goal(state([], r, Rs)) :-
   setEquals(Rs, [rw, ld, nr]).

successor(state([L|Ls], l, Rs), row(X, right), state(NewL, r, NewR)) :-
   setMember(X, [L|Ls]),
   setDelete(X, [L|Ls], NewL),
   setInsert(X, Rs, NewR),
   legal(NewL). 
	    
successor(state(Ls, r, [R|Rs]), row(X, left), state(NewL, l, NewR)) :-
   setMember(X, [R|Rs]),
   setDelete(X, [R|Rs], NewR),
   setInsert(X, Ls, NewL),
   legal(NewR).
			
successor(state(Ls, l, Rs), row(empty, right), state(Ls, r, Rs)) :- 
   legal(Ls). 
			    
successor(state(Ls, r, Rs), row(empty, left), state(Ls, l, Rs)) :- 
   legal(Rs).    
			        
legal(Xs) :- 
  \+ (setMember(rw, Xs), setMember(ld, Xs)), 
  \+ (setMember(ld, Xs), setMember(nr, Xs)).

sameState(state(L1s, B, R1s), state(L2s, B, R2s)) :-
   setEquals(L1s, L2s), setEquals(R1s, R2s).