TORPAcyc is applied to the string rewriting system 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 1 1 0 2 0 1 2 3 -> 5 4 4 5 2 5 5 2 3 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 4 2 1 1 5 1 0 0 0 2 5 -> 5 5 0 3 0 1 4 5 2 5 5 4 5 4 2 0 2 2 3 0 0 2 -> 5 3 4 5 0 3 2 1 1 2 2 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 1 4 0 0 2 4 0 3 3 2 0 3 1 -> 1 5 0 5 0 2 0 5 1 0 1 2 5 5 4 1 4 1 3 0 0 2 1 5 4 1 0 0 -> 2 3 0 2 5 4 4 3 0 4 1 2 0 4 2 4 4 0 0 0 4 0 3 5 0 3 3 -> 5 1 0 1 0 1 3 5 3 5 5 0 0 3 1 2 5 3 3 0 2 2 5 3 2 3 3 3 2 1 -> 1 1 0 0 4 1 2 1 0 5 0 0 3 5 0 4 1 3 1 2 5 0 3 4 3 1 5 4 1 5 2 0 5 -> 3 1 0 4 2 0 5 2 4 4 2 2 1 1 1 5 1 3 4 5 1 0 0 3 1 2 4 2 3 5 2 0 4 1 -> 1 3 0 0 4 2 2 5 3 1 0 1 2 1 5 0 1 4 1 1 0 3 3 2 5 0 0 3 0 3 2 4 1 4 0 2 4 2 -> 4 3 4 2 1 4 2 4 3 3 2 2 2 1 1 1 5 3 2 5 3 2 1 0 1 3 1 3 3 0 0 3 2 5 3 0 3 0 -> 5 1 0 3 2 4 0 0 3 2 1 5 1 3 0 5 1 3 1 0 2 2 3 3 5 0 0 5 0 3 1 3 0 1 2 1 5 5 1 -> 0 0 3 2 5 2 5 2 3 2 1 2 5 4 3 4 5 0 4 1 0 4 2 3 3 5 4 3 5 0 2 0 4 5 0 2 0 2 4 -> 4 5 4 5 4 1 1 2 5 0 4 3 1 5 4 3 1 5 4 0 4 1 4 2 3 1 3 4 2 4 1 5 1 4 0 4 5 2 0 0 3 4 -> 4 3 4 1 3 5 1 1 4 3 1 5 1 3 1 2 4 2 1 3 interpretation of 0: 5 interpretation of 1: 4 interpretation of 2: 4 interpretation of 3: 8 interpretation of 4: 5 interpretation of 5: 3 remove rule 23 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 1 1 0 2 0 1 2 3 -> 5 4 4 5 2 5 5 2 3 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 4 2 1 1 5 1 0 0 0 2 5 -> 5 5 0 3 0 1 4 5 2 5 5 4 5 4 2 0 2 2 3 0 0 2 -> 5 3 4 5 0 3 2 1 1 2 2 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 1 4 0 0 2 4 0 3 3 2 0 3 1 -> 1 5 0 5 0 2 0 5 1 0 1 2 5 5 4 1 4 1 3 0 0 2 1 5 4 1 0 0 -> 2 3 0 2 5 4 4 3 0 4 1 2 0 4 2 4 4 0 0 0 4 0 3 5 0 3 3 -> 5 1 0 1 0 1 3 5 3 5 5 0 0 3 1 2 5 3 3 0 2 2 5 3 2 3 3 3 2 1 -> 1 1 0 0 4 1 2 1 0 5 0 0 3 5 0 4 1 3 1 2 5 0 3 4 3 1 5 4 1 5 2 0 5 -> 3 1 0 4 2 0 5 2 4 4 2 2 1 1 1 5 1 3 4 5 1 0 0 3 1 2 4 2 3 5 2 0 4 1 -> 1 3 0 0 4 2 2 5 3 1 0 1 2 1 5 0 1 4 1 1 0 3 3 2 5 0 0 3 0 3 2 4 1 4 0 2 4 2 -> 4 3 4 2 1 4 2 4 3 3 2 2 2 1 1 1 5 3 2 5 3 2 1 0 1 3 1 3 3 0 0 3 2 5 3 0 3 0 -> 5 1 0 3 2 4 0 0 3 2 1 5 1 3 0 5 1 3 1 1 0 4 2 3 3 5 4 3 5 0 2 0 4 5 0 2 0 2 4 -> 4 5 4 5 4 1 1 2 5 0 4 3 1 5 4 3 1 5 4 0 4 1 4 2 3 1 3 4 2 4 1 5 1 4 0 4 5 2 0 0 3 4 -> 4 3 4 1 3 5 1 1 4 3 1 5 1 3 1 2 4 2 1 3 interpretation of 0: 5 interpretation of 1: 4 interpretation of 2: 4 interpretation of 3: 8 interpretation of 4: 5 interpretation of 5: 3 remove rule 23 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 1 1 0 2 0 1 2 3 -> 5 4 4 5 2 5 5 2 3 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 4 2 1 1 5 1 0 0 0 2 5 -> 5 5 0 3 0 1 4 5 2 5 5 4 5 4 2 0 2 2 3 0 0 2 -> 5 3 4 5 0 3 2 1 1 2 2 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 1 4 0 0 2 4 0 3 3 2 0 3 1 -> 1 5 0 5 0 2 0 5 1 0 1 2 5 5 4 1 4 1 3 0 0 2 1 5 4 1 0 0 -> 2 3 0 2 5 4 4 3 0 4 1 2 0 4 2 4 4 0 0 0 4 0 3 5 0 3 3 -> 5 1 0 1 0 1 3 5 3 5 5 0 0 3 1 2 5 3 3 0 2 2 5 3 2 3 3 3 2 1 -> 1 1 0 0 4 1 2 1 0 5 0 0 3 5 0 4 1 3 1 2 5 0 3 4 3 1 5 4 1 5 2 0 5 -> 3 1 0 4 2 0 5 2 4 4 2 2 1 1 1 5 1 3 4 5 1 0 0 3 1 2 4 2 3 5 2 0 4 1 -> 1 3 0 0 4 2 2 5 3 1 0 1 2 1 5 0 1 4 1 1 0 3 3 2 5 0 0 3 0 3 2 4 1 4 0 2 4 2 -> 4 3 4 2 1 4 2 4 3 3 2 2 2 1 1 1 5 3 2 5 3 2 1 0 1 3 1 3 3 0 0 3 2 5 3 0 3 0 -> 5 1 0 3 2 4 0 0 3 2 1 5 1 3 0 5 1 3 1 1 4 2 3 1 3 4 2 4 1 5 1 4 0 4 5 2 0 0 3 4 -> 4 3 4 1 3 5 1 1 4 3 1 5 1 3 1 2 4 2 1 3 interpretation of 0: 6 interpretation of 1: 5 interpretation of 2: 5 interpretation of 3: 10 interpretation of 4: 7 interpretation of 5: 5 remove rule 22 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 1 1 0 2 0 1 2 3 -> 5 4 4 5 2 5 5 2 3 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 4 2 1 1 5 1 0 0 0 2 5 -> 5 5 0 3 0 1 4 5 2 5 5 4 5 4 2 0 2 2 3 0 0 2 -> 5 3 4 5 0 3 2 1 1 2 2 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 1 4 0 0 2 4 0 3 3 2 0 3 1 -> 1 5 0 5 0 2 0 5 1 0 1 2 5 5 4 1 4 1 3 0 0 2 1 5 4 1 0 0 -> 2 3 0 2 5 4 4 3 0 4 1 2 0 4 2 4 4 0 0 0 4 0 3 5 0 3 3 -> 5 1 0 1 0 1 3 5 3 5 5 0 0 3 1 2 5 3 3 0 2 2 5 3 2 3 3 3 2 1 -> 1 1 0 0 4 1 2 1 0 5 0 0 3 5 0 4 1 3 1 2 5 0 3 4 3 1 5 4 1 5 2 0 5 -> 3 1 0 4 2 0 5 2 4 4 2 2 1 1 1 5 1 3 4 5 1 0 0 3 1 2 4 2 3 5 2 0 4 1 -> 1 3 0 0 4 2 2 5 3 1 0 1 2 1 5 0 1 4 1 1 0 3 3 2 5 0 0 3 0 3 2 4 1 4 0 2 4 2 -> 4 3 4 2 1 4 2 4 3 3 2 2 2 1 1 1 5 3 2 1 4 2 3 1 3 4 2 4 1 5 1 4 0 4 5 2 0 0 3 4 -> 4 3 4 1 3 5 1 1 4 3 1 5 1 3 1 2 4 2 1 3 interpretation of 0: 5 interpretation of 1: 4 interpretation of 2: 5 interpretation of 3: 7 interpretation of 4: 6 interpretation of 5: 5 remove rule 19 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 1 1 0 2 0 1 2 3 -> 5 4 4 5 2 5 5 2 3 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 4 2 1 1 5 1 0 0 0 2 5 -> 5 5 0 3 0 1 4 5 2 5 5 4 5 4 2 0 2 2 3 0 0 2 -> 5 3 4 5 0 3 2 1 1 2 2 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 1 4 0 0 2 4 0 3 3 2 0 3 1 -> 1 5 0 5 0 2 0 5 1 0 1 2 5 5 4 1 4 1 3 0 0 2 1 5 4 1 0 0 -> 2 3 0 2 5 4 4 3 0 4 1 2 0 4 2 4 4 0 0 0 4 0 3 5 0 3 3 -> 5 1 0 1 0 1 3 5 3 5 5 0 0 3 1 2 5 3 3 0 2 2 5 3 2 3 3 3 2 1 -> 1 1 0 0 4 1 2 1 0 5 0 0 3 5 0 4 1 1 3 4 5 1 0 0 3 1 2 4 2 3 5 2 0 4 1 -> 1 3 0 0 4 2 2 5 3 1 0 1 2 1 5 0 1 4 1 1 0 3 3 2 5 0 0 3 0 3 2 4 1 4 0 2 4 2 -> 4 3 4 2 1 4 2 4 3 3 2 2 2 1 1 1 5 3 2 1 4 2 3 1 3 4 2 4 1 5 1 4 0 4 5 2 0 0 3 4 -> 4 3 4 1 3 5 1 1 4 3 1 5 1 3 1 2 4 2 1 3 interpretation of 0: 5 interpretation of 