Here three things have to be maintained: 

1.   �The snail never climbs a negative distance. If the fatigue factor drops the snail's climbing distance below zero, the snail does not climb at all that day.� It means, at any time of its climbing, if its figure factor drops its climbing distance less then zero, from that day the snail would not climb, but just slides at night. So there is no way to be succeeded at this situation. 

2.   The snail climbs at day and slide at night. It does not slide if it become succeed. So any day it reaches the height and crossing the wall it becomes succeed on that day. 

3.   The snail will fail if it reaches the ground i.e. when its height from ground is less then zero(!) it become fail.