CMP.13:5.3 - Independent ranges lose the determining relation

Let input b be either 0 or 1. Execute x=b; y=b, then test whether x!=y. Independent intervals give x∈[0,1] and y∈[0,1]. Their product contains (0,1), so it cannot exclude the unequal branch.

Recover the construction: both assignments use the same b. Retain x=y, or keep the two input cases separate. Each choice excludes the unequal branch. The shared equality is the needed distinction; refining both independent endpoint ranges cannot recover it.

If the second assignment becomes y=1-b, both inputs take the unequal branch. A retained relation must be derived again from the changed operation. The earlier equality is an invalid assumption in the new computation.