State machine solving a language problem

sm.hs

-- http://math.feld.cvut.cz/demlova/teaching/jag/cjag812.pdf   cviceni 12.1

automat :: String -> Bool
automat input = automat_h input 0 False

automat2 :: String -> Bool
automat2 input = automat_h2 input ['z'] 1

automat_h :: String -> Int -> Bool -> Bool
automat_h ('a':xs) count False = automat_h xs (count + 1) False 
automat_h ('b':xs) count False = automat_h xs (count + 1) False
automat_h ('c':xs) count False = automat_h xs count True
automat_h ('a':xs) count True = automat_h xs (count - 1) True 
automat_h ('b':xs) count True = automat_h xs (count - 1) True
automat_h "" count _ = (count /= 0)

automat_h2 :: String -> [Char] -> Int -> Bool
automat_h2 ('c':xs) stack 1 = automat_h2 xs stack 2
automat_h2 (x:xs) stack 1 = automat_h2 xs ('a':stack) 1  
automat_h2 ('a':xs) ('a':ss) 2 = automat_h2 xs ss 2
automat_h2 ('a':xs) ('z':_) 2 = True
automat_h2 "" ('a':_) 2 = True
automat_h2 _ _ _ = False