135.55/104.24	MAYBE
137.98/104.92	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
137.98/104.92	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
137.98/104.92	
137.98/104.92	
137.98/104.92	H-Termination with start terms of the given HASKELL could not be shown:
137.98/104.92	
137.98/104.92	(0) HASKELL
137.98/104.92	(1) LR [EQUIVALENT, 0 ms]
137.98/104.92	(2) HASKELL
137.98/104.92	(3) CR [EQUIVALENT, 0 ms]
137.98/104.92	(4) HASKELL
137.98/104.92	(5) BR [EQUIVALENT, 0 ms]
137.98/104.92	(6) HASKELL
137.98/104.92	(7) COR [EQUIVALENT, 17 ms]
137.98/104.92	(8) HASKELL
137.98/104.92	(9) LetRed [EQUIVALENT, 0 ms]
137.98/104.92	(10) HASKELL
137.98/104.92	(11) NumRed [SOUND, 0 ms]
137.98/104.92	(12) HASKELL
137.98/104.92	
137.98/104.92	
137.98/104.92	----------------------------------------
137.98/104.92	
137.98/104.92	(0)
137.98/104.92	Obligation:
137.98/104.92	mainModule Main 
137.98/104.92	module FiniteMap where {
137.98/104.92	import qualified Main;
137.98/104.92	import qualified Maybe;
137.98/104.92	import qualified Prelude;
137.98/104.92	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
137.98/104.92	
137.98/104.92	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
137.98/104.92	}
137.98/104.92	addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
137.98/104.92	addToFM fm key elt = addToFM_C (\old new ->new) fm key elt;
137.98/104.92	
137.98/104.92	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
137.98/104.92	addToFM_C combiner EmptyFM key elt = unitFM key elt;
137.98/104.92	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
137.98/104.92	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
137.98/104.92	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
137.98/104.92	
137.98/104.92	emptyFM :: FiniteMap a b;
137.98/104.92	emptyFM = EmptyFM;
137.98/104.92	
137.98/104.92	findMax :: FiniteMap b a  ->  (b,a);
137.98/104.92	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
137.98/104.92	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
137.98/104.92	
137.98/104.92	findMin :: FiniteMap a b  ->  (a,b);
137.98/104.92	findMin (Branch key elt _ EmptyFM _) = (key,elt);
137.98/104.92	findMin (Branch key elt _ fm_l _) = findMin fm_l;
137.98/104.92	
137.98/104.92	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
137.98/104.92	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
137.98/104.92	 | size_r > sIZE_RATIO * size_l = case fm_R of { 
137.98/104.92	Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R
137.98/104.92	 | otherwise -> double_L fm_L fm_R; 
137.98/104.92	 } 
137.98/104.92	 | size_l > sIZE_RATIO * size_r = case fm_L of { 
137.98/104.92	Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R
137.98/104.92	 | otherwise -> double_R fm_L fm_R; 
137.98/104.92	 } 
137.98/104.92	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
137.98/104.92	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);
137.98/104.92	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);
137.98/104.92	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;
137.98/104.92	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);
137.98/104.92	size_l = sizeFM fm_L;
137.98/104.92	size_r = sizeFM fm_R;
137.98/104.92	 };
137.98/104.92	
137.98/104.92	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
137.98/104.92	mkBranch which key elt fm_l fm_r = let { 
137.98/104.92	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
137.98/104.92	} in result where { 
137.98/104.92	balance_ok = True;
137.98/104.92	left_ok = case fm_l of { 
137.98/104.92	EmptyFM-> True; 
137.98/104.92	Branch left_key _ _ _ _-> let { 
137.98/104.92	biggest_left_key = fst (findMax fm_l);
137.98/104.92	} in biggest_left_key < key; 
137.98/104.92	 } ;
137.98/104.92	left_size = sizeFM fm_l;
137.98/104.92	right_ok = case fm_r of { 
137.98/104.92	EmptyFM-> True; 
137.98/104.92	Branch right_key _ _ _ _-> let { 
137.98/104.92	smallest_right_key = fst (findMin fm_r);
137.98/104.92	} in key < smallest_right_key; 
137.98/104.92	 } ;
137.98/104.92	right_size = sizeFM fm_r;
137.98/104.92	unbox :: Int  ->  Int;
137.98/104.92	unbox x = x;
137.98/104.92	 };
137.98/104.92	
137.98/104.92	sIZE_RATIO :: Int;
137.98/104.92	sIZE_RATIO = 5;
137.98/104.92	
137.98/104.92	sizeFM :: FiniteMap b a  ->  Int;
137.98/104.92	sizeFM EmptyFM = 0;
137.98/104.92	sizeFM (Branch _ _ size _ _) = size;
137.98/104.92	
137.98/104.92	unitFM :: a  ->  b  ->  FiniteMap a b;
137.98/104.92	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
137.98/104.92	
137.98/104.92	}
137.98/104.92	module Maybe where {
137.98/104.92	import qualified FiniteMap;
137.98/104.92	import qualified Main;
137.98/104.92	import qualified Prelude;
137.98/104.92	}
137.98/104.92	module Main where {
137.98/104.92	import qualified FiniteMap;
137.98/104.92	import qualified Maybe;
137.98/104.92	import qualified Prelude;
137.98/104.92	}
137.98/104.92	
137.98/104.92	----------------------------------------
137.98/104.92	
137.98/104.92	(1) LR (EQUIVALENT)
137.98/104.92	Lambda Reductions:
137.98/104.92	The following Lambda expression
137.98/104.92	"\oldnew->new"
137.98/104.92	is transformed to
137.98/104.92	"addToFM0 old new = new;
137.98/104.92	"
137.98/104.92	
137.98/104.92	----------------------------------------
