/* The weak well-founded model for the following program*/
%r(1,2).
%r(2,3).
%r(3,4).
%p(X,Y) :- r(X,Y), not q(Y).
%q(X) :- r(Y,X), not p(X,Y).

/* Domain definition predicates*/
xdom(1).
xdom(2).
xdom(3).
xdom(4).
ydom(1).
ydom(2).
ydom(3).
ydom(4).

/* EDB */
/* complete the r predicate r =<rplus,rminus> */
/* 16 tuples */
rplus(1,2).
rplus(2,3).
rplus(3,4).

/* IDB */
/* the IDB has two rules */
/* qcomplement for the first rule */
qcomplementplus(X) :- qminus(X).
qcomplementminus(X) :- qplus(X).

/* join this with r to get p */
pplus(X,Y) :- rplus(X,Y),qcomplementplus(Y).
pminus(X,Y) :- xdom(X),ydom(Y),not(rplus(X,Y)).
pminus(X,Y) :- xdom(X),qcomplementminus(Y).

/* second rule defines q */
/* pcomplement rule*/
pcomplementplus(X,Y) :- pminus(X,Y).
pcomplementminus(X,Y) :- pplus(X,Y).

/* join this with r and project first column to get q */
/* the join is stored in predicate temp */
tempplus(Y,X) :- rplus(Y,X),pcomplementplus(X,Y).
tempminus(Y,X) :- ydom(Y),xdom(X),not(rplus(Y,X)).
tempminus(Y,X) :- pcomplementminus(X,Y).
/* project second column from temp to get q */
qplus(X) :- tempplus(_,X).
temp1(X,Y) :- xdom(X),ydom(Y).
temp2(Y) :- temp1(X,Y),not(tempminus(X,Y)).
qminus(X) :- xdom(X), not(temp2(X)).

punknown(X,Y) :- xdom(X),ydom(Y),not(pplus(X,Y)),not(pminus(X,Y)).
qunknown(X) :- xdom(X),not(qplus(X)),not(qminus(X)).