108.38/78.67	MAYBE
111.00/79.38	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
111.00/79.38	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
111.00/79.38	
111.00/79.38	
111.00/79.38	H-Termination with start terms of the given HASKELL could not be shown:
111.00/79.38	
111.00/79.38	(0) HASKELL
111.00/79.38	(1) CR [EQUIVALENT, 0 ms]
111.00/79.38	(2) HASKELL
111.00/79.38	(3) BR [EQUIVALENT, 0 ms]
111.00/79.38	(4) HASKELL
111.00/79.38	(5) COR [EQUIVALENT, 20 ms]
111.00/79.38	(6) HASKELL
111.00/79.38	(7) LetRed [EQUIVALENT, 0 ms]
111.00/79.38	(8) HASKELL
111.00/79.38	(9) NumRed [SOUND, 0 ms]
111.00/79.38	(10) HASKELL
111.00/79.38	
111.00/79.38	
111.00/79.38	----------------------------------------
111.00/79.38	
111.00/79.38	(0)
111.00/79.38	Obligation:
111.00/79.38	mainModule Main 
111.00/79.38	module FiniteMap where {
111.00/79.38	import qualified Main;
111.00/79.38	import qualified Maybe;
111.00/79.38	import qualified Prelude;
111.00/79.38	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
111.00/79.38	
111.00/79.38	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
111.00/79.38	}
111.00/79.38	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
111.00/79.38	addToFM_C combiner EmptyFM key elt = unitFM key elt;
111.00/79.38	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt  | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
111.00/79.38	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
111.00/79.38	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
111.00/79.38	
111.00/79.38	emptyFM :: FiniteMap a b;
111.00/79.38	emptyFM = EmptyFM;
111.00/79.38	
111.00/79.38	findMax :: FiniteMap b a  ->  (b,a);
111.00/79.38	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
111.00/79.38	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
111.00/79.38	
111.00/79.38	findMin :: FiniteMap a b  ->  (a,b);
111.00/79.38	findMin (Branch key elt _ EmptyFM _) = (key,elt);
111.00/79.38	findMin (Branch key elt _ fm_l _) = findMin fm_l;
111.00/79.38	
111.00/79.38	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
111.00/79.38	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
111.00/79.38	 | size_r > sIZE_RATIO * size_l = case fm_R of { 
111.00/79.38	Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R
111.00/79.38	 | otherwise -> double_L fm_L fm_R; 
111.00/79.38	 } 
111.00/79.38	 | size_l > sIZE_RATIO * size_r = case fm_L of { 
111.00/79.38	Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R
111.00/79.38	 | otherwise -> double_R fm_L fm_R; 
111.00/79.38	 } 
111.00/79.38	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
111.00/79.38	double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
111.00/79.38	double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
111.00/79.38	single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
111.00/79.38	single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
111.00/79.38	size_l = sizeFM fm_L;
111.00/79.38	size_r = sizeFM fm_R;
111.00/79.38	 };
111.00/79.38	
111.00/79.38	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
111.00/79.38	mkBranch which key elt fm_l fm_r = let { 
111.00/79.38	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
111.00/79.38	} in result where { 
111.00/79.38	balance_ok = True;
111.00/79.38	left_ok = case fm_l of { 
111.00/79.38	EmptyFM-> True; 
111.00/79.38	Branch left_key _ _ _ _-> let { 
111.00/79.38	biggest_left_key = fst (findMax fm_l);
111.00/79.38	} in biggest_left_key < key; 
111.00/79.38	 } ;
111.00/79.38	left_size = sizeFM fm_l;
111.00/79.38	right_ok = case fm_r of { 
111.00/79.38	EmptyFM-> True; 
111.00/79.38	Branch right_key _ _ _ _-> let { 
111.00/79.38	smallest_right_key = fst (findMin fm_r);
111.00/79.38	} in key < smallest_right_key; 
111.00/79.38	 } ;
111.00/79.38	right_size = sizeFM fm_r;
111.00/79.38	unbox :: Int  ->  Int;
111.00/79.38	unbox x = x;
111.00/79.38	 };
111.00/79.38	
111.00/79.38	sIZE_RATIO :: Int;
111.00/79.38	sIZE_RATIO = 5;
111.00/79.38	
111.00/79.38	sizeFM :: FiniteMap b a  ->  Int;
111.00/79.38	sizeFM EmptyFM = 0;
111.00/79.38	sizeFM (Branch _ _ size _ _) = size;
111.00/79.38	
111.00/79.38	unitFM :: a  ->  b  ->  FiniteMap a b;
111.00/79.38	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
111.00/79.38	
111.00/79.38	}
111.00/79.38	module Maybe where {
111.00/79.38	import qualified FiniteMap;
111.00/79.38	import qualified Main;
111.00/79.38	import qualified Prelude;
111.00/79.38	}
111.00/79.38	module Main where {
111.00/79.38	import qualified FiniteMap;
111.00/79.38	import qualified Maybe;
111.00/79.38	import qualified Prelude;
111.00/79.38	}
111.00/79.38	
111.00/79.38	----------------------------------------
111.00/79.38	
111.00/79.38	(1) CR (EQUIVALENT)
111.00/79.38	Case Reductions:
111.00/79.38	The following Case expression
111.00/79.38	"case fm_r of {
111.00/79.38	EmptyFM  -> True;
111.00/79.38	Branch right_key _ _ _ _  -> let {
111.00/79.38	smallest_right_key  = fst (findMin fm_r);
