#
# A one point, we couldn't handling this analysis of value-based dependences.
# Now we can :-)
#

Pos := {[In_1,In_2] -> [i,j] :	1 <= i,j <= 100 &&
				In_1 = 1+2j+i && 2i+In_2 = 1 };

ko := {[In_1,In_2] -> [i,j] :	1+In_1+2j = 4i && In_2+i+2j = 0 &&
				1 <= i <= 100 && 1 <= j <= 100};

kf := {[i,j] -> [i',j'] :	1 <= i,i',j,j' <= 100 && i < i' &&
				4i = 2+2j+2j'+i' && 2i' = 1+2j+i };

k := ko join kf;

k intersection Pos;
example (k intersection Pos);
Pos;
Pos - (ko join kf);
Pos - k;
answer := Pos - k;
answer;
answer intersection {[7,-7] -> [4,1]};
gist answer given Pos;