1: 4 interpretation of 2: 4 interpretation of 3: 8 interpretation of 4: 5 interpretation of 5: 3 remove rule 18 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 1 1 0 2 0 1 2 3 -> 5 4 4 5 2 5 5 2 3 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 4 2 1 1 5 1 0 0 0 2 5 -> 5 5 0 3 0 1 4 5 2 5 5 4 5 4 2 0 2 2 3 0 0 2 -> 5 3 4 5 0 3 2 1 1 2 2 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 1 4 0 0 2 4 0 3 3 2 0 3 1 -> 1 5 0 5 0 2 0 5 1 0 1 2 5 5 4 1 4 1 3 0 0 2 1 5 4 1 0 0 -> 2 3 0 2 5 4 4 3 0 4 1 2 0 4 2 4 4 0 0 0 4 0 3 5 0 3 3 -> 5 1 0 1 0 1 3 5 3 5 5 0 0 3 1 3 4 5 1 0 0 3 1 2 4 2 3 5 2 0 4 1 -> 1 3 0 0 4 2 2 5 3 1 0 1 2 1 5 0 1 4 1 1 0 3 3 2 5 0 0 3 0 3 2 4 1 4 0 2 4 2 -> 4 3 4 2 1 4 2 4 3 3 2 2 2 1 1 1 5 3 2 1 4 2 3 1 3 4 2 4 1 5 1 4 0 4 5 2 0 0 3 4 -> 4 3 4 1 3 5 1 1 4 3 1 5 1 3 1 2 4 2 1 3 interpretation of 0: 6 interpretation of 1: 5 interpretation of 2: 6 interpretation of 3: 9 interpretation of 4: 7 interpretation of 5: 6 remove rule 17 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 1 1 0 2 0 1 2 3 -> 5 4 4 5 2 5 5 2 3 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 4 2 1 1 5 1 0 0 0 2 5 -> 5 5 0 3 0 1 4 5 2 5 5 4 5 4 2 0 2 2 3 0 0 2 -> 5 3 4 5 0 3 2 1 1 2 2 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 1 4 0 0 2 4 0 3 3 2 0 3 1 -> 1 5 0 5 0 2 0 5 1 0 1 2 5 5 4 1 4 1 3 0 0 2 1 5 4 1 0 0 -> 2 3 0 2 5 4 4 3 0 4 1 2 0 1 3 4 5 1 0 0 3 1 2 4 2 3 5 2 0 4 1 -> 1 3 0 0 4 2 2 5 3 1 0 1 2 1 5 0 1 4 1 1 0 3 3 2 5 0 0 3 0 3 2 4 1 4 0 2 4 2 -> 4 3 4 2 1 4 2 4 3 3 2 2 2 1 1 1 5 3 2 1 4 2 3 1 3 4 2 4 1 5 1 4 0 4 5 2 0 0 3 4 -> 4 3 4 1 3 5 1 1 4 3 1 5 1 3 1 2 4 2 1 3 interpretation of 0: 5 interpretation of 1: 4 interpretation of 2: 4 interpretation of 3: 8 interpretation of 4: 6 interpretation of 5: 4 remove rule 19 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 1 1 0 2 0 1 2 3 -> 5 4 4 5 2 5 5 2 3 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 4 2 1 1 5 1 0 0 0 2 5 -> 5 5 0 3 0 1 4 5 2 5 5 4 5 4 2 0 2 2 3 0 0 2 -> 5 3 4 5 0 3 2 1 1 2 2 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 1 4 0 0 2 4 0 3 3 2 0 3 1 -> 1 5 0 5 0 2 0 5 1 0 1 2 5 5 4 1 4 1 3 0 0 2 1 5 4 1 0 0 -> 2 3 0 2 5 4 4 3 0 4 1 2 0 1 3 4 5 1 0 0 3 1 2 4 2 3 5 2 0 4 1 -> 1 3 0 0 4 2 2 5 3 1 0 1 2 1 5 0 1 4 1 1 0 3 3 2 5 0 0 3 0 3 2 4 1 4 0 2 4 2 -> 4 3 4 2 1 4 2 4 3 3 2 2 2 1 1 1 5 3 2 interpretation of 0: 5 interpretation of 1: 4 interpretation of 2: 5 interpretation of 3: 7 interpretation of 4: 6 interpretation of 5: 5 remove rule 15 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 1 1 0 2 0 1 2 3 -> 5 4 4 5 2 5 5 2 3 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 4 2 1 1 5 1 0 0 0 2 5 -> 5 5 0 3 0 1 