module Exercise_7 where

import Data.List
import Data.Maybe

{-WETT-}
trancl :: Eq a => [(Integer,(a,a))] -> [(Integer,(a,a))]
trancl rel = if eqRel recStep curStep then curStep else trancl curStep where 
    tranclCalc rel = filter (\(d, (a,b)) -> not (lessThan d (a,b) trans)) trans where 
        trans = nub ([((d+e), (a,c)) | (d, (a,b)) <- rel, (e, (b',c)) <- rel, b == b'] ++ rel)
        lessThan d (a,b) [] = False
        lessThan d (a,b) ((e, (a',b')):rels)
            | a == a' && b == b' && e < d = True
            | otherwise = lessThan d (a,b) rels
    curStep = tranclCalc rel
    recStep = tranclCalc curStep
    eqRel recStep curStep = length recStep == length curStep && and [x `elem` curStep | x <- recStep]
{-TTEW-}