In this constructed illustration, use Boolean a,b,c, groups {a,b} and {c}, and measurements s=a+b and v=c. Assign A1=(1+a)(1+c) to the first group and A2=(1+a+b)(2-c) to the second. Each uses the other group only through its measurement. Let W_s be the sum of 1+a in the first fiber. Then B1=(1+v)W_s and B2=(1+s)(2-v).

s	W_s	B1*B2 at v=0	B1*B2 at v=1
0	1	2	2
1	3	12	12
2	2	12	12

The six contributions total 52, matching direct evaluation over eight assignments. Other candidate tuples have empty fibers. This is a weighted illustration, not a SAT count or speedup; v is a measurement, not the polynomial parameter.