109.13/79.60	MAYBE
111.62/80.32	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
111.62/80.32	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
111.62/80.32	
111.62/80.32	
111.62/80.32	H-Termination with start terms of the given HASKELL could not be shown:
111.62/80.32	
111.62/80.32	(0) HASKELL
111.62/80.32	(1) LR [EQUIVALENT, 0 ms]
111.62/80.32	(2) HASKELL
111.62/80.32	(3) CR [EQUIVALENT, 0 ms]
111.62/80.32	(4) HASKELL
111.62/80.32	(5) BR [EQUIVALENT, 0 ms]
111.62/80.32	(6) HASKELL
111.62/80.32	(7) COR [EQUIVALENT, 21 ms]
111.62/80.32	(8) HASKELL
111.62/80.32	(9) LetRed [EQUIVALENT, 0 ms]
111.62/80.32	(10) HASKELL
111.62/80.32	(11) NumRed [SOUND, 0 ms]
111.62/80.32	(12) HASKELL
111.62/80.32	
111.62/80.32	
111.62/80.32	----------------------------------------
111.62/80.32	
111.62/80.32	(0)
111.62/80.32	Obligation:
111.62/80.32	mainModule Main 
111.62/80.32	module FiniteMap where {
111.62/80.32	import qualified Main;
111.62/80.32	import qualified Maybe;
111.62/80.32	import qualified Prelude;
111.62/80.32	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
111.62/80.32	
111.62/80.32	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
111.62/80.32	}
111.62/80.32	addListToFM :: Ord a => FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
111.62/80.32	addListToFM fm key_elt_pairs = addListToFM_C (\old new ->new) fm key_elt_pairs;
111.62/80.32	
111.62/80.32	addListToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
111.62/80.32	addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 
111.62/80.32	add fmap (key,elt) = addToFM_C combiner fmap key elt;
111.62/80.32	 };
111.62/80.32	
111.62/80.32	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
111.62/80.32	addToFM_C combiner EmptyFM key elt = unitFM key elt;
111.62/80.32	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt  | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
111.62/80.32	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
111.62/80.32	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
111.62/80.32	
111.62/80.32	emptyFM :: FiniteMap a b;
111.62/80.32	emptyFM = EmptyFM;
111.62/80.32	
111.62/80.32	findMax :: FiniteMap b a  ->  (b,a);
111.62/80.32	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
111.62/80.32	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
111.62/80.32	
111.62/80.32	findMin :: FiniteMap b a  ->  (b,a);
111.62/80.32	findMin (Branch key elt _ EmptyFM _) = (key,elt);
111.62/80.32	findMin (Branch key elt _ fm_l _) = findMin fm_l;
111.62/80.32	
111.62/80.32	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
111.62/80.32	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
111.62/80.32	 | size_r > sIZE_RATIO * size_l = case fm_R of { 
111.62/80.32	Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R
111.62/80.32	 | otherwise -> double_L fm_L fm_R; 
111.62/80.32	 } 
111.62/80.32	 | size_l > sIZE_RATIO * size_r = case fm_L of { 
111.62/80.32	Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R
111.62/80.32	 | otherwise -> double_R fm_L fm_R; 
111.62/80.32	 } 
111.62/80.32	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
111.62/80.32	double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
111.62/80.32	double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
111.62/80.32	single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
111.62/80.32	single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
111.62/80.32	size_l = sizeFM fm_L;
111.62/80.32	size_r = sizeFM fm_R;
111.62/80.32	 };
111.62/80.32	
111.62/80.32	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
111.62/80.32	mkBranch which key elt fm_l fm_r = let { 
111.62/80.32	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
111.62/80.32	} in result where { 
111.62/80.32	balance_ok = True;
111.62/80.32	left_ok = case fm_l of { 
111.62/80.32	EmptyFM-> True; 
111.62/80.32	Branch left_key _ _ _ _-> let { 
111.62/80.32	biggest_left_key = fst (findMax fm_l);
111.62/80.32	} in biggest_left_key < key; 
111.62/80.32	 } ;
111.62/80.32	left_size = sizeFM fm_l;
111.62/80.32	right_ok = case fm_r of { 
111.62/80.32	EmptyFM-> True; 
111.62/80.32	Branch right_key _ _ _ _-> let { 
111.62/80.32	smallest_right_key = fst (findMin fm_r);
111.62/80.32	} in key < smallest_right_key; 
111.62/80.32	 } ;
111.62/80.32	right_size = sizeFM fm_r;
111.62/80.32	unbox :: Int  ->  Int;
111.62/80.32	unbox x = x;
111.62/80.32	 };
111.62/80.32	
111.62/80.32	sIZE_RATIO :: Int;
111.62/80.32	sIZE_RATIO = 5;
111.62/80.32	
111.62/80.32	sizeFM :: FiniteMap b a  ->  Int;
111.62/80.32	sizeFM EmptyFM = 0;
111.62/80.32	sizeFM (Branch _ _ size _ _) = size;
111.62/80.32	
111.62/80.32	unitFM :: a  ->  b  ->  FiniteMap a b;
111.62/80.32	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
111.62/80.32	
111.62/80.32	}
111.62/80.32	module Maybe where {
111.62/80.32	import qualified FiniteMap;
111.62/80.32	import qualified Main;
111.62/80.32	import qualified Prelude;
111.62/80.32	}
111.62/80.32	module Main where {
111.62/80.32	import qualified FiniteMap;
111.62/80.32	import qualified Maybe;
111.62/80.32	import qualified Prelude;
111.62/80.32	}
111.62/80.32	
111.62/80.32	----------------------------------------
111.62/80.32	
111.62/80.32	(1) LR (EQUIVALENT)
111.62/80.32	Lambda Reductions:
111.62/80.32	The following Lambda expression
111.62/80.32	"\oldnew->new"
111.62/80.32	is transformed to
111.62/80.32	"addListToFM0 old new = new;
111.62/80.32	"
111.62/80.32	
111.62/80.32	----------------------------------------
111.62/80.32	
111.62/80.32	(2)
111.62/80.32	Obligation:
111.62/80.32	mainModule Main 
111.62/80.32	module FiniteMap where {
111.62/80.32	import qualified Main;
111.62/80.32	import qualified Maybe;
111.62/80.32	import qualified Prelude;
111.62/80.32	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
111.62/80.32	
111.62/80.32	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
111.62/80.32	}
111.62/80.32	addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a;
111.62/80.32	addListToFM fm key_elt_pairs = addListToFM_C addListToFM0 fm key_elt_pairs;
111.62/80.32	
111.62/80.32	addListToFM0 old new = new;
111.62/80.32	
111.62/80.32	addListToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a;
111.62/80.32	addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 
111.62/80.32	add fmap (key,elt) = addToFM_C combiner fmap key elt;
111.62/80.32	 };
111.62/80.32	
111.62/80.32	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
111.62/80.32	addToFM_C combiner EmptyFM key elt = unitFM key elt;
111.62/80.32	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt  | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
111.62/80.32	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
111.62/80.32	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
111.62/80.32	
111.62/80.32	emptyFM :: FiniteMap b a;
111.62/80.32	emptyFM = EmptyFM;
111.62/80.32	
111.62/80.32	findMax :: FiniteMap b a  ->  (b,a);
111.62/80.32	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
111.62/80.32	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
111.62/80.32	
111.62/80.32	findMin :: FiniteMap a b  ->  (a,b);
111.62/80.32	findMin (Branch key elt _ EmptyFM _) = (key,elt);
111.62/80.32	findMin (Branch key elt _ fm_l _) = findMin fm_l;
111.62/80.32	
111.62/80.32	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
111.62/80.32	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
111.62/80.32	 | size_r > sIZE_RATIO * size_l = case fm_R of { 
111.62/80.32	Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R
111.62/80.32	 | otherwise -> double_L fm_L fm_R; 
111.62/80.32	 } 
111.62/80.32	 | size_l > sIZE_RATIO * size_r = case fm_L of { 
111.62/80.32	Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R
111.62/80.32	 | otherwise -> double_R fm_L fm_R; 
111.62/80.32	 } 
111.62/80.32	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
111.62/80.32	double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
111.62/80.32	double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
111.62/80.32	single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
111.62/80.32	single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
111.62/80.32	size_l = sizeFM fm_L;
111.62/80.32	size_r = sizeFM fm_R;
111.62/80.32	 };
111.62/80.32	
111.62/80.32	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
111.62/80.32	mkBranch which key elt fm_l fm_r = let { 
111.62/80.32	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
111.62/80.32	} in result where { 
111.62/80.32	balance_ok = True;
111.62/80.32	left_ok = case fm_l of { 
111.62/80.32	EmptyFM-> True; 
111.62/80.32	Branch left_key _ _ _ _-> let { 
111.62/80.32	biggest_left_key = fst (findMax fm_l);
111.62/80.32	} in biggest_left_key < key; 
111.62/80.32	 } ;
111.62/80.32	left_size = sizeFM fm_l;
111.62/80.32	right_ok = case fm_r of { 
111.62/80.32	EmptyFM-> True; 
111.62/80.32	Branch right_key _ _ _ _-> let { 
111.62/80.32	smallest_right_key = fst (findMin fm_r);
111.62/80.32	} in key < smallest_right_key; 
111.62/80.32	 } ;
111.62/80.32	right_size = sizeFM fm_r;
111.62/80.32	unbox :: Int  ->  Int;
111.62/80.32	unbox x = x;
111.62/80.32	 };
111.62/80.32	
111.62/80.32	sIZE_RATIO :: Int;
111.62/80.32	sIZE_RATIO = 5;
111.62/80.32	
111.62/80.32	sizeFM :: FiniteMap a b  ->  Int;
111.62/80.32	sizeFM EmptyFM = 0;
111.62/80.32	sizeFM (Branch _ _ size _ _) = size;
111.62/80.32	
111.62/80.32	unitFM :: a  ->  b  ->  FiniteMap a b;
111.62/80.32	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
111.62/80.32	
111.62/80.32	}
111.62/80.32	module Maybe where {
111.62/80.32	import qualified FiniteMap;
111.62/80.32	import qualified Main;
111.62/80.32	import qualified Prelude;
111.62/80.32	}
111.62/80.32	module Main where {
111.62/80.32	import qualified FiniteMap;
111.62/80.32	import qualified Maybe;
111.62/80.32	import qualified Prelude;
111.62/80.32	}
111.62/80.32	
111.62/80.32	----------------------------------------
111.98/80.44	
111.98/80.44	(3) CR (EQUIVALENT)
111.98/80.44	Case Reductions:
111.98/80.44	The following Case expression
111.98/80.44	"case fm_r of {
111.98/80.44	EmptyFM  -> True;
111.98/80.44	Branch right_key _ _ _ _  -> let {
111.98/80.44	smallest_right_key  = fst (findMin fm_r);
111.98/80.44	} in key < smallest_right_key}
111.98/80.44	"
111.98/80.44	is transformed to
111.98/80.44	"right_ok0 fm_r key EmptyFM = True;
111.98/80.44	right_ok0 fm_r key (Branch right_key _ _ _ _) = let {
111.98/80.44	smallest_right_key  = fst (findMin fm_r);
111.98/80.44	} in key < smallest_right_key;
111.98/80.44	"
111.98/80.44	The following Case expression
111.98/80.44	"case fm_l of {
111.98/80.44	EmptyFM  -> True;
111.98/80.44	Branch left_key _ _ _ _  -> let {
111.98/80.44	biggest_left_key  = fst (findMax fm_l);
111.98/80.44	} in biggest_left_key < key}
111.98/80.44	"
111.98/80.44	is transformed to
111.98/80.44	"left_ok0 fm_l key EmptyFM = True;
111.98/80.44	left_ok0 fm_l key (Branch left_key _ _ _ _) = let {
111.98/80.44	biggest_left_key  = fst (findMax fm_l);
111.98/80.44	} in biggest_left_key < key;
111.98/80.44	"
111.98/80.44	The following Case expression
111.98/80.44	"case fm_R of {
111.98/80.44	Branch _ _ _ fm_rl fm_rr |sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R}
111.98/80.44	"
111.98/80.44	is transformed to
111.98/80.44	"mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R;
111.98/80.44	"
111.98/80.44	The following Case expression
111.98/80.44	"case fm_L of {
111.98/80.44	Branch _ _ _ fm_ll fm_lr |sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R}
111.98/80.44	"
111.98/80.44	is transformed to
111.98/80.44	"mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R;
111.98/80.44	"
111.98/80.44	
111.98/80.44	----------------------------------------
111.98/80.44	
111.98/80.44	(4)
111.98/80.44	Obligation:
111.98/80.44	mainModule Main 
111.98/80.44	module FiniteMap where {
111.98/80.44	import qualified Main;
111.98/80.44	import qualified Maybe;
111.98/80.44	import qualified Prelude;
111.98/80.44	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
111.98/80.44	
111.98/80.44	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
111.98/80.44	}
111.98/80.44	addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a;
111.98/80.44	addListToFM fm key_elt_pairs = addListToFM_C addListToFM0 fm key_elt_pairs;
111.98/80.44	
111.98/80.44	addListToFM0 old new = new;
111.98/80.44	
111.98/80.44	addListToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a;
111.98/80.44	addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 
111.98/80.44	add fmap (key,elt) = addToFM_C combiner fmap key elt;
111.98/80.44	 };
111.98/80.44	
111.98/80.44	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
111.98/80.44	addToFM_C combiner EmptyFM key elt = unitFM key elt;
111.98/80.44	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt  | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
111.98/80.44	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
111.98/80.44	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
111.98/80.44	
111.98/80.44	emptyFM :: FiniteMap b a;
111.98/80.44	emptyFM = EmptyFM;
111.98/80.44	
111.98/80.44	findMax :: FiniteMap b a  ->  (b,a);
111.98/80.44	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
111.98/80.44	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
111.98/80.44	
111.98/80.44	findMin :: FiniteMap b a  ->  (b,a);
111.98/80.44	findMin (Branch key elt _ EmptyFM _) = (key,elt);
111.98/80.44	findMin (Branch key elt _ fm_l _) = findMin fm_l;
111.98/80.44	
111.98/80.44	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
111.98/80.44	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
111.98/80.44	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
111.98/80.44	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
111.98/80.44	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
111.98/80.44	double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
111.98/80.44	double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
111.98/80.44	mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr)  | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R
111.98/80.44	 | otherwise = double_L fm_L fm_R;
111.98/80.44	mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr)  | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R
111.98/80.44	 | otherwise = double_R fm_L fm_R;
111.98/80.44	single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
111.98/80.44	single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
111.98/80.44	size_l = sizeFM fm_L;
111.98/80.44	size_r = sizeFM fm_R;
111.98/80.44	 };
111.98/80.44	
111.98/80.44	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
111.98/80.44	mkBranch which key elt fm_l fm_r = let { 
111.98/80.44	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
111.98/80.44	} in result where { 
111.98/80.44	balance_ok = True;
111.98/80.44	left_ok = left_ok0 fm_l key fm_l;
111.98/80.44	left_ok0 fm_l key EmptyFM = True;
111.98/80.44	left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 
111.98/80.44	biggest_left_key = fst (findMax fm_l);
111.98/80.44	} in biggest_left_key < key;
111.98/80.44	left_size = sizeFM fm_l;
111.98/80.44	right_ok = right_ok0 fm_r key fm_r;
111.98/80.44	right_ok0 fm_r key EmptyFM = True;
111.98/80.44	right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 
111.98/80.44	smallest_right_key = fst (findMin fm_r);
111.98/80.44	} in key < smallest_right_key;
111.98/80.44	right_size = sizeFM fm_r;
111.98/80.44	unbox :: Int  ->  Int;
111.98/80.44	unbox x = x;
111.98/80.44	 };
111.98/80.44	
111.98/80.44	sIZE_RATIO :: Int;
111.98/80.44	sIZE_RATIO = 5;
111.98/80.44	
111.98/80.44	sizeFM :: FiniteMap a b  ->  Int;
111.98/80.44	sizeFM EmptyFM = 0;
111.98/80.44	sizeFM (Branch _ _ size _ _) = size;
111.98/80.44	
111.98/80.44	unitFM :: a  ->  b  ->  FiniteMap a b;
111.98/80.44	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
111.98/80.44	
111.98/80.44	}
111.98/80.44	module Maybe where {
111.98/80.44	import qualified FiniteMap;
111.98/80.44	import qualified Main;
111.98/80.44	import qualified Prelude;
111.98/80.44	}
111.98/80.44	module Main where {
111.98/80.44	import qualified FiniteMap;
111.98/80.44	import qualified Maybe;
111.98/80.44	import qualified Prelude;
111.98/80.44	}
111.98/80.44	
111.98/80.44	----------------------------------------
111.98/80.44	
111.98/80.44	(5) BR (EQUIVALENT)
111.98/80.44	Replaced joker patterns by fresh variables and removed binding patterns.
111.98/80.44	----------------------------------------
111.98/80.44	
111.98/80.44	(6)
111.98/80.44	Obligation:
111.98/80.44	mainModule Main 
111.98/80.44	module FiniteMap where {
111.98/80.44	import qualified Main;
111.98/80.44	import qualified Maybe;
111.98/80.44	import qualified Prelude;
111.98/80.44	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
111.98/80.44	
111.98/80.44	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
111.98/80.44	}
111.98/80.44	addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a;
111.98/80.44	addListToFM fm key_elt_pairs = addListToFM_C addListToFM0 fm key_elt_pairs;
111.98/80.44	
111.98/80.44	addListToFM0 old new = new;
111.98/80.44	
111.98/80.44	addListToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
111.98/80.44	addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 
111.98/80.44	add fmap (key,elt) = addToFM_C combiner fmap key elt;
111.98/80.44	 };
111.98/80.44	
111.98/80.44	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
111.98/80.44	addToFM_C combiner EmptyFM key elt = unitFM key elt;
111.98/80.44	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt  | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
111.98/80.44	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
111.98/80.44	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
111.98/80.44	
111.98/80.44	emptyFM :: FiniteMap a b;
111.98/80.44	emptyFM = EmptyFM;
111.98/80.44	
111.98/80.44	findMax :: FiniteMap b a  ->  (b,a);
111.98/80.44	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
111.98/80.44	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
111.98/80.44	
111.98/80.44	findMin :: FiniteMap b a  ->  (b,a);
111.98/80.44	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
111.98/80.44	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
111.98/80.44	
111.98/80.44	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
111.98/80.44	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
111.98/80.44	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
111.98/80.44	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
111.98/80.44	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
111.98/80.44	double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
111.98/80.44	double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
111.98/80.44	mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr)  | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R
111.98/80.44	 | otherwise = double_L fm_L fm_R;
111.98/80.44	mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr)  | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R
111.98/80.44	 | otherwise = double_R fm_L fm_R;
111.98/80.44	single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
111.98/80.44	single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
111.98/80.44	size_l = sizeFM fm_L;
111.98/80.44	size_r = sizeFM fm_R;
111.98/80.44	 };
111.98/80.44	
111.98/80.44	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
111.98/80.44	mkBranch which key elt fm_l fm_r = let { 
111.98/80.44	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
111.98/80.44	} in result where { 
111.98/80.44	balance_ok = True;
111.98/80.44	left_ok = left_ok0 fm_l key fm_l;
111.98/80.44	left_ok0 fm_l key EmptyFM = True;
111.98/80.44	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
111.98/80.44	biggest_left_key = fst (findMax fm_l);
111.98/80.44	} in biggest_left_key < key;
111.98/80.44	left_size = sizeFM fm_l;
111.98/80.44	right_ok = right_ok0 fm_r key fm_r;
111.98/80.44	right_ok0 fm_r key EmptyFM = True;
111.98/80.44	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
111.98/80.44	smallest_right_key = fst (findMin fm_r);
111.98/80.44	} in key < smallest_right_key;
111.98/80.44	right_size = sizeFM fm_r;
111.98/80.44	unbox :: Int  ->  Int;
111.98/80.44	unbox x = x;
111.98/80.44	 };
111.98/80.44	
111.98/80.44	sIZE_RATIO :: Int;
111.98/80.44	sIZE_RATIO = 5;
111.98/80.44	
111.98/80.44	sizeFM :: FiniteMap b a  ->  Int;
111.98/80.44	sizeFM EmptyFM = 0;
111.98/80.44	sizeFM (Branch vz wu size wv ww) = size;
111.98/80.44	
111.98/80.44	unitFM :: b  ->  a  ->  FiniteMap b a;
111.98/80.44	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
111.98/80.44	
111.98/80.44	}
111.98/80.44	module Maybe where {
111.98/80.44	import qualified FiniteMap;
111.98/80.44	import qualified Main;
111.98/80.44	import qualified Prelude;
111.98/80.44	}
111.98/80.44	module Main where {
111.98/80.44	import qualified FiniteMap;
111.98/80.44	import qualified Maybe;
111.98/80.44	import qualified Prelude;
111.98/80.44	}
111.98/80.44	
111.98/80.44	----------------------------------------
111.98/80.44	
111.98/80.44	(7) COR (EQUIVALENT)
111.98/80.44	Cond Reductions:
111.98/80.44	The following Function with conditions
111.98/80.44	"undefined |Falseundefined;
111.98/80.44	"
111.98/80.44	is transformed to
111.98/80.44	"undefined  = undefined1;
111.98/80.44	"
111.98/80.44	"undefined0 True = undefined;
111.98/80.44	"
111.98/80.44	"undefined1  = undefined0 False;
111.98/80.44	"
111.98/80.44	The following Function with conditions
111.98/80.44	"addToFM_C combiner EmptyFM key elt = unitFM key elt;
111.98/80.44	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt|new_key < keymkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r|new_key > keymkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)|otherwiseBranch new_key (combiner elt new_elt) size fm_l fm_r;
111.98/80.44	"
111.98/80.44	is transformed to
111.98/80.44	"addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
111.98/80.44	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt;
111.98/80.44	"
111.98/80.44	"addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r;
111.98/80.44	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key);
111.98/80.44	"
111.98/80.44	"addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r;
111.98/80.44	"
111.98/80.44	"addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt);
111.98/80.44	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise;
111.98/80.44	"
111.98/80.44	"addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key);
111.98/80.44	"
111.98/80.44	"addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
111.98/80.44	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
111.98/80.44	"
111.98/80.44	The following Function with conditions
111.98/80.44	"mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R;
111.98/80.44	"
111.98/80.44	is transformed to
111.98/80.44	"mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
111.98/80.44	"
111.98/80.44	"mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
111.98/80.44	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
111.98/80.44	"
111.98/80.44	"mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
111.98/80.44	"
111.98/80.44	"mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
111.98/80.44	"
111.98/80.44	The following Function with conditions
111.98/80.44	"mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R;
111.98/80.44	"
111.98/80.44	is transformed to
111.98/80.44	"mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
111.98/80.44	"
111.98/80.44	"mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
111.98/80.44	"
111.98/80.44	"mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
111.98/80.44	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
111.98/80.44	"
111.98/80.44	"mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
111.98/80.44	"
111.98/80.44	The following Function with conditions
111.98/80.44	"mkBalBranch key elt fm_L fm_R|size_l + size_r < 2mkBranch 1 key elt fm_L fm_R|size_r > sIZE_RATIO * size_lmkBalBranch0 fm_L fm_R fm_R|size_l > sIZE_RATIO * size_rmkBalBranch1 fm_L fm_R fm_L|otherwisemkBranch 2 key elt fm_L fm_R where {
111.98/80.44	double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
111.98/80.44	;
111.98/80.44	double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
111.98/80.44	;
111.98/80.44	mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R;
111.98/80.44	;
111.98/80.44	mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R;
111.98/80.44	;
111.98/80.44	single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
111.98/80.44	;
111.98/80.44	single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
111.98/80.44	;
111.98/80.44	size_l  = sizeFM fm_L;
111.98/80.44	;
111.98/80.44	size_r  = sizeFM fm_R;
111.98/80.44	} 
111.98/80.44	;
111.98/80.44	"
111.98/80.44	is transformed to
111.98/80.44	"mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
111.98/80.44	"
111.98/80.44	"mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
111.98/80.44	double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
111.98/80.44	;
111.98/80.44	double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
111.98/80.44	;
111.98/80.44	mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
111.98/80.44	;
111.98/80.44	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
111.98/80.44	;
111.98/80.44	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
111.98/80.44	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
111.98/80.44	;
111.98/80.44	mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
111.98/80.44	;
111.98/80.44	mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
111.98/80.44	;
111.98/80.44	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
111.98/80.44	;
111.98/80.44	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
111.98/80.44	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
111.98/80.44	;
111.98/80.44	mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
111.98/80.44	;
111.98/80.44	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
111.98/80.44	;
111.98/80.44	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
111.98/80.44	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
111.98/80.44	;
111.98/80.44	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
111.98/80.44	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
111.98/80.44	;
111.98/80.44	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
111.98/80.44	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
111.98/80.44	;
111.98/80.44	single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
111.98/80.44	;
111.98/80.44	single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
111.98/80.44	;
111.98/80.44	size_l  = sizeFM fm_L;
111.98/80.44	;
111.98/80.44	size_r  = sizeFM fm_R;
111.98/80.44	} 
111.98/80.44	;
111.98/80.44	"
111.98/80.44	
111.98/80.44	----------------------------------------
111.98/80.44	
111.98/80.44	(8)
111.98/80.44	Obligation:
112.36/80.50	mainModule Main 
112.36/80.50	module FiniteMap where {
112.36/80.50	import qualified Main;
112.36/80.50	import qualified Maybe;
112.36/80.50	import qualified Prelude;
112.36/80.50	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
112.36/80.50	
112.36/80.50	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
112.36/80.50	}
112.36/80.50	addListToFM :: Ord a => FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
112.36/80.50	addListToFM fm key_elt_pairs = addListToFM_C addListToFM0 fm key_elt_pairs;
112.36/80.50	
112.36/80.50	addListToFM0 old new = new;
112.36/80.50	
112.36/80.50	addListToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
112.36/80.50	addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 
112.36/80.50	add fmap (key,elt) = addToFM_C combiner fmap key elt;
112.36/80.50	 };
112.36/80.50	
112.36/80.50	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
112.36/80.50	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
112.36/80.50	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt;
112.36/80.50	
112.36/80.50	addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r;
112.36/80.50	
112.36/80.50	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt);
112.36/80.50	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise;
112.36/80.50	
112.36/80.50	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r;
112.36/80.50	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key);
112.36/80.50	
112.36/80.50	addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key);
112.36/80.50	
112.36/80.50	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
112.36/80.50	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
112.36/80.50	
112.36/80.50	emptyFM :: FiniteMap a b;
112.36/80.50	emptyFM = EmptyFM;
112.36/80.50	
112.36/80.50	findMax :: FiniteMap a b  ->  (a,b);
112.36/80.50	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
112.36/80.50	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
112.36/80.50	
112.36/80.50	findMin :: FiniteMap b a  ->  (b,a);
112.36/80.50	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
112.36/80.50	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
112.36/80.50	
112.36/80.50	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
112.36/80.50	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
112.36/80.50	
112.36/80.50	mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 
112.36/80.50	double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
112.36/80.50	double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
112.36/80.50	mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
112.36/80.50	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
112.36/80.50	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
112.36/80.50	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
112.36/80.50	mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
112.36/80.50	mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
112.36/80.50	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
112.36/80.50	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
112.36/80.50	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
112.36/80.50	mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
112.36/80.50	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
112.36/80.50	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
112.36/80.50	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
112.36/80.50	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
112.36/80.50	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
112.36/80.50	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
112.36/80.50	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
112.36/80.50	single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
112.36/80.50	single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
112.36/80.50	size_l = sizeFM fm_L;
112.36/80.50	size_r = sizeFM fm_R;
112.36/80.50	 };
112.36/80.50	
112.36/80.50	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
112.36/80.50	mkBranch which key elt fm_l fm_r = let { 
112.36/80.50	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
112.36/80.50	} in result where { 
112.36/80.50	balance_ok = True;
112.36/80.50	left_ok = left_ok0 fm_l key fm_l;
112.36/80.50	left_ok0 fm_l key EmptyFM = True;
112.36/80.50	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
112.36/80.50	biggest_left_key = fst (findMax fm_l);
112.36/80.50	} in biggest_left_key < key;
112.36/80.50	left_size = sizeFM fm_l;
112.36/80.50	right_ok = right_ok0 fm_r key fm_r;
112.36/80.50	right_ok0 fm_r key EmptyFM = True;
112.36/80.50	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
112.36/80.50	smallest_right_key = fst (findMin fm_r);
112.36/80.50	} in key < smallest_right_key;
112.36/80.50	right_size = sizeFM fm_r;
112.36/80.50	unbox :: Int  ->  Int;
112.36/80.50	unbox x = x;
112.36/80.50	 };
112.36/80.50	
112.36/80.50	sIZE_RATIO :: Int;
112.36/80.50	sIZE_RATIO = 5;
112.36/80.50	
112.36/80.50	sizeFM :: FiniteMap a b  ->  Int;
112.36/80.50	sizeFM EmptyFM = 0;
112.36/80.50	sizeFM (Branch vz wu size wv ww) = size;
112.36/80.50	
112.36/80.50	unitFM :: a  ->  b  ->  FiniteMap a b;
112.36/80.50	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
112.36/80.50	
112.36/80.50	}
112.36/80.50	module Maybe where {
112.36/80.50	import qualified FiniteMap;
112.36/80.50	import qualified Main;
112.36/80.50	import qualified Prelude;
112.36/80.50	}
112.36/80.50	module Main where {
112.36/80.50	import qualified FiniteMap;
112.36/80.50	import qualified Maybe;
112.36/80.50	import qualified Prelude;
112.36/80.50	}
112.36/80.50	
112.36/80.50	----------------------------------------
112.36/80.50	
112.36/80.50	(9) LetRed (EQUIVALENT)
112.36/80.50	Let/Where Reductions:
112.36/80.50	The bindings of the following Let/Where expression
112.36/80.50	"mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
112.36/80.50	double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
112.36/80.50	;
112.36/80.50	double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
112.36/80.50	;
112.36/80.50	mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
112.36/80.50	;
112.36/80.50	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
112.36/80.50	;
112.36/80.50	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
112.36/80.50	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
112.36/80.50	;
112.36/80.50	mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
112.36/80.50	;
112.36/80.50	mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
112.36/80.50	;
112.36/80.50	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
112.36/80.50	;
112.36/80.50	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
112.36/80.50	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
112.36/80.50	;
112.36/80.50	mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
112.36/80.50	;
112.36/80.50	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
112.36/80.50	;
112.36/80.50	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
112.36/80.50	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
112.36/80.50	;
112.36/80.50	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
112.36/80.50	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
112.36/80.50	;
112.36/80.50	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
112.36/80.50	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
112.36/80.50	;
112.36/80.50	single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
112.36/80.50	;
112.36/80.50	single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
112.46/80.55	;
112.46/80.55	size_l  = sizeFM fm_L;
112.46/80.55	;
112.46/80.55	size_r  = sizeFM fm_R;
112.46/80.55	} 
112.46/80.55	"
112.46/80.55	are unpacked to the following functions on top level
112.46/80.55	"mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
112.46/80.55	"
112.46/80.55	"mkBalBranch6Single_R vwx vwy vwz vxu (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 vwx vwy fm_lr fm_r);
112.46/80.55	"
112.46/80.55	"mkBalBranch6Double_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 vwx vwy fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
112.46/80.55	"
112.46/80.55	"mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Single_L vwx vwy vwz vxu fm_L fm_R;
112.46/80.55	mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
112.46/80.55	"
112.46/80.55	"mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
112.46/80.55	"
112.46/80.55	"mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
112.46/80.55	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_l vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_r vwx vwy vwz vxu);
112.46/80.55	"
112.46/80.55	"mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
112.46/80.55	"
112.46/80.55	"mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
112.46/80.55	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
112.46/80.55	"
112.46/80.55	"mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vwz;
112.46/80.55	"
112.46/80.55	"mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vxu;
112.46/80.55	"
112.46/80.55	"mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Single_R vwx vwy vwz vxu fm_L fm_R;
112.46/80.55	mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
112.46/80.55	"
112.46/80.55	"mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
112.46/80.55	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_r vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_l vwx vwy vwz vxu);
112.46/80.55	"
112.46/80.55	"mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
112.46/80.55	"
112.46/80.55	"mkBalBranch6Single_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 vwx vwy fm_l fm_rl) fm_rr;
112.46/80.55	"
112.46/80.55	"mkBalBranch6Double_R vwx vwy vwz vxu (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 vwx vwy fm_lrr fm_r);
112.46/80.55	"
112.46/80.55	"mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Double_L vwx vwy vwz vxu fm_L fm_R;
112.46/80.55	"
112.46/80.55	"mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Double_R vwx vwy vwz vxu fm_L fm_R;
112.46/80.55	"
112.46/80.55	"mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
112.46/80.55	"
112.46/80.55	The bindings of the following Let/Where expression
112.46/80.55	"foldl add fm key_elt_pairs where {
112.46/80.55	add fmap (key,elt) = addToFM_C combiner fmap key elt;
112.46/80.55	} 
112.46/80.55	"
112.46/80.55	are unpacked to the following functions on top level
112.46/80.55	"addListToFM_CAdd vxv fmap (key,elt) = addToFM_C vxv fmap key elt;
112.46/80.55	"
112.46/80.55	The bindings of the following Let/Where expression
112.46/80.55	"let {
112.46/80.55	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
112.46/80.55	} in result where {
112.46/80.55	balance_ok  = True;
112.46/80.55	;
112.46/80.55	left_ok  = left_ok0 fm_l key fm_l;
112.46/80.55	;
112.46/80.55	left_ok0 fm_l key EmptyFM = True;
112.46/80.55	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let {
112.46/80.55	biggest_left_key  = fst (findMax fm_l);
112.46/80.55	} in biggest_left_key < key;
112.46/80.55	;
112.46/80.55	left_size  = sizeFM fm_l;
112.46/80.55	;
112.46/80.55	right_ok  = right_ok0 fm_r key fm_r;
112.46/80.55	;
112.46/80.55	right_ok0 fm_r key EmptyFM = True;
112.46/80.55	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let {
112.46/80.55	smallest_right_key  = fst (findMin fm_r);
112.46/80.55	} in key < smallest_right_key;
112.46/80.55	;
112.46/80.55	right_size  = sizeFM fm_r;
112.46/80.55	;
112.46/80.55	unbox x = x;
112.46/80.55	} 
112.46/80.55	"
112.46/80.55	are unpacked to the following functions on top level
112.46/80.55	"mkBranchRight_size vxw vxx vxy = sizeFM vxw;
112.46/80.55	"
112.46/80.55	"mkBranchBalance_ok vxw vxx vxy = True;
112.46/80.55	"
112.46/80.55	"mkBranchUnbox vxw vxx vxy x = x;
112.46/80.55	"
112.46/80.55	"mkBranchRight_ok vxw vxx vxy = mkBranchRight_ok0 vxw vxx vxy vxw vxx vxw;
112.46/80.55	"
112.46/80.55	"mkBranchLeft_size vxw vxx vxy = sizeFM vxy;
112.46/80.55	"
112.46/80.55	"mkBranchLeft_ok vxw vxx vxy = mkBranchLeft_ok0 vxw vxx vxy vxy vxx vxy;
112.46/80.55	"
112.46/80.55	"mkBranchLeft_ok0 vxw vxx vxy fm_l key EmptyFM = True;
112.46/80.55	mkBranchLeft_ok0 vxw vxx vxy fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
112.46/80.55	"
112.46/80.55	"mkBranchRight_ok0 vxw vxx vxy fm_r key EmptyFM = True;
112.46/80.55	mkBranchRight_ok0 vxw vxx vxy fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
112.46/80.55	"
112.46/80.55	The bindings of the following Let/Where expression
112.46/80.55	"let {
112.46/80.55	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
112.46/80.55	} in result"
112.46/80.55	are unpacked to the following functions on top level
112.46/80.55	"mkBranchResult vxz vyu vyv vyw = Branch vxz vyu (mkBranchUnbox vyv vxz vyw (1 + mkBranchLeft_size vyv vxz vyw + mkBranchRight_size vyv vxz vyw)) vyw vyv;
112.46/80.55	"
112.46/80.55	The bindings of the following Let/Where expression
112.46/80.55	"let {
112.46/80.55	biggest_left_key  = fst (findMax fm_l);
112.46/80.55	} in biggest_left_key < key"
112.46/80.55	are unpacked to the following functions on top level
112.46/80.55	"mkBranchLeft_ok0Biggest_left_key vyx = fst (findMax vyx);
112.46/80.55	"
112.46/80.55	The bindings of the following Let/Where expression
112.46/80.55	"let {
112.46/80.55	smallest_right_key  = fst (findMin fm_r);
112.46/80.55	} in key < smallest_right_key"
112.46/80.55	are unpacked to the following functions on top level
112.46/80.55	"mkBranchRight_ok0Smallest_right_key vyy = fst (findMin vyy);
112.46/80.55	"
112.46/80.55	
112.46/80.55	----------------------------------------
112.46/80.55	
112.46/80.55	(10)
112.46/80.55	Obligation:
112.46/80.55	mainModule Main 
112.46/80.55	module FiniteMap where {
112.46/80.55	import qualified Main;
112.46/80.55	import qualified Maybe;
112.46/80.55	import qualified Prelude;
112.46/80.55	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
112.46/80.55	
112.46/80.55	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
112.46/80.55	}
112.46/80.55	addListToFM :: Ord a => FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
112.46/80.55	addListToFM fm key_elt_pairs = addListToFM_C addListToFM0 fm key_elt_pairs;
112.46/80.55	
112.46/80.55	addListToFM0 old new = new;
112.46/80.55	
112.46/80.55	addListToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
112.46/80.55	addListToFM_C combiner fm key_elt_pairs = foldl (addListToFM_CAdd combiner) fm key_elt_pairs;
112.46/80.55	
112.46/80.55	addListToFM_CAdd vxv fmap (key,elt) = addToFM_C vxv fmap key elt;
112.46/80.55	
112.46/80.55	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
112.46/80.55	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
112.46/80.55	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt;
112.46/80.55	
112.46/80.55	addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r;
112.46/80.55	
112.46/80.55	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt);
112.46/80.55	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise;
112.46/80.55	
112.46/80.55	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r;
112.46/80.55	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key);
112.46/80.55	
112.46/80.55	addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key);
112.46/80.55	
112.46/80.55	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
112.46/80.55	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
112.46/80.55	
112.46/80.55	emptyFM :: FiniteMap b a;
112.46/80.55	emptyFM = EmptyFM;
112.46/80.55	
112.46/80.55	findMax :: FiniteMap b a  ->  (b,a);
112.46/80.55	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
112.46/80.55	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
112.46/80.55	
112.46/80.55	findMin :: FiniteMap a b  ->  (a,b);
112.46/80.55	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
112.46/80.55	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
112.46/80.55	
112.46/80.55	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
112.46/80.55	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
112.46/80.55	
112.46/80.55	mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 key elt fm_L fm_R key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_L fm_R + mkBalBranch6Size_r key elt fm_L fm_R < 2);
112.46/80.55	
112.46/80.55	mkBalBranch6Double_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 vwx vwy fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
112.46/80.55	
112.46/80.55	mkBalBranch6Double_R vwx vwy vwz vxu (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 vwx vwy fm_lrr fm_r);
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Double_L vwx vwy vwz vxu fm_L fm_R;
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Single_L vwx vwy vwz vxu fm_L fm_R;
112.46/80.55	mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Double_R vwx vwy vwz vxu fm_L fm_R;
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Single_R vwx vwy vwz vxu fm_L fm_R;
112.46/80.55	mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
112.46/80.55	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
112.46/80.55	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_l vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_r vwx vwy vwz vxu);
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
112.46/80.55	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_r vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_l vwx vwy vwz vxu);
112.46/80.55	
112.46/80.55	mkBalBranch6Single_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 vwx vwy fm_l fm_rl) fm_rr;
112.46/80.55	
112.46/80.55	mkBalBranch6Single_R vwx vwy vwz vxu (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 vwx vwy fm_lr fm_r);
112.46/80.55	
112.46/80.55	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vwz;
112.46/80.55	
112.46/80.55	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vxu;
112.46/80.55	
112.46/80.55	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
112.46/80.55	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_r fm_l;
112.46/80.55	
112.46/80.55	mkBranchBalance_ok vxw vxx vxy = True;
112.46/80.55	
112.46/80.55	mkBranchLeft_ok vxw vxx vxy = mkBranchLeft_ok0 vxw vxx vxy vxy vxx vxy;
112.46/80.55	
112.46/80.55	mkBranchLeft_ok0 vxw vxx vxy fm_l key EmptyFM = True;
112.46/80.55	mkBranchLeft_ok0 vxw vxx vxy fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
112.46/80.55	
112.46/80.55	mkBranchLeft_ok0Biggest_left_key vyx = fst (findMax vyx);
112.46/80.55	
112.46/80.55	mkBranchLeft_size vxw vxx vxy = sizeFM vxy;
112.46/80.55	
112.46/80.55	mkBranchResult vxz vyu vyv vyw = Branch vxz vyu (mkBranchUnbox vyv vxz vyw (1 + mkBranchLeft_size vyv vxz vyw + mkBranchRight_size vyv vxz vyw)) vyw vyv;
112.46/80.55	
112.46/80.55	mkBranchRight_ok vxw vxx vxy = mkBranchRight_ok0 vxw vxx vxy vxw vxx vxw;
112.46/80.55	
112.46/80.55	mkBranchRight_ok0 vxw vxx vxy fm_r key EmptyFM = True;
112.46/80.55	mkBranchRight_ok0 vxw vxx vxy fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
112.46/80.55	
112.46/80.55	mkBranchRight_ok0Smallest_right_key vyy = fst (findMin vyy);
112.46/80.55	
112.46/80.55	mkBranchRight_size vxw vxx vxy = sizeFM vxw;
112.46/80.55	
112.46/80.55	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)));
112.46/80.55	mkBranchUnbox vxw vxx vxy x = x;
112.46/80.55	
112.46/80.55	sIZE_RATIO :: Int;
112.46/80.55	sIZE_RATIO = 5;
112.46/80.55	
112.46/80.55	sizeFM :: FiniteMap b a  ->  Int;
112.46/80.55	sizeFM EmptyFM = 0;
112.46/80.55	sizeFM (Branch vz wu size wv ww) = size;
112.46/80.55	
112.46/80.55	unitFM :: a  ->  b  ->  FiniteMap a b;
112.46/80.55	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
112.46/80.55	
112.46/80.55	}
112.46/80.55	module Maybe where {
112.46/80.55	import qualified FiniteMap;
112.46/80.55	import qualified Main;
112.46/80.55	import qualified Prelude;
112.46/80.55	}
112.46/80.55	module Main where {
112.46/80.55	import qualified FiniteMap;
112.46/80.55	import qualified Maybe;
112.46/80.55	import qualified Prelude;
112.46/80.55	}
112.46/80.55	
112.46/80.55	----------------------------------------
112.46/80.55	
112.46/80.55	(11) NumRed (SOUND)
112.46/80.55	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
112.46/80.55	----------------------------------------
112.46/80.55	
112.46/80.55	(12)
112.46/80.55	Obligation:
112.46/80.55	mainModule Main 
112.46/80.55	module FiniteMap where {
112.46/80.55	import qualified Main;
112.46/80.55	import qualified Maybe;
112.46/80.55	import qualified Prelude;
112.46/80.55	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
112.46/80.55	
112.46/80.55	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
112.46/80.55	}
112.46/80.55	addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a;
112.46/80.55	addListToFM fm key_elt_pairs = addListToFM_C addListToFM0 fm key_elt_pairs;
112.46/80.55	
112.46/80.55	addListToFM0 old new = new;
112.46/80.55	
112.46/80.55	addListToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a;
112.46/80.55	addListToFM_C combiner fm key_elt_pairs = foldl (addListToFM_CAdd combiner) fm key_elt_pairs;
112.46/80.55	
112.46/80.55	addListToFM_CAdd vxv fmap (key,elt) = addToFM_C vxv fmap key elt;
112.46/80.55	
112.46/80.55	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
112.46/80.55	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
112.46/80.55	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt;
112.46/80.55	
112.46/80.55	addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r;
112.46/80.55	
112.46/80.55	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt);
112.46/80.55	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise;
112.46/80.55	
112.46/80.55	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r;
112.46/80.55	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key);
112.46/80.55	
112.46/80.55	addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key);
112.46/80.55	
112.46/80.55	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
112.46/80.55	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
112.46/80.55	
112.46/80.55	emptyFM :: FiniteMap a b;
112.46/80.55	emptyFM = EmptyFM;
112.46/80.55	
112.46/80.55	findMax :: FiniteMap a b  ->  (a,b);
112.46/80.55	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
112.46/80.55	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
112.46/80.55	
112.46/80.55	findMin :: FiniteMap a b  ->  (a,b);
112.46/80.55	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
112.46/80.55	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
112.46/80.55	
112.46/80.55	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
112.46/80.55	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
112.46/80.55	
112.46/80.55	mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 key elt fm_L fm_R key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_L fm_R + mkBalBranch6Size_r key elt fm_L fm_R < Pos (Succ (Succ Zero)));
112.46/80.55	
112.46/80.55	mkBalBranch6Double_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) key_rl elt_rl (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) vwx vwy fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr);
112.46/80.55	
112.46/80.55	mkBalBranch6Double_R vwx vwy vwz vxu (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) key_lr elt_lr (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))) key_l elt_l fm_ll fm_lrl) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) vwx vwy fm_lrr fm_r);
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Double_L vwx vwy vwz vxu fm_L fm_R;
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Single_L vwx vwy vwz vxu fm_L fm_R;
112.46/80.55	mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr);
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Double_R vwx vwy vwz vxu fm_L fm_R;
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Single_R vwx vwy vwz vxu fm_L fm_R;
112.46/80.55	mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < Pos (Succ (Succ Zero)) * sizeFM fm_ll);
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R;
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
112.46/80.55	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
112.46/80.55	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_l vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_r vwx vwy vwz vxu);
112.46/80.55	
112.46/80.55	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R;
112.46/80.55	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_r vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_l vwx vwy vwz vxu);
112.46/80.55	
112.46/80.55	mkBalBranch6Single_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch (Pos (Succ (Succ (Succ Zero)))) key_r elt_r (mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) vwx vwy fm_l fm_rl) fm_rr;
112.46/80.55	
112.46/80.55	mkBalBranch6Single_R vwx vwy vwz vxu (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))) key_l elt_l fm_ll (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) vwx vwy fm_lr fm_r);
112.46/80.55	
112.46/80.55	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vwz;
112.46/80.55	
112.46/80.55	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vxu;
112.46/80.55	
112.46/80.55	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
112.46/80.55	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_r fm_l;
112.46/80.55	
112.46/80.55	mkBranchBalance_ok vxw vxx vxy = True;
112.46/80.55	
112.46/80.55	mkBranchLeft_ok vxw vxx vxy = mkBranchLeft_ok0 vxw vxx vxy vxy vxx vxy;
112.46/80.55	
112.46/80.55	mkBranchLeft_ok0 vxw vxx vxy fm_l key EmptyFM = True;
112.46/80.55	mkBranchLeft_ok0 vxw vxx vxy fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
112.46/80.55	
112.46/80.55	mkBranchLeft_ok0Biggest_left_key vyx = fst (findMax vyx);
112.46/80.55	
112.46/80.55	mkBranchLeft_size vxw vxx vxy = sizeFM vxy;
112.46/80.55	
112.46/80.55	mkBranchResult vxz vyu vyv vyw = Branch vxz vyu (mkBranchUnbox vyv vxz vyw (Pos (Succ Zero) + mkBranchLeft_size vyv vxz vyw + mkBranchRight_size vyv vxz vyw)) vyw vyv;
112.46/80.55	
112.46/80.55	mkBranchRight_ok vxw vxx vxy = mkBranchRight_ok0 vxw vxx vxy vxw vxx vxw;
112.46/80.55	
112.46/80.55	mkBranchRight_ok0 vxw vxx vxy fm_r key EmptyFM = True;
112.46/80.55	mkBranchRight_ok0 vxw vxx vxy fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
112.46/80.55	
112.46/80.55	mkBranchRight_ok0Smallest_right_key vyy = fst (findMin vyy);
112.46/80.55	
112.46/80.55	mkBranchRight_size vxw vxx vxy = sizeFM vxw;
112.46/80.55	
112.46/80.55	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)));
112.46/80.55	mkBranchUnbox vxw vxx vxy x = x;
112.46/80.55	
112.46/80.55	sIZE_RATIO :: Int;
112.46/80.55	sIZE_RATIO = Pos (Succ (Succ (Succ (Succ (Succ Zero)))));
112.46/80.55	
112.46/80.55	sizeFM :: FiniteMap b a  ->  Int;
112.46/80.55	sizeFM EmptyFM = Pos Zero;
112.46/80.55	sizeFM (Branch vz wu size wv ww) = size;
112.46/80.55	
112.46/80.55	unitFM :: b  ->  a  ->  FiniteMap b a;
112.46/80.55	unitFM key elt = Branch key elt (Pos (Succ Zero)) emptyFM emptyFM;
112.46/80.55	
112.46/80.55	}
112.46/80.55	module Maybe where {
112.46/80.55	import qualified FiniteMap;
112.46/80.55	import qualified Main;
112.46/80.55	import qualified Prelude;
112.46/80.55	}
112.46/80.55	module Main where {
112.46/80.55	import qualified FiniteMap;
112.46/80.55	import qualified Maybe;
112.46/80.55	import qualified Prelude;
112.46/80.55	}
112.46/80.59	EOF