137.98/104.92	
137.98/104.92	(2)
137.98/104.92	Obligation:
137.98/104.92	mainModule Main 
137.98/104.92	module FiniteMap where {
137.98/104.92	import qualified Main;
137.98/104.92	import qualified Maybe;
137.98/104.92	import qualified Prelude;
137.98/104.92	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
137.98/104.92	
137.98/104.92	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
137.98/104.92	}
137.98/104.92	addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
137.98/104.92	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
137.98/104.92	
137.98/104.92	addToFM0 old new = new;
137.98/104.92	
137.98/104.92	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
137.98/104.92	addToFM_C combiner EmptyFM key elt = unitFM key elt;
137.98/104.92	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
137.98/104.92	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
137.98/104.92	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
137.98/104.92	
137.98/104.92	emptyFM :: FiniteMap b a;
137.98/104.92	emptyFM = EmptyFM;
137.98/104.92	
137.98/104.92	findMax :: FiniteMap b a  ->  (b,a);
137.98/104.93	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
137.98/104.93	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
137.98/104.93	
137.98/104.93	findMin :: FiniteMap a b  ->  (a,b);
137.98/104.93	findMin (Branch key elt _ EmptyFM _) = (key,elt);
137.98/104.93	findMin (Branch key elt _ fm_l _) = findMin fm_l;
137.98/104.93	
137.98/104.93	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
137.98/104.93	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
137.98/104.93	 | size_r > sIZE_RATIO * size_l = case fm_R of { 
137.98/104.93	Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R
137.98/104.93	 | otherwise -> double_L fm_L fm_R; 
137.98/104.93	 } 
137.98/104.93	 | size_l > sIZE_RATIO * size_r = case fm_L of { 
137.98/104.93	Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R
137.98/104.93	 | otherwise -> double_R fm_L fm_R; 
137.98/104.93	 } 
137.98/104.93	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
137.98/104.93	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);
137.98/104.93	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);
137.98/104.93	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;
137.98/104.93	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);
137.98/104.93	size_l = sizeFM fm_L;
137.98/104.93	size_r = sizeFM fm_R;
137.98/104.93	 };
137.98/104.93	
137.98/104.93	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
137.98/104.93	mkBranch which key elt fm_l fm_r = let { 
137.98/104.93	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
137.98/104.93	} in result where { 
137.98/104.93	balance_ok = True;
137.98/104.93	left_ok = case fm_l of { 
137.98/104.93	EmptyFM-> True; 
137.98/104.93	Branch left_key _ _ _ _-> let { 
137.98/104.93	biggest_left_key = fst (findMax fm_l);
137.98/104.93	} in biggest_left_key < key; 
137.98/104.93	 } ;
137.98/104.93	left_size = sizeFM fm_l;
137.98/104.93	right_ok = case fm_r of { 
137.98/104.93	EmptyFM-> True; 
137.98/104.93	Branch right_key _ _ _ _-> let { 
137.98/104.93	smallest_right_key = fst (findMin fm_r);
137.98/104.93	} in key < smallest_right_key; 
137.98/104.93	 } ;
137.98/104.93	right_size = sizeFM fm_r;
137.98/104.93	unbox :: Int  ->  Int;
137.98/104.93	unbox x = x;
137.98/104.93	 };
137.98/104.93	
137.98/104.93	sIZE_RATIO :: Int;
137.98/104.93	sIZE_RATIO = 5;
137.98/104.93	
137.98/104.93	sizeFM :: FiniteMap b a  ->  Int;
137.98/104.93	sizeFM EmptyFM = 0;
137.98/104.93	sizeFM (Branch _ _ size _ _) = size;
137.98/104.93	
137.98/104.93	unitFM :: b  ->  a  ->  FiniteMap b a;
137.98/104.93	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
137.98/104.93	
137.98/104.93	}
137.98/104.93	module Maybe where {
137.98/104.93	import qualified FiniteMap;
137.98/104.93	import qualified Main;
137.98/104.93	import qualified Prelude;
137.98/104.93	}
137.98/104.93	module Main where {
137.98/104.93	import qualified FiniteMap;
137.98/104.93	import qualified Maybe;
137.98/104.93	import qualified Prelude;
137.98/104.93	}
137.98/104.93	
137.98/104.93	----------------------------------------
137.98/104.93	
137.98/104.93	(3) CR (EQUIVALENT)
137.98/104.93	Case Reductions:
137.98/104.93	The following Case expression
137.98/104.93	"case fm_r of {
137.98/104.93	EmptyFM  -> True;
137.98/104.93	Branch right_key _ _ _ _  -> let {
137.98/104.93	smallest_right_key  = fst (findMin fm_r);
137.98/104.93	} in key < smallest_right_key}
137.98/104.93	"
137.98/104.93	is transformed to
137.98/104.93	"right_ok0 fm_r key EmptyFM = True;
137.98/104.93	right_ok0 fm_r key (Branch right_key _ _ _ _) = let {
137.98/104.93	smallest_right_key  = fst (findMin fm_r);
137.98/104.93	} in key < smallest_right_key;
137.98/104.93	"
137.98/104.93	The following Case expression
137.98/104.93	"case fm_l of {
137.98/104.93	EmptyFM  -> True;
137.98/104.93	Branch left_key _ _ _ _  -> let {
138.88/105.16	biggest_left_key  = fst (findMax fm_l);
138.88/105.16	} in biggest_left_key < key}
138.88/105.16	"
138.88/105.16	is transformed to
138.88/105.16	"left_ok0 fm_l key EmptyFM = True;
138.88/105.16	left_ok0 fm_l key (Branch left_key _ _ _ _) = let {
138.88/105.16	biggest_left_key  = fst (findMax fm_l);
138.88/105.16	} in biggest_left_key < key;
138.88/105.16	"
138.88/105.16	The following Case expression
138.88/105.16	"case fm_R of {
138.88/105.16	Branch _ _ _ fm_rl fm_rr |sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R}
138.88/105.16	"
138.88/105.16	is transformed to
138.88/105.16	"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;
138.88/105.16	"
138.88/105.16	The following Case expression
138.88/105.16	"case fm_L of {
138.88/105.16	Branch _ _ _ fm_ll fm_lr |sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R}
138.88/105.16	"
138.88/105.16	is transformed to
138.88/105.16	"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;
138.88/105.16	"
138.88/105.16	
138.88/105.16	----------------------------------------
138.88/105.16	
138.88/105.16	(4)
138.88/105.16	Obligation:
138.88/105.16	mainModule Main 
138.88/105.16	module FiniteMap where {
138.88/105.16	import qualified Main;
138.88/105.16	import qualified Maybe;
138.88/105.16	import qualified Prelude;
138.88/105.16	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
138.88/105.16	
138.88/105.16	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
138.88/105.16	}
138.88/105.16	addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
138.88/105.16	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
138.88/105.16	
138.88/105.16	addToFM0 old new = new;
138.88/105.16	
138.88/105.16	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
138.88/105.16	addToFM_C combiner EmptyFM key elt = unitFM key elt;
138.88/105.16	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
138.88/105.16	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
138.88/105.16	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
138.88/105.16	
138.88/105.16	emptyFM :: FiniteMap b a;
138.88/105.16	emptyFM = EmptyFM;
138.88/105.16	
138.88/105.16	findMax :: FiniteMap a b  ->  (a,b);
138.88/105.16	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
138.88/105.16	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
138.88/105.16	
138.88/105.16	findMin :: FiniteMap b a  ->  (b,a);
138.88/105.16	findMin (Branch key elt _ EmptyFM _) = (key,elt);
138.88/105.16	findMin (Branch key elt _ fm_l _) = findMin fm_l;
138.88/105.16	
138.88/105.16	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
138.88/105.16	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
138.88/105.16	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
138.88/105.16	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
138.88/105.16	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
138.88/105.16	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);
138.88/105.16	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);
138.88/105.16	mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr)  | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R
138.88/105.16	 | otherwise = double_L fm_L fm_R;
138.88/105.16	mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr)  | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R
138.88/105.16	 | otherwise = double_R fm_L fm_R;
138.88/105.16	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;
138.88/105.16	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);
138.88/105.16	size_l = sizeFM fm_L;
138.88/105.16	size_r = sizeFM fm_R;
138.88/105.16	 };
138.88/105.16	
138.88/105.16	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
138.88/105.16	mkBranch which key elt fm_l fm_r = let { 
138.88/105.16	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
138.88/105.16	} in result where { 
138.88/105.16	balance_ok = True;
138.88/105.16	left_ok = left_ok0 fm_l key fm_l;
138.88/105.16	left_ok0 fm_l key EmptyFM = True;
138.88/105.16	left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 
138.88/105.16	biggest_left_key = fst (findMax fm_l);
138.88/105.16	} in biggest_left_key < key;
138.88/105.16	left_size = sizeFM fm_l;
138.88/105.16	right_ok = right_ok0 fm_r key fm_r;
138.88/105.16	right_ok0 fm_r key EmptyFM = True;
138.88/105.16	right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 
138.88/105.16	smallest_right_key = fst (findMin fm_r);
138.88/105.16	} in key < smallest_right_key;
138.88/105.16	right_size = sizeFM fm_r;
138.88/105.16	unbox :: Int  ->  Int;
138.88/105.16	unbox x = x;
138.88/105.16	 };
138.88/105.16	
138.88/105.16	sIZE_RATIO :: Int;
138.88/105.16	sIZE_RATIO = 5;
138.88/105.16	
138.88/105.16	sizeFM :: FiniteMap b a  ->  Int;
138.88/105.16	sizeFM EmptyFM = 0;
138.88/105.16	sizeFM (Branch _ _ size _ _) = size;
138.88/105.16	
138.88/105.16	unitFM :: b  ->  a  ->  FiniteMap b a;
138.88/105.16	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
138.88/105.16	
138.88/105.16	}
138.88/105.16	module Maybe where {
138.88/105.16	import qualified FiniteMap;
138.88/105.16	import qualified Main;
138.88/105.16	import qualified Prelude;
138.88/105.16	}
138.88/105.16	module Main where {
138.88/105.16	import qualified FiniteMap;
138.88/105.16	import qualified Maybe;
138.88/105.16	import qualified Prelude;
138.88/105.16	}
138.88/105.16	
138.88/105.16	----------------------------------------
138.88/105.16	
138.88/105.16	(5) BR (EQUIVALENT)
138.88/105.16	Replaced joker patterns by fresh variables and removed binding patterns.