111.00/79.38	} in key < smallest_right_key}
111.00/79.38	"
111.00/79.38	is transformed to
111.00/79.38	"right_ok0 fm_r key EmptyFM = True;
111.00/79.38	right_ok0 fm_r key (Branch right_key _ _ _ _) = let {
111.00/79.38	smallest_right_key  = fst (findMin fm_r);
111.00/79.38	} in key < smallest_right_key;
111.00/79.38	"
111.00/79.38	The following Case expression
111.00/79.38	"case fm_l of {
111.00/79.38	EmptyFM  -> True;
111.00/79.38	Branch left_key _ _ _ _  -> let {
111.00/79.38	biggest_left_key  = fst (findMax fm_l);
111.00/79.38	} in biggest_left_key < key}
111.00/79.38	"
111.00/79.38	is transformed to
111.00/79.38	"left_ok0 fm_l key EmptyFM = True;
111.00/79.38	left_ok0 fm_l key (Branch left_key _ _ _ _) = let {
111.00/79.38	biggest_left_key  = fst (findMax fm_l);
111.00/79.38	} in biggest_left_key < key;
111.00/79.38	"
111.00/79.38	The following Case expression
111.00/79.38	"case fm_R of {
111.00/79.38	Branch _ _ _ fm_rl fm_rr |sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R}
111.00/79.38	"
111.00/79.38	is transformed to
111.00/79.38	"mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R;
111.00/79.38	"
111.00/79.38	The following Case expression
111.00/79.38	"case fm_L of {
111.00/79.38	Branch _ _ _ fm_ll fm_lr |sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R}
111.00/79.38	"
111.00/79.38	is transformed to
111.00/79.38	"mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R;
111.00/79.38	"
111.00/79.38	
111.00/79.38	----------------------------------------
111.00/79.38	
111.00/79.38	(2)
111.00/79.38	Obligation:
111.00/79.38	mainModule Main 
111.00/79.38	module FiniteMap where {
111.00/79.38	import qualified Main;
111.00/79.38	import qualified Maybe;
111.00/79.38	import qualified Prelude;
111.00/79.38	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
111.00/79.38	
111.00/79.38	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
111.00/79.38	}
111.00/79.38	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
111.00/79.38	addToFM_C combiner EmptyFM key elt = unitFM key elt;
111.00/79.38	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt  | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
111.00/79.38	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
111.00/79.38	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
111.00/79.38	
111.00/79.38	emptyFM :: FiniteMap a b;
111.00/79.38	emptyFM = EmptyFM;
111.00/79.38	
111.00/79.38	findMax :: FiniteMap a b  ->  (a,b);
111.00/79.38	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
111.00/79.38	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
111.00/79.38	
111.00/79.38	findMin :: FiniteMap a b  ->  (a,b);
111.00/79.38	findMin (Branch key elt _ EmptyFM _) = (key,elt);
111.00/79.38	findMin (Branch key elt _ fm_l _) = findMin fm_l;
111.00/79.38	
111.00/79.38	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
111.00/79.38	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
111.00/79.38	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
111.00/79.38	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
111.00/79.38	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
111.00/79.38	double_L fm_l (Branch key_r elt_r _ (Branch key_rl elt_rl _ fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
111.00/79.38	double_R (Branch key_l elt_l _ fm_ll (Branch key_lr elt_lr _ fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
111.00/79.38	mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr)  | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R
111.00/79.38	 | otherwise = double_L fm_L fm_R;
111.00/79.38	mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr)  | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R
111.00/79.38	 | otherwise = double_R fm_L fm_R;
111.00/79.38	single_L fm_l (Branch key_r elt_r _ fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
111.00/79.38	single_R (Branch key_l elt_l _ fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
111.00/79.38	size_l = sizeFM fm_L;
111.00/79.38	size_r = sizeFM fm_R;
111.00/79.38	 };
111.00/79.38	
111.00/79.38	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
111.00/79.38	mkBranch which key elt fm_l fm_r = let { 
111.00/79.38	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
111.00/79.38	} in result where { 
111.00/79.38	balance_ok = True;
111.00/79.38	left_ok = left_ok0 fm_l key fm_l;
111.00/79.38	left_ok0 fm_l key EmptyFM = True;
111.00/79.38	left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 
111.00/79.38	biggest_left_key = fst (findMax fm_l);
111.00/79.38	} in biggest_left_key < key;
111.00/79.38	left_size = sizeFM fm_l;
111.00/79.38	right_ok = right_ok0 fm_r key fm_r;
111.00/79.38	right_ok0 fm_r key EmptyFM = True;
111.00/79.38	right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 
111.00/79.38	smallest_right_key = fst (findMin fm_r);
111.00/79.38	} in key < smallest_right_key;
111.16/79.42	right_size = sizeFM fm_r;
