/**
?- traverse([i,happy],[[i,apple],[apple,happy]],_).

Yes

traverse([i,happy],[[i,apple],[apple,happy], [i,appleseed], [appleseed,apple]],  _).


**/

/** 

traverse(+Pair,+Facts,-Facts2)

Pair is form [Subject,Object]
Facts is in form of list of pairs

**/

traverse([Subject,Object],Facts,Facts2) :- 
	traverse1(Subject,Object1,Facts,Facts1), 
	traverse1(Object1,Object,Facts1,Facts2).

/**

traverse(+Pair,+Facts,-Facts2)

As for traverse/1

**/

traverse1(Subject,Object,Facts,Facts3) :-
	delete(Facts,[Subject,Object],Facts2), 
	traverse2([Subject,Object],Facts2,Facts3),!.

/**  

traverse2([+Pair,+Terminator],+Facts,-Facts1) 

where terms are described as for traverse/1.

**/

traverse2([Subject,Object],Facts,Facts3) :-
	member([Subject,Object1],Facts), member([Object1,Object],Facts),
	traverse([Subject,Object],Facts,Facts3).
traverse2([Subject,Object],Facts,Facts) :-
	not(member([Subject,Object1],Facts)),
	not(member([Object1,Object],Facts)).