138.88/105.16	----------------------------------------
138.88/105.16	
138.88/105.16	(6)
138.88/105.16	Obligation:
138.88/105.16	mainModule Main 
138.88/105.16	module FiniteMap where {
138.88/105.16	import qualified Main;
138.88/105.16	import qualified Maybe;
138.88/105.16	import qualified Prelude;
138.88/105.16	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
138.88/105.16	
138.88/105.16	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
138.88/105.16	}
138.88/105.16	addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
138.88/105.16	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
138.88/105.16	
138.88/105.16	addToFM0 old new = new;
138.88/105.16	
138.88/105.16	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
138.88/105.16	addToFM_C combiner EmptyFM key elt = unitFM key elt;
138.88/105.16	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
138.88/105.16	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
138.88/105.16	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
138.88/105.16	
138.88/105.16	emptyFM :: FiniteMap b a;
138.88/105.16	emptyFM = EmptyFM;
138.88/105.16	
138.88/105.16	findMax :: FiniteMap b a  ->  (b,a);
138.88/105.16	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
138.88/105.16	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
138.88/105.16	
138.88/105.16	findMin :: FiniteMap a b  ->  (a,b);
138.88/105.16	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
138.88/105.16	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
138.88/105.16	
138.88/105.16	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
138.88/105.16	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
138.88/105.16	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
138.88/105.16	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
138.88/105.16	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
138.88/105.16	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);
138.88/105.16	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);
138.88/105.16	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
138.88/105.16	 | otherwise = double_L fm_L fm_R;
138.88/105.16	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
138.88/105.16	 | otherwise = double_R fm_L fm_R;
138.88/105.16	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;
138.88/105.16	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);
138.88/105.16	size_l = sizeFM fm_L;
138.88/105.16	size_r = sizeFM fm_R;
138.88/105.16	 };
138.88/105.16	
138.88/105.16	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
138.88/105.16	mkBranch which key elt fm_l fm_r = let { 
138.88/105.16	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
138.88/105.16	} in result where { 
138.88/105.16	balance_ok = True;
138.88/105.16	left_ok = left_ok0 fm_l key fm_l;
138.88/105.16	left_ok0 fm_l key EmptyFM = True;
138.88/105.16	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
138.88/105.16	biggest_left_key = fst (findMax fm_l);
138.88/105.16	} in biggest_left_key < key;
138.88/105.16	left_size = sizeFM fm_l;
138.88/105.16	right_ok = right_ok0 fm_r key fm_r;
138.88/105.16	right_ok0 fm_r key EmptyFM = True;
138.88/105.16	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
138.88/105.16	smallest_right_key = fst (findMin fm_r);
138.88/105.16	} in key < smallest_right_key;
138.88/105.16	right_size = sizeFM fm_r;
138.88/105.16	unbox :: Int  ->  Int;
138.88/105.16	unbox x = x;
138.88/105.16	 };
138.88/105.16	
138.88/105.16	sIZE_RATIO :: Int;
138.88/105.16	sIZE_RATIO = 5;
138.88/105.16	
138.88/105.16	sizeFM :: FiniteMap b a  ->  Int;
138.88/105.16	sizeFM EmptyFM = 0;
138.88/105.16	sizeFM (Branch vz wu size wv ww) = size;
138.88/105.16	
138.88/105.16	unitFM :: a  ->  b  ->  FiniteMap a b;
138.88/105.16	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
138.88/105.16	
138.88/105.16	}
138.88/105.16	module Maybe where {
138.88/105.16	import qualified FiniteMap;
138.88/105.16	import qualified Main;
138.88/105.16	import qualified Prelude;
138.88/105.16	}
138.88/105.16	module Main where {
138.88/105.16	import qualified FiniteMap;
138.88/105.16	import qualified Maybe;
138.88/105.16	import qualified Prelude;
138.88/105.16	}
138.88/105.16	
138.88/105.16	----------------------------------------
138.88/105.16	
138.88/105.16	(7) COR (EQUIVALENT)
138.88/105.16	Cond Reductions:
138.88/105.16	The following Function with conditions
138.88/105.16	"undefined |Falseundefined;
138.88/105.16	"
138.88/105.16	is transformed to
138.88/105.16	"undefined  = undefined1;
138.88/105.16	"
138.88/105.16	"undefined0 True = undefined;
138.88/105.16	"
138.88/105.16	"undefined1  = undefined0 False;
138.88/105.16	"
138.88/105.16	The following Function with conditions
138.88/105.16	"addToFM_C combiner EmptyFM key elt = unitFM key elt;
138.88/105.16	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;
138.88/105.16	"
138.88/105.16	is transformed to
138.88/105.16	"addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
138.88/105.16	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;
138.88/105.16	"
138.88/105.16	"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;
138.88/105.16	"
138.88/105.16	"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;
138.88/105.16	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);
138.88/105.16	"
138.88/105.16	"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);
138.88/105.16	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;
138.88/105.16	"
138.88/105.16	"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);
138.88/105.16	"
138.88/105.16	"addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
138.88/105.16	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
138.88/105.16	"
138.88/105.16	The following Function with conditions
138.88/105.16	"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;
138.88/105.16	"
138.88/105.16	is transformed to
138.88/105.16	"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);
138.88/105.16	"
138.88/105.16	"mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
138.88/105.16	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;
138.88/105.16	"
138.88/105.16	"mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
138.88/105.16	"
138.88/105.16	"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);
138.88/105.16	"
138.88/105.16	The following Function with conditions
138.88/105.16	"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;
138.88/105.16	"
138.88/105.16	is transformed to
138.88/105.16	"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);
138.88/105.16	"
138.88/105.16	"mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
138.88/105.16	"
138.88/105.16	"mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
138.88/105.16	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;
138.88/105.16	"
138.88/105.16	"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);
138.88/105.16	"
138.88/105.16	The following Function with conditions
138.88/105.16	"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 {
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	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;
138.88/105.16	;
138.88/105.16	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;
138.88/105.16	;
138.88/105.16	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;
138.88/105.16	;
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	size_l  = sizeFM fm_L;
138.88/105.16	;
138.88/105.16	size_r  = sizeFM fm_R;
138.88/105.16	} 
138.88/105.16	;
138.88/105.16	"
138.88/105.16	is transformed to
138.88/105.16	"mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
138.88/105.16	"
138.88/105.16	"mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
138.88/105.16	;
138.88/105.16	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
138.88/105.16	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;
138.88/105.16	;
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
138.88/105.16	;
138.88/105.16	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
138.88/105.16	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;
138.88/105.16	;
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
138.88/105.16	;
138.88/105.16	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
138.88/105.16	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
138.88/105.16	;
138.88/105.16	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
138.88/105.16	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
138.88/105.16	;
138.88/105.16	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
138.88/105.16	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
138.88/105.16	;
138.88/105.16	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;
138.88/105.16	;
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	size_l  = sizeFM fm_L;
138.88/105.16	;
138.88/105.16	size_r  = sizeFM fm_R;
138.88/105.16	} 
138.88/105.16	;
138.88/105.16	"
138.88/105.16	
138.88/105.16	----------------------------------------
138.88/105.16	
138.88/105.16	(8)
138.88/105.16	Obligation:
138.88/105.16	mainModule Main 
138.88/105.16	module FiniteMap where {
138.88/105.16	import qualified Main;
138.88/105.16	import qualified Maybe;
138.88/105.16	import qualified Prelude;
138.88/105.16	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
138.88/105.16	
138.88/105.16	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
138.88/105.16	}
138.88/105.16	addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
138.88/105.16	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
138.88/105.16	
138.88/105.16	addToFM0 old new = new;
138.88/105.16	
138.88/105.16	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
138.88/105.16	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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);
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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;
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
138.88/105.16	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
138.88/105.16	
138.88/105.16	emptyFM :: FiniteMap b a;
138.88/105.16	emptyFM = EmptyFM;
138.88/105.16	
138.88/105.16	findMax :: FiniteMap b a  ->  (b,a);
138.88/105.16	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
138.88/105.16	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
138.88/105.16	
138.88/105.16	findMin :: FiniteMap b a  ->  (b,a);
138.88/105.16	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
138.88/105.16	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
138.88/105.16	
138.88/105.16	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
138.88/105.16	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
138.88/105.16	
138.88/105.16	mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 
138.88/105.16	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);
138.88/105.16	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);
138.88/105.16	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);
138.88/105.16	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
138.88/105.16	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
138.88/105.16	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;
138.88/105.16	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);
138.88/105.16	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);
138.88/105.16	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
138.88/105.16	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
138.88/105.16	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;
138.88/105.16	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);
138.88/105.16	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
138.88/105.16	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
138.88/105.16	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
138.88/105.16	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
138.88/105.16	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
138.88/105.16	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
138.88/105.16	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
138.88/105.16	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;
138.88/105.16	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);
138.88/105.16	size_l = sizeFM fm_L;
138.88/105.16	size_r = sizeFM fm_R;
138.88/105.16	 };
138.88/105.16	
138.88/105.16	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
138.88/105.16	mkBranch which key elt fm_l fm_r = let { 
138.88/105.16	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
138.88/105.16	} in result where { 
138.88/105.16	balance_ok = True;
138.88/105.16	left_ok = left_ok0 fm_l key fm_l;
138.88/105.16	left_ok0 fm_l key EmptyFM = True;
138.88/105.16	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
138.88/105.16	biggest_left_key = fst (findMax fm_l);
138.88/105.16	} in biggest_left_key < key;
138.88/105.16	left_size = sizeFM fm_l;
138.88/105.16	right_ok = right_ok0 fm_r key fm_r;
138.88/105.16	right_ok0 fm_r key EmptyFM = True;
138.88/105.16	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
138.88/105.16	smallest_right_key = fst (findMin fm_r);
138.88/105.16	} in key < smallest_right_key;
138.88/105.16	right_size = sizeFM fm_r;
138.88/105.16	unbox :: Int  ->  Int;
138.88/105.16	unbox x = x;
138.88/105.16	 };
138.88/105.16	
138.88/105.16	sIZE_RATIO :: Int;
138.88/105.16	sIZE_RATIO = 5;
138.88/105.16	
138.88/105.16	sizeFM :: FiniteMap b a  ->  Int;
138.88/105.16	sizeFM EmptyFM = 0;
138.88/105.16	sizeFM (Branch vz wu size wv ww) = size;
138.88/105.16	
138.88/105.16	unitFM :: b  ->  a  ->  FiniteMap b a;
138.88/105.16	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
138.88/105.16	
138.88/105.16	}
138.88/105.16	module Maybe where {
138.88/105.16	import qualified FiniteMap;
138.88/105.16	import qualified Main;
138.88/105.16	import qualified Prelude;
138.88/105.16	}
138.88/105.16	module Main where {
138.88/105.16	import qualified FiniteMap;
138.88/105.16	import qualified Maybe;
138.88/105.16	import qualified Prelude;
138.88/105.16	}
138.88/105.16	
138.88/105.16	----------------------------------------
138.88/105.16	
138.88/105.16	(9) LetRed (EQUIVALENT)
138.88/105.16	Let/Where Reductions:
138.88/105.16	The bindings of the following Let/Where expression
138.88/105.16	"mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
138.88/105.16	;
138.88/105.16	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
138.88/105.16	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;
138.88/105.16	;
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
138.88/105.16	;
138.88/105.16	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
138.88/105.16	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;
138.88/105.16	;
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
138.88/105.16	;
138.88/105.16	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
138.88/105.16	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
138.88/105.16	;
138.88/105.16	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
138.88/105.16	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
138.88/105.16	;
138.88/105.16	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
138.88/105.16	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
138.88/105.16	;
138.88/105.16	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;
138.88/105.16	;
138.88/105.16	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);
138.88/105.16	;
138.88/105.16	size_l  = sizeFM fm_L;
138.88/105.16	;
138.88/105.16	size_r  = sizeFM fm_R;
138.88/105.16	} 
138.88/105.16	"
138.88/105.16	are unpacked to the following functions on top level
138.88/105.16	"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);
138.88/105.16	"
138.88/105.16	"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;
138.88/105.16	"
138.88/105.16	"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;
138.88/105.16	"
138.88/105.16	"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);
138.88/105.16	"
138.88/105.16	"mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
138.88/105.16	"
138.88/105.16	"mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
138.88/105.16	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);
138.88/105.16	"
138.88/105.16	"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);
138.88/105.16	"
138.88/105.16	"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;
138.88/105.16	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;
138.88/105.16	"
138.88/105.16	"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);
138.88/105.16	"
138.88/105.16	"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;
138.88/105.16	"
138.88/105.16	"mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
138.88/105.16	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
138.88/105.16	"
138.88/105.16	"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);
138.88/105.16	"
138.88/105.16	"mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vwz;
138.88/105.16	"
138.88/105.16	"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;
138.88/105.16	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;
138.88/105.16	"
138.88/105.16	"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);
138.88/105.16	"
138.88/105.16	"mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
138.88/105.16	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);
138.88/105.16	"
138.88/105.16	"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);
138.88/105.16	"
138.88/105.16	"mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vxu;
138.88/105.16	"
138.88/105.16	The bindings of the following Let/Where expression
138.88/105.16	"let {
138.88/105.16	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
138.88/105.16	} in result where {
138.88/105.16	balance_ok  = True;
138.88/105.16	;
138.88/105.16	left_ok  = left_ok0 fm_l key fm_l;
138.88/105.16	;
138.88/105.16	left_ok0 fm_l key EmptyFM = True;
138.88/105.16	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let {
138.88/105.16	biggest_left_key  = fst (findMax fm_l);
138.88/105.16	} in biggest_left_key < key;
138.88/105.16	;
138.88/105.16	left_size  = sizeFM fm_l;
138.88/105.16	;
138.88/105.16	right_ok  = right_ok0 fm_r key fm_r;
138.88/105.16	;
138.88/105.16	right_ok0 fm_r key EmptyFM = True;
138.88/105.16	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let {
138.88/105.16	smallest_right_key  = fst (findMin fm_r);
138.88/105.16	} in key < smallest_right_key;
