9.89/4.51	YES
12.86/5.26	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.86/5.26	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.86/5.26	
12.86/5.26	
12.86/5.26	H-Termination with start terms of the given HASKELL could be proven:
12.86/5.26	
12.86/5.26	(0) HASKELL
12.86/5.26	(1) LR [EQUIVALENT, 0 ms]
12.86/5.26	(2) HASKELL
12.86/5.26	(3) CR [EQUIVALENT, 0 ms]
12.86/5.26	(4) HASKELL
12.86/5.26	(5) BR [EQUIVALENT, 0 ms]
12.86/5.26	(6) HASKELL
12.86/5.26	(7) COR [EQUIVALENT, 19 ms]
12.86/5.26	(8) HASKELL
12.86/5.26	(9) LetRed [EQUIVALENT, 0 ms]
12.86/5.26	(10) HASKELL
12.86/5.26	(11) NumRed [SOUND, 0 ms]
12.86/5.26	(12) HASKELL
12.86/5.26	(13) Narrow [EQUIVALENT, 22 ms]
12.86/5.26	(14) YES
12.86/5.26	
12.86/5.26	
12.86/5.26	----------------------------------------
12.86/5.26	
12.86/5.26	(0)
12.86/5.26	Obligation:
12.86/5.26	mainModule Main 
12.86/5.26	module FiniteMap where {
12.86/5.26	import qualified Main;
12.86/5.26	import qualified Maybe;
12.86/5.26	import qualified Prelude;
12.86/5.26	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.86/5.26	
12.86/5.26	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.86/5.26	}
12.86/5.26	addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
12.86/5.26	addToFM fm key elt = addToFM_C (\old new ->new) fm key elt;
12.86/5.26	
12.86/5.26	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
13.59/5.47	addToFM_C combiner EmptyFM key elt = unitFM key elt;
13.59/5.47	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
13.59/5.47	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
13.59/5.47	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
13.59/5.47	
13.59/5.47	emptyFM :: FiniteMap b a;
13.59/5.47	emptyFM = EmptyFM;
13.59/5.47	
13.59/5.47	findMax :: FiniteMap a b  ->  (a,b);
13.59/5.47	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
13.59/5.47	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
13.59/5.47	
13.59/5.47	findMin :: FiniteMap a b  ->  (a,b);
13.59/5.47	findMin (Branch key elt _ EmptyFM _) = (key,elt);
13.59/5.47	findMin (Branch key elt _ fm_l _) = findMin fm_l;
13.59/5.47	
13.59/5.47	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
13.59/5.47	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
13.59/5.47	 | size_r > sIZE_RATIO * size_l = case fm_R of { 
13.59/5.47	Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R
13.59/5.47	 | otherwise -> double_L fm_L fm_R; 
13.59/5.47	 } 
13.59/5.47	 | size_l > sIZE_RATIO * size_r = case fm_L of { 
13.59/5.47	Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R
13.59/5.47	 | otherwise -> double_R fm_L fm_R; 
13.59/5.47	 } 
13.59/5.47	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
13.59/5.47	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);
13.59/5.47	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);
13.59/5.47	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;
13.59/5.47	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);
13.59/5.47	size_l = sizeFM fm_L;
13.59/5.47	size_r = sizeFM fm_R;
13.59/5.47	 };
13.59/5.47	
13.59/5.47	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
13.59/5.47	mkBranch which key elt fm_l fm_r = let { 
13.59/5.47	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
13.59/5.47	} in result where { 
13.59/5.47	balance_ok = True;
13.59/5.47	left_ok = case fm_l of { 
13.59/5.47	EmptyFM-> True; 
13.59/5.47	Branch left_key _ _ _ _-> let { 
13.59/5.47	biggest_left_key = fst (findMax fm_l);
13.59/5.47	} in biggest_left_key < key; 
13.59/5.47	 } ;
13.59/5.47	left_size = sizeFM fm_l;
13.59/5.47	right_ok = case fm_r of { 
13.59/5.47	EmptyFM-> True; 
13.59/5.47	Branch right_key _ _ _ _-> let { 
13.59/5.47	smallest_right_key = fst (findMin fm_r);
13.59/5.47	} in key < smallest_right_key; 
13.59/5.47	 } ;
13.59/5.47	right_size = sizeFM fm_r;
13.59/5.47	unbox :: Int  ->  Int;
13.59/5.47	unbox x = x;
13.59/5.47	 };
13.59/5.47	
13.59/5.47	sIZE_RATIO :: Int;
13.59/5.47	sIZE_RATIO = 5;
13.59/5.47	
13.59/5.47	sizeFM :: FiniteMap b a  ->  Int;
13.59/5.47	sizeFM EmptyFM = 0;
13.59/5.47	sizeFM (Branch _ _ size _ _) = size;
13.59/5.47	
13.59/5.47	unitFM :: a  ->  b  ->  FiniteMap a b;
13.59/5.47	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
13.59/5.47	
13.59/5.47	}
13.59/5.47	module Maybe where {
13.59/5.47	import qualified FiniteMap;
13.59/5.47	import qualified Main;
13.59/5.47	import qualified Prelude;
13.59/5.47	}
13.59/5.47	module Main where {
13.59/5.47	import qualified FiniteMap;
13.59/5.47	import qualified Maybe;
13.59/5.47	import qualified Prelude;
13.59/5.47	}
13.59/5.47	
13.59/5.47	----------------------------------------
13.59/5.47	
13.59/5.47	(1) LR (EQUIVALENT)
13.59/5.47	Lambda Reductions:
13.59/5.47	The following Lambda expression
13.59/5.47	"\oldnew->new"
13.59/5.47	is transformed to
13.59/5.47	"addToFM0 old new = new;
13.59/5.47	"
13.59/5.47	
13.59/5.47	----------------------------------------
13.59/5.47	
13.59/5.47	(2)
13.59/5.47	Obligation:
13.59/5.47	mainModule Main 
13.59/5.47	module FiniteMap where {
13.59/5.47	import qualified Main;
13.59/5.47	import qualified Maybe;
13.59/5.47	import qualified Prelude;
13.59/5.47	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
13.59/5.47	
13.59/5.47	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
13.59/5.47	}
13.59/5.47	addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
13.59/5.47	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
13.59/5.47	
13.59/5.47	addToFM0 old new = new;
13.59/5.47	
13.59/5.47	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
13.59/5.47	addToFM_C combiner EmptyFM key elt = unitFM key elt;
13.59/5.47	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
13.59/5.47	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
13.59/5.47	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
13.59/5.47	
13.59/5.47	emptyFM :: FiniteMap a b;
13.59/5.47	emptyFM = EmptyFM;
13.59/5.47	
13.59/5.47	findMax :: FiniteMap b a  ->  (b,a);
13.59/5.47	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
13.59/5.47	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
13.59/5.47	
13.59/5.47	findMin :: FiniteMap b a  ->  (b,a);
