Shift overflow bouncer counter

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

• It has both a bouncer and a counter on the tape.
• Increment: when the bouncer finish a loop, the counter is increased by one.
• Overflow: when the counter overflows, the bouncer is reset to nearly empty, and the original location of the bouncer becomes part of the counter (this is imprecise and sometimes it has more complex behavior).

Examples

• 1RB0RE_1LC0RA_1LD0LB_1LA0LB_1RF1RA_---0RD (bbch)
• 1RB1RE_1LC---_0LD0LC_1RD0RA_1RE0RF_0LA1LD (bbch)
• 1RB0RF_1LC1RB_0RD0LB_---0LE_1RE0RA_1RD1RE (bbch)
• 1RB3LA3LB1RA3RA_2LA2LB---4RA4LA (bbch)