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