138.88/105.16	;
138.88/105.16	right_size  = sizeFM fm_r;
138.88/105.16	;
138.88/105.16	unbox x = x;
138.88/105.16	} 
138.88/105.16	"
138.88/105.16	are unpacked to the following functions on top level
138.88/105.16	"mkBranchLeft_size vxv vxw vxx = sizeFM vxv;
138.88/105.16	"
138.88/105.16	"mkBranchBalance_ok vxv vxw vxx = True;
138.88/105.16	"
138.88/105.16	"mkBranchRight_size vxv vxw vxx = sizeFM vxw;
138.88/105.16	"
138.88/105.16	"mkBranchRight_ok0 vxv vxw vxx fm_r key EmptyFM = True;
138.88/105.16	mkBranchRight_ok0 vxv vxw vxx fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
138.88/105.16	"
138.88/105.16	"mkBranchLeft_ok0 vxv vxw vxx fm_l key EmptyFM = True;
138.88/105.16	mkBranchLeft_ok0 vxv vxw vxx fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
138.88/105.16	"
138.88/105.16	"mkBranchLeft_ok vxv vxw vxx = mkBranchLeft_ok0 vxv vxw vxx vxv vxx vxv;
138.88/105.16	"
138.88/105.16	"mkBranchUnbox vxv vxw vxx x = x;
138.88/105.16	"
138.88/105.16	"mkBranchRight_ok vxv vxw vxx = mkBranchRight_ok0 vxv vxw vxx vxw vxx vxw;
138.88/105.16	"
138.88/105.16	The bindings of the following Let/Where expression
138.88/105.16	"let {
138.88/105.16	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
138.88/105.16	} in result"
138.88/105.16	are unpacked to the following functions on top level
138.88/105.16	"mkBranchResult vxy vxz vyu vyv = Branch vxy vxz (mkBranchUnbox vyu vyv vxy (1 + mkBranchLeft_size vyu vyv vxy + mkBranchRight_size vyu vyv vxy)) vyu vyv;
138.88/105.16	"
138.88/105.16	The bindings of the following Let/Where expression
138.88/105.16	"let {
138.88/105.16	smallest_right_key  = fst (findMin fm_r);
138.88/105.16	} in key < smallest_right_key"
138.88/105.16	are unpacked to the following functions on top level
138.88/105.16	"mkBranchRight_ok0Smallest_right_key vyw = fst (findMin vyw);
138.88/105.16	"
138.88/105.16	The bindings of the following Let/Where expression
138.88/105.16	"let {
138.88/105.16	biggest_left_key  = fst (findMax fm_l);
138.88/105.16	} in biggest_left_key < key"
138.88/105.16	are unpacked to the following functions on top level
138.88/105.16	"mkBranchLeft_ok0Biggest_left_key vyx = fst (findMax vyx);
138.88/105.16	"
138.88/105.16	
138.88/105.16	----------------------------------------
138.88/105.16	
138.88/105.16	(10)
138.88/105.16	Obligation:
138.88/105.16	mainModule Main 
138.88/105.16	module FiniteMap where {
138.88/105.16	import qualified Main;
138.88/105.16	import qualified Maybe;
138.88/105.16	import qualified Prelude;
138.88/105.16	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
138.88/105.16	
138.88/105.16	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
138.88/105.16	}
138.88/105.16	addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
138.88/105.16	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
138.88/105.16	
138.88/105.16	addToFM0 old new = new;
138.88/105.16	
138.88/105.16	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
138.88/105.16	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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);
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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;
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
138.88/105.16	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
138.88/105.16	
138.88/105.16	emptyFM :: FiniteMap a b;
138.88/105.16	emptyFM = EmptyFM;
138.88/105.16	
138.88/105.16	findMax :: FiniteMap b a  ->  (b,a);
138.88/105.16	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
138.88/105.16	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
138.88/105.16	
138.88/105.16	findMin :: FiniteMap b a  ->  (b,a);
138.88/105.16	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
138.88/105.16	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
138.88/105.16	
138.88/105.16	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
138.88/105.16	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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;
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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;
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
138.88/105.16	
138.88/105.16	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
138.88/105.16	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
138.88/105.16	
138.88/105.16	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
138.88/105.16	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);
138.88/105.16	
138.88/105.16	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vwz;
138.88/105.16	
138.88/105.16	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vxu;
138.88/105.16	
138.88/105.16	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
138.88/105.16	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r;
138.88/105.16	
138.88/105.16	mkBranchBalance_ok vxv vxw vxx = True;
138.88/105.16	
138.88/105.16	mkBranchLeft_ok vxv vxw vxx = mkBranchLeft_ok0 vxv vxw vxx vxv vxx vxv;
138.88/105.16	
138.88/105.16	mkBranchLeft_ok0 vxv vxw vxx fm_l key EmptyFM = True;
138.88/105.16	mkBranchLeft_ok0 vxv vxw vxx fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
138.88/105.16	
138.88/105.16	mkBranchLeft_ok0Biggest_left_key vyx = fst (findMax vyx);
138.88/105.16	
138.88/105.16	mkBranchLeft_size vxv vxw vxx = sizeFM vxv;
138.88/105.16	
138.88/105.16	mkBranchResult vxy vxz vyu vyv = Branch vxy vxz (mkBranchUnbox vyu vyv vxy (1 + mkBranchLeft_size vyu vyv vxy + mkBranchRight_size vyu vyv vxy)) vyu vyv;
138.88/105.16	
138.88/105.16	mkBranchRight_ok vxv vxw vxx = mkBranchRight_ok0 vxv vxw vxx vxw vxx vxw;
138.88/105.16	
138.88/105.16	mkBranchRight_ok0 vxv vxw vxx fm_r key EmptyFM = True;
138.88/105.16	mkBranchRight_ok0 vxv vxw vxx fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
138.88/105.16	
138.88/105.16	mkBranchRight_ok0Smallest_right_key vyw = fst (findMin vyw);
138.88/105.16	
138.88/105.16	mkBranchRight_size vxv vxw vxx = sizeFM vxw;
138.88/105.16	
138.88/105.16	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)));
138.88/105.16	mkBranchUnbox vxv vxw vxx x = x;