13.59/5.47	findMin (Branch key elt _ EmptyFM _) = (key,elt);
13.59/5.47	findMin (Branch key elt _ fm_l _) = findMin fm_l;
13.59/5.47	
13.59/5.47	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
13.59/5.47	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
13.59/5.47	 | size_r > sIZE_RATIO * size_l = case fm_R of { 
13.59/5.47	Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R
13.59/5.47	 | otherwise -> double_L fm_L fm_R; 
13.59/5.47	 } 
13.59/5.47	 | size_l > sIZE_RATIO * size_r = case fm_L of { 
13.59/5.47	Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R
13.59/5.47	 | otherwise -> double_R fm_L fm_R; 
13.59/5.47	 } 
13.59/5.47	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
13.59/5.47	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);
13.59/5.47	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);
13.59/5.47	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;
13.59/5.47	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);
13.59/5.47	size_l = sizeFM fm_L;
13.59/5.47	size_r = sizeFM fm_R;
13.59/5.47	 };
13.59/5.47	
13.59/5.47	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
13.59/5.47	mkBranch which key elt fm_l fm_r = let { 
13.59/5.47	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
13.59/5.47	} in result where { 
13.59/5.47	balance_ok = True;
13.59/5.47	left_ok = case fm_l of { 
13.59/5.47	EmptyFM-> True; 
13.59/5.47	Branch left_key _ _ _ _-> let { 
13.59/5.47	biggest_left_key = fst (findMax fm_l);
13.59/5.47	} in biggest_left_key < key; 
13.59/5.47	 } ;
13.59/5.47	left_size = sizeFM fm_l;
13.59/5.47	right_ok = case fm_r of { 
13.59/5.47	EmptyFM-> True; 
13.59/5.47	Branch right_key _ _ _ _-> let { 
13.59/5.47	smallest_right_key = fst (findMin fm_r);
13.59/5.47	} in key < smallest_right_key; 
13.59/5.47	 } ;
13.59/5.47	right_size = sizeFM fm_r;
13.59/5.47	unbox :: Int  ->  Int;
13.59/5.47	unbox x = x;
13.59/5.47	 };
13.59/5.47	
13.59/5.47	sIZE_RATIO :: Int;
13.59/5.47	sIZE_RATIO = 5;
13.59/5.47	
13.59/5.47	sizeFM :: FiniteMap a b  ->  Int;
13.59/5.47	sizeFM EmptyFM = 0;
13.59/5.47	sizeFM (Branch _ _ size _ _) = size;
13.59/5.47	
13.59/5.47	unitFM :: b  ->  a  ->  FiniteMap b a;
13.59/5.47	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
13.59/5.47	
13.59/5.47	}
13.59/5.47	module Maybe where {
13.59/5.47	import qualified FiniteMap;
13.59/5.47	import qualified Main;
13.59/5.47	import qualified Prelude;
13.59/5.47	}
13.59/5.47	module Main where {
13.59/5.47	import qualified FiniteMap;
13.59/5.47	import qualified Maybe;
13.59/5.47	import qualified Prelude;
13.59/5.47	}
13.59/5.47	
13.59/5.47	----------------------------------------
13.59/5.47	
13.59/5.47	(3) CR (EQUIVALENT)
13.59/5.47	Case Reductions:
13.59/5.47	The following Case expression
13.59/5.47	"case fm_r of {
13.59/5.47	EmptyFM  -> True;
13.59/5.47	Branch right_key _ _ _ _  -> let {
13.59/5.47	smallest_right_key  = fst (findMin fm_r);
13.59/5.47	} in key < smallest_right_key}
13.59/5.47	"
13.59/5.47	is transformed to
13.59/5.47	"right_ok0 fm_r key EmptyFM = True;
13.59/5.47	right_ok0 fm_r key (Branch right_key _ _ _ _) = let {
13.59/5.47	smallest_right_key  = fst (findMin fm_r);
13.59/5.47	} in key < smallest_right_key;
13.59/5.47	"
13.59/5.47	The following Case expression
13.59/5.47	"case fm_l of {
13.59/5.47	EmptyFM  -> True;
13.59/5.47	Branch left_key _ _ _ _  -> let {
13.59/5.47	biggest_left_key  = fst (findMax fm_l);
13.59/5.47	} in biggest_left_key < key}
13.59/5.47	"
13.59/5.47	is transformed to
13.59/5.47	"left_ok0 fm_l key EmptyFM = True;
13.59/5.47	left_ok0 fm_l key (Branch left_key _ _ _ _) = let {
13.59/5.47	biggest_left_key  = fst (findMax fm_l);
13.59/5.47	} in biggest_left_key < key;
13.59/5.47	"
13.59/5.47	The following Case expression
13.59/5.47	"case fm_R of {
13.59/5.47	Branch _ _ _ fm_rl fm_rr |sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R}
13.59/5.47	"
13.59/5.47	is transformed to
13.59/5.47	"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;
13.59/5.47	"
13.59/5.47	The following Case expression
13.59/5.47	"case fm_L of {
13.59/5.47	Branch _ _ _ fm_ll fm_lr |sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R}
13.59/5.47	"
13.59/5.47	is transformed to
13.59/5.47	"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;
13.59/5.47	"
13.59/5.47	
13.59/5.47	----------------------------------------
13.59/5.47	
13.59/5.47	(4)
13.59/5.47	Obligation:
13.59/5.47	mainModule Main 
13.59/5.47	module FiniteMap where {
13.59/5.47	import qualified Main;
13.59/5.47	import qualified Maybe;
13.59/5.47	import qualified Prelude;
13.59/5.47	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
13.59/5.47	
13.59/5.47	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
13.59/5.47	}
13.59/5.47	addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
13.59/5.47	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
13.59/5.47	
13.59/5.47	addToFM0 old new = new;
13.59/5.47	
13.59/5.47	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
13.59/5.47	addToFM_C combiner EmptyFM key elt = unitFM key elt;
13.59/5.47	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
13.59/5.47	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
13.59/5.47	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
13.59/5.47	
13.59/5.47	emptyFM :: FiniteMap a b;
13.59/5.47	emptyFM = EmptyFM;
13.59/5.47	
13.59/5.47	findMax :: FiniteMap a b  ->  (a,b);
13.59/5.47	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
13.59/5.47	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
13.59/5.47	
13.59/5.47	findMin :: FiniteMap b a  ->  (b,a);
13.59/5.47	findMin (Branch key elt _ EmptyFM _) = (key,elt);
13.59/5.47	findMin (Branch key elt _ fm_l _) = findMin fm_l;
13.59/5.47	
13.59/5.47	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
13.59/5.47	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
13.59/5.47	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
13.59/5.47	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
13.59/5.47	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
13.59/5.47	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);
