Shift overflow counter

Shift overflow counter is an informal class of Turing machines. A typical Turing machine in this class has the following behavior:

it represents digits as short fixed-length blocks of symbols
it spends most of it's time implementing basic double counter until one of the sides overflows (expands) which leads to changing the offsets of blocks, making them non-valid representations of digits
after “Counter Phase” there is a “Reset Phase” where the contents are “reparsed”, creating a new double counter configuration. The new configuration could lead to halting.

Examples