45.51/11.86 NO 45.51/11.86 45.51/11.86 45.51/11.86 The system was reversed. 45.51/11.86 45.51/11.86 Remains to prove termination of the 6-rule system 45.51/11.86 { b a a -> a b c , 45.51/11.86 c b a -> b c c , 45.51/11.86 c a b -> a a a , 45.51/11.86 b a b ->= b a c , 45.51/11.86 c b b ->= a c c , 45.51/11.86 a c a ->= b b a } 45.51/11.86 45.51/11.86 45.51/11.86 Loop of length 34 starting with a string of length 12 using right expansion 45.51/11.86 and the encoding {a=b, b=a, c=c}: 45.51/11.86 45.51/11.86 .aba.bbbaaaaab 45.51/11.86 rule aba ->= abc at position 0 45.51/11.86 .abc.bbbaaaaab 45.51/11.86 rule bcb ->= aab at position 1 45.51/11.86 .aaab.bbaaaaab 45.51/11.86 rule abb -> bac at position 2 45.51/11.86 .aabac.baaaaab 45.51/11.86 rule cba -> bbb at position 4 45.51/11.86 .aababbb.aaaab 45.51/11.86 rule abb -> bac at position 3 45.51/11.86 .aabbacb.aaaab 45.51/11.86 rule abb -> bac at position 1 45.51/11.86 .abacacb.aaaab 45.51/11.86 rule aba ->= abc at position 0 45.51/11.86 .abccacb.aaaab 45.51/11.86 rule cba -> bbb at position 5 45.51/11.86 .abccabbb.aaab 45.51/11.86 rule abb -> bac at position 4 45.51/11.86 .abccbacb.aaab 45.51/11.86 rule cba -> bbb at position 3 45.51/11.86 .abcbbbcb.aaab 45.51/11.86 rule bcb ->= aab at position 1 45.51/11.86 .aaabbbcb.aaab 45.51/11.86 rule abb -> bac at position 2 45.51/11.86 .aabacbcb.aaab 45.51/11.86 rule aba ->= abc at position 1 45.51/11.86 .aabccbcb.aaab 45.51/11.86 rule bcb ->= aab at position 5 45.51/11.86 .aabccaab.aaab 45.51/11.86 rule caa ->= bcc at position 4 45.51/11.86 .aabcbccb.aaab 45.51/11.86 rule cba -> bbb at position 6 45.51/11.86 .aabcbcbbb.aab 45.51/11.86 rule bcb ->= aab at position 4 45.51/11.86 .aabcaabbb.aab 45.51/11.86 rule abb -> bac at position 5 45.51/11.86 .aabcabacb.aab 45.51/11.86 rule aba ->= abc at position 4 45.51/11.86 .aabcabccb.aab 45.51/11.86 rule cba -> bbb at position 7 45.51/11.86 .aabcabcbbb.ab 45.51/11.86 rule bcb ->= aab at position 5 45.51/11.86 .aabcaaabbb.ab 45.51/11.86 rule caa ->= bcc at position 3 45.51/11.86 .aabbccabbb.ab 45.51/11.86 rule abb -> bac at position 6 45.51/11.86 .aabbccbacb.ab 45.51/11.86 rule cba -> bbb at position 5 45.51/11.86 .aabbcbbbcb.ab 45.51/11.86 rule bcb ->= aab at position 3 45.51/11.86 .aabaabbbcb.ab 45.51/11.86 rule aba ->= abc at position 1 45.51/11.86 .aabcabbbcb.ab 45.51/11.86 rule abb -> bac at position 4 45.51/11.86 .aabcbacbcb.ab 45.51/11.86 rule cba -> bbb at position 3 45.51/11.86 .aabbbbcbcb.ab 45.51/11.86 rule abb -> bac at position 1 45.51/11.86 .abacbbcbcb.ab 45.51/11.86 rule bcb ->= aab at position 5 45.51/11.86 .abacbaabcb.ab 45.51/11.86 rule cba -> bbb at position 3 45.51/11.86 .ababbbabcb.ab 45.51/11.86 rule bcb ->= aab at position 7 45.51/11.86 .ababbbaaab.ab 45.51/11.86 rule aba ->= abc at position 8 45.51/11.86 .ababbbaaabc.b 45.51/11.86 rule bcb ->= aab at position 9 45.51/11.86 .ababbbaaaaab. 45.66/11.90 EOF