13.59/5.47	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);
13.59/5.47	mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr)  | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R
13.59/5.47	 | otherwise = double_L fm_L fm_R;
13.59/5.47	mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr)  | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R
13.59/5.47	 | otherwise = double_R fm_L fm_R;
13.59/5.47	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;
13.59/5.47	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);
13.59/5.47	size_l = sizeFM fm_L;
13.59/5.47	size_r = sizeFM fm_R;
13.59/5.47	 };
13.59/5.47	
13.59/5.47	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
13.59/5.47	mkBranch which key elt fm_l fm_r = let { 
13.59/5.47	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
13.59/5.47	} in result where { 
13.59/5.47	balance_ok = True;
13.59/5.47	left_ok = left_ok0 fm_l key fm_l;
13.59/5.47	left_ok0 fm_l key EmptyFM = True;
13.59/5.47	left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 
13.59/5.47	biggest_left_key = fst (findMax fm_l);
13.59/5.47	} in biggest_left_key < key;
13.59/5.47	left_size = sizeFM fm_l;
13.59/5.47	right_ok = right_ok0 fm_r key fm_r;
13.59/5.47	right_ok0 fm_r key EmptyFM = True;
13.59/5.47	right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 
13.59/5.47	smallest_right_key = fst (findMin fm_r);
13.59/5.47	} in key < smallest_right_key;
13.59/5.47	right_size = sizeFM fm_r;
13.59/5.47	unbox :: Int  ->  Int;
13.59/5.47	unbox x = x;
13.59/5.47	 };
13.59/5.47	
13.59/5.47	sIZE_RATIO :: Int;
13.59/5.47	sIZE_RATIO = 5;
13.59/5.47	
13.59/5.47	sizeFM :: FiniteMap a b  ->  Int;
13.59/5.47	sizeFM EmptyFM = 0;
13.59/5.47	sizeFM (Branch _ _ size _ _) = size;
13.59/5.47	
13.59/5.47	unitFM :: a  ->  b  ->  FiniteMap a b;
13.59/5.47	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
13.59/5.47	
13.59/5.47	}
13.59/5.47	module Maybe where {
13.59/5.47	import qualified FiniteMap;
13.59/5.47	import qualified Main;
13.59/5.47	import qualified Prelude;
13.59/5.47	}
13.59/5.47	module Main where {
13.59/5.47	import qualified FiniteMap;
13.59/5.47	import qualified Maybe;
13.59/5.47	import qualified Prelude;
13.59/5.47	}
13.59/5.47	
13.59/5.47	----------------------------------------
13.59/5.47	
13.59/5.47	(5) BR (EQUIVALENT)
13.59/5.47	Replaced joker patterns by fresh variables and removed binding patterns.
13.59/5.47	----------------------------------------
13.59/5.47	
13.59/5.47	(6)
13.59/5.47	Obligation:
13.59/5.47	mainModule Main 
13.59/5.47	module FiniteMap where {
13.59/5.47	import qualified Main;
13.59/5.47	import qualified Maybe;
13.59/5.47	import qualified Prelude;
13.59/5.47	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
13.59/5.47	
13.59/5.47	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
13.59/5.47	}
13.59/5.47	addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
13.59/5.47	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
13.59/5.47	
13.59/5.47	addToFM0 old new = new;
13.59/5.47	
13.59/5.47	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
13.59/5.47	addToFM_C combiner EmptyFM key elt = unitFM key elt;
13.59/5.47	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
13.59/5.47	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
13.59/5.47	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
13.59/5.47	
13.59/5.47	emptyFM :: FiniteMap a b;
13.59/5.47	emptyFM = EmptyFM;
13.59/5.47	
13.59/5.47	findMax :: FiniteMap b a  ->  (b,a);
13.59/5.47	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
13.59/5.47	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
13.59/5.47	
13.59/5.47	findMin :: FiniteMap a b  ->  (a,b);
13.59/5.47	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
13.59/5.47	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
13.59/5.47	
13.59/5.47	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
13.59/5.47	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
13.59/5.47	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
13.59/5.47	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
13.59/5.47	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
13.59/5.47	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);
13.59/5.47	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);
13.59/5.47	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
13.59/5.47	 | otherwise = double_L fm_L fm_R;
13.59/5.47	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
13.59/5.47	 | otherwise = double_R fm_L fm_R;
13.59/5.47	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;
13.59/5.47	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);
13.59/5.47	size_l = sizeFM fm_L;
13.59/5.47	size_r = sizeFM fm_R;
13.59/5.47	 };
13.59/5.47	
13.59/5.47	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
13.59/5.47	mkBranch which key elt fm_l fm_r = let { 
13.59/5.47	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
13.59/5.47	} in result where { 
13.59/5.47	balance_ok = True;
13.59/5.47	left_ok = left_ok0 fm_l key fm_l;
13.59/5.47	left_ok0 fm_l key EmptyFM = True;
13.59/5.47	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
13.59/5.47	biggest_left_key = fst (findMax fm_l);
13.59/5.47	} in biggest_left_key < key;
13.59/5.47	left_size = sizeFM fm_l;
13.59/5.47	right_ok = right_ok0 fm_r key fm_r;
13.59/5.47	right_ok0 fm_r key EmptyFM = True;
13.59/5.47	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
13.59/5.47	smallest_right_key = fst (findMin fm_r);
13.59/5.47	} in key < smallest_right_key;
13.59/5.47	right_size = sizeFM fm_r;
13.59/5.47	unbox :: Int  ->  Int;
13.59/5.47	unbox x = x;
13.59/5.47	 };
13.59/5.47	
13.59/5.47	sIZE_RATIO :: Int;
13.59/5.47	sIZE_RATIO = 5;
13.59/5.47	
13.59/5.47	sizeFM :: FiniteMap b a  ->  Int;
13.59/5.47	sizeFM EmptyFM = 0;
13.59/5.47	sizeFM (Branch vz wu size wv ww) = size;
13.59/5.47	
13.59/5.47	unitFM :: a  ->  b  ->  FiniteMap a b;
13.59/5.47	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
13.59/5.47	
13.59/5.47	}
13.59/5.47	module Maybe where {
13.59/5.47	import qualified FiniteMap;
13.59/5.47	import qualified Main;
13.59/5.47	import qualified Prelude;