4 5 2 5 5 4 5 4 2 0 2 2 3 0 0 2 -> 5 3 4 5 0 3 2 1 1 2 2 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 4 1 4 1 3 0 0 2 1 5 4 1 0 0 -> 2 3 0 2 5 4 4 3 0 4 1 2 0 1 3 4 5 1 0 0 3 1 2 4 2 3 5 2 0 4 1 -> 1 3 0 0 4 2 2 5 3 1 0 1 2 1 5 0 1 4 1 1 0 3 3 2 5 0 0 3 0 3 2 4 1 4 0 2 4 2 -> 4 3 4 2 1 4 2 4 3 3 2 2 2 1 1 1 5 3 2 interpretation of 0: 5 interpretation of 1: 4 interpretation of 2: 4 interpretation of 3: 8 interpretation of 4: 6 interpretation of 5: 4 remove rule 12 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 1 1 0 2 0 1 2 3 -> 5 4 4 5 2 5 5 2 3 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 4 2 1 1 5 1 0 0 0 2 5 -> 5 5 0 3 0 1 4 5 2 5 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 4 1 4 1 3 0 0 2 1 5 4 1 0 0 -> 2 3 0 2 5 4 4 3 0 4 1 2 0 1 3 4 5 1 0 0 3 1 2 4 2 3 5 2 0 4 1 -> 1 3 0 0 4 2 2 5 3 1 0 1 2 1 5 0 1 4 1 1 0 3 3 2 5 0 0 3 0 3 2 4 1 4 0 2 4 2 -> 4 3 4 2 1 4 2 4 3 3 2 2 2 1 1 1 5 3 2 interpretation of 0: 5 interpretation of 1: 4 interpretation of 2: 5 interpretation of 3: 7 interpretation of 4: 6 interpretation of 5: 5 remove rule 11 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 1 1 0 2 0 1 2 3 -> 5 4 4 5 2 5 5 2 3 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 4 1 4 1 3 0 0 2 1 5 4 1 0 0 -> 2 3 0 2 5 4 4 3 0 4 1 2 0 1 3 4 5 1 0 0 3 1 2 4 2 3 5 2 0 4 1 -> 1 3 0 0 4 2 2 5 3 1 0 1 2 1 5 0 1 4 1 1 0 3 3 2 5 0 0 3 0 3 2 4 1 4 0 2 4 2 -> 4 3 4 2 1 4 2 4 3 3 2 2 2 1 1 1 5 3 2 interpretation of 0: 5 interpretation of 1: 4 interpretation of 2: 4 interpretation of 3: 8 interpretation of 4: 6 interpretation of 5: 4 remove rule 14 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 1 1 0 2 0 1 2 3 -> 5 4 4 5 2 5 5 2 3 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 4 1 4 1 3 0 0 2 1 5 4 1 0 0 -> 2 3 0 2 5 4 4 3 0 4 1 2 0 1 0 3 3 2 5 0 0 3 0 3 2 4 1 4 0 2 4 2 -> 4 3 4 2 1 4 2 4 3 3 2 2 2 1 1 1 5 3 2 interpretation of 0: 2 interpretation of 1: 4 interpretation of 2: 0 interpretation of 3: 2 interpretation of 4: 1 interpretation of 5: 0 remove rule 9 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 4 1 4 1 3 0 0 2 1 5 4 1 0 0 -> 2 3 0 2 5 4 4 3 0 4 1 2 0 1 0 3 3 2 5 0 0 3 0 3 2 4 1 4 0 2 4 2 -> 4 3 4 2 1 4 2 4 3 3 2 2 2 1 1 1 5 3 2 interpretation of 0: 2 interpretation of 1: 4 interpretation of 2: 0 interpretation of 3: 1 interpretation of 4: 0 interpretation of 5: 0 remove rule 12 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 1 0 3 3 2 5 0 0 3 0 3 2 4 1 4 0 2 4 2 -> 4 3 4 2 1 4 2 4 3 3 2 2 2 1 1 1 5 3 2 interpretation of 0: 2 interpretation of 1: 3 interpretation of 2: 0 interpretation of 3: 3 interpretation of 4: 0 interpretation of 5: 1 remove rule 12 