The state transition table:
S1 S0 IN NS1 NS0 OUT ---------------------- 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 1 0 1 1 1 1 0 1
The state transition diagram:
Circuit operation:
INPUT OUTPUT STATE ---------------------- 00 0 1 01 1 0 00 0 1 01 0 0 10 0 0 11 1 1 10 1 0 00 1 1 11 0 0 01 1 0 00
Destroy the topmost AND gate (with two bubbled inputs).
There are a number of ways you can do this; here's one: