101.61/78.58	MAYBE
103.65/79.23	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
103.65/79.23	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
103.65/79.23	
103.65/79.23	
103.65/79.23	H-Termination with start terms of the given HASKELL could not be shown:
103.65/79.23	
103.65/79.23	(0) HASKELL
103.65/79.23	(1) LR [EQUIVALENT, 0 ms]
103.65/79.23	(2) HASKELL
103.65/79.23	(3) CR [EQUIVALENT, 0 ms]
103.65/79.23	(4) HASKELL
103.65/79.23	(5) BR [EQUIVALENT, 0 ms]
103.65/79.23	(6) HASKELL
103.65/79.23	(7) COR [EQUIVALENT, 22 ms]
103.65/79.23	(8) HASKELL
103.65/79.23	(9) LetRed [EQUIVALENT, 0 ms]
103.65/79.23	(10) HASKELL
103.65/79.23	(11) NumRed [SOUND, 0 ms]
103.65/79.23	(12) HASKELL
103.65/79.23	
103.65/79.23	
103.65/79.23	----------------------------------------
103.65/79.23	
103.65/79.23	(0)
103.65/79.23	Obligation:
103.65/79.23	mainModule Main 
103.65/79.23	module FiniteMap where {
103.65/79.23	import qualified Main;
103.65/79.23	import qualified Maybe;
103.65/79.23	import qualified Prelude;
103.65/79.23	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
103.65/79.23	
103.65/79.23	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
103.65/79.23	}
103.65/79.23	addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
103.65/79.23	addToFM fm key elt = addToFM_C (\old new ->new) fm key elt;
103.65/79.23	
103.65/79.23	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
103.65/79.23	addToFM_C combiner EmptyFM key elt = unitFM key elt;
103.65/79.23	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
103.65/79.23	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
103.65/79.23	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
103.65/79.23	
103.65/79.23	emptyFM :: FiniteMap a b;
103.65/79.23	emptyFM = EmptyFM;
103.65/79.23	
103.65/79.23	findMax :: FiniteMap a b  ->  (a,b);
103.65/79.23	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
103.65/79.23	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
103.65/79.23	
103.65/79.23	findMin :: FiniteMap b a  ->  (b,a);
103.65/79.23	findMin (Branch key elt _ EmptyFM _) = (key,elt);
103.65/79.23	findMin (Branch key elt _ fm_l _) = findMin fm_l;
103.65/79.23	
103.65/79.23	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
103.65/79.23	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
103.65/79.23	 | size_r > sIZE_RATIO * size_l = case fm_R of { 
103.65/79.23	Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R
103.65/79.23	 | otherwise -> double_L fm_L fm_R; 
103.65/79.23	 } 
103.65/79.23	 | size_l > sIZE_RATIO * size_r = case fm_L of { 
103.65/79.23	Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R
103.65/79.23	 | otherwise -> double_R fm_L fm_R; 
103.65/79.23	 } 
103.65/79.23	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
103.65/79.23	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);
103.65/79.23	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);
103.65/79.23	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;
103.65/79.23	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);
103.65/79.23	size_l = sizeFM fm_L;
103.65/79.23	size_r = sizeFM fm_R;
103.65/79.23	 };
103.65/79.23	
103.65/79.23	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
103.65/79.23	mkBranch which key elt fm_l fm_r = let { 
103.65/79.23	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
103.65/79.23	} in result where { 
103.65/79.23	balance_ok = True;
103.65/79.23	left_ok = case fm_l of { 
103.65/79.23	EmptyFM-> True; 
103.65/79.23	Branch left_key _ _ _ _-> let { 
103.65/79.23	biggest_left_key = fst (findMax fm_l);
103.65/79.23	} in biggest_left_key < key; 
103.65/79.23	 } ;
103.65/79.23	left_size = sizeFM fm_l;
103.65/79.23	right_ok = case fm_r of { 
103.65/79.23	EmptyFM-> True; 
103.65/79.23	Branch right_key _ _ _ _-> let { 
103.65/79.23	smallest_right_key = fst (findMin fm_r);
103.65/79.23	} in key < smallest_right_key; 
103.65/79.23	 } ;
103.65/79.23	right_size = sizeFM fm_r;
103.65/79.23	unbox :: Int  ->  Int;
103.65/79.23	unbox x = x;
103.65/79.23	 };
103.65/79.23	
103.65/79.23	sIZE_RATIO :: Int;
103.65/79.23	sIZE_RATIO = 5;
103.65/79.23	
103.65/79.23	sizeFM :: FiniteMap a b  ->  Int;
103.65/79.23	sizeFM EmptyFM = 0;
103.65/79.23	sizeFM (Branch _ _ size _ _) = size;
103.65/79.23	
103.65/79.23	unitFM :: b  ->  a  ->  FiniteMap b a;
103.65/79.23	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
103.65/79.23	
103.65/79.23	}
103.65/79.23	module Maybe where {
103.65/79.23	import qualified FiniteMap;
103.65/79.23	import qualified Main;
103.65/79.23	import qualified Prelude;
103.65/79.23	}
103.65/79.23	module Main where {
103.65/79.23	import qualified FiniteMap;
103.65/79.23	import qualified Maybe;
103.65/79.23	import qualified Prelude;
103.65/79.23	}
103.65/79.23	
103.65/79.23	----------------------------------------
103.65/79.23	
103.65/79.23	(1) LR (EQUIVALENT)
103.65/79.23	Lambda Reductions:
103.65/79.23	The following Lambda expression
103.65/79.23	"\oldnew->new"
103.65/79.23	is transformed to
103.65/79.23	"addToFM0 old new = new;
103.65/79.23	"
103.65/79.23	
103.65/79.23	----------------------------------------
103.65/79.23	
103.65/79.23	(2)
103.65/79.23	Obligation:
103.65/79.23	mainModule Main 
103.65/79.23	module FiniteMap where {
103.65/79.23	import qualified Main;
103.65/79.23	import qualified Maybe;
103.65/79.23	import qualified Prelude;
103.65/79.23	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
103.65/79.23	
103.65/79.23	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
103.65/79.23	}
103.65/79.23	addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
103.65/79.23	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
103.65/79.23	
103.65/79.23	addToFM0 old new = new;
103.65/79.23	
103.65/79.23	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
103.65/79.23	addToFM_C combiner EmptyFM key elt = unitFM key elt;
103.65/79.23	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
103.65/79.23	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
103.65/79.23	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
103.65/79.23	
103.65/79.23	emptyFM :: FiniteMap a b;
103.65/79.23	emptyFM = EmptyFM;
103.65/79.23	
103.65/79.23	findMax :: FiniteMap b a  ->  (b,a);
104.00/79.23	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
104.00/79.23	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
104.00/79.23	
104.00/79.23	findMin :: FiniteMap b a  ->  (b,a);
104.00/79.23	findMin (Branch key elt _ EmptyFM _) = (key,elt);
104.00/79.23	findMin (Branch key elt _ fm_l _) = findMin fm_l;
104.00/79.23	
104.00/79.23	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
104.00/79.23	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
104.00/79.23	 | size_r > sIZE_RATIO * size_l = case fm_R of { 
104.00/79.23	Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R
104.00/79.23	 | otherwise -> double_L fm_L fm_R; 
104.00/79.23	 } 
104.00/79.23	 | size_l > sIZE_RATIO * size_r = case fm_L of { 
104.00/79.23	Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R
104.00/79.23	 | otherwise -> double_R fm_L fm_R; 
104.00/79.23	 } 
104.00/79.23	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
104.00/79.23	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);
104.00/79.23	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);
104.00/79.23	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;
104.00/79.23	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);
104.00/79.23	size_l = sizeFM fm_L;
104.00/79.23	size_r = sizeFM fm_R;
104.00/79.23	 };
104.00/79.23	
104.00/79.23	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
104.00/79.23	mkBranch which key elt fm_l fm_r = let { 
104.00/79.23	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
104.00/79.23	} in result where { 
104.00/79.23	balance_ok = True;
104.00/79.23	left_ok = case fm_l of { 
104.00/79.23	EmptyFM-> True; 
104.00/79.23	Branch left_key _ _ _ _-> let { 
104.00/79.23	biggest_left_key = fst (findMax fm_l);
104.00/79.23	} in biggest_left_key < key; 
104.00/79.23	 } ;
104.00/79.23	left_size = sizeFM fm_l;
104.00/79.23	right_ok = case fm_r of { 
104.00/79.23	EmptyFM-> True; 
104.00/79.23	Branch right_key _ _ _ _-> let { 
104.00/79.23	smallest_right_key = fst (findMin fm_r);
104.00/79.23	} in key < smallest_right_key; 
104.00/79.23	 } ;
104.00/79.23	right_size = sizeFM fm_r;
104.00/79.23	unbox :: Int  ->  Int;
104.00/79.23	unbox x = x;
104.00/79.23	 };
104.00/79.23	
104.00/79.23	sIZE_RATIO :: Int;
104.00/79.23	sIZE_RATIO = 5;
104.00/79.23	
104.00/79.23	sizeFM :: FiniteMap b a  ->  Int;
104.00/79.23	sizeFM EmptyFM = 0;
104.00/79.23	sizeFM (Branch _ _ size _ _) = size;
104.00/79.23	
104.00/79.23	unitFM :: a  ->  b  ->  FiniteMap a b;
104.00/79.23	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
104.00/79.23	
104.00/79.23	}
104.00/79.23	module Maybe where {
104.00/79.23	import qualified FiniteMap;
104.00/79.23	import qualified Main;
104.00/79.23	import qualified Prelude;
104.00/79.23	}
104.00/79.23	module Main where {
104.00/79.23	import qualified FiniteMap;
104.00/79.23	import qualified Maybe;
104.00/79.23	import qualified Prelude;
104.00/79.23	}
104.00/79.23	
104.00/79.23	----------------------------------------
104.00/79.23	
104.00/79.23	(3) CR (EQUIVALENT)
104.00/79.23	Case Reductions:
104.00/79.23	The following Case expression
104.00/79.23	"case fm_r of {
104.00/79.23	EmptyFM  -> True;
104.00/79.23	Branch right_key _ _ _ _  -> let {
104.00/79.23	smallest_right_key  = fst (findMin fm_r);
104.00/79.23	} in key < smallest_right_key}
104.00/79.23	"
104.00/79.23	is transformed to
104.00/79.23	"right_ok0 fm_r key EmptyFM = True;
104.00/79.23	right_ok0 fm_r key (Branch right_key _ _ _ _) = let {
104.00/79.23	smallest_right_key  = fst (findMin fm_r);
104.00/79.23	} in key < smallest_right_key;
104.00/79.23	"
104.00/79.23	The following Case expression
104.00/79.23	"case fm_l of {
104.00/79.23	EmptyFM  -> True;
104.00/79.23	Branch left_key _ _ _ _  -> let {
104.55/79.42	biggest_left_key  = fst (findMax fm_l);
104.55/79.42	} in biggest_left_key < key}
104.55/79.42	"
104.55/79.42	is transformed to
104.55/79.42	"left_ok0 fm_l key EmptyFM = True;
104.55/79.42	left_ok0 fm_l key (Branch left_key _ _ _ _) = let {
104.55/79.42	biggest_left_key  = fst (findMax fm_l);
104.55/79.42	} in biggest_left_key < key;
104.55/79.42	"
104.55/79.42	The following Case expression
104.55/79.42	"case fm_R of {
104.55/79.42	Branch _ _ _ fm_rl fm_rr |sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R}
104.55/79.42	"
104.55/79.42	is transformed to
104.55/79.42	"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;
104.55/79.42	"
104.55/79.42	The following Case expression
104.55/79.42	"case fm_L of {
104.55/79.42	Branch _ _ _ fm_ll fm_lr |sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R}
104.55/79.42	"
104.55/79.42	is transformed to
104.55/79.42	"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;
104.55/79.42	"
104.55/79.42	
104.55/79.42	----------------------------------------
104.55/79.42	
104.55/79.42	(4)
104.55/79.42	Obligation:
104.55/79.42	mainModule Main 
104.55/79.42	module FiniteMap where {
104.55/79.42	import qualified Main;
104.55/79.42	import qualified Maybe;
104.55/79.42	import qualified Prelude;
104.55/79.42	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
104.55/79.42	
104.55/79.42	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
104.55/79.42	}
104.55/79.42	addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
104.55/79.42	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
104.55/79.42	
104.55/79.42	addToFM0 old new = new;
104.55/79.42	
104.55/79.42	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
104.55/79.42	addToFM_C combiner EmptyFM key elt = unitFM key elt;
104.55/79.42	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
104.55/79.42	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
104.55/79.42	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
104.55/79.42	
104.55/79.42	emptyFM :: FiniteMap a b;
104.55/79.42	emptyFM = EmptyFM;
104.55/79.42	
104.55/79.42	findMax :: FiniteMap b a  ->  (b,a);
104.55/79.42	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
104.55/79.42	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
104.55/79.42	
104.55/79.42	findMin :: FiniteMap a b  ->  (a,b);
104.55/79.42	findMin (Branch key elt _ EmptyFM _) = (key,elt);
104.55/79.42	findMin (Branch key elt _ fm_l _) = findMin fm_l;
104.55/79.42	
104.55/79.42	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
104.55/79.42	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
104.55/79.42	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
104.55/79.42	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
104.55/79.42	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
104.55/79.42	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);
104.55/79.42	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);
104.55/79.42	mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr)  | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R
104.55/79.42	 | otherwise = double_L fm_L fm_R;
104.55/79.42	mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr)  | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R
104.55/79.42	 | otherwise = double_R fm_L fm_R;
104.55/79.42	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;
104.55/79.42	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);
104.55/79.42	size_l = sizeFM fm_L;
104.55/79.42	size_r = sizeFM fm_R;
104.55/79.42	 };
104.55/79.42	
104.55/79.42	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
104.55/79.42	mkBranch which key elt fm_l fm_r = let { 
104.55/79.42	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
104.55/79.42	} in result where { 
104.55/79.42	balance_ok = True;
104.55/79.42	left_ok = left_ok0 fm_l key fm_l;
104.55/79.42	left_ok0 fm_l key EmptyFM = True;
104.55/79.42	left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 
104.55/79.42	biggest_left_key = fst (findMax fm_l);
104.55/79.42	} in biggest_left_key < key;
104.55/79.42	left_size = sizeFM fm_l;
104.55/79.42	right_ok = right_ok0 fm_r key fm_r;
104.55/79.42	right_ok0 fm_r key EmptyFM = True;
104.55/79.42	right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 
104.55/79.42	smallest_right_key = fst (findMin fm_r);
104.55/79.42	} in key < smallest_right_key;
104.55/79.42	right_size = sizeFM fm_r;
104.55/79.42	unbox :: Int  ->  Int;
104.55/79.42	unbox x = x;
104.55/79.42	 };
104.55/79.42	
104.55/79.42	sIZE_RATIO :: Int;
104.55/79.42	sIZE_RATIO = 5;
104.55/79.42	
104.55/79.42	sizeFM :: FiniteMap b a  ->  Int;
104.55/79.42	sizeFM EmptyFM = 0;
104.55/79.42	sizeFM (Branch _ _ size _ _) = size;
104.55/79.42	
104.55/79.42	unitFM :: a  ->  b  ->  FiniteMap a b;
104.55/79.42	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
104.55/79.42	
104.55/79.42	}
104.55/79.42	module Maybe where {
104.55/79.42	import qualified FiniteMap;
104.55/79.42	import qualified Main;
104.55/79.42	import qualified Prelude;
104.55/79.42	}
104.55/79.42	module Main where {
104.55/79.42	import qualified FiniteMap;
104.55/79.42	import qualified Maybe;
104.55/79.42	import qualified Prelude;
104.55/79.42	}
104.55/79.42	
104.55/79.42	----------------------------------------
104.55/79.42	
104.55/79.42	(5) BR (EQUIVALENT)
104.55/79.42	Replaced joker patterns by fresh variables and removed binding patterns.
104.55/79.42	----------------------------------------
104.55/79.42	
104.55/79.42	(6)
104.55/79.42	Obligation:
104.55/79.42	mainModule Main 
104.55/79.42	module FiniteMap where {
104.55/79.42	import qualified Main;
104.55/79.42	import qualified Maybe;
104.55/79.42	import qualified Prelude;
104.55/79.42	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
104.55/79.42	
104.55/79.42	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
104.55/79.42	}
104.55/79.42	addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
104.55/79.42	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
104.55/79.42	
104.55/79.42	addToFM0 old new = new;
104.55/79.42	
104.55/79.42	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
104.55/79.42	addToFM_C combiner EmptyFM key elt = unitFM key elt;
104.55/79.42	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
104.55/79.42	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
104.55/79.42	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
104.55/79.42	
104.55/79.42	emptyFM :: FiniteMap b a;
104.55/79.42	emptyFM = EmptyFM;
104.55/79.42	
104.55/79.42	findMax :: FiniteMap b a  ->  (b,a);
104.55/79.42	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
104.55/79.42	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
104.55/79.42	
104.55/79.42	findMin :: FiniteMap a b  ->  (a,b);
104.55/79.42	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
104.55/79.42	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
104.55/79.42	
104.55/79.42	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
104.55/79.42	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
104.55/79.42	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
104.55/79.42	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
104.55/79.42	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
104.55/79.42	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);
104.55/79.42	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);
104.55/79.42	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
104.55/79.42	 | otherwise = double_L fm_L fm_R;
104.55/79.42	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
104.55/79.42	 | otherwise = double_R fm_L fm_R;
104.55/79.42	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;
104.55/79.42	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);
104.55/79.42	size_l = sizeFM fm_L;
104.55/79.42	size_r = sizeFM fm_R;
104.55/79.42	 };
104.55/79.42	
104.55/79.42	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
104.55/79.42	mkBranch which key elt fm_l fm_r = let { 
104.55/79.42	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
104.55/79.42	} in result where { 
104.55/79.42	balance_ok = True;
104.55/79.42	left_ok = left_ok0 fm_l key fm_l;
104.55/79.42	left_ok0 fm_l key EmptyFM = True;
104.55/79.42	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
104.55/79.42	biggest_left_key = fst (findMax fm_l);
104.55/79.42	} in biggest_left_key < key;
104.55/79.42	left_size = sizeFM fm_l;
104.55/79.42	right_ok = right_ok0 fm_r key fm_r;
104.55/79.42	right_ok0 fm_r key EmptyFM = True;
104.55/79.42	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
104.55/79.42	smallest_right_key = fst (findMin fm_r);
104.55/79.42	} in key < smallest_right_key;
104.55/79.42	right_size = sizeFM fm_r;
104.55/79.42	unbox :: Int  ->  Int;
104.55/79.42	unbox x = x;
104.55/79.42	 };
104.55/79.42	
104.55/79.42	sIZE_RATIO :: Int;
104.55/79.42	sIZE_RATIO = 5;
104.55/79.42	
104.55/79.42	sizeFM :: FiniteMap a b  ->  Int;
104.55/79.42	sizeFM EmptyFM = 0;
104.55/79.42	sizeFM (Branch vz wu size wv ww) = size;
104.55/79.42	
104.55/79.42	unitFM :: b  ->  a  ->  FiniteMap b a;
104.55/79.42	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
104.55/79.42	
104.55/79.42	}
104.55/79.42	module Maybe where {
104.55/79.42	import qualified FiniteMap;
104.55/79.42	import qualified Main;
104.55/79.42	import qualified Prelude;
104.55/79.42	}
104.55/79.42	module Main where {
104.55/79.42	import qualified FiniteMap;
104.55/79.42	import qualified Maybe;
104.55/79.42	import qualified Prelude;
104.55/79.42	}
104.55/79.42	
104.55/79.42	----------------------------------------
104.55/79.42	
104.55/79.42	(7) COR (EQUIVALENT)
104.55/79.42	Cond Reductions:
104.55/79.42	The following Function with conditions
104.55/79.42	"undefined |Falseundefined;
104.55/79.42	"
104.55/79.42	is transformed to
104.55/79.42	"undefined  = undefined1;
104.55/79.42	"
104.55/79.42	"undefined0 True = undefined;
104.55/79.42	"
104.55/79.42	"undefined1  = undefined0 False;
104.55/79.42	"
104.55/79.42	The following Function with conditions
104.55/79.42	"addToFM_C combiner EmptyFM key elt = unitFM key elt;
104.55/79.42	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;
104.55/79.42	"
104.55/79.42	is transformed to
104.55/79.42	"addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
104.55/79.42	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;
104.55/79.42	"
104.55/79.42	"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;
104.55/79.42	"
104.55/79.42	"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);
104.55/79.42	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;
104.55/79.42	"
104.55/79.42	"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;
104.55/79.42	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);
104.55/79.42	"
104.55/79.42	"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);
104.55/79.42	"
104.55/79.42	"addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
104.55/79.42	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
104.55/79.42	"
104.55/79.42	The following Function with conditions
104.55/79.42	"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;
104.55/79.42	"
104.55/79.42	is transformed to
104.55/79.42	"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);
104.55/79.42	"
104.55/79.42	"mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
104.55/79.42	"
104.55/79.42	"mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
104.55/79.42	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;
104.55/79.42	"
104.55/79.42	"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);
104.55/79.42	"
104.55/79.42	The following Function with conditions
104.55/79.42	"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;
104.55/79.42	"
104.55/79.42	is transformed to
104.55/79.42	"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);
104.55/79.42	"
104.55/79.42	"mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
104.55/79.42	"
104.55/79.42	"mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
104.55/79.42	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;
104.55/79.42	"
104.55/79.42	"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);
104.55/79.42	"
104.55/79.42	The following Function with conditions
104.55/79.42	"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 {
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	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;
104.55/79.42	;
104.55/79.42	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;
104.55/79.42	;
104.55/79.42	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;
104.55/79.42	;
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	size_l  = sizeFM fm_L;
104.55/79.42	;
104.55/79.42	size_r  = sizeFM fm_R;
104.55/79.42	} 
104.55/79.42	;
104.55/79.42	"
104.55/79.42	is transformed to
104.55/79.42	"mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
104.55/79.42	"
104.55/79.42	"mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
104.55/79.42	;
104.55/79.42	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
104.55/79.42	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;
104.55/79.42	;
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
104.55/79.42	;
104.55/79.42	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
104.55/79.42	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;
104.55/79.42	;
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
104.55/79.42	;
104.55/79.42	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
104.55/79.42	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
104.55/79.42	;
104.55/79.42	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
104.55/79.42	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
104.55/79.42	;
104.55/79.42	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
104.55/79.42	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
104.55/79.42	;
104.55/79.42	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;
104.55/79.42	;
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	size_l  = sizeFM fm_L;
104.55/79.42	;
104.55/79.42	size_r  = sizeFM fm_R;
104.55/79.42	} 
104.55/79.42	;
104.55/79.42	"
104.55/79.42	
104.55/79.42	----------------------------------------
104.55/79.42	
104.55/79.42	(8)
104.55/79.42	Obligation:
104.55/79.42	mainModule Main 
104.55/79.42	module FiniteMap where {
104.55/79.42	import qualified Main;
104.55/79.42	import qualified Maybe;
104.55/79.42	import qualified Prelude;
104.55/79.42	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
104.55/79.42	
104.55/79.42	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
104.55/79.42	}
104.55/79.42	addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
104.55/79.42	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
104.55/79.42	
104.55/79.42	addToFM0 old new = new;
104.55/79.42	
104.55/79.42	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
104.55/79.42	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
104.55/79.42	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;
104.55/79.42	
104.55/79.42	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;
104.55/79.42	
104.55/79.42	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);
104.55/79.42	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;
104.55/79.42	
104.55/79.42	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;
104.55/79.42	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);
104.55/79.42	
104.55/79.42	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);
104.55/79.42	
104.55/79.42	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
104.55/79.42	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
104.55/79.42	
104.55/79.42	emptyFM :: FiniteMap b a;
104.55/79.42	emptyFM = EmptyFM;
104.55/79.42	
104.55/79.42	findMax :: FiniteMap b a  ->  (b,a);
104.55/79.42	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
104.55/79.42	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
104.55/79.42	
104.55/79.42	findMin :: FiniteMap a b  ->  (a,b);
104.55/79.42	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
104.55/79.42	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
104.55/79.42	
104.55/79.42	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
104.55/79.42	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
104.55/79.42	
104.55/79.42	mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 
104.55/79.42	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);
104.55/79.42	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);
104.55/79.42	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);
104.55/79.42	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
104.55/79.42	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
104.55/79.42	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;
104.55/79.42	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);
104.55/79.42	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);
104.55/79.42	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
104.55/79.42	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
104.55/79.42	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;
104.55/79.42	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);
104.55/79.42	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
104.55/79.42	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
104.55/79.42	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
104.55/79.42	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
104.55/79.42	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
104.55/79.42	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
104.55/79.42	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
104.55/79.42	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;
104.55/79.42	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);
104.55/79.42	size_l = sizeFM fm_L;
104.55/79.42	size_r = sizeFM fm_R;
104.55/79.42	 };
104.55/79.42	
104.55/79.42	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
104.55/79.42	mkBranch which key elt fm_l fm_r = let { 
104.55/79.42	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
104.55/79.42	} in result where { 
104.55/79.42	balance_ok = True;
104.55/79.42	left_ok = left_ok0 fm_l key fm_l;
104.55/79.42	left_ok0 fm_l key EmptyFM = True;
104.55/79.42	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
104.55/79.42	biggest_left_key = fst (findMax fm_l);
104.55/79.42	} in biggest_left_key < key;
104.55/79.42	left_size = sizeFM fm_l;
104.55/79.42	right_ok = right_ok0 fm_r key fm_r;
104.55/79.42	right_ok0 fm_r key EmptyFM = True;
104.55/79.42	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
104.55/79.42	smallest_right_key = fst (findMin fm_r);
104.55/79.42	} in key < smallest_right_key;
104.55/79.42	right_size = sizeFM fm_r;
104.55/79.42	unbox :: Int  ->  Int;
104.55/79.42	unbox x = x;
104.55/79.42	 };
104.55/79.42	
104.55/79.42	sIZE_RATIO :: Int;
104.55/79.42	sIZE_RATIO = 5;
104.55/79.42	
104.55/79.42	sizeFM :: FiniteMap a b  ->  Int;
104.55/79.42	sizeFM EmptyFM = 0;
104.55/79.42	sizeFM (Branch vz wu size wv ww) = size;
104.55/79.42	
104.55/79.42	unitFM :: a  ->  b  ->  FiniteMap a b;
104.55/79.42	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
104.55/79.42	
104.55/79.42	}
104.55/79.42	module Maybe where {
104.55/79.42	import qualified FiniteMap;
104.55/79.42	import qualified Main;
104.55/79.42	import qualified Prelude;
104.55/79.42	}
104.55/79.42	module Main where {
104.55/79.42	import qualified FiniteMap;
104.55/79.42	import qualified Maybe;
104.55/79.42	import qualified Prelude;
104.55/79.42	}
104.55/79.42	
104.55/79.42	----------------------------------------
104.55/79.42	
104.55/79.42	(9) LetRed (EQUIVALENT)
104.55/79.42	Let/Where Reductions:
104.55/79.42	The bindings of the following Let/Where expression
104.55/79.42	"mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
104.55/79.42	;
104.55/79.42	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
104.55/79.42	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;
104.55/79.42	;
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
104.55/79.42	;
104.55/79.42	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
104.55/79.42	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;
104.55/79.42	;
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
104.55/79.42	;
104.55/79.42	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
104.55/79.42	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
104.55/79.42	;
104.55/79.42	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
104.55/79.42	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
104.55/79.42	;
104.55/79.42	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
104.55/79.42	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
104.55/79.42	;
104.55/79.42	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;
104.55/79.42	;
104.55/79.42	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);
104.55/79.42	;
104.55/79.42	size_l  = sizeFM fm_L;
104.55/79.42	;
104.55/79.42	size_r  = sizeFM fm_R;
104.55/79.42	} 
104.55/79.42	"
104.55/79.42	are unpacked to the following functions on top level
104.55/79.42	"mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vwx;
104.55/79.42	"
104.55/79.42	"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;
104.55/79.42	"
104.55/79.42	"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);
104.55/79.42	"
104.55/79.42	"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 vwy vwz fm_l fm_rl) fm_rr;
104.55/79.42	"
104.55/79.42	"mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
104.55/79.42	"
104.55/79.42	"mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
104.55/79.42	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);
104.55/79.42	"
104.55/79.42	"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);
104.86/79.46	"
104.86/79.46	"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 vwy vwz fm_lr fm_r);
104.86/79.46	"
104.86/79.46	"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;
104.86/79.46	"
104.86/79.46	"mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
104.86/79.46	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
104.86/79.46	"
104.86/79.46	"mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vxu;
104.86/79.46	"
104.86/79.46	"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);
104.86/79.46	"
104.86/79.46	"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 vwy vwz fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
104.86/79.46	"
104.86/79.46	"mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
104.86/79.46	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);
104.86/79.46	"
104.86/79.46	"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 vwy vwz fm_lrr fm_r);
104.86/79.46	"
104.86/79.46	"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;
104.86/79.46	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;
104.86/79.46	"
104.86/79.46	"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);
104.86/79.46	"
104.86/79.46	"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;
104.86/79.46	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;
104.86/79.46	"
104.86/79.46	The bindings of the following Let/Where expression
104.86/79.46	"let {
104.86/79.46	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
104.86/79.46	} in result where {
104.86/79.46	balance_ok  = True;
104.86/79.46	;
104.86/79.46	left_ok  = left_ok0 fm_l key fm_l;
104.86/79.46	;
104.86/79.46	left_ok0 fm_l key EmptyFM = True;
104.86/79.46	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let {
104.86/79.46	biggest_left_key  = fst (findMax fm_l);
104.86/79.46	} in biggest_left_key < key;
104.86/79.46	;
104.86/79.46	left_size  = sizeFM fm_l;
104.86/79.46	;
104.86/79.46	right_ok  = right_ok0 fm_r key fm_r;
104.86/79.46	;
104.86/79.46	right_ok0 fm_r key EmptyFM = True;
104.86/79.46	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let {
104.86/79.46	smallest_right_key  = fst (findMin fm_r);
104.86/79.46	} in key < smallest_right_key;
104.86/79.46	;
104.86/79.46	right_size  = sizeFM fm_r;
104.86/79.46	;
104.86/79.46	unbox x = x;
104.86/79.46	} 
104.86/79.46	"
104.86/79.46	are unpacked to the following functions on top level
104.86/79.46	"mkBranchBalance_ok vxv vxw vxx = True;
104.86/79.46	"
104.86/79.46	"mkBranchLeft_ok0 vxv vxw vxx fm_l key EmptyFM = True;
104.86/79.46	mkBranchLeft_ok0 vxv vxw vxx fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
104.86/79.46	"
104.86/79.46	"mkBranchRight_ok0 vxv vxw vxx fm_r key EmptyFM = True;
104.86/79.46	mkBranchRight_ok0 vxv vxw vxx fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
104.86/79.46	"
104.86/79.46	"mkBranchLeft_ok vxv vxw vxx = mkBranchLeft_ok0 vxv vxw vxx vxv vxw vxv;
104.86/79.46	"
104.86/79.46	"mkBranchUnbox vxv vxw vxx x = x;
104.86/79.46	"
104.86/79.46	"mkBranchRight_size vxv vxw vxx = sizeFM vxx;
104.86/79.46	"
104.86/79.46	"mkBranchRight_ok vxv vxw vxx = mkBranchRight_ok0 vxv vxw vxx vxx vxw vxx;
104.86/79.46	"
104.86/79.46	"mkBranchLeft_size vxv vxw vxx = sizeFM vxv;
104.86/79.46	"
104.86/79.46	The bindings of the following Let/Where expression
104.86/79.46	"let {
104.86/79.46	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
104.86/79.46	} in result"
104.86/79.46	are unpacked to the following functions on top level
104.86/79.46	"mkBranchResult vxy vxz vyu vyv = Branch vxy vxz (mkBranchUnbox vyu vxy vyv (1 + mkBranchLeft_size vyu vxy vyv + mkBranchRight_size vyu vxy vyv)) vyu vyv;
104.86/79.46	"
104.86/79.46	The bindings of the following Let/Where expression
104.86/79.46	"let {
104.86/79.46	biggest_left_key  = fst (findMax fm_l);
104.86/79.46	} in biggest_left_key < key"
104.86/79.46	are unpacked to the following functions on top level
104.86/79.46	"mkBranchLeft_ok0Biggest_left_key vyw = fst (findMax vyw);
104.86/79.46	"
