#lang racket

(require racklog)

(define %edge
  (%rel ()
        [('a 'b)]
        [('a 'g)]
        [('b 'c)]
        [('c 'a)]))


(define %select
  (%rel (x xs y ys)
        [(x (cons x xs) xs)]
        [(y (cons x xs) (cons x ys))
         (%select y xs ys)]))

(define %hamilton
  (%rel (x xs y z zs)
        [(x (list y x))]
        [(x (cons x (cons z xs)))
         (%or
          (%edge x z)
          (%edge z x))
         (%hamilton x (cons z xs))]
        [(x (cons y (cons z xs)))
         (%not (%select y xs zs))
         (%not (%= x z))
         (%or
          (%edge y z)
          (%edge z y))
         (%hamilton x (cons z xs))]))

(eq? (%which () (%hamilton 'a '(a b c a))) '())
(eq? (%which () (%hamilton 'a '(a b a g a))) #f)