98.49/70.89	MAYBE
102.76/72.11	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
102.76/72.11	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
102.76/72.11	
102.76/72.11	
102.76/72.11	H-Termination with start terms of the given HASKELL could not be shown:
102.76/72.11	
102.76/72.11	(0) HASKELL
102.76/72.11	(1) LR [EQUIVALENT, 0 ms]
102.76/72.11	(2) HASKELL
102.76/72.11	(3) CR [EQUIVALENT, 0 ms]
102.76/72.11	(4) HASKELL
102.76/72.11	(5) BR [EQUIVALENT, 0 ms]
102.76/72.11	(6) HASKELL
102.76/72.11	(7) COR [EQUIVALENT, 23 ms]
102.76/72.11	(8) HASKELL
102.76/72.11	(9) LetRed [EQUIVALENT, 0 ms]
102.76/72.11	(10) HASKELL
102.76/72.11	(11) NumRed [SOUND, 0 ms]
102.76/72.11	(12) HASKELL
102.76/72.11	
102.76/72.11	
102.76/72.11	----------------------------------------
102.76/72.11	
102.76/72.11	(0)
102.76/72.11	Obligation:
102.76/72.11	mainModule Main 
102.76/72.11	module FiniteMap where {
102.76/72.11	import qualified Main;
102.76/72.11	import qualified Maybe;
102.76/72.11	import qualified Prelude;
102.76/72.11	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
102.76/72.11	
102.76/72.11	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
102.76/72.11	}
102.76/72.11	addListToFM :: Ord a => FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
102.76/72.11	addListToFM fm key_elt_pairs = addListToFM_C (\old new ->new) fm key_elt_pairs;
102.76/72.11	
102.76/72.11	addListToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
102.76/72.11	addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 
102.76/72.11	add fmap (key,elt) = addToFM_C combiner fmap key elt;
102.76/72.11	 };
102.76/72.11	
102.76/72.11	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
102.76/72.11	addToFM_C combiner EmptyFM key elt = unitFM key elt;
102.76/72.11	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
102.76/72.11	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
102.76/72.11	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
102.76/72.11	
102.76/72.11	emptyFM :: FiniteMap a b;
102.76/72.11	emptyFM = EmptyFM;
102.76/72.11	
102.76/72.11	findMax :: FiniteMap a b  ->  (a,b);
102.76/72.11	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
102.76/72.11	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
102.76/72.11	
102.76/72.11	findMin :: FiniteMap a b  ->  (a,b);
102.76/72.11	findMin (Branch key elt _ EmptyFM _) = (key,elt);
102.76/72.11	findMin (Branch key elt _ fm_l _) = findMin fm_l;
102.76/72.11	
102.76/72.11	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
102.76/72.11	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
102.76/72.11	 | size_r > sIZE_RATIO * size_l = case fm_R of { 
102.76/72.11	Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R
102.76/72.11	 | otherwise -> double_L fm_L fm_R; 
102.76/72.11	 } 
102.76/72.11	 | size_l > sIZE_RATIO * size_r = case fm_L of { 
102.76/72.11	Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R
102.76/72.11	 | otherwise -> double_R fm_L fm_R; 
102.76/72.11	 } 
102.76/72.11	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
102.76/72.11	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);
102.76/72.11	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);
102.76/72.11	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;
102.76/72.11	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);
102.76/72.11	size_l = sizeFM fm_L;
102.76/72.11	size_r = sizeFM fm_R;
102.76/72.11	 };
102.76/72.11	
102.76/72.11	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
102.76/72.11	mkBranch which key elt fm_l fm_r = let { 
102.76/72.11	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
102.76/72.11	} in result where { 
102.76/72.11	balance_ok = True;
102.76/72.11	left_ok = case fm_l of { 
102.76/72.11	EmptyFM-> True; 
102.76/72.11	Branch left_key _ _ _ _-> let { 
102.76/72.11	biggest_left_key = fst (findMax fm_l);
102.76/72.11	} in biggest_left_key < key; 
102.76/72.11	 } ;
102.76/72.11	left_size = sizeFM fm_l;
102.76/72.11	right_ok = case fm_r of { 
102.76/72.11	EmptyFM-> True; 
102.76/72.11	Branch right_key _ _ _ _-> let { 
102.76/72.11	smallest_right_key = fst (findMin fm_r);
102.76/72.11	} in key < smallest_right_key; 
102.76/72.11	 } ;
102.76/72.11	right_size = sizeFM fm_r;
102.76/72.11	unbox :: Int  ->  Int;
102.76/72.11	unbox x = x;
102.76/72.11	 };
102.76/72.11	
102.76/72.11	sIZE_RATIO :: Int;
102.76/72.11	sIZE_RATIO = 5;
102.76/72.11	
102.76/72.11	sizeFM :: FiniteMap a b  ->  Int;
102.76/72.11	sizeFM EmptyFM = 0;
102.76/72.11	sizeFM (Branch _ _ size _ _) = size;
102.76/72.11	
102.76/72.11	unitFM :: a  ->  b  ->  FiniteMap a b;
102.76/72.11	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
102.76/72.11	
102.76/72.11	}
102.76/72.11	module Maybe where {
102.76/72.11	import qualified FiniteMap;
102.76/72.11	import qualified Main;
102.76/72.11	import qualified Prelude;
102.76/72.11	}
102.76/72.11	module Main where {
102.76/72.11	import qualified FiniteMap;
102.76/72.11	import qualified Maybe;
102.76/72.11	import qualified Prelude;
102.76/72.11	}
102.76/72.11	
102.76/72.11	----------------------------------------
102.76/72.11	
102.76/72.11	(1) LR (EQUIVALENT)
102.76/72.11	Lambda Reductions:
102.76/72.11	The following Lambda expression
102.76/72.11	"\oldnew->new"
102.76/72.11	is transformed to
102.76/72.11	"addListToFM0 old new = new;
102.76/72.11	"
102.76/72.11	
102.76/72.11	----------------------------------------
102.76/72.11	
102.76/72.11	(2)
102.76/72.11	Obligation:
102.76/72.11	mainModule Main 
102.76/72.11	module FiniteMap where {
102.76/72.11	import qualified Main;
102.76/72.11	import qualified Maybe;
102.76/72.11	import qualified Prelude;
102.76/72.11	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
102.76/72.11	
102.76/72.11	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
102.76/72.11	}
102.76/72.11	addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a;
102.76/72.11	addListToFM fm key_elt_pairs = addListToFM_C addListToFM0 fm key_elt_pairs;
102.76/72.11	
102.76/72.11	addListToFM0 old new = new;
102.76/72.11	
102.76/72.11	addListToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a;
102.76/72.11	addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 
102.76/72.11	add fmap (key,elt) = addToFM_C combiner fmap key elt;
102.76/72.11	 };
102.76/72.11	
102.76/72.11	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
102.76/72.11	addToFM_C combiner EmptyFM key elt = unitFM key elt;
102.76/72.11	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
102.76/72.11	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
102.76/72.11	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
102.76/72.11	
102.76/72.11	emptyFM :: FiniteMap a b;
102.76/72.11	emptyFM = EmptyFM;
102.76/72.11	
102.76/72.11	findMax :: FiniteMap b a  ->  (b,a);
102.76/72.11	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
102.76/72.11	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
102.76/72.11	
102.76/72.11	findMin :: FiniteMap a b  ->  (a,b);
102.76/72.11	findMin (Branch key elt _ EmptyFM _) = (key,elt);
102.76/72.11	findMin (Branch key elt _ fm_l _) = findMin fm_l;
102.76/72.11	
102.76/72.11	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
102.76/72.11	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
102.76/72.11	 | size_r > sIZE_RATIO * size_l = case fm_R of { 
102.76/72.11	Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R
102.76/72.11	 | otherwise -> double_L fm_L fm_R; 
102.76/72.11	 } 
102.76/72.11	 | size_l > sIZE_RATIO * size_r = case fm_L of { 
102.76/72.11	Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R
102.76/72.11	 | otherwise -> double_R fm_L fm_R; 
102.76/72.11	 } 
102.76/72.11	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
102.76/72.11	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);
102.76/72.11	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);
102.76/72.11	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;
102.76/72.11	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);
102.76/72.11	size_l = sizeFM fm_L;
102.76/72.11	size_r = sizeFM fm_R;
102.76/72.11	 };
102.76/72.11	
102.76/72.11	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
102.76/72.11	mkBranch which key elt fm_l fm_r = let { 
102.76/72.11	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
102.76/72.11	} in result where { 
102.76/72.11	balance_ok = True;
102.76/72.11	left_ok = case fm_l of { 
102.76/72.11	EmptyFM-> True; 
102.76/72.11	Branch left_key _ _ _ _-> let { 
102.76/72.11	biggest_left_key = fst (findMax fm_l);
102.76/72.11	} in biggest_left_key < key; 
102.76/72.11	 } ;
102.76/72.11	left_size = sizeFM fm_l;
102.76/72.11	right_ok = case fm_r of { 
102.76/72.11	EmptyFM-> True; 
102.76/72.11	Branch right_key _ _ _ _-> let { 
102.76/72.11	smallest_right_key = fst (findMin fm_r);
102.76/72.11	} in key < smallest_right_key; 
102.76/72.11	 } ;
102.76/72.11	right_size = sizeFM fm_r;
102.76/72.11	unbox :: Int  ->  Int;
102.76/72.11	unbox x = x;
102.76/72.11	 };
102.76/72.11	
102.76/72.11	sIZE_RATIO :: Int;
102.76/72.11	sIZE_RATIO = 5;
102.76/72.11	
102.76/72.11	sizeFM :: FiniteMap a b  ->  Int;
102.76/72.11	sizeFM EmptyFM = 0;
102.76/72.11	sizeFM (Branch _ _ size _ _) = size;
102.76/72.11	
102.76/72.11	unitFM :: b  ->  a  ->  FiniteMap b a;
102.76/72.11	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
102.76/72.11	
102.76/72.11	}
102.76/72.11	module Maybe where {
102.76/72.11	import qualified FiniteMap;
102.76/72.11	import qualified Main;
102.76/72.11	import qualified Prelude;
102.76/72.11	}
102.76/72.11	module Main where {
102.76/72.11	import qualified FiniteMap;
102.76/72.11	import qualified Maybe;
102.76/72.11	import qualified Prelude;
102.76/72.11	}
102.76/72.11	
102.76/72.11	----------------------------------------
102.76/72.11	
102.76/72.11	(3) CR (EQUIVALENT)
102.76/72.11	Case Reductions:
102.76/72.11	The following Case expression
102.76/72.11	"case fm_r of {
102.76/72.11	EmptyFM  -> True;
102.76/72.11	Branch right_key _ _ _ _  -> let {
102.76/72.11	smallest_right_key  = fst (findMin fm_r);
102.76/72.11	} in key < smallest_right_key}
102.76/72.11	"
102.76/72.11	is transformed to
102.76/72.11	"right_ok0 fm_r key EmptyFM = True;
102.76/72.11	right_ok0 fm_r key (Branch right_key _ _ _ _) = let {
102.76/72.11	smallest_right_key  = fst (findMin fm_r);
102.76/72.11	} in key < smallest_right_key;
102.76/72.11	"
102.76/72.11	The following Case expression
102.76/72.11	"case fm_l of {
102.76/72.11	EmptyFM  -> True;
102.76/72.11	Branch left_key _ _ _ _  -> let {
102.76/72.11	biggest_left_key  = fst (findMax fm_l);
102.76/72.11	} in biggest_left_key < key}
102.76/72.11	"
102.76/72.11	is transformed to
102.76/72.11	"left_ok0 fm_l key EmptyFM = True;
102.76/72.11	left_ok0 fm_l key (Branch left_key _ _ _ _) = let {
102.76/72.11	biggest_left_key  = fst (findMax fm_l);
102.76/72.11	} in biggest_left_key < key;
102.76/72.11	"
102.76/72.11	The following Case expression
102.76/72.11	"case fm_R of {
102.76/72.11	Branch _ _ _ fm_rl fm_rr |sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R}
102.76/72.11	"
102.76/72.11	is transformed to
102.76/72.11	"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;
102.76/72.11	"
102.76/72.11	The following Case expression
102.76/72.11	"case fm_L of {
102.76/72.11	Branch _ _ _ fm_ll fm_lr |sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R}
102.76/72.11	"
102.76/72.11	is transformed to
102.76/72.11	"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;
102.76/72.11	"
102.76/72.11	
102.76/72.11	----------------------------------------
102.76/72.11	
102.76/72.11	(4)
102.76/72.11	Obligation:
102.76/72.11	mainModule Main 
102.76/72.11	module FiniteMap where {
102.76/72.11	import qualified Main;
102.76/72.11	import qualified Maybe;
102.76/72.11	import qualified Prelude;
102.76/72.11	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
102.76/72.11	
102.76/72.11	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
102.76/72.11	}
102.76/72.11	addListToFM :: Ord a => FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
102.76/72.11	addListToFM fm key_elt_pairs = addListToFM_C addListToFM0 fm key_elt_pairs;
102.76/72.11	
102.76/72.11	addListToFM0 old new = new;
102.76/72.11	
102.76/72.11	addListToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a;
102.76/72.11	addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 
102.76/72.11	add fmap (key,elt) = addToFM_C combiner fmap key elt;
102.76/72.11	 };
102.76/72.11	
102.76/72.11	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
102.76/72.11	addToFM_C combiner EmptyFM key elt = unitFM key elt;
102.76/72.11	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
102.76/72.11	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
102.76/72.11	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
102.76/72.11	
102.76/72.11	emptyFM :: FiniteMap a b;
102.76/72.11	emptyFM = EmptyFM;
102.76/72.11	
102.76/72.11	findMax :: FiniteMap b a  ->  (b,a);
102.76/72.11	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
102.76/72.11	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
102.76/72.11	
102.76/72.11	findMin :: FiniteMap a b  ->  (a,b);
102.76/72.11	findMin (Branch key elt _ EmptyFM _) = (key,elt);
102.76/72.11	findMin (Branch key elt _ fm_l _) = findMin fm_l;
102.76/72.11	
102.76/72.11	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
102.76/72.11	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
102.76/72.11	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
102.76/72.11	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
102.76/72.11	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
102.76/72.11	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);
102.76/72.11	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);
102.76/72.11	mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr)  | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R
102.76/72.11	 | otherwise = double_L fm_L fm_R;
102.76/72.11	mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr)  | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R
102.76/72.11	 | otherwise = double_R fm_L fm_R;
102.76/72.11	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;
102.76/72.11	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);
102.76/72.11	size_l = sizeFM fm_L;
102.76/72.11	size_r = sizeFM fm_R;
102.76/72.11	 };
102.76/72.11	
102.76/72.11	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
102.76/72.11	mkBranch which key elt fm_l fm_r = let { 
102.76/72.11	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
102.76/72.11	} in result where { 
102.76/72.11	balance_ok = True;
102.76/72.11	left_ok = left_ok0 fm_l key fm_l;
102.76/72.11	left_ok0 fm_l key EmptyFM = True;
102.76/72.11	left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 
102.76/72.11	biggest_left_key = fst (findMax fm_l);
102.76/72.11	} in biggest_left_key < key;
102.76/72.11	left_size = sizeFM fm_l;
102.76/72.11	right_ok = right_ok0 fm_r key fm_r;
102.76/72.11	right_ok0 fm_r key EmptyFM = True;
102.76/72.11	right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 
102.76/72.11	smallest_right_key = fst (findMin fm_r);
102.76/72.11	} in key < smallest_right_key;
102.76/72.11	right_size = sizeFM fm_r;
102.76/72.11	unbox :: Int  ->  Int;
102.76/72.11	unbox x = x;
102.76/72.11	 };
102.76/72.11	
102.76/72.11	sIZE_RATIO :: Int;
102.76/72.11	sIZE_RATIO = 5;
102.76/72.11	
102.76/72.11	sizeFM :: FiniteMap a b  ->  Int;
102.76/72.11	sizeFM EmptyFM = 0;
102.76/72.11	sizeFM (Branch _ _ size _ _) = size;
102.76/72.11	
102.76/72.11	unitFM :: b  ->  a  ->  FiniteMap b a;
102.76/72.11	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
102.76/72.11	
102.76/72.11	}
102.76/72.11	module Maybe where {
102.76/72.11	import qualified FiniteMap;
102.76/72.11	import qualified Main;
102.76/72.11	import qualified Prelude;
102.76/72.11	}
102.76/72.11	module Main where {
102.76/72.11	import qualified FiniteMap;
102.76/72.11	import qualified Maybe;
102.76/72.11	import qualified Prelude;
102.76/72.11	}
102.76/72.11	
102.76/72.11	----------------------------------------
102.76/72.11	
102.76/72.11	(5) BR (EQUIVALENT)
102.76/72.11	Replaced joker patterns by fresh variables and removed binding patterns.
102.76/72.11	----------------------------------------
102.76/72.11	
102.76/72.11	(6)
102.76/72.11	Obligation:
102.76/72.11	mainModule Main 
102.76/72.11	module FiniteMap where {
102.76/72.11	import qualified Main;
102.76/72.11	import qualified Maybe;
102.76/72.11	import qualified Prelude;
102.76/72.11	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
102.76/72.11	
102.76/72.11	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
102.76/72.11	}
102.76/72.11	addListToFM :: Ord b => FiniteMap b a  ->  [(b,a)]  ->  FiniteMap b a;
102.76/72.11	addListToFM fm key_elt_pairs = addListToFM_C addListToFM0 fm key_elt_pairs;
102.76/72.11	
102.76/72.11	addListToFM0 old new = new;
102.76/72.11	
102.76/72.11	addListToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
102.76/72.11	addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 
102.76/72.11	add fmap (key,elt) = addToFM_C combiner fmap key elt;
102.76/72.11	 };
102.76/72.11	
102.76/72.11	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
102.76/72.11	addToFM_C combiner EmptyFM key elt = unitFM key elt;
102.76/72.11	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
102.76/72.11	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
102.76/72.11	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
102.76/72.11	
102.76/72.11	emptyFM :: FiniteMap b a;
102.76/72.11	emptyFM = EmptyFM;
102.76/72.11	
102.76/72.11	findMax :: FiniteMap a b  ->  (a,b);
102.76/72.11	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
102.76/72.11	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
102.76/72.11	
102.76/72.11	findMin :: FiniteMap a b  ->  (a,b);
102.76/72.11	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
102.76/72.11	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
102.76/72.11	
102.76/72.11	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
102.76/72.11	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
102.76/72.11	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
102.76/72.11	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
102.76/72.11	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
102.76/72.11	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);
102.76/72.11	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);
102.76/72.11	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
102.76/72.11	 | otherwise = double_L fm_L fm_R;
102.76/72.11	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
102.76/72.11	 | otherwise = double_R fm_L fm_R;
102.76/72.11	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;
102.76/72.11	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);
102.76/72.11	size_l = sizeFM fm_L;
103.66/72.30	size_r = sizeFM fm_R;
103.66/72.30	 };
103.66/72.30	
103.66/72.30	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
103.66/72.30	mkBranch which key elt fm_l fm_r = let { 
103.66/72.30	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
103.66/72.30	} in result where { 
103.66/72.30	balance_ok = True;
103.66/72.30	left_ok = left_ok0 fm_l key fm_l;
103.66/72.30	left_ok0 fm_l key EmptyFM = True;
103.66/72.30	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
103.66/72.30	biggest_left_key = fst (findMax fm_l);
103.66/72.30	} in biggest_left_key < key;
103.66/72.30	left_size = sizeFM fm_l;
103.66/72.30	right_ok = right_ok0 fm_r key fm_r;
103.66/72.30	right_ok0 fm_r key EmptyFM = True;
103.66/72.30	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
103.66/72.30	smallest_right_key = fst (findMin fm_r);
103.66/72.30	} in key < smallest_right_key;
103.66/72.30	right_size = sizeFM fm_r;
103.66/72.30	unbox :: Int  ->  Int;
103.66/72.30	unbox x = x;
103.66/72.30	 };
103.66/72.30	
103.66/72.30	sIZE_RATIO :: Int;
103.66/72.30	sIZE_RATIO = 5;
103.66/72.30	
103.66/72.30	sizeFM :: FiniteMap a b  ->  Int;
103.66/72.30	sizeFM EmptyFM = 0;
103.66/72.30	sizeFM (Branch vz wu size wv ww) = size;
103.66/72.30	
103.66/72.30	unitFM :: a  ->  b  ->  FiniteMap a b;
103.66/72.30	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
103.66/72.30	
103.66/72.30	}
103.66/72.30	module Maybe where {
103.66/72.30	import qualified FiniteMap;
103.66/72.30	import qualified Main;
103.66/72.30	import qualified Prelude;
103.66/72.30	}
103.66/72.30	module Main where {
103.66/72.30	import qualified FiniteMap;
103.66/72.30	import qualified Maybe;
103.66/72.30	import qualified Prelude;
103.66/72.30	}
103.66/72.30	
103.66/72.30	----------------------------------------
103.66/72.30	
103.66/72.30	(7) COR (EQUIVALENT)
103.66/72.30	Cond Reductions:
103.66/72.30	The following Function with conditions
103.66/72.30	"compare x y|x == yEQ|x <= yLT|otherwiseGT;
103.66/72.30	"
103.66/72.30	is transformed to
103.66/72.30	"compare x y = compare3 x y;
103.66/72.30	"
103.66/72.30	"compare1 x y True = LT;
103.66/72.30	compare1 x y False = compare0 x y otherwise;
103.66/72.30	"
103.66/72.30	"compare2 x y True = EQ;
103.66/72.30	compare2 x y False = compare1 x y (x <= y);
103.66/72.30	"
103.66/72.30	"compare0 x y True = GT;
103.66/72.30	"
103.66/72.30	"compare3 x y = compare2 x y (x == y);
103.66/72.30	"
103.66/72.30	The following Function with conditions
103.66/72.30	"undefined |Falseundefined;
103.66/72.30	"
103.66/72.30	is transformed to
103.66/72.30	"undefined  = undefined1;
103.66/72.30	"
103.66/72.30	"undefined0 True = undefined;
103.66/72.30	"
103.66/72.30	"undefined1  = undefined0 False;
103.66/72.30	"
103.66/72.30	The following Function with conditions
103.66/72.30	"addToFM_C combiner EmptyFM key elt = unitFM key elt;
103.66/72.30	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;
103.66/72.30	"
103.66/72.30	is transformed to
103.66/72.30	"addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
103.66/72.30	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;
103.66/72.30	"
103.66/72.30	"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);
103.66/72.30	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;
103.66/72.30	"
103.66/72.30	"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;
103.66/72.30	"
103.66/72.30	"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;
103.66/72.30	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);
103.66/72.30	"
103.66/72.30	"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);
103.66/72.30	"
103.66/72.30	"addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
103.66/72.30	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
103.66/72.30	"
103.66/72.30	The following Function with conditions
103.66/72.30	"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;
103.66/72.30	"
103.66/72.30	is transformed to
103.66/72.30	"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);
103.66/72.30	"
103.66/72.30	"mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
103.66/72.30	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;
103.66/72.30	"
103.66/72.30	"mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
103.66/72.30	"
103.66/72.30	"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);
103.66/72.30	"
103.66/72.30	The following Function with conditions
103.66/72.30	"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;
103.66/72.30	"
103.66/72.30	is transformed to
103.66/72.30	"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);
103.66/72.30	"
103.66/72.30	"mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
103.66/72.30	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;
103.66/72.30	"
103.66/72.30	"mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
103.66/72.30	"
103.66/72.30	"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);
103.66/72.30	"
103.66/72.30	The following Function with conditions
103.66/72.30	"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 {
103.66/72.30	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);
103.66/72.30	;
103.66/72.30	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);
103.66/72.30	;
103.66/72.30	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;
103.66/72.30	;
103.66/72.30	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;
103.66/72.30	;
103.66/72.30	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;
103.66/72.30	;
103.66/72.30	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);
103.66/72.30	;
103.66/72.30	size_l  = sizeFM fm_L;
103.66/72.30	;
103.66/72.30	size_r  = sizeFM fm_R;
103.66/72.30	} 
103.66/72.30	;
103.66/72.30	"
103.66/72.30	is transformed to
103.66/72.30	"mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
103.66/72.30	"
103.66/72.30	"mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
103.66/72.30	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);
103.66/72.30	;
103.66/72.30	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);
103.66/72.30	;
103.66/72.30	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);
103.66/72.30	;
103.66/72.30	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
103.66/72.30	;
103.66/72.30	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
103.66/72.30	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;
103.66/72.30	;
103.66/72.30	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);
103.66/72.30	;
103.66/72.30	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);
103.66/72.30	;
103.66/72.30	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
103.66/72.30	;
103.66/72.30	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
103.66/72.30	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;
103.66/72.30	;
103.66/72.30	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);
103.66/72.30	;
103.66/72.30	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
103.66/72.30	;
103.66/72.30	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
103.66/72.30	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
103.66/72.30	;
103.66/72.30	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
103.66/72.30	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
103.66/72.30	;
103.66/72.30	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
103.66/72.30	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
103.66/72.30	;
103.66/72.30	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;
103.97/72.35	;
103.97/72.35	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);
103.97/72.35	;
103.97/72.35	size_l  = sizeFM fm_L;
103.97/72.35	;
103.97/72.35	size_r  = sizeFM fm_R;
103.97/72.35	} 
103.97/72.35	;
103.97/72.35	"
103.97/72.35	
103.97/72.35	----------------------------------------
103.97/72.35	
103.97/72.35	(8)
103.97/72.35	Obligation:
103.97/72.35	mainModule Main 
103.97/72.35	module FiniteMap where {
103.97/72.35	import qualified Main;
103.97/72.35	import qualified Maybe;
103.97/72.35	import qualified Prelude;
103.97/72.35	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
103.97/72.35	
103.97/72.35	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
103.97/72.35	}
103.97/72.35	addListToFM :: Ord a => FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
103.97/72.35	addListToFM fm key_elt_pairs = addListToFM_C addListToFM0 fm key_elt_pairs;
103.97/72.35	
103.97/72.35	addListToFM0 old new = new;
103.97/72.35	
103.97/72.35	addListToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
103.97/72.35	addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 
103.97/72.35	add fmap (key,elt) = addToFM_C combiner fmap key elt;
103.97/72.35	 };
103.97/72.35	
103.97/72.35	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
103.97/72.35	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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);
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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;
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
103.97/72.35	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
103.97/72.35	
103.97/72.35	emptyFM :: FiniteMap b a;
103.97/72.35	emptyFM = EmptyFM;
103.97/72.35	
103.97/72.35	findMax :: FiniteMap a b  ->  (a,b);
103.97/72.35	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
103.97/72.35	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
103.97/72.35	
103.97/72.35	findMin :: FiniteMap b a  ->  (b,a);
103.97/72.35	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
103.97/72.35	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
103.97/72.35	
103.97/72.35	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
103.97/72.35	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
103.97/72.35	
103.97/72.35	mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 
103.97/72.35	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);
103.97/72.35	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);
103.97/72.35	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);
103.97/72.35	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
103.97/72.35	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
103.97/72.35	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;
103.97/72.35	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);
103.97/72.35	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);
103.97/72.35	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
103.97/72.35	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
103.97/72.35	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;
103.97/72.35	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);
103.97/72.35	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
103.97/72.35	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
103.97/72.35	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
103.97/72.35	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
103.97/72.35	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
103.97/72.35	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
103.97/72.35	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
103.97/72.35	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;
103.97/72.35	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);
103.97/72.35	size_l = sizeFM fm_L;
103.97/72.35	size_r = sizeFM fm_R;
103.97/72.35	 };
103.97/72.35	
103.97/72.35	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
103.97/72.35	mkBranch which key elt fm_l fm_r = let { 
103.97/72.35	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
103.97/72.35	} in result where { 
103.97/72.35	balance_ok = True;
103.97/72.35	left_ok = left_ok0 fm_l key fm_l;
103.97/72.35	left_ok0 fm_l key EmptyFM = True;
103.97/72.35	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
103.97/72.35	biggest_left_key = fst (findMax fm_l);
103.97/72.35	} in biggest_left_key < key;
103.97/72.35	left_size = sizeFM fm_l;
103.97/72.35	right_ok = right_ok0 fm_r key fm_r;
103.97/72.35	right_ok0 fm_r key EmptyFM = True;
103.97/72.35	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
103.97/72.35	smallest_right_key = fst (findMin fm_r);
103.97/72.35	} in key < smallest_right_key;
103.97/72.35	right_size = sizeFM fm_r;
103.97/72.35	unbox :: Int  ->  Int;
103.97/72.35	unbox x = x;
103.97/72.35	 };
103.97/72.35	
103.97/72.35	sIZE_RATIO :: Int;
103.97/72.35	sIZE_RATIO = 5;
103.97/72.35	
103.97/72.35	sizeFM :: FiniteMap a b  ->  Int;
103.97/72.35	sizeFM EmptyFM = 0;
103.97/72.35	sizeFM (Branch vz wu size wv ww) = size;
103.97/72.35	
103.97/72.35	unitFM :: b  ->  a  ->  FiniteMap b a;
103.97/72.35	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
103.97/72.35	
103.97/72.35	}
103.97/72.35	module Maybe where {
103.97/72.35	import qualified FiniteMap;
103.97/72.35	import qualified Main;
103.97/72.35	import qualified Prelude;
103.97/72.35	}
103.97/72.35	module Main where {
103.97/72.35	import qualified FiniteMap;
103.97/72.35	import qualified Maybe;
103.97/72.35	import qualified Prelude;
103.97/72.35	}
103.97/72.35	
103.97/72.35	----------------------------------------
103.97/72.35	
103.97/72.35	(9) LetRed (EQUIVALENT)
103.97/72.35	Let/Where Reductions:
103.97/72.35	The bindings of the following Let/Where expression
103.97/72.35	"mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
103.97/72.35	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);
103.97/72.35	;
103.97/72.35	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);
103.97/72.35	;
103.97/72.35	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);
103.97/72.35	;
103.97/72.35	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
103.97/72.35	;
103.97/72.35	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
103.97/72.35	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;
103.97/72.35	;
103.97/72.35	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);
103.97/72.35	;
103.97/72.35	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);
103.97/72.35	;
103.97/72.35	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
103.97/72.35	;
103.97/72.35	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
103.97/72.35	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;
103.97/72.35	;
103.97/72.35	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);
103.97/72.35	;
103.97/72.35	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
103.97/72.35	;
103.97/72.35	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
103.97/72.35	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
103.97/72.35	;
103.97/72.35	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
103.97/72.35	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
103.97/72.35	;
103.97/72.35	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
103.97/72.35	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
103.97/72.35	;
103.97/72.35	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;
103.97/72.35	;
103.97/72.35	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);
103.97/72.35	;
103.97/72.35	size_l  = sizeFM fm_L;
103.97/72.35	;
103.97/72.35	size_r  = sizeFM fm_R;
103.97/72.35	} 
103.97/72.35	"
103.97/72.35	are unpacked to the following functions on top level
103.97/72.35	"mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
103.97/72.35	"
103.97/72.35	"mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
103.97/72.35	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
103.97/72.35	"
103.97/72.35	"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);
103.97/72.35	"
103.97/72.35	"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);
103.97/72.35	"
103.97/72.35	"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);
103.97/72.35	"
103.97/72.35	"mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
103.97/72.35	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);
103.97/72.35	"
103.97/72.35	"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;
103.97/72.35	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;
103.97/72.35	"
103.97/72.35	"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);
103.97/72.35	"
103.97/72.35	"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;
103.97/72.35	"
103.97/72.35	"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);
103.97/72.35	"
103.97/72.35	"mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vwz;
103.97/72.35	"
103.97/72.35	"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;
103.97/72.35	"
103.97/72.35	"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);
103.97/72.35	"
103.97/72.35	"mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vxu;
103.97/72.35	"
103.97/72.35	"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;
103.97/72.35	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;
103.97/72.35	"
103.97/72.35	"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;
103.97/72.35	"
103.97/72.35	"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);
103.97/72.35	"
103.97/72.35	"mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
103.97/72.35	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);
103.97/72.35	"
103.97/72.35	The bindings of the following Let/Where expression
103.97/72.35	"foldl add fm key_elt_pairs where {
103.97/72.35	add fmap (key,elt) = addToFM_C combiner fmap key elt;
103.97/72.35	} 
103.97/72.35	"
103.97/72.35	are unpacked to the following functions on top level
103.97/72.35	"addListToFM_CAdd vxv fmap (key,elt) = addToFM_C vxv fmap key elt;
103.97/72.35	"
103.97/72.35	The bindings of the following Let/Where expression
103.97/72.35	"let {
103.97/72.35	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
103.97/72.35	} in result where {
103.97/72.35	balance_ok  = True;
103.97/72.35	;
103.97/72.35	left_ok  = left_ok0 fm_l key fm_l;
103.97/72.35	;
103.97/72.35	left_ok0 fm_l key EmptyFM = True;
103.97/72.35	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let {
103.97/72.35	biggest_left_key  = fst (findMax fm_l);
103.97/72.35	} in biggest_left_key < key;
103.97/72.35	;
103.97/72.35	left_size  = sizeFM fm_l;
103.97/72.35	;
103.97/72.35	right_ok  = right_ok0 fm_r key fm_r;
103.97/72.35	;
103.97/72.35	right_ok0 fm_r key EmptyFM = True;
103.97/72.35	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let {
103.97/72.35	smallest_right_key  = fst (findMin fm_r);
103.97/72.35	} in key < smallest_right_key;
103.97/72.35	;
103.97/72.35	right_size  = sizeFM fm_r;
103.97/72.35	;
103.97/72.35	unbox x = x;
103.97/72.35	} 
103.97/72.35	"
103.97/72.35	are unpacked to the following functions on top level
103.97/72.35	"mkBranchUnbox vxw vxx vxy x = x;
103.97/72.35	"
103.97/72.35	"mkBranchLeft_ok vxw vxx vxy = mkBranchLeft_ok0 vxw vxx vxy vxw vxx vxw;
103.97/72.35	"
103.97/72.35	"mkBranchRight_ok0 vxw vxx vxy fm_r key EmptyFM = True;
103.97/72.35	mkBranchRight_ok0 vxw vxx vxy fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
103.97/72.35	"
103.97/72.35	"mkBranchLeft_size vxw vxx vxy = sizeFM vxw;
103.97/72.35	"
103.97/72.35	"mkBranchRight_size vxw vxx vxy = sizeFM vxy;
103.97/72.35	"
103.97/72.35	"mkBranchBalance_ok vxw vxx vxy = True;
103.97/72.35	"
103.97/72.35	"mkBranchLeft_ok0 vxw vxx vxy fm_l key EmptyFM = True;
103.97/72.35	mkBranchLeft_ok0 vxw vxx vxy fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
103.97/72.35	"
103.97/72.35	"mkBranchRight_ok vxw vxx vxy = mkBranchRight_ok0 vxw vxx vxy vxy vxx vxy;
103.97/72.35	"
103.97/72.35	The bindings of the following Let/Where expression
103.97/72.35	"let {
103.97/72.35	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
103.97/72.35	} in result"
103.97/72.35	are unpacked to the following functions on top level
103.97/72.35	"mkBranchResult vxz vyu vyv vyw = Branch vxz vyu (mkBranchUnbox vyv vxz vyw (1 + mkBranchLeft_size vyv vxz vyw + mkBranchRight_size vyv vxz vyw)) vyv vyw;
103.97/72.35	"
103.97/72.35	The bindings of the following Let/Where expression
103.97/72.35	"let {
103.97/72.35	smallest_right_key  = fst (findMin fm_r);
103.97/72.35	} in key < smallest_right_key"
103.97/72.35	are unpacked to the following functions on top level
103.97/72.35	"mkBranchRight_ok0Smallest_right_key vyx = fst (findMin vyx);
103.97/72.35	"
103.97/72.35	The bindings of the following Let/Where expression
103.97/72.35	"let {
103.97/72.35	biggest_left_key  = fst (findMax fm_l);
103.97/72.35	} in biggest_left_key < key"
103.97/72.35	are unpacked to the following functions on top level
103.97/72.35	"mkBranchLeft_ok0Biggest_left_key vyy = fst (findMax vyy);
103.97/72.35	"
103.97/72.35	
103.97/72.35	----------------------------------------
103.97/72.35	
103.97/72.35	(10)
103.97/72.35	Obligation:
103.97/72.35	mainModule Main 
103.97/72.35	module FiniteMap where {
103.97/72.35	import qualified Main;
103.97/72.35	import qualified Maybe;
103.97/72.35	import qualified Prelude;
103.97/72.35	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
103.97/72.35	
103.97/72.35	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
103.97/72.35	}
103.97/72.35	addListToFM :: Ord a => FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
103.97/72.35	addListToFM fm key_elt_pairs = addListToFM_C addListToFM0 fm key_elt_pairs;
103.97/72.35	
103.97/72.35	addListToFM0 old new = new;
103.97/72.35	
103.97/72.35	addListToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
103.97/72.35	addListToFM_C combiner fm key_elt_pairs = foldl (addListToFM_CAdd combiner) fm key_elt_pairs;
103.97/72.35	
103.97/72.35	addListToFM_CAdd vxv fmap (key,elt) = addToFM_C vxv fmap key elt;
103.97/72.35	
103.97/72.35	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
103.97/72.35	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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);
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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;
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
103.97/72.35	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
103.97/72.35	
103.97/72.35	emptyFM :: FiniteMap a b;
103.97/72.35	emptyFM = EmptyFM;
103.97/72.35	
103.97/72.35	findMax :: FiniteMap a b  ->  (a,b);
103.97/72.35	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
103.97/72.35	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
103.97/72.35	
103.97/72.35	findMin :: FiniteMap b a  ->  (b,a);
103.97/72.35	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
103.97/72.35	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
103.97/72.35	
103.97/72.35	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
103.97/72.35	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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;
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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;
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
103.97/72.35	
103.97/72.35	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
103.97/72.35	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
103.97/72.35	
103.97/72.35	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
103.97/72.35	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);
103.97/72.35	
103.97/72.35	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vwz;
103.97/72.35	
103.97/72.35	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vxu;
103.97/72.35	
103.97/72.35	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
103.97/72.35	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r;
103.97/72.35	
103.97/72.35	mkBranchBalance_ok vxw vxx vxy = True;
103.97/72.35	
103.97/72.35	mkBranchLeft_ok vxw vxx vxy = mkBranchLeft_ok0 vxw vxx vxy vxw vxx vxw;
103.97/72.35	
103.97/72.35	mkBranchLeft_ok0 vxw vxx vxy fm_l key EmptyFM = True;
103.97/72.35	mkBranchLeft_ok0 vxw vxx vxy fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
103.97/72.35	
103.97/72.35	mkBranchLeft_ok0Biggest_left_key vyy = fst (findMax vyy);
103.97/72.35	
103.97/72.35	mkBranchLeft_size vxw vxx vxy = sizeFM vxw;
103.97/72.35	
103.97/72.35	mkBranchResult vxz vyu vyv vyw = Branch vxz vyu (mkBranchUnbox vyv vxz vyw (1 + mkBranchLeft_size vyv vxz vyw + mkBranchRight_size vyv vxz vyw)) vyv vyw;
103.97/72.35	
103.97/72.35	mkBranchRight_ok vxw vxx vxy = mkBranchRight_ok0 vxw vxx vxy vxy vxx vxy;
103.97/72.35	
103.97/72.35	mkBranchRight_ok0 vxw vxx vxy fm_r key EmptyFM = True;
103.97/72.35	mkBranchRight_ok0 vxw vxx vxy fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
103.97/72.35	
103.97/72.35	mkBranchRight_ok0Smallest_right_key vyx = fst (findMin vyx);
103.97/72.35	
103.97/72.35	mkBranchRight_size vxw vxx vxy = sizeFM vxy;
103.97/72.35	
103.97/72.35	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)));
103.97/72.35	mkBranchUnbox vxw vxx vxy x = x;
103.97/72.35	
103.97/72.35	sIZE_RATIO :: Int;
103.97/72.35	sIZE_RATIO = 5;
103.97/72.35	
103.97/72.35	sizeFM :: FiniteMap a b  ->  Int;
103.97/72.35	sizeFM EmptyFM = 0;
103.97/72.35	sizeFM (Branch vz wu size wv ww) = size;
103.97/72.35	
103.97/72.35	unitFM :: b  ->  a  ->  FiniteMap b a;
103.97/72.35	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
103.97/72.35	
103.97/72.35	}
103.97/72.35	module Maybe where {
103.97/72.35	import qualified FiniteMap;
103.97/72.35	import qualified Main;
103.97/72.35	import qualified Prelude;
103.97/72.35	}
103.97/72.35	module Main where {
103.97/72.35	import qualified FiniteMap;
103.97/72.35	import qualified Maybe;
103.97/72.35	import qualified Prelude;
103.97/72.35	}
103.97/72.35	
103.97/72.35	----------------------------------------
103.97/72.35	
103.97/72.35	(11) NumRed (SOUND)
103.97/72.35	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
103.97/72.35	----------------------------------------
103.97/72.35	
103.97/72.35	(12)
103.97/72.35	Obligation:
103.97/72.35	mainModule Main 
103.97/72.35	module FiniteMap where {
103.97/72.35	import qualified Main;
103.97/72.35	import qualified Maybe;
103.97/72.35	import qualified Prelude;
103.97/72.35	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
103.97/72.35	
103.97/72.35	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
103.97/72.35	}
103.97/72.35	addListToFM :: Ord a => FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
103.97/72.35	addListToFM fm key_elt_pairs = addListToFM_C addListToFM0 fm key_elt_pairs;
103.97/72.35	
103.97/72.35	addListToFM0 old new = new;
103.97/72.35	
103.97/72.35	addListToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
103.97/72.35	addListToFM_C combiner fm key_elt_pairs = foldl (addListToFM_CAdd combiner) fm key_elt_pairs;
103.97/72.35	
103.97/72.35	addListToFM_CAdd vxv fmap (key,elt) = addToFM_C vxv fmap key elt;
103.97/72.35	
103.97/72.35	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
103.97/72.35	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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);
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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;
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
103.97/72.35	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
103.97/72.35	
103.97/72.35	emptyFM :: FiniteMap a b;
103.97/72.35	emptyFM = EmptyFM;
103.97/72.35	
103.97/72.35	findMax :: FiniteMap a b  ->  (a,b);
103.97/72.35	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
103.97/72.35	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
103.97/72.35	
103.97/72.35	findMin :: FiniteMap a b  ->  (a,b);
103.97/72.35	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
103.97/72.35	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
103.97/72.35	
103.97/72.35	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
103.97/72.35	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
103.97/72.35	
103.97/72.35	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)));
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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;
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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;
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R;
103.97/72.35	
103.97/72.35	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
103.97/72.35	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
103.97/72.35	
103.97/72.35	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
103.97/72.35	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);
103.97/72.35	
103.97/72.35	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R;
103.97/72.35	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);
103.97/72.35	
103.97/72.35	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;
103.97/72.35	
103.97/72.35	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);
103.97/72.35	
103.97/72.35	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vwz;
103.97/72.35	
103.97/72.35	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vxu;
103.97/72.35	
103.97/72.35	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
103.97/72.35	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r;
103.97/72.35	
103.97/72.35	mkBranchBalance_ok vxw vxx vxy = True;
103.97/72.35	
103.97/72.35	mkBranchLeft_ok vxw vxx vxy = mkBranchLeft_ok0 vxw vxx vxy vxw vxx vxw;
103.97/72.35	
103.97/72.35	mkBranchLeft_ok0 vxw vxx vxy fm_l key EmptyFM = True;
103.97/72.35	mkBranchLeft_ok0 vxw vxx vxy fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
103.97/72.35	
103.97/72.35	mkBranchLeft_ok0Biggest_left_key vyy = fst (findMax vyy);
103.97/72.35	
103.97/72.35	mkBranchLeft_size vxw vxx vxy = sizeFM vxw;
103.97/72.35	
103.97/72.35	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)) vyv vyw;
103.97/72.35	
103.97/72.35	mkBranchRight_ok vxw vxx vxy = mkBranchRight_ok0 vxw vxx vxy vxy vxx vxy;
103.97/72.35	
103.97/72.35	mkBranchRight_ok0 vxw vxx vxy fm_r key EmptyFM = True;
103.97/72.35	mkBranchRight_ok0 vxw vxx vxy fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
103.97/72.35	
103.97/72.35	mkBranchRight_ok0Smallest_right_key vyx = fst (findMin vyx);
103.97/72.35	
103.97/72.35	mkBranchRight_size vxw vxx vxy = sizeFM vxy;
103.97/72.35	
103.97/72.35	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)));
103.97/72.35	mkBranchUnbox vxw vxx vxy x = x;
103.97/72.35	
103.97/72.35	sIZE_RATIO :: Int;
103.97/72.35	sIZE_RATIO = Pos (Succ (Succ (Succ (Succ (Succ Zero)))));
103.97/72.35	
103.97/72.35	sizeFM :: FiniteMap a b  ->  Int;
103.97/72.35	sizeFM EmptyFM = Pos Zero;
103.97/72.35	sizeFM (Branch vz wu size wv ww) = size;
103.97/72.35	
103.97/72.35	unitFM :: b  ->  a  ->  FiniteMap b a;
103.97/72.35	unitFM key elt = Branch key elt (Pos (Succ Zero)) emptyFM emptyFM;
103.97/72.35	
103.97/72.35	}
103.97/72.35	module Maybe where {
103.97/72.35	import qualified FiniteMap;
103.97/72.35	import qualified Main;
103.97/72.35	import qualified Prelude;
103.97/72.35	}
103.97/72.35	module Main where {
103.97/72.35	import qualified FiniteMap;
103.97/72.35	import qualified Maybe;
103.97/72.35	import qualified Prelude;
103.97/72.35	}
103.97/72.39	EOF