13.59/5.47	}
13.59/5.47	module Main where {
13.59/5.47	import qualified FiniteMap;
13.59/5.47	import qualified Maybe;
13.59/5.47	import qualified Prelude;
13.59/5.47	}
13.59/5.47	
13.59/5.47	----------------------------------------
13.59/5.47	
13.59/5.47	(7) COR (EQUIVALENT)
13.59/5.47	Cond Reductions:
13.59/5.47	The following Function with conditions
13.59/5.47	"undefined |Falseundefined;
13.59/5.47	"
13.59/5.47	is transformed to
13.59/5.47	"undefined  = undefined1;
13.59/5.47	"
13.59/5.47	"undefined0 True = undefined;
13.59/5.47	"
13.59/5.47	"undefined1  = undefined0 False;
13.59/5.47	"
13.59/5.47	The following Function with conditions
13.59/5.47	"addToFM_C combiner EmptyFM key elt = unitFM key elt;
13.59/5.47	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;
13.59/5.47	"
13.59/5.47	is transformed to
13.59/5.47	"addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
13.59/5.47	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;
13.59/5.47	"
13.59/5.47	"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);
13.59/5.47	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;
13.59/5.47	"
13.59/5.47	"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;
13.59/5.47	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);
13.59/5.47	"
13.59/5.47	"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;
13.59/5.47	"
13.59/5.47	"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);
13.59/5.47	"
13.59/5.47	"addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
13.59/5.47	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
13.59/5.47	"
13.59/5.47	The following Function with conditions
13.59/5.47	"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;
13.59/5.47	"
13.59/5.47	is transformed to
13.59/5.47	"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);
13.59/5.47	"
13.59/5.47	"mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
13.59/5.47	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;
13.59/5.47	"
13.59/5.47	"mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
13.59/5.47	"
13.59/5.47	"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);
13.59/5.47	"
13.59/5.47	The following Function with conditions
13.59/5.47	"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;
13.59/5.47	"
13.59/5.47	is transformed to
13.59/5.47	"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);
13.59/5.47	"
13.59/5.47	"mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
13.59/5.47	"
13.59/5.47	"mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
13.59/5.47	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;
13.59/5.47	"
13.59/5.47	"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);
13.59/5.47	"
13.59/5.47	The following Function with conditions
13.59/5.47	"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 {
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	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;
13.59/5.47	;
13.59/5.47	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;
13.59/5.47	;
13.59/5.47	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;
13.59/5.47	;
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	size_l  = sizeFM fm_L;
13.59/5.47	;
13.59/5.47	size_r  = sizeFM fm_R;
13.59/5.47	} 
13.59/5.47	;
13.59/5.47	"
13.59/5.47	is transformed to
13.59/5.47	"mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
13.59/5.47	"
13.59/5.47	"mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
13.59/5.47	;
13.59/5.47	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
13.59/5.47	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;
13.59/5.47	;
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
13.59/5.47	;
13.59/5.47	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
13.59/5.47	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;
13.59/5.47	;
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
13.59/5.47	;
13.59/5.47	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
13.59/5.47	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
13.59/5.47	;
13.59/5.47	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
13.59/5.47	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
13.59/5.47	;
13.59/5.47	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
13.59/5.47	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
13.59/5.47	;
13.59/5.47	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;
13.59/5.47	;
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	size_l  = sizeFM fm_L;
13.59/5.47	;
13.59/5.47	size_r  = sizeFM fm_R;
13.59/5.47	} 
13.59/5.47	;
13.59/5.47	"
13.59/5.47	
13.59/5.47	----------------------------------------
13.59/5.47	
13.59/5.47	(8)
13.59/5.47	Obligation:
13.59/5.47	mainModule Main 
13.59/5.47	module FiniteMap where {
13.59/5.47	import qualified Main;
13.59/5.47	import qualified Maybe;
13.59/5.47	import qualified Prelude;
13.59/5.47	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
13.59/5.47	
13.59/5.47	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
13.59/5.47	}
13.59/5.47	addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
13.59/5.47	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
13.59/5.47	
13.59/5.47	addToFM0 old new = new;
13.59/5.47	
13.59/5.47	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
13.59/5.47	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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);
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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;
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
13.59/5.47	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
13.59/5.47	
13.59/5.47	emptyFM :: FiniteMap b a;
13.59/5.47	emptyFM = EmptyFM;
13.59/5.47	
13.59/5.47	findMax :: FiniteMap b a  ->  (b,a);
13.59/5.47	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
13.59/5.47	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
13.59/5.47	
13.59/5.47	findMin :: FiniteMap a b  ->  (a,b);
13.59/5.47	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
13.59/5.47	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
13.59/5.47	
13.59/5.47	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