138.88/105.16	
138.88/105.16	sIZE_RATIO :: Int;
138.88/105.16	sIZE_RATIO = 5;
138.88/105.16	
138.88/105.16	sizeFM :: FiniteMap b a  ->  Int;
138.88/105.16	sizeFM EmptyFM = 0;
138.88/105.16	sizeFM (Branch vz wu size wv ww) = size;
138.88/105.16	
138.88/105.16	unitFM :: a  ->  b  ->  FiniteMap a b;
138.88/105.16	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
138.88/105.16	
138.88/105.16	}
138.88/105.16	module Maybe where {
138.88/105.16	import qualified FiniteMap;
138.88/105.16	import qualified Main;
138.88/105.16	import qualified Prelude;
138.88/105.16	}
138.88/105.16	module Main where {
138.88/105.16	import qualified FiniteMap;
138.88/105.16	import qualified Maybe;
138.88/105.16	import qualified Prelude;
138.88/105.16	}
138.88/105.16	
138.88/105.16	----------------------------------------
138.88/105.16	
138.88/105.16	(11) NumRed (SOUND)
138.88/105.16	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
138.88/105.16	----------------------------------------
138.88/105.16	
138.88/105.16	(12)
138.88/105.16	Obligation:
138.88/105.16	mainModule Main 
138.88/105.16	module FiniteMap where {
138.88/105.16	import qualified Main;
138.88/105.16	import qualified Maybe;
138.88/105.16	import qualified Prelude;
138.88/105.16	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
138.88/105.16	
138.88/105.16	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
138.88/105.16	}
138.88/105.16	addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
138.88/105.16	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
138.88/105.16	
138.88/105.16	addToFM0 old new = new;
138.88/105.16	
138.88/105.16	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
138.88/105.16	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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);
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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;
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
138.88/105.16	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
138.88/105.16	
138.88/105.16	emptyFM :: FiniteMap b a;
138.88/105.16	emptyFM = EmptyFM;
138.88/105.16	
138.88/105.16	findMax :: FiniteMap b a  ->  (b,a);
138.88/105.16	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
138.88/105.16	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
138.88/105.16	
138.88/105.16	findMin :: FiniteMap b a  ->  (b,a);
138.88/105.16	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
138.88/105.16	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
138.88/105.16	
138.88/105.16	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
138.88/105.16	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
138.88/105.16	
138.88/105.16	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)));
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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;
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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;
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R;
138.88/105.16	
138.88/105.16	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
138.88/105.16	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
138.88/105.16	
138.88/105.16	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
138.88/105.16	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);
138.88/105.16	
138.88/105.16	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R;
138.88/105.16	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);
138.88/105.16	
138.88/105.16	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;
138.88/105.16	
138.88/105.16	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);
138.88/105.16	
138.88/105.16	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vwz;
138.88/105.16	
138.88/105.16	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vxu;
138.88/105.16	
138.88/105.16	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
138.88/105.16	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r;
138.88/105.16	
138.88/105.16	mkBranchBalance_ok vxv vxw vxx = True;
138.88/105.16	
138.88/105.16	mkBranchLeft_ok vxv vxw vxx = mkBranchLeft_ok0 vxv vxw vxx vxv vxx vxv;
138.88/105.16	
138.88/105.16	mkBranchLeft_ok0 vxv vxw vxx fm_l key EmptyFM = True;
138.88/105.16	mkBranchLeft_ok0 vxv vxw vxx fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
138.88/105.16	
138.88/105.16	mkBranchLeft_ok0Biggest_left_key vyx = fst (findMax vyx);
138.88/105.16	
138.88/105.16	mkBranchLeft_size vxv vxw vxx = sizeFM vxv;
138.88/105.16	
138.88/105.16	mkBranchResult vxy vxz vyu vyv = Branch vxy vxz (mkBranchUnbox vyu vyv vxy (Pos (Succ Zero) + mkBranchLeft_size vyu vyv vxy + mkBranchRight_size vyu vyv vxy)) vyu vyv;
138.88/105.16	
138.88/105.16	mkBranchRight_ok vxv vxw vxx = mkBranchRight_ok0 vxv vxw vxx vxw vxx vxw;
138.88/105.16	
138.88/105.16	mkBranchRight_ok0 vxv vxw vxx fm_r key EmptyFM = True;
138.88/105.16	mkBranchRight_ok0 vxv vxw vxx fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
138.88/105.16	
138.88/105.16	mkBranchRight_ok0Smallest_right_key vyw = fst (findMin vyw);
138.88/105.16	
138.88/105.16	mkBranchRight_size vxv vxw vxx = sizeFM vxw;
138.88/105.16	
138.88/105.16	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)));
138.88/105.16	mkBranchUnbox vxv vxw vxx x = x;
138.88/105.16	
138.88/105.16	sIZE_RATIO :: Int;
138.88/105.16	sIZE_RATIO = Pos (Succ (Succ (Succ (Succ (Succ Zero)))));
138.88/105.16	
138.88/105.16	sizeFM :: FiniteMap b a  ->  Int;
138.88/105.16	sizeFM EmptyFM = Pos Zero;
138.88/105.16	sizeFM (Branch vz wu size wv ww) = size;
138.88/105.16	
138.88/105.16	unitFM :: b  ->  a  ->  FiniteMap b a;
138.88/105.16	unitFM key elt = Branch key elt (Pos (Succ Zero)) emptyFM emptyFM;
138.88/105.16	
138.88/105.16	}
138.88/105.16	module Maybe where {
138.88/105.16	import qualified FiniteMap;
138.88/105.16	import qualified Main;
138.88/105.16	import qualified Prelude;
138.88/105.16	}
138.88/105.16	module Main where {
138.88/105.16	import qualified FiniteMap;
138.88/105.16	import qualified Maybe;
138.88/105.16	import qualified Prelude;
138.88/105.16	}
139.07/105.24	EOF