111.16/79.42	unbox :: Int  ->  Int;
111.16/79.42	unbox x = x;
111.16/79.42	 };
111.16/79.42	
111.16/79.42	sIZE_RATIO :: Int;
111.16/79.42	sIZE_RATIO = 5;
111.16/79.42	
111.16/79.42	sizeFM :: FiniteMap b a  ->  Int;
111.16/79.42	sizeFM EmptyFM = 0;
111.16/79.42	sizeFM (Branch _ _ size _ _) = size;
111.16/79.42	
111.16/79.42	unitFM :: b  ->  a  ->  FiniteMap b a;
111.16/79.42	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
111.16/79.42	
111.16/79.42	}
111.16/79.42	module Maybe where {
111.16/79.42	import qualified FiniteMap;
111.16/79.42	import qualified Main;
111.16/79.42	import qualified Prelude;
111.16/79.42	}
111.16/79.42	module Main where {
111.16/79.42	import qualified FiniteMap;
111.16/79.42	import qualified Maybe;
111.16/79.42	import qualified Prelude;
111.16/79.42	}
111.16/79.42	
111.16/79.42	----------------------------------------
111.16/79.42	
111.16/79.42	(3) BR (EQUIVALENT)
111.16/79.42	Replaced joker patterns by fresh variables and removed binding patterns.
111.16/79.42	----------------------------------------
111.16/79.42	
111.16/79.42	(4)
111.16/79.42	Obligation:
111.16/79.42	mainModule Main 
111.16/79.42	module FiniteMap where {
111.16/79.42	import qualified Main;
111.16/79.42	import qualified Maybe;
111.16/79.42	import qualified Prelude;
111.16/79.42	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
111.16/79.42	
111.16/79.42	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
111.16/79.42	}
111.16/79.42	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
111.16/79.42	addToFM_C combiner EmptyFM key elt = unitFM key elt;
111.16/79.42	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt  | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
111.16/79.42	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
111.16/79.42	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
111.16/79.42	
111.16/79.42	emptyFM :: FiniteMap a b;
111.16/79.42	emptyFM = EmptyFM;
111.16/79.42	
111.16/79.42	findMax :: FiniteMap b a  ->  (b,a);
111.16/79.42	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
111.16/79.42	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
111.16/79.42	
111.16/79.42	findMin :: FiniteMap a b  ->  (a,b);
111.16/79.42	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
111.16/79.42	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
111.16/79.42	
111.16/79.42	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
111.16/79.42	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
111.16/79.42	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
111.16/79.42	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
111.16/79.42	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
111.16/79.42	double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
111.16/79.42	double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
111.16/79.42	mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr)  | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R
111.16/79.42	 | otherwise = double_L fm_L fm_R;
111.16/79.42	mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr)  | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R
111.16/79.42	 | otherwise = double_R fm_L fm_R;
111.16/79.42	single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
111.16/79.42	single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
111.16/79.42	size_l = sizeFM fm_L;
111.16/79.42	size_r = sizeFM fm_R;
111.16/79.42	 };
111.16/79.42	
111.16/79.42	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
111.16/79.42	mkBranch which key elt fm_l fm_r = let { 
111.16/79.42	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
111.16/79.42	} in result where { 
111.16/79.42	balance_ok = True;
111.16/79.42	left_ok = left_ok0 fm_l key fm_l;
111.16/79.42	left_ok0 fm_l key EmptyFM = True;
111.16/79.42	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
111.16/79.42	biggest_left_key = fst (findMax fm_l);
111.16/79.42	} in biggest_left_key < key;
111.16/79.42	left_size = sizeFM fm_l;
111.16/79.42	right_ok = right_ok0 fm_r key fm_r;
111.16/79.42	right_ok0 fm_r key EmptyFM = True;
111.16/79.42	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
111.16/79.42	smallest_right_key = fst (findMin fm_r);
111.16/79.42	} in key < smallest_right_key;
111.16/79.42	right_size = sizeFM fm_r;
111.16/79.42	unbox :: Int  ->  Int;
111.16/79.42	unbox x = x;
111.16/79.42	 };
111.16/79.42	
111.16/79.42	sIZE_RATIO :: Int;
111.16/79.42	sIZE_RATIO = 5;
111.16/79.42	
111.16/79.42	sizeFM :: FiniteMap a b  ->  Int;
111.16/79.42	sizeFM EmptyFM = 0;
111.16/79.42	sizeFM (Branch vz wu size wv ww) = size;
111.16/79.42	
111.16/79.42	unitFM :: b  ->  a  ->  FiniteMap b a;
111.16/79.42	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
111.16/79.42	
111.16/79.42	}
111.16/79.42	module Maybe where {
111.16/79.42	import qualified FiniteMap;
111.16/79.42	import qualified Main;
111.16/79.42	import qualified Prelude;
111.16/79.42	}
111.16/79.42	module Main where {
