TORPAcyc is applied to the string rewriting system 2 1 -> 4 1 3 4 -> 4 2 2 4 -> 3 2 Normal matrix interpretation interpretation of 2: / 1 2 \ \ 0 2 / interpretation of 1: / 1 0 \ \ 2 0 / interpretation of 4: / 1 0 \ \ 0 2 / interpretation of 3: / 1 1 \ \ 0 2 / remove rule 1 continue with: 3 4 -> 4 2 2 4 -> 3 2 interpretation of 2: 0 interpretation of 1: 0 interpretation of 4: 9 interpretation of 3: 1 remove rule 2 continue with: 3 4 -> 4 2 interpretation of 2: 7 interpretation of 1: 0 interpretation of 4: 10 interpretation of 3: 8 remove rule 1 termination has been proved