13.59/5.47	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
13.59/5.47	
13.59/5.47	mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 
13.59/5.47	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);
13.59/5.47	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);
13.59/5.47	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);
13.59/5.47	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
13.59/5.47	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
13.59/5.47	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;
13.59/5.47	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);
13.59/5.47	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);
13.59/5.47	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
13.59/5.47	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
13.59/5.47	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;
13.59/5.47	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);
13.59/5.47	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
13.59/5.47	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
13.59/5.47	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
13.59/5.47	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
13.59/5.47	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
13.59/5.47	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
13.59/5.47	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
13.59/5.47	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;
13.59/5.47	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);
13.59/5.47	size_l = sizeFM fm_L;
13.59/5.47	size_r = sizeFM fm_R;
13.59/5.47	 };
13.59/5.47	
13.59/5.47	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
13.59/5.47	mkBranch which key elt fm_l fm_r = let { 
13.59/5.47	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
13.59/5.47	} in result where { 
13.59/5.47	balance_ok = True;
13.59/5.47	left_ok = left_ok0 fm_l key fm_l;
13.59/5.47	left_ok0 fm_l key EmptyFM = True;
13.59/5.47	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
13.59/5.47	biggest_left_key = fst (findMax fm_l);
13.59/5.47	} in biggest_left_key < key;
13.59/5.47	left_size = sizeFM fm_l;
13.59/5.47	right_ok = right_ok0 fm_r key fm_r;
13.59/5.47	right_ok0 fm_r key EmptyFM = True;
13.59/5.47	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
13.59/5.47	smallest_right_key = fst (findMin fm_r);
13.59/5.47	} in key < smallest_right_key;
13.59/5.47	right_size = sizeFM fm_r;
13.59/5.47	unbox :: Int  ->  Int;
13.59/5.47	unbox x = x;
13.59/5.47	 };
13.59/5.47	
13.59/5.47	sIZE_RATIO :: Int;
13.59/5.47	sIZE_RATIO = 5;
13.59/5.47	
13.59/5.47	sizeFM :: FiniteMap b a  ->  Int;
13.59/5.47	sizeFM EmptyFM = 0;
13.59/5.47	sizeFM (Branch vz wu size wv ww) = size;
13.59/5.47	
13.59/5.47	unitFM :: b  ->  a  ->  FiniteMap b a;
13.59/5.47	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
13.59/5.47	
13.59/5.47	}
13.59/5.47	module Maybe where {
13.59/5.47	import qualified FiniteMap;
13.59/5.47	import qualified Main;
13.59/5.47	import qualified Prelude;
13.59/5.47	}
13.59/5.47	module Main where {
13.59/5.47	import qualified FiniteMap;
13.59/5.47	import qualified Maybe;
13.59/5.47	import qualified Prelude;
13.59/5.47	}
13.59/5.47	
13.59/5.47	----------------------------------------
13.59/5.47	
13.59/5.47	(9) LetRed (EQUIVALENT)
13.59/5.47	Let/Where Reductions:
13.59/5.47	The bindings of the following Let/Where expression
13.59/5.47	"mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
13.59/5.47	;
13.59/5.47	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
13.59/5.47	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;
13.59/5.47	;
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
13.59/5.47	;
13.59/5.47	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
13.59/5.47	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;
13.59/5.47	;
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
13.59/5.47	;
13.59/5.47	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
13.59/5.47	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
13.59/5.47	;
13.59/5.47	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
13.59/5.47	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
13.59/5.47	;
13.59/5.47	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
13.59/5.47	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
13.59/5.47	;
13.59/5.47	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;
13.59/5.47	;
13.59/5.47	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);
13.59/5.47	;
13.59/5.47	size_l  = sizeFM fm_L;
13.59/5.47	;
13.59/5.47	size_r  = sizeFM fm_R;
13.59/5.47	} 
13.59/5.47	"
13.59/5.47	are unpacked to the following functions on top level
13.59/5.47	"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);
13.59/5.47	"
13.59/5.47	"mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
13.59/5.47	"
13.59/5.47	"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);
13.59/5.47	"
13.59/5.47	"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);
13.59/5.47	"
13.59/5.47	"mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vwz;
13.59/5.47	"
13.59/5.47	"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);
13.59/5.47	"
13.59/5.47	"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;
13.59/5.47	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;
13.59/5.47	"
13.59/5.47	"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;
13.59/5.47	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;
13.59/5.47	"
13.59/5.47	"mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
13.59/5.47	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);
13.59/5.47	"
13.59/5.47	"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;
13.59/5.47	"
13.59/5.47	"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);
13.59/5.47	"
13.59/5.47	"mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vxu;
13.59/5.47	"
13.59/5.47	"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;
13.59/5.47	"
13.59/5.47	"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);
13.59/5.47	"
13.59/5.47	"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;
13.59/5.47	"
