module Exercise_7 where
import Data.List

{-WETT-}

tuplefilter :: Eq e => [(k,e)] -> (k -> k -> Bool) -> [(k,e)]
tuplefilter xs f = aux xs [] [] f
    where
        aux [] fs bs f = fs++bs
        aux (x:xs) fs [] f = aux xs [] (x:fs) f
        aux (x:xs) fs (b:bs) f 
            | snd x == snd b = if (f (fst x) (fst b)) then (aux xs [] (fs++[x]++bs) f) else (aux xs [] (fs++[b]++bs) f)
            | otherwise = aux (x:xs) (fs++[b]) bs f

comp :: Eq b => [(Integer,(a,b))] -> [(Integer,(b,c))] -> [(Integer,(a,c))]
comp xs ys = [(xi+yi, (xa, yb)) | (xi, (xa, xb)) <- xs, (yi, (ya, yb)) <- ys, xb == ya]

subset [] ys = True
subset (x:xs) ys = elem x ys && subset xs ys
setEquality xs ys = subset xs ys && subset ys xs

trancl :: Eq a => [(Integer,(a,a))] -> [(Integer,(a,a))]
trancl xs = if (setEquality newval xs) then newval else trancl newval
    where
        newval = tuplefilter ((comp xs xs) ++ xs) (<)

{-TTEW-}