104.86/79.46	The bindings of the following Let/Where expression
104.86/79.46	"let {
104.86/79.46	smallest_right_key  = fst (findMin fm_r);
104.86/79.46	} in key < smallest_right_key"
104.86/79.46	are unpacked to the following functions on top level
104.86/79.46	"mkBranchRight_ok0Smallest_right_key vyx = fst (findMin vyx);
104.86/79.46	"
104.86/79.46	
104.86/79.46	----------------------------------------
104.86/79.46	
104.86/79.46	(10)
104.86/79.46	Obligation:
104.86/79.46	mainModule Main 
104.86/79.46	module FiniteMap where {
104.86/79.46	import qualified Main;
104.86/79.46	import qualified Maybe;
104.86/79.46	import qualified Prelude;
104.86/79.46	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
104.86/79.46	
104.86/79.46	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
104.86/79.46	}
104.86/79.46	addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
104.86/79.46	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
104.86/79.46	
104.86/79.46	addToFM0 old new = new;
104.86/79.46	
104.86/79.46	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
104.86/79.46	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
104.86/79.46	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;
104.86/79.46	
104.86/79.46	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;
104.86/79.46	
104.86/79.46	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);
104.86/79.46	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;
104.86/79.46	
104.86/79.46	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;
104.86/79.46	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);
104.86/79.46	
104.86/79.46	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);
104.86/79.46	
104.86/79.46	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
104.86/79.46	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
104.86/79.46	
104.86/79.46	emptyFM :: FiniteMap b a;
104.86/79.46	emptyFM = EmptyFM;
104.86/79.46	
104.86/79.46	findMax :: FiniteMap a b  ->  (a,b);
104.86/79.46	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
104.86/79.46	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
104.86/79.46	
104.86/79.46	findMin :: FiniteMap a b  ->  (a,b);
104.86/79.46	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
104.86/79.46	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
104.86/79.46	
104.86/79.46	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
104.86/79.46	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
104.86/79.46	
104.86/79.46	mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 fm_L key elt fm_R key elt fm_L fm_R (mkBalBranch6Size_l fm_L key elt fm_R + mkBalBranch6Size_r fm_L key elt fm_R < 2);
104.86/79.46	
104.86/79.46	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 vwy vwz fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
104.86/79.46	
104.86/79.46	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 vwy vwz fm_lrr fm_r);
104.86/79.46	
104.86/79.46	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);
104.86/79.46	
104.86/79.46	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;
104.86/79.46	
104.86/79.46	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;
104.86/79.46	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;
104.86/79.46	
104.86/79.46	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);
104.86/79.46	
104.86/79.46	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);
104.86/79.46	
104.86/79.46	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;
104.86/79.46	
104.86/79.46	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;
104.86/79.46	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;
104.86/79.46	
104.86/79.46	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);
104.86/79.46	
104.86/79.46	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
104.86/79.46	
104.86/79.46	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
104.86/79.46	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
104.86/79.46	
104.86/79.46	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
104.86/79.46	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);
104.86/79.46	
104.86/79.46	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
104.86/79.46	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);
104.86/79.46	
104.86/79.46	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 vwy vwz fm_l fm_rl) fm_rr;
104.86/79.46	
104.86/79.46	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 vwy vwz fm_lr fm_r);
104.86/79.46	
104.86/79.46	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vwx;
104.86/79.46	
104.86/79.46	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vxu;
104.86/79.46	
104.86/79.46	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
104.86/79.46	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r;
104.86/79.46	
104.86/79.46	mkBranchBalance_ok vxv vxw vxx = True;
104.86/79.46	
104.86/79.46	mkBranchLeft_ok vxv vxw vxx = mkBranchLeft_ok0 vxv vxw vxx vxv vxw vxv;
104.86/79.46	
104.86/79.46	mkBranchLeft_ok0 vxv vxw vxx fm_l key EmptyFM = True;
104.86/79.46	mkBranchLeft_ok0 vxv vxw vxx fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
104.86/79.46	
104.86/79.46	mkBranchLeft_ok0Biggest_left_key vyw = fst (findMax vyw);
104.86/79.46	
104.86/79.46	mkBranchLeft_size vxv vxw vxx = sizeFM vxv;
104.86/79.46	
104.86/79.46	mkBranchResult vxy vxz vyu vyv = Branch vxy vxz (mkBranchUnbox vyu vxy vyv (1 + mkBranchLeft_size vyu vxy vyv + mkBranchRight_size vyu vxy vyv)) vyu vyv;
104.86/79.46	
104.86/79.46	mkBranchRight_ok vxv vxw vxx = mkBranchRight_ok0 vxv vxw vxx vxx vxw vxx;
104.86/79.46	
104.86/79.46	mkBranchRight_ok0 vxv vxw vxx fm_r key EmptyFM = True;
104.86/79.46	mkBranchRight_ok0 vxv vxw vxx fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
104.86/79.46	
104.86/79.46	mkBranchRight_ok0Smallest_right_key vyx = fst (findMin vyx);
104.86/79.46	
104.86/79.46	mkBranchRight_size vxv vxw vxx = sizeFM vxx;
104.86/79.46	
104.86/79.46	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)));
104.86/79.46	mkBranchUnbox vxv vxw vxx x = x;
104.86/79.46	
104.86/79.46	sIZE_RATIO :: Int;
104.86/79.46	sIZE_RATIO = 5;
104.86/79.46	
104.86/79.46	sizeFM :: FiniteMap a b  ->  Int;
104.86/79.46	sizeFM EmptyFM = 0;
104.86/79.46	sizeFM (Branch vz wu size wv ww) = size;
104.86/79.46	
104.86/79.46	unitFM :: a  ->  b  ->  FiniteMap a b;
104.86/79.46	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
104.86/79.46	
104.86/79.46	}
104.86/79.46	module Maybe where {
104.86/79.46	import qualified FiniteMap;
104.86/79.46	import qualified Main;
104.86/79.46	import qualified Prelude;
104.86/79.46	}
104.86/79.46	module Main where {
104.86/79.46	import qualified FiniteMap;
104.86/79.46	import qualified Maybe;
104.86/79.46	import qualified Prelude;
