Bell eats counter

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

• It has both a bell and a counter on the tape.
• Increment: when the bouncer in the bell finishes a period, the counter is increased by one.
• Overflow: when the bouncer in the bell overflows, the bell eats the lowest digit of the counter (the counter is halved), and the bouncer in the bell is reset.

A Coq proof of a kind of typical behavior doesn't halt.

Examples

1RB1RE_0RC1RD_1LA1RC_1LC---_1LF0RE_0LF0LA

1RB---_1RC0RA_1LD1RA_1LE0LD_0RE1RF_0RB0LF

1RB0LE_0RC---_1LC0RD_0RB1RA_1LF1LE_0LA1LF (more complex than typical ones)

1RB3LB---3RA0LA_2LA3LB4RB1RB2RA