successors' :: Problem a => a -> [Traced a]
successors' startRiver = concat (map cycleDetect (nub (successors'' [startRiver] [] [Traced startRiver []])))

--Since we want to generate all possible states, we have to generate past the solution.
--However, this means that the solution is not the 'current' part of Traced, though we want that.
--cycleDetect finds instances of Traced whose trace contains a solution,
--then cuts back to that solution, maintaining the original Traced in the process.
cycleDetect :: Problem a => Traced a -> [Traced a]
cycleDetect (Traced x xs) |elem True (map a xs) = [c,Traced (head b) (tail b)]
                          |otherwise = [c]
                          where a = (\x -> isSolution x)
                                b = dropWhile (\x -> not(isSolution x)) xs
                                c = Traced x xs