104.86/79.46	}
104.86/79.46	
104.86/79.46	----------------------------------------
104.86/79.46	
104.86/79.46	(11) NumRed (SOUND)
104.86/79.46	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
104.86/79.46	----------------------------------------
104.86/79.46	
104.86/79.46	(12)
104.86/79.46	Obligation:
104.86/79.46	mainModule Main 
104.86/79.46	module FiniteMap where {
104.86/79.46	import qualified Main;
104.86/79.46	import qualified Maybe;
104.86/79.46	import qualified Prelude;
104.86/79.46	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
104.86/79.46	
104.86/79.46	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
104.86/79.46	}
104.86/79.46	addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
104.86/79.46	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
104.86/79.46	
104.86/79.46	addToFM0 old new = new;
104.86/79.46	
104.86/79.46	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
104.86/79.46	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
104.86/79.46	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;
104.86/79.46	
104.86/79.46	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;
104.86/79.46	
104.86/79.46	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);
104.86/79.46	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;
104.86/79.46	
104.86/79.46	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;
104.86/79.46	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);
104.86/79.46	
104.86/79.46	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);
104.86/79.46	
104.86/79.46	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
104.86/79.46	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
104.86/79.46	
104.86/79.46	emptyFM :: FiniteMap b a;
104.86/79.46	emptyFM = EmptyFM;
104.86/79.46	
104.86/79.46	findMax :: FiniteMap b a  ->  (b,a);
104.86/79.46	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
104.86/79.46	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
104.86/79.46	
104.86/79.46	findMin :: FiniteMap a b  ->  (a,b);
104.86/79.46	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
104.86/79.46	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
104.86/79.46	
104.86/79.46	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
104.86/79.46	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
104.86/79.46	
104.86/79.46	mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 fm_L key elt fm_R key elt fm_L fm_R (mkBalBranch6Size_l fm_L key elt fm_R + mkBalBranch6Size_r fm_L key elt fm_R < Pos (Succ (Succ Zero)));
104.86/79.46	
104.86/79.46	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))))))) vwy vwz fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr);
104.86/79.46	
104.86/79.46	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))))))))))))) vwy vwz fm_lrr fm_r);
104.86/79.46	
104.86/79.46	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);
104.86/79.46	
104.86/79.46	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;
104.86/79.46	
104.86/79.46	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;
104.86/79.46	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;
104.86/79.46	
104.86/79.46	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);
104.86/79.46	
104.86/79.46	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);
104.86/79.46	
104.86/79.46	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;
104.86/79.46	
104.86/79.46	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;
104.86/79.46	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;
104.86/79.46	
104.86/79.46	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);
104.86/79.46	
104.86/79.46	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R;
104.86/79.46	
104.86/79.46	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
104.86/79.46	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
104.86/79.46	
104.86/79.46	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
104.86/79.46	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);
104.86/79.46	
104.86/79.46	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R;
104.86/79.46	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);
104.86/79.46	
104.86/79.46	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))))) vwy vwz fm_l fm_rl) fm_rr;
104.86/79.46	
104.86/79.46	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)))))))))) vwy vwz fm_lr fm_r);
104.86/79.46	
104.86/79.46	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vwx;
104.86/79.46	
104.86/79.46	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vxu;
104.86/79.46	
104.86/79.46	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
104.86/79.46	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r;
104.86/79.46	
104.86/79.46	mkBranchBalance_ok vxv vxw vxx = True;
104.86/79.46	
104.86/79.46	mkBranchLeft_ok vxv vxw vxx = mkBranchLeft_ok0 vxv vxw vxx vxv vxw vxv;
104.86/79.46	
104.86/79.46	mkBranchLeft_ok0 vxv vxw vxx fm_l key EmptyFM = True;
104.86/79.46	mkBranchLeft_ok0 vxv vxw vxx fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
104.86/79.46	
104.86/79.46	mkBranchLeft_ok0Biggest_left_key vyw = fst (findMax vyw);
104.86/79.46	
104.86/79.46	mkBranchLeft_size vxv vxw vxx = sizeFM vxv;
104.86/79.46	
104.86/79.46	mkBranchResult vxy vxz vyu vyv = Branch vxy vxz (mkBranchUnbox vyu vxy vyv (Pos (Succ Zero) + mkBranchLeft_size vyu vxy vyv + mkBranchRight_size vyu vxy vyv)) vyu vyv;
104.86/79.46	
104.86/79.46	mkBranchRight_ok vxv vxw vxx = mkBranchRight_ok0 vxv vxw vxx vxx vxw vxx;
104.86/79.46	
104.86/79.46	mkBranchRight_ok0 vxv vxw vxx fm_r key EmptyFM = True;
104.86/79.46	mkBranchRight_ok0 vxv vxw vxx fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
104.86/79.46	
104.86/79.46	mkBranchRight_ok0Smallest_right_key vyx = fst (findMin vyx);
104.86/79.46	
104.86/79.46	mkBranchRight_size vxv vxw vxx = sizeFM vxx;
104.86/79.46	
104.86/79.46	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)));
104.86/79.46	mkBranchUnbox vxv vxw vxx x = x;
104.86/79.46	
104.86/79.46	sIZE_RATIO :: Int;
104.86/79.46	sIZE_RATIO = Pos (Succ (Succ (Succ (Succ (Succ Zero)))));
104.86/79.46	
104.86/79.46	sizeFM :: FiniteMap a b  ->  Int;
104.86/79.46	sizeFM EmptyFM = Pos Zero;
104.86/79.46	sizeFM (Branch vz wu size wv ww) = size;
104.86/79.46	
104.86/79.46	unitFM :: a  ->  b  ->  FiniteMap a b;
104.86/79.46	unitFM key elt = Branch key elt (Pos (Succ Zero)) emptyFM emptyFM;
104.86/79.46	
104.86/79.46	}
104.86/79.46	module Maybe where {
104.86/79.46	import qualified FiniteMap;
104.86/79.46	import qualified Main;
104.86/79.46	import qualified Prelude;
104.86/79.46	}
104.86/79.46	module Main where {
104.86/79.46	import qualified FiniteMap;
104.86/79.46	import qualified Maybe;
104.86/79.46	import qualified Prelude;
104.86/79.46	}
104.86/79.50	EOF