TORPAcyc is applied to the string rewriting system R E -> L E a L -> L Aa b L -> L Ab R Aa -> a R R Ab -> b R a b L -> b a R Normal matrix interpretation interpretation of R: / 1 1 \ \ 1 0 / interpretation of E: / 1 0 \ \ 0 0 / interpretation of L: / 1 1 \ \ 1 0 / interpretation of a: / 2 0 \ \ 0 1 / interpretation of Aa: / 1 0 \ \ 1 2 / interpretation of b: / 2 1 \ \ 0 1 / interpretation of Ab: / 1 0 \ \ 2 2 / remove rule 6 continue with: R E -> L E a L -> L Aa b L -> L Ab R Aa -> a R R Ab -> b R interpretation of R: 4 interpretation of E: 10 interpretation of L: 3 interpretation of a: 0 interpretation of Aa: 0 interpretation of b: 2 interpretation of Ab: 2 remove rule 1 continue with: a L -> L Aa b L -> L Ab R Aa -> a R R Ab -> b R Tropical matrix interpretation interpretation of R: / 0 - \ \ 0 - / interpretation of E: / 0 0 \ \ 0 0 / interpretation of L: / 2 2 \ \ - 0 / interpretation of a: / 3 2 \ \ - 1 / interpretation of Aa: / 2 - \ \ - 0 / interpretation of b: / 1 2 \ \ - 1 / interpretation of Ab: / 2 - \ \ 0 0 / remove rule 4 continue with: a L -> L Aa b L -> L Ab R Aa -> a R interpretation of R: 1 interpretation of E: 1 interpretation of L: 0 interpretation of a: 0 interpretation of Aa: 0 interpretation of b: 1 interpretation of Ab: 0 remove rule 2 continue with: a L -> L Aa R Aa -> a R Tropical matrix interpretation interpretation of R: / 0 - \ \ 0 - / interpretation of E: / 0 0 \ \ 0 0 / interpretation of L: / 0 - \ \ - - / interpretation of a: / 2 0 \ \ - 0 / interpretation of Aa: / 1 - \ \ 1 0 / interpretation of b: / 0 0 \ \ 0 0 / interpretation of Ab: / 0 0 \ \ 0 0 / remove rule 1 continue with: R Aa -> a R interpretation of R: 2 interpretation of E: 1 interpretation of L: 1 interpretation of a: 6 interpretation of Aa: 10 interpretation of b: 0 interpretation of Ab: 0 remove rule 1 termination has been proved