111.16/79.42	import qualified FiniteMap;
111.16/79.42	import qualified Maybe;
111.16/79.42	import qualified Prelude;
111.16/79.42	}
111.16/79.42	
111.16/79.42	----------------------------------------
111.16/79.42	
111.16/79.42	(5) COR (EQUIVALENT)
111.16/79.42	Cond Reductions:
111.16/79.42	The following Function with conditions
111.16/79.42	"compare x y|x == yEQ|x <= yLT|otherwiseGT;
111.16/79.42	"
111.16/79.42	is transformed to
111.16/79.42	"compare x y = compare3 x y;
111.16/79.42	"
111.16/79.42	"compare0 x y True = GT;
111.16/79.42	"
111.16/79.42	"compare1 x y True = LT;
111.16/79.42	compare1 x y False = compare0 x y otherwise;
111.16/79.42	"
111.16/79.42	"compare2 x y True = EQ;
111.16/79.42	compare2 x y False = compare1 x y (x <= y);
111.16/79.42	"
111.16/79.42	"compare3 x y = compare2 x y (x == y);
111.16/79.42	"
111.16/79.42	The following Function with conditions
111.16/79.42	"undefined |Falseundefined;
111.16/79.42	"
111.16/79.42	is transformed to
111.16/79.42	"undefined  = undefined1;
111.16/79.42	"
111.16/79.42	"undefined0 True = undefined;
111.16/79.42	"
111.16/79.42	"undefined1  = undefined0 False;
111.16/79.42	"
111.16/79.42	The following Function with conditions
111.16/79.42	"addToFM_C combiner EmptyFM key elt = unitFM key elt;
111.16/79.42	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt|new_key < keymkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r|new_key > keymkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)|otherwiseBranch new_key (combiner elt new_elt) size fm_l fm_r;
111.16/79.42	"
111.16/79.42	is transformed to
111.16/79.42	"addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
111.16/79.42	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt;
111.16/79.42	"
111.16/79.42	"addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r;
111.16/79.42	"
111.16/79.42	"addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt);
111.16/79.42	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise;
111.16/79.42	"
111.16/79.42	"addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r;
111.16/79.42	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key);
111.16/79.42	"
111.16/79.42	"addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key);
111.16/79.42	"
111.16/79.42	"addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
111.16/79.42	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
111.16/79.42	"
111.16/79.42	The following Function with conditions
111.16/79.42	"mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R;
111.16/79.42	"
111.16/79.42	is transformed to
111.16/79.42	"mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
111.16/79.42	"
111.16/79.42	"mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
111.16/79.42	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
111.16/79.42	"
111.16/79.42	"mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
111.16/79.42	"
111.16/79.42	"mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
111.16/79.42	"
111.16/79.42	The following Function with conditions
111.16/79.42	"mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R;
111.16/79.42	"
111.16/79.42	is transformed to
111.16/79.42	"mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
111.16/79.42	"
111.16/79.42	"mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
111.16/79.42	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
111.16/79.42	"
111.16/79.42	"mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
111.16/79.42	"
111.16/79.42	"mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
111.16/79.42	"
111.16/79.42	The following Function with conditions
111.16/79.42	"mkBalBranch key elt fm_L fm_R|size_l + size_r < 2mkBranch 1 key elt fm_L fm_R|size_r > sIZE_RATIO * size_lmkBalBranch0 fm_L fm_R fm_R|size_l > sIZE_RATIO * size_rmkBalBranch1 fm_L fm_R fm_L|otherwisemkBranch 2 key elt fm_L fm_R where {
111.16/79.42	double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
111.16/79.42	;
111.16/79.42	double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
111.16/79.42	;
111.16/79.42	mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R;
111.16/79.42	;
111.16/79.42	mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R;
111.16/79.42	;
111.16/79.42	single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
111.16/79.42	;
111.16/79.42	single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
111.16/79.42	;
111.16/79.42	size_l  = sizeFM fm_L;
111.16/79.42	;
111.16/79.42	size_r  = sizeFM fm_R;
111.16/79.42	} 
111.16/79.42	;
111.16/79.42	"
111.16/79.42	is transformed to
111.16/79.42	"mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
111.16/79.42	"
111.16/79.42	"mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
111.16/79.42	double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
111.16/79.42	;
111.16/79.42	double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
111.16/79.42	;
111.16/79.42	mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
