 FIND_NEXT_STATE: The machine first marks (1) with y the configuration \(q_{CC,i}S_{CC,j}\) of the rightmost (and so last) complete configuration computed by U in the B part of the tape and (2) with x the configuration \(q_{q,m}S_{q,n}\) of the leftmost quintuple which is not preceded by a marked (with the letter z) semicolon in the A part of the tape. The two configurations are compared. If they are identical, the machine moves to MARK_OPERATIONS, if not, it marks the semicolon preceding \(q_{q,m}S_{q,n}\) with z and goes to FIND_NEXT_STATE. This is easily achieved using the function COMPARE_ALL which means that, whatever the outcome of the comparison, the marks x and y will be erased. For instance, suppose that \(T_n = T_{\textrm{Simple}}\) and that the last complete configuration of \(T_{\textrm{Simple}}\) as computed by U is: 