13.59/5.47	"mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
13.59/5.47	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
13.59/5.47	"
13.59/5.47	"mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
13.59/5.47	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);
13.59/5.47	"
13.59/5.47	"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);
13.59/5.47	"
13.59/5.47	The bindings of the following Let/Where expression
13.59/5.47	"let {
13.59/5.47	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
13.59/5.47	} in result where {
13.59/5.47	balance_ok  = True;
13.59/5.47	;
13.59/5.47	left_ok  = left_ok0 fm_l key fm_l;
13.59/5.47	;
13.59/5.47	left_ok0 fm_l key EmptyFM = True;
13.59/5.47	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let {
13.59/5.47	biggest_left_key  = fst (findMax fm_l);
13.59/5.47	} in biggest_left_key < key;
13.59/5.47	;
13.59/5.47	left_size  = sizeFM fm_l;
13.59/5.47	;
13.59/5.47	right_ok  = right_ok0 fm_r key fm_r;
13.59/5.47	;
13.59/5.47	right_ok0 fm_r key EmptyFM = True;
13.59/5.47	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let {
13.59/5.47	smallest_right_key  = fst (findMin fm_r);
13.59/5.47	} in key < smallest_right_key;
13.59/5.47	;
13.59/5.47	right_size  = sizeFM fm_r;
13.59/5.47	;
13.59/5.47	unbox x = x;
13.59/5.47	} 
13.59/5.47	"
13.59/5.47	are unpacked to the following functions on top level
13.59/5.47	"mkBranchUnbox vxv vxw vxx x = x;
13.59/5.47	"
13.59/5.47	"mkBranchRight_size vxv vxw vxx = sizeFM vxv;
13.59/5.47	"
13.59/5.47	"mkBranchLeft_ok vxv vxw vxx = mkBranchLeft_ok0 vxv vxw vxx vxw vxx vxw;
13.59/5.47	"
13.59/5.47	"mkBranchLeft_size vxv vxw vxx = sizeFM vxw;
13.59/5.47	"
13.59/5.47	"mkBranchBalance_ok vxv vxw vxx = True;
13.59/5.47	"
13.59/5.47	"mkBranchLeft_ok0 vxv vxw vxx fm_l key EmptyFM = True;
13.59/5.47	mkBranchLeft_ok0 vxv vxw vxx fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
13.59/5.47	"
13.59/5.47	"mkBranchRight_ok0 vxv vxw vxx fm_r key EmptyFM = True;
13.59/5.47	mkBranchRight_ok0 vxv vxw vxx fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
13.59/5.47	"
13.59/5.47	"mkBranchRight_ok vxv vxw vxx = mkBranchRight_ok0 vxv vxw vxx vxv vxx vxv;
13.59/5.47	"
13.59/5.47	The bindings of the following Let/Where expression
13.59/5.47	"let {
13.59/5.47	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
13.59/5.47	} in result"
13.59/5.47	are unpacked to the following functions on top level
13.59/5.47	"mkBranchResult vxy vxz vyu vyv = Branch vxy vxz (mkBranchUnbox vyu vyv vxy (1 + mkBranchLeft_size vyu vyv vxy + mkBranchRight_size vyu vyv vxy)) vyv vyu;
13.59/5.47	"
13.59/5.47	The bindings of the following Let/Where expression
13.59/5.47	"let {
13.59/5.47	biggest_left_key  = fst (findMax fm_l);
13.59/5.47	} in biggest_left_key < key"
13.59/5.47	are unpacked to the following functions on top level
13.59/5.47	"mkBranchLeft_ok0Biggest_left_key vyw = fst (findMax vyw);
13.59/5.47	"
13.59/5.47	The bindings of the following Let/Where expression
13.59/5.47	"let {
13.59/5.47	smallest_right_key  = fst (findMin fm_r);
13.59/5.47	} in key < smallest_right_key"
13.59/5.47	are unpacked to the following functions on top level
13.59/5.47	"mkBranchRight_ok0Smallest_right_key vyx = fst (findMin vyx);
13.59/5.47	"
13.59/5.47	
13.59/5.47	----------------------------------------
13.59/5.47	
13.59/5.47	(10)
13.59/5.47	Obligation:
13.59/5.47	mainModule Main 
13.59/5.47	module FiniteMap where {
13.59/5.47	import qualified Main;
13.59/5.47	import qualified Maybe;
13.59/5.47	import qualified Prelude;
13.59/5.47	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
13.59/5.47	
13.59/5.47	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
13.59/5.47	}
13.59/5.47	addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
13.59/5.47	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
13.59/5.47	
13.59/5.47	addToFM0 old new = new;
13.59/5.47	
13.59/5.47	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
13.59/5.47	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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);
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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;
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
13.59/5.47	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
13.59/5.47	
13.59/5.47	emptyFM :: FiniteMap a b;
13.59/5.47	emptyFM = EmptyFM;
13.59/5.47	
13.59/5.47	findMax :: FiniteMap a b  ->  (a,b);
13.59/5.47	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
13.59/5.47	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
13.59/5.47	
13.59/5.47	findMin :: FiniteMap b a  ->  (b,a);
13.59/5.47	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
13.59/5.47	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
13.59/5.47	
13.59/5.47	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
13.59/5.47	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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;
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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;
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
13.59/5.47	
13.59/5.47	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
13.59/5.47	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
13.59/5.47	
13.59/5.47	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
13.59/5.47	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);
13.59/5.47	
13.59/5.47	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vwz;
13.59/5.47	
13.59/5.47	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vxu;
13.59/5.47	
13.59/5.47	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
13.59/5.47	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_r fm_l;
13.59/5.47	
13.59/5.47	mkBranchBalance_ok vxv vxw vxx = True;
13.59/5.47	
13.59/5.47	mkBranchLeft_ok vxv vxw vxx = mkBranchLeft_ok0 vxv vxw vxx vxw vxx vxw;
13.59/5.47	
13.59/5.47	mkBranchLeft_ok0 vxv vxw vxx fm_l key EmptyFM = True;
13.59/5.47	mkBranchLeft_ok0 vxv vxw vxx fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
13.59/5.47	
13.59/5.47	mkBranchLeft_ok0Biggest_left_key vyw = fst (findMax vyw);