111.16/79.42	;
111.16/79.42	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
111.16/79.42	;
111.16/79.42	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
111.16/79.42	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
111.16/79.42	;
111.16/79.42	mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
111.16/79.42	;
111.16/79.42	mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
111.16/79.42	;
111.16/79.42	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
111.16/79.42	;
111.16/79.42	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
111.16/79.42	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
111.16/79.42	;
111.16/79.42	mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
111.16/79.42	;
111.16/79.42	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
111.16/79.42	;
111.16/79.42	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
111.16/79.42	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
111.16/79.42	;
111.16/79.42	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
111.16/79.42	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
111.16/79.42	;
111.16/79.42	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
111.16/79.42	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
111.16/79.42	;
111.16/79.42	single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
111.16/79.42	;
111.16/79.42	single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
111.16/79.42	;
111.16/79.42	size_l  = sizeFM fm_L;
111.16/79.42	;
111.16/79.42	size_r  = sizeFM fm_R;
111.16/79.42	} 
111.16/79.42	;
111.16/79.42	"
111.16/79.42	
111.16/79.42	----------------------------------------
111.16/79.42	
111.16/79.42	(6)
111.16/79.42	Obligation:
111.16/79.42	mainModule Main 
111.16/79.42	module FiniteMap where {
111.16/79.42	import qualified Main;
111.16/79.42	import qualified Maybe;
111.16/79.42	import qualified Prelude;
111.16/79.42	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
111.16/79.42	
111.16/79.42	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
111.16/79.42	}
111.16/79.42	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
111.16/79.42	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
111.16/79.42	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt;
111.16/79.42	
111.16/79.42	addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r;
111.16/79.42	
111.16/79.42	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt);
111.16/79.43	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise;
111.16/79.43	
111.16/79.43	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r;
111.16/79.43	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key);
111.16/79.43	
111.16/79.43	addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key);
111.16/79.43	
111.16/79.43	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
111.16/79.43	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
111.16/79.43	
111.16/79.43	emptyFM :: FiniteMap b a;
111.16/79.43	emptyFM = EmptyFM;
111.16/79.43	
111.16/79.43	findMax :: FiniteMap b a  ->  (b,a);
111.16/79.43	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
111.16/79.43	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
111.16/79.43	
111.16/79.43	findMin :: FiniteMap b a  ->  (b,a);
111.16/79.43	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
111.16/79.43	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
111.16/79.43	
111.16/79.43	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
111.16/79.43	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
111.16/79.43	
111.16/79.43	mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 
111.16/79.43	double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
111.16/79.43	double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
111.16/79.43	mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
111.16/79.43	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
111.16/79.43	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
111.16/79.43	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
111.16/79.43	mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
111.16/79.43	mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
111.16/79.43	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
111.16/79.43	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
111.16/79.43	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
111.16/79.43	mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
111.16/79.43	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
111.16/79.43	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
111.16/79.43	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
111.16/79.43	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
111.16/79.43	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
111.16/79.43	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
111.16/79.43	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