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 interpretation of 0: 0 interpretation of 1: 2 interpretation of 2: 1 interpretation of 3: 0 interpretation of 4: 0 interpretation of 5: 0 remove rule 11 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 5 1 0 3 -> 5 5 0 3 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 interpretation of 0: 1 interpretation of 1: 2 interpretation of 2: 0 interpretation of 3: 2 interpretation of 4: 0 interpretation of 5: 0 remove rule 5 continue with: 0 1 0 2 -> 2 2 2 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 interpretation of 0: 0 interpretation of 1: 1 interpretation of 2: 0 interpretation of 3: 0 interpretation of 4: 0 interpretation of 5: 0 remove rule 1 continue with: 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 interpretation of 0: 0 interpretation of 1: 3 interpretation of 2: 1 interpretation of 3: 0 interpretation of 4: 0 interpretation of 5: 0 remove rule 8 continue with: 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 interpretation of 0: 2 interpretation of 1: 4 interpretation of 2: 2 interpretation of 3: 5 interpretation of 4: 1 interpretation of 5: 3 remove rule 7 continue with: 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 interpretation of 0: 4 interpretation of 1: 6 interpretation of 2: 0 interpretation of 3: 4 interpretation of 4: 3 interpretation of 5: 2 remove rule 6 continue with: 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 1 3 5 1 0 4 -> 4 0 0 0 1 4 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 interpretation of 0: 3 interpretation of 1: 2 interpretation of 2: 0 interpretation of 3: 4 interpretation of 4: 0 interpretation of 5: 1 remove rule 4 continue with: 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 interpretation of 0: 0 interpretation of 1: 4 interpretation of 2: 0 interpretation of 3: 2 interpretation of 4: 2 interpretation of 5: 1 remove rule 4 continue with: 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 1 2 0 4 1 -> 2 5 2 2 interpretation of 0: 4 interpretation of 1: 5 interpretation of 2: 3 interpretation of 3: 1 interpretation of 4: 2 interpretation of 5: 2 remove rule 3 continue with: 0 1 1 1 -> 3 1 0 4 5 1 4 -> 1 5 4 4 interpretation of 0: 0 interpretation of 1: 3 interpretation of 2: 2 interpretation of 3: 1 interpretation of 4: 0 interpretation of 5: 0 remove rule 1 continue with: 4 5 1 4 -> 1 5 4 4 Tropical matrix interpretation interpretation of 0: / 0 0 \ \ 0 0 / interpretation of 1: / 2 3 \ \ 0 0 / interpretation of 2: / 0 0 \ \ 0 0 / interpretation of 3: / 0 0 \ \ 0 0 / interpretation of 4: / 3 3 \ \ 2 0 / interpretation of 5: / 0 2 \ \ 1 3 / remove rule 1 termination has been proved