13.59/5.47	
13.59/5.47	mkBranchLeft_size vxv vxw vxx = sizeFM vxw;
13.59/5.47	
13.59/5.47	mkBranchResult vxy vxz vyu vyv = Branch vxy vxz (mkBranchUnbox vyu vyv vxy (1 + mkBranchLeft_size vyu vyv vxy + mkBranchRight_size vyu vyv vxy)) vyv vyu;
13.59/5.47	
13.59/5.47	mkBranchRight_ok vxv vxw vxx = mkBranchRight_ok0 vxv vxw vxx vxv vxx vxv;
13.59/5.47	
13.59/5.47	mkBranchRight_ok0 vxv vxw vxx fm_r key EmptyFM = True;
13.59/5.47	mkBranchRight_ok0 vxv vxw vxx fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
13.59/5.47	
13.59/5.47	mkBranchRight_ok0Smallest_right_key vyx = fst (findMin vyx);
13.59/5.47	
13.59/5.47	mkBranchRight_size vxv vxw vxx = sizeFM vxv;
13.59/5.47	
13.59/5.47	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)));
13.59/5.47	mkBranchUnbox vxv vxw vxx x = x;
13.59/5.47	
13.59/5.47	sIZE_RATIO :: Int;
13.59/5.47	sIZE_RATIO = 5;
13.59/5.47	
13.59/5.47	sizeFM :: FiniteMap a b  ->  Int;
13.59/5.47	sizeFM EmptyFM = 0;
13.59/5.47	sizeFM (Branch vz wu size wv ww) = size;
13.59/5.47	
13.59/5.47	unitFM :: a  ->  b  ->  FiniteMap a b;
13.59/5.47	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
13.59/5.47	
13.59/5.47	}
13.59/5.47	module Maybe where {
13.59/5.47	import qualified FiniteMap;
13.59/5.47	import qualified Main;
13.59/5.47	import qualified Prelude;
13.59/5.47	}
13.59/5.47	module Main where {
13.59/5.47	import qualified FiniteMap;
13.59/5.47	import qualified Maybe;
13.59/5.47	import qualified Prelude;
13.59/5.47	}
13.59/5.47	
13.59/5.47	----------------------------------------
13.59/5.47	
13.59/5.47	(11) NumRed (SOUND)
13.59/5.47	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
13.59/5.47	----------------------------------------
13.59/5.47	
13.59/5.47	(12)
13.59/5.47	Obligation:
13.59/5.47	mainModule Main 
13.59/5.47	module FiniteMap where {
13.59/5.47	import qualified Main;
13.59/5.47	import qualified Maybe;
13.59/5.47	import qualified Prelude;
13.59/5.47	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
13.59/5.47	
13.59/5.47	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
13.59/5.47	}
13.59/5.47	addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
13.59/5.47	addToFM fm key elt = addToFM_C addToFM0 fm key elt;
13.59/5.47	
13.59/5.47	addToFM0 old new = new;
13.59/5.47	
13.59/5.47	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
13.59/5.47	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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);
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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;
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
13.59/5.47	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
13.59/5.47	
13.59/5.47	emptyFM :: FiniteMap b a;
13.59/5.47	emptyFM = EmptyFM;
13.59/5.47	
13.59/5.47	findMax :: FiniteMap a b  ->  (a,b);
13.59/5.47	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
13.59/5.47	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
13.59/5.47	
13.59/5.47	findMin :: FiniteMap a b  ->  (a,b);
13.59/5.47	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
13.59/5.47	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
13.59/5.47	
13.59/5.47	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
13.59/5.47	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
13.59/5.47	
13.59/5.47	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)));
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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;
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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;
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R;
13.59/5.47	
13.59/5.47	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
13.59/5.47	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
13.59/5.47	
13.59/5.47	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
13.59/5.47	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);
13.59/5.47	
13.59/5.47	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R;
13.59/5.47	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);
13.59/5.47	
13.59/5.47	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;
13.59/5.47	
13.59/5.47	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);
13.59/5.47	
13.59/5.47	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vwz;
13.59/5.47	
13.59/5.47	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vxu;
13.59/5.47	
13.59/5.47	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
13.59/5.47	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_r fm_l;
13.59/5.47	
13.59/5.47	mkBranchBalance_ok vxv vxw vxx = True;
13.59/5.47	
13.59/5.47	mkBranchLeft_ok vxv vxw vxx = mkBranchLeft_ok0 vxv vxw vxx vxw vxx vxw;
13.59/5.47	
13.59/5.47	mkBranchLeft_ok0 vxv vxw vxx fm_l key EmptyFM = True;
13.59/5.47	mkBranchLeft_ok0 vxv vxw vxx fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
13.59/5.47	
13.59/5.47	mkBranchLeft_ok0Biggest_left_key vyw = fst (findMax vyw);
13.59/5.47	
13.59/5.47	mkBranchLeft_size vxv vxw vxx = sizeFM vxw;
13.59/5.47	
13.59/5.47	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)) vyv vyu;
13.59/5.47	
13.59/5.47	mkBranchRight_ok vxv vxw vxx = mkBranchRight_ok0 vxv vxw vxx vxv vxx vxv;
13.59/5.48	
13.59/5.48	mkBranchRight_ok0 vxv vxw vxx fm_r key EmptyFM = True;
13.59/5.48	mkBranchRight_ok0 vxv vxw vxx fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
13.59/5.48	
13.59/5.48	mkBranchRight_ok0Smallest_right_key vyx = fst (findMin vyx);
13.59/5.48	
13.59/5.48	mkBranchRight_size vxv vxw vxx = sizeFM vxv;
13.59/5.48	
13.59/5.48	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)));
13.59/5.48	mkBranchUnbox vxv vxw vxx x = x;
13.59/5.48	
13.59/5.48	sIZE_RATIO :: Int;
13.59/5.48	sIZE_RATIO = Pos (Succ (Succ (Succ (Succ (Succ Zero)))));
13.59/5.48	
13.59/5.48	sizeFM :: FiniteMap b a  ->  Int;
13.59/5.48	sizeFM EmptyFM = Pos Zero;
13.59/5.48	sizeFM (Branch vz wu size wv ww) = size;
13.59/5.48	
13.59/5.48	unitFM :: b  ->  a  ->  FiniteMap b a;
13.59/5.48	unitFM key elt = Branch key elt (Pos (Succ Zero)) emptyFM emptyFM;
13.59/5.48	
13.59/5.48	}
13.59/5.48	module Maybe where {