111.16/79.43	single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
111.16/79.43	single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
111.16/79.43	size_l = sizeFM fm_L;
111.16/79.43	size_r = sizeFM fm_R;
111.16/79.43	 };
111.16/79.43	
111.16/79.43	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
111.16/79.43	mkBranch which key elt fm_l fm_r = let { 
111.16/79.43	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
111.16/79.43	} in result where { 
111.16/79.43	balance_ok = True;
111.16/79.43	left_ok = left_ok0 fm_l key fm_l;
111.16/79.43	left_ok0 fm_l key EmptyFM = True;
111.16/79.43	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
111.16/79.43	biggest_left_key = fst (findMax fm_l);
111.16/79.43	} in biggest_left_key < key;
111.16/79.43	left_size = sizeFM fm_l;
111.16/79.43	right_ok = right_ok0 fm_r key fm_r;
111.16/79.43	right_ok0 fm_r key EmptyFM = True;
111.16/79.43	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
111.20/79.48	smallest_right_key = fst (findMin fm_r);
111.20/79.48	} in key < smallest_right_key;
111.20/79.48	right_size = sizeFM fm_r;
111.20/79.48	unbox :: Int  ->  Int;
111.20/79.48	unbox x = x;
111.20/79.48	 };
111.20/79.48	
111.20/79.48	sIZE_RATIO :: Int;
111.20/79.48	sIZE_RATIO = 5;
111.20/79.48	
111.20/79.48	sizeFM :: FiniteMap a b  ->  Int;
111.20/79.48	sizeFM EmptyFM = 0;
111.20/79.48	sizeFM (Branch vz wu size wv ww) = size;
111.20/79.48	
111.20/79.48	unitFM :: a  ->  b  ->  FiniteMap a b;
111.20/79.48	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
111.20/79.48	
111.20/79.48	}
111.20/79.48	module Maybe where {
111.20/79.48	import qualified FiniteMap;
111.20/79.48	import qualified Main;
111.20/79.48	import qualified Prelude;
111.20/79.48	}
111.20/79.48	module Main where {
111.20/79.48	import qualified FiniteMap;
111.20/79.48	import qualified Maybe;
111.20/79.48	import qualified Prelude;
111.20/79.48	}
111.20/79.48	
111.20/79.48	----------------------------------------
111.20/79.48	
111.20/79.48	(7) LetRed (EQUIVALENT)
111.20/79.48	Let/Where Reductions:
111.20/79.48	The bindings of the following Let/Where expression
111.20/79.48	"mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
111.20/79.48	double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
111.20/79.48	;
111.20/79.48	double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
111.20/79.48	;
111.20/79.48	mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
111.20/79.48	;
111.20/79.48	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
111.20/79.48	;
111.20/79.48	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
111.20/79.48	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
111.20/79.48	;
111.20/79.48	mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
111.20/79.48	;
111.20/79.48	mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
111.20/79.48	;
111.20/79.48	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
111.20/79.48	;
111.20/79.48	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
111.20/79.48	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
111.20/79.48	;
111.20/79.48	mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
111.20/79.48	;
111.20/79.48	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
111.20/79.48	;
111.20/79.48	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
111.20/79.48	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
111.20/79.48	;
111.20/79.48	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
111.20/79.48	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
111.20/79.48	;
111.20/79.48	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
111.20/79.48	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
111.20/79.48	;
111.20/79.48	single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
111.20/79.48	;
111.20/79.48	single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
111.20/79.48	;
111.20/79.48	size_l  = sizeFM fm_L;
111.20/79.48	;
111.20/79.48	size_r  = sizeFM fm_R;
111.20/79.48	} 
111.20/79.48	"
111.20/79.48	are unpacked to the following functions on top level
111.20/79.48	"mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vwx;
111.20/79.48	"
111.20/79.48	"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);
111.20/79.48	"
111.20/79.48	"mkBalBranch6Single_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 vwy vwz fm_l fm_rl) fm_rr;
111.20/79.48	"
111.20/79.48	"mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vxu;
111.20/79.48	"
111.20/79.48	"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;
111.20/79.48	"
111.20/79.48	"mkBalBranch6Single_R vwx vwy vwz vxu (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 vwy vwz fm_lr fm_r);
111.20/79.48	"
111.20/79.48	"mkBalBranch6Double_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 vwy vwz fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
111.20/79.48	"
111.20/79.48	"mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
111.20/79.48	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);
