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