13.59/5.48	import qualified FiniteMap;
13.59/5.48	import qualified Main;
13.59/5.48	import qualified Prelude;
13.59/5.48	}
13.59/5.48	module Main where {
13.59/5.48	import qualified FiniteMap;
13.59/5.48	import qualified Maybe;
13.59/5.48	import qualified Prelude;
13.59/5.48	}
13.59/5.48	
13.59/5.48	----------------------------------------
13.59/5.48	
13.59/5.48	(13) Narrow (EQUIVALENT)
13.59/5.48	Haskell To QDPs
13.59/5.48	
13.59/5.48	digraph dp_graph {
13.59/5.48	node [outthreshold=100, inthreshold=100];1[label="FiniteMap.addToFM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
13.59/5.48	3[label="FiniteMap.addToFM vyy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
13.59/5.48	4[label="FiniteMap.addToFM vyy3 vyy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
13.59/5.48	5[label="FiniteMap.addToFM vyy3 vyy4 vyy5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3];
13.59/5.48	6[label="FiniteMap.addToFM_C FiniteMap.addToFM0 vyy3 vyy4 vyy5",fontsize=16,color="burlywood",shape="box"];31[label="vyy3/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];6 -> 31[label="",style="solid", color="burlywood", weight=9];
13.59/5.48	31 -> 7[label="",style="solid", color="burlywood", weight=3];
13.59/5.48	32[label="vyy3/FiniteMap.Branch vyy30 vyy31 vyy32 vyy33 vyy34",fontsize=10,color="white",style="solid",shape="box"];6 -> 32[label="",style="solid", color="burlywood", weight=9];
13.59/5.48	32 -> 8[label="",style="solid", color="burlywood", weight=3];
13.59/5.48	7[label="FiniteMap.addToFM_C FiniteMap.addToFM0 FiniteMap.EmptyFM vyy4 vyy5",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
13.59/5.48	8[label="FiniteMap.addToFM_C FiniteMap.addToFM0 (FiniteMap.Branch vyy30 vyy31 vyy32 vyy33 vyy34) vyy4 vyy5",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
13.59/5.48	9[label="FiniteMap.addToFM_C4 FiniteMap.addToFM0 FiniteMap.EmptyFM vyy4 vyy5",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
13.59/5.48	10[label="FiniteMap.addToFM_C3 FiniteMap.addToFM0 (FiniteMap.Branch vyy30 vyy31 vyy32 vyy33 vyy34) vyy4 vyy5",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
13.59/5.48	11[label="FiniteMap.unitFM vyy4 vyy5",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
13.59/5.48	12[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 vyy30 vyy31 vyy32 vyy33 vyy34 vyy4 vyy5 (vyy4 < vyy30)",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
13.59/5.48	13[label="FiniteMap.Branch vyy4 vyy5 (Pos (Succ Zero)) FiniteMap.emptyFM FiniteMap.emptyFM",fontsize=16,color="green",shape="box"];13 -> 15[label="",style="dashed", color="green", weight=3];
13.59/5.48	13 -> 16[label="",style="dashed", color="green", weight=3];
13.59/5.48	14[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 vyy30 vyy31 vyy32 vyy33 vyy34 vyy4 vyy5 (compare vyy4 vyy30 == LT)",fontsize=16,color="burlywood",shape="box"];33[label="vyy4/()",fontsize=10,color="white",style="solid",shape="box"];14 -> 33[label="",style="solid", color="burlywood", weight=9];
13.59/5.48	33 -> 17[label="",style="solid", color="burlywood", weight=3];
13.59/5.48	15[label="FiniteMap.emptyFM",fontsize=16,color="black",shape="triangle"];15 -> 18[label="",style="solid", color="black", weight=3];
13.59/5.48	16 -> 15[label="",style="dashed", color="red", weight=0];
13.59/5.48	16[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];17[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 vyy30 vyy31 vyy32 vyy33 vyy34 () vyy5 (compare () vyy30 == LT)",fontsize=16,color="burlywood",shape="box"];34[label="vyy30/()",fontsize=10,color="white",style="solid",shape="box"];17 -> 34[label="",style="solid", color="burlywood", weight=9];
13.59/5.48	34 -> 19[label="",style="solid", color="burlywood", weight=3];
13.59/5.48	18[label="FiniteMap.EmptyFM",fontsize=16,color="green",shape="box"];19[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 () vyy31 vyy32 vyy33 vyy34 () vyy5 (compare () () == LT)",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3];
13.59/5.48	20[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 () vyy31 vyy32 vyy33 vyy34 () vyy5 (EQ == LT)",fontsize=16,color="black",shape="box"];20 -> 21[label="",style="solid", color="black", weight=3];
13.59/5.48	21[label="FiniteMap.addToFM_C2 FiniteMap.addToFM0 () vyy31 vyy32 vyy33 vyy34 () vyy5 False",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3];
13.59/5.48	22[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 () vyy31 vyy32 vyy33 vyy34 () vyy5 (() > ())",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3];
13.59/5.48	23[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 () vyy31 vyy32 vyy33 vyy34 () vyy5 (compare () () == GT)",fontsize=16,color="black",shape="box"];23 -> 24[label="",style="solid", color="black", weight=3];
13.59/5.48	24[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 () vyy31 vyy32 vyy33 vyy34 () vyy5 (EQ == GT)",fontsize=16,color="black",shape="box"];24 -> 25[label="",style="solid", color="black", weight=3];
13.59/5.48	25[label="FiniteMap.addToFM_C1 FiniteMap.addToFM0 () vyy31 vyy32 vyy33 vyy34 () vyy5 False",fontsize=16,color="black",shape="box"];25 -> 26[label="",style="solid", color="black", weight=3];
13.59/5.48	26[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 () vyy31 vyy32 vyy33 vyy34 () vyy5 otherwise",fontsize=16,color="black",shape="box"];26 -> 27[label="",style="solid", color="black", weight=3];
13.59/5.48	27[label="FiniteMap.addToFM_C0 FiniteMap.addToFM0 () vyy31 vyy32 vyy33 vyy34 () vyy5 True",fontsize=16,color="black",shape="box"];27 -> 28[label="",style="solid", color="black", weight=3];
13.59/5.48	28[label="FiniteMap.Branch () (FiniteMap.addToFM0 vyy31 vyy5) vyy32 vyy33 vyy34",fontsize=16,color="green",shape="box"];28 -> 29[label="",style="dashed", color="green", weight=3];
13.59/5.48	29[label="FiniteMap.addToFM0 vyy31 vyy5",fontsize=16,color="black",shape="box"];29 -> 30[label="",style="solid", color="black", weight=3];
13.59/5.48	30[label="vyy5",fontsize=16,color="green",shape="box"];}
13.59/5.48	
13.59/5.48	----------------------------------------
13.59/5.48	
13.59/5.48	(14)
13.59/5.48	YES
13.60/8.10	EOF