111.20/79.48	"
111.20/79.48	"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;
111.20/79.48	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;
111.20/79.48	"
111.20/79.48	"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;
111.20/79.48	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;
111.20/79.48	"
111.20/79.48	"mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
111.20/79.48	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);
111.20/79.48	"
111.20/79.48	"mkBalBranch6Double_R vwx vwy vwz vxu (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 vwy vwz fm_lrr fm_r);
111.20/79.48	"
111.20/79.48	"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;
111.20/79.48	"
111.20/79.48	"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);
111.20/79.48	"
111.20/79.48	"mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
111.20/79.48	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
111.20/79.48	"
111.20/79.48	"mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
111.20/79.48	"
111.20/79.48	"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);
111.20/79.48	"
111.20/79.48	"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);
111.20/79.48	"
111.20/79.48	The bindings of the following Let/Where expression
111.20/79.48	"let {
111.20/79.48	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
111.20/79.48	} in result where {
111.20/79.48	balance_ok  = True;
111.20/79.48	;
111.20/79.48	left_ok  = left_ok0 fm_l key fm_l;
111.20/79.48	;
111.20/79.48	left_ok0 fm_l key EmptyFM = True;
111.20/79.48	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let {
111.20/79.48	biggest_left_key  = fst (findMax fm_l);
111.20/79.48	} in biggest_left_key < key;
111.20/79.48	;
111.20/79.48	left_size  = sizeFM fm_l;
111.20/79.48	;
111.20/79.48	right_ok  = right_ok0 fm_r key fm_r;
111.20/79.48	;
111.20/79.48	right_ok0 fm_r key EmptyFM = True;
111.20/79.48	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let {
111.20/79.48	smallest_right_key  = fst (findMin fm_r);
111.20/79.48	} in key < smallest_right_key;
111.20/79.48	;
111.20/79.48	right_size  = sizeFM fm_r;
111.20/79.48	;
111.20/79.48	unbox x = x;
111.20/79.48	} 
111.20/79.48	"
111.20/79.48	are unpacked to the following functions on top level
111.20/79.48	"mkBranchUnbox vxv vxw vxx x = x;
111.20/79.48	"
111.20/79.48	"mkBranchBalance_ok vxv vxw vxx = True;
111.20/79.48	"
111.20/79.48	"mkBranchLeft_ok vxv vxw vxx = mkBranchLeft_ok0 vxv vxw vxx vxv vxw vxv;
111.20/79.48	"
111.20/79.48	"mkBranchRight_size vxv vxw vxx = sizeFM vxx;
111.20/79.48	"
111.20/79.48	"mkBranchRight_ok vxv vxw vxx = mkBranchRight_ok0 vxv vxw vxx vxx vxw vxx;
111.20/79.48	"
111.20/79.48	"mkBranchLeft_size vxv vxw vxx = sizeFM vxv;
111.20/79.48	"
111.20/79.48	"mkBranchRight_ok0 vxv vxw vxx fm_r key EmptyFM = True;
111.20/79.48	mkBranchRight_ok0 vxv vxw vxx fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
111.20/79.48	"
111.20/79.48	"mkBranchLeft_ok0 vxv vxw vxx fm_l key EmptyFM = True;
111.20/79.48	mkBranchLeft_ok0 vxv vxw vxx fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
111.20/79.48	"
111.20/79.48	The bindings of the following Let/Where expression
111.20/79.48	"let {
111.20/79.48	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
111.20/79.48	} in result"
111.20/79.48	are unpacked to the following functions on top level
111.20/79.48	"mkBranchResult vxy vxz vyu vyv = Branch vxy vxz (mkBranchUnbox vyu vxy vyv (1 + mkBranchLeft_size vyu vxy vyv + mkBranchRight_size vyu vxy vyv)) vyu vyv;
111.20/79.48	"
111.20/79.48	The bindings of the following Let/Where expression
111.20/79.48	"let {
111.20/79.48	smallest_right_key  = fst (findMin fm_r);
111.20/79.48	} in key < smallest_right_key"
111.20/79.48	are unpacked to the following functions on top level
111.20/79.48	"mkBranchRight_ok0Smallest_right_key vyw = fst (findMin vyw);
111.20/79.48	"
111.20/79.48	The bindings of the following Let/Where expression
111.20/79.48	"let {
111.20/79.48	biggest_left_key  = fst (findMax fm_l);
111.20/79.48	} in biggest_left_key < key"
111.20/79.48	are unpacked to the following functions on top level
111.20/79.48	"mkBranchLeft_ok0Biggest_left_key vyx = fst (findMax vyx);
111.20/79.48	"
111.20/79.48	
111.20/79.48	----------------------------------------
111.20/79.48	
111.20/79.48	(8)
111.20/79.48	Obligation:
111.20/79.48	mainModule Main 
111.20/79.48	module FiniteMap where {
111.20/79.48	import qualified Main;
111.20/79.48	import qualified Maybe;
111.20/79.48	import qualified Prelude;
111.20/79.48	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
111.20/79.48	
111.20/79.48	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
111.20/79.48	}
111.20/79.48	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
111.20/79.48	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
111.20/79.48	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt;
111.20/79.48	
111.20/79.48	addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r;
111.20/79.48	
111.20/79.48	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt);
111.20/79.48	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise;
111.20/79.48	
111.20/79.48	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r;
111.20/79.48	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key);
111.20/79.48	
111.20/79.48	addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key);
111.20/79.48	
111.20/79.48	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
111.20/79.48	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
111.20/79.48	
111.20/79.48	emptyFM :: FiniteMap a b;
111.20/79.48	emptyFM = EmptyFM;
111.20/79.48	
111.20/79.48	findMax :: FiniteMap a b  ->  (a,b);
111.20/79.48	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
111.20/79.48	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
111.20/79.48	
111.20/79.48	findMin :: FiniteMap b a  ->  (b,a);
111.20/79.48	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
111.20/79.48	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
111.20/79.48	
111.20/79.48	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
111.20/79.48	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
111.20/79.48	
111.20/79.48	mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 fm_R key elt fm_L key elt fm_L fm_R (mkBalBranch6Size_l fm_R key elt fm_L + mkBalBranch6Size_r fm_R key elt fm_L < 2);
111.20/79.48	
111.20/79.48	mkBalBranch6Double_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 vwy vwz fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
111.20/79.48	
111.20/79.48	mkBalBranch6Double_R vwx vwy vwz vxu (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 vwy vwz fm_lrr fm_r);
111.20/79.48	
111.20/79.48	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);
111.20/79.48	
111.20/79.48	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;
111.20/79.48	
111.20/79.48	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;
111.20/79.48	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;
111.20/79.48	
111.20/79.48	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);
111.20/79.48	
111.20/79.48	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);
111.20/79.48	
111.20/79.48	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;
111.20/79.48	
111.20/79.48	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;
111.20/79.48	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;
111.20/79.48	
111.20/79.48	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);
111.20/79.48	
111.20/79.48	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
111.20/79.48	
111.20/79.48	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
111.20/79.48	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
111.20/79.48	
111.20/79.48	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
111.20/79.48	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);
111.20/79.48	
111.20/79.48	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
111.20/79.48	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);
111.20/79.48	
111.20/79.48	mkBalBranch6Single_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 vwy vwz fm_l fm_rl) fm_rr;
111.20/79.48	
111.20/79.48	mkBalBranch6Single_R vwx vwy vwz vxu (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 vwy vwz fm_lr fm_r);
111.20/79.48	
111.20/79.48	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vxu;
111.20/79.48	
111.20/79.48	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vwx;
111.20/79.48	
111.20/79.48	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
111.20/79.48	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r;
111.20/79.48	
111.20/79.48	mkBranchBalance_ok vxv vxw vxx = True;
111.20/79.48	
111.20/79.48	mkBranchLeft_ok vxv vxw vxx = mkBranchLeft_ok0 vxv vxw vxx vxv vxw vxv;
111.20/79.48	
111.20/79.48	mkBranchLeft_ok0 vxv vxw vxx fm_l key EmptyFM = True;
111.20/79.48	mkBranchLeft_ok0 vxv vxw vxx fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
111.20/79.48	
111.20/79.48	mkBranchLeft_ok0Biggest_left_key vyx = fst (findMax vyx);
111.20/79.48	
111.20/79.48	mkBranchLeft_size vxv vxw vxx = sizeFM vxv;
111.20/79.48	
111.20/79.48	mkBranchResult vxy vxz vyu vyv = Branch vxy vxz (mkBranchUnbox vyu vxy vyv (1 + mkBranchLeft_size vyu vxy vyv + mkBranchRight_size vyu vxy vyv)) vyu vyv;
111.20/79.48	
111.20/79.48	mkBranchRight_ok vxv vxw vxx = mkBranchRight_ok0 vxv vxw vxx vxx vxw vxx;
111.20/79.48	
111.20/79.48	mkBranchRight_ok0 vxv vxw vxx fm_r key EmptyFM = True;
111.20/79.48	mkBranchRight_ok0 vxv vxw vxx fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
111.20/79.48	
111.20/79.48	mkBranchRight_ok0Smallest_right_key vyw = fst (findMin vyw);
111.20/79.48	
111.20/79.48	mkBranchRight_size vxv vxw vxx = sizeFM vxx;
111.20/79.48	
111.20/79.48	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)));
111.20/79.48	mkBranchUnbox vxv vxw vxx x = x;
111.20/79.48	
111.