 3 0 0 2 3 2 3 3 0 2 4 5 2 1 2 0 2 5 1 -> 3 1 3 0 5 0 2 2 4 0 4 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 15 continue with: 0 1 0 2 -> 3 4 4 2 0 0 3 -> 3 4 1 5 3 5 0 1 -> 5 2 3 0 0 0 1 2 2 3 -> 4 0 2 2 3 0 5 3 1 4 3 -> 1 4 0 5 2 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 4 0 2 3 0 0 2 -> 2 4 0 3 4 4 2 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 2 5 5 0 1 1 5 1 4 2 3 3 -> 4 2 3 0 3 0 0 2 3 2 3 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 14 continue with: 0 1 0 2 -> 3 4 4 2 0 0 3 -> 3 4 1 5 3 5 0 1 -> 5 2 3 0 0 0 1 2 2 3 -> 4 0 2 2 3 0 5 3 1 4 3 -> 1 4 0 5 2 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 4 0 2 3 0 0 2 -> 2 4 0 3 4 4 2 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 7 continue with: 0 1 0 2 -> 3 4 4 2 0 0 3 -> 3 4 1 5 3 5 0 1 -> 5 2 3 0 0 0 1 2 2 3 -> 4 0 2 2 3 0 5 3 1 4 3 -> 1 4 0 5 2 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 5 continue with: 0 1 0 2 -> 3 4 4 2 0 0 3 -> 3 4 1 5 3 5 0 1 -> 5 2 3 0 0 0 1 2 2 3 -> 4 0 2 2 3 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 4 continue with: 0 1 0 2 -> 3 4 4 2 0 0 3 -> 3 4 1 5 3 5 0 1 -> 5 2 3 0 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 3 continue with: 0 1 0 2 -> 3 4 4 2 0 0 3 -> 3 4 1 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 2 continue with: 0 1 0 2 -> 3 4 4 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 1 continue with: 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 2 1 5 5 3 0 1 3 3 3 1 2 0 5 2 0 3 5 2 2 2 -> 3 0 3 3 4 0 1 4 5 1 3 3 3 4 1 2 1 3 2 1 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 1 interpretation of 3: 1 interpretation of 4: 1 interpretation of 5: 1 remove rule 13 continue with: 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 5 4 0 0 3 2 5 3 0 3 0 4 5 0 4 4 5 1 1 1 3 -> 5 2 5 1 0 3 5 3 2 1 0 0 5 5 4 5 4 4 2 2 2 interpretation of 0: 1 interpretation of 1: 2 interpretation of 2: 0 interpretation of 3: 1 interpretation of 4: 3 interpretation of 5: 0 remove rule 13 continue with: 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 0 5 3 5 1 0 5 1 2 4 4 5 0 -> 0 3 1 0 4 5 5 2 5 5 2 4 0 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 0 interpretation of 3: 1 interpretation of 4: 3 interpretation of 5: 0 remove rule 8 continue with: 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 1 5 5 2 4 2 4 0 3 3 0 -> 1 3 5 4 5 5 5 3 2 4 2 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 interpretation of 0: 1 interpretation of 1: 1 interpretation of 2: 0 interpretation of 3: 1 interpretation of 4: 3 interpretation of 5: 0 remove rule 7 continue with: 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 2 2 1 3 4 0 1 1 4 2 2 2 0 4 4 2 4 4 -> 4 3 4 4 5 5 0 1 0 1 3 2 5 5 1 1 4 4 interpretation of 0: 2 interpretation of 1: 3 interpretation of 2: 0 interpretation of 3: 3 interpretation of 4: 8 interpretation of 5: 0 remove rule 10 continue with: 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 0 4 0 0 1 3 5 0 -> 5 0 0 0 3 5 5 3 2 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 interpretation of 0: 0 interpretation of 1: 2 interpretation of 2: 0 interpretation of 3: 1 interpretation of 4: 2 interpretation of 5: 0 remove rule 3 continue with: 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 4 4 3 2 0 1 1 4 0 2 -> 2 3 4 0 0 1 2 1 3 4 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 interpretation of 0: 0 interpretation of 1: 3 interpretation of 2: 0 interpretation of 3: 1 interpretation of 4: 2 interpretation of 5: 0 remove rule 5 continue with: 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 5 3 5 4 4 2 2 2 1 -> 5 0 3 0 0 4 5 2 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 interpretation of 0: 1 interpretation of 1: 5 interpretation of 2: 0 interpretation of 3: 3 interpretation of 4: 4 interpretation of 5: 2 remove rule 3 continue with: 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 2 5 2 4 1 5 3 3 1 0 2 5 3 -> 2 3 1 3 3 5 1 2 0 3 2 3 0 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 interpretation of 0: 1 interpretation of 1: 0 interpretation of 2: 0 interpretation of 3: 0 interpretation of 4: 0 interpretation of 5: 1 remove rule 4 continue with: 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 2 5 5 3 5 3 1 3 1 2 5 0 0 -> 2 5 5 5 0 4 5 5 1 1 3 2 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 interpretation of 0: 5 interpretation of 1: 6 interpretation of 2: 1 interpretation of 3: 4 interpretation of 4: 0 interpretation of 5: 5 remove rule 4 continue with: 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 1 4 0 4 1 5 0 2 -> 3 3 2 2 3 0 3 3 4 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 interpretation of 0: 0 interpretation of 1: 0 interpretation of 2: 0 interpretation of 3: 0 interpretation of 4: 1 interpretation of 5: 0 remove rule 2 continue with: 2 0 4 3 5 3 3 1 -> 2 1 2 2 2 0 3 1 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 interpretation of 0: 0 interpretation of 1: 0 interpretation of 2: 0 interpretation of 3: 1 interpretation of 4: 0 interpretation of 5: 0 remove rule 1 continue with: 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 3 5 3 3 1 2 4 0 4 3 5 4 2 1 -> 5 2 0 1 4 4 3 3 3 5 3 4 1 2 Tropical matrix interpretation interpretation of 0: / 3 0 \ \ 1 3 / interpretation of 1: / 1 0 \ \ 0 2 / interpretation of 2: / 0 3 \ \ 0 0 / interpretation of 3: / 1 0 \ \ - 0 / interpretation of 4: / 2 0 \ \ 0 2 / interpretation of 5: / 2 0 \ \ - - / remove rule 2 continue with: 2 0 4 2 3 3 3 5 4 2 -> 3 4 4 2 0 2 3 3 5 2 Tropical matrix interpretation interpretation of 0: / 0 - \ \ - - / interpretation of 1: / 0 0 \ \ 0 0 / interpretation of 2: / 0 - \ \ - - / interpretation of 3: / 0 1 \ \ - - / interpretation of 4: / 2 2 \ \ 0 - / interpretation of 5: / 3 2 \ \ 0 2 / remove rule 1 termination has been proved