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:
