TORPAcyc is applied to the string rewriting system 0 P -> 1 P 1 P -> c P 0 c -> 1 0 1 c -> c 0 P 0 -> P 1 0 0 Tropical matrix interpretation interpretation of 0: / 0 - \ \ - - / interpretation of P: / 1 0 \ \ - 0 / interpretation of 1: / 0 - \ \ 0 - / interpretation of c: / 0 - \ \ 0 2 / remove rule 5 continue with: 0 P -> 1 P 1 P -> c P 0 c -> 1 0 1 c -> c 0 Normal matrix interpretation interpretation of 0: / 1 2 \ \ 0 2 / interpretation of P: / 2 0 \ \ 2 0 / interpretation of 1: / 1 1 \ \ 0 2 / interpretation of c: / 1 0 \ \ 0 2 / remove rule 1 remove rule 2 continue with: 0 c -> 1 0 1 c -> c 0 interpretation of 0: 0 interpretation of P: 0 interpretation of 1: 1 interpretation of c: 9 remove rule 2 continue with: 0 c -> 1 0 interpretation of 0: 8 interpretation of P: 10 interpretation of 1: 7 interpretation of c: 9 remove rule 1 termination has been proved