How will z decide when to emit an output and when to ask for input?
and 0 ≤ x ≤
Then z must lie between a/c and b/d
(Unless c + dx vanishes on (0, ), but ignore this possibility for now)
If a/c and b/d have the same integer part n, then z can output n
Otherwise, it needs more information and should request a term from x
This will tend to narrow the interval of uncertainty