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