(VAR f x xs y ys )
(RULES 
        app(app(app(if,true),xs),ys) -> xs
        app(app(app(if,false),xs),ys) -> ys
        app(app(lt,app(s,x)),app(s,y)) -> app(app(lt,x),y)
        app(app(lt,0),app(s,y)) -> true
        app(app(lt,y),0) -> false
        app(app(eq,x),x) -> true
        app(app(eq,app(s,x)),0) -> false
        app(app(eq,0),app(s,x)) -> false
        app(app(merge,xs),nil) -> xs
        app(app(merge,nil),ys) -> ys
        app(app(merge,app(app(cons,x),xs)),app(app(cons,y),ys)) -> app(app(app(if,app(app(lt,x),y)),app(app(cons,x),app(app(merge,xs),app(app(cons,y),ys)))),app(app(app(if,app(app(eq,x),y)),app(app(cons,x),app(app(merge,xs),ys))),app(app(cons,y),app(app(merge,app(app(cons,x),xs)),ys))))
        app(app(map,f),nil) -> nil
        app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs))
        app(app(mult,0),x) -> 0
        app(app(mult,app(s,x)),y) -> app(app(plus,y),app(app(mult,x),y))
        app(app(plus,0),x) -> 0
        app(app(plus,app(s,x)),y) -> app(s,app(app(plus,x),y))
        list1 -> app(app(map,app(mult,app(s,app(s,0)))),hamming)
        list2 -> app(app(map,app(mult,app(s,app(s,app(s,0))))),hamming)
        list3 -> app(app(map,app(mult,app(s,app(s,app(s,app(s,app(s,0))))))),hamming)
        hamming -> app(app(cons,app(s,0)),app(app(merge,list1),app(app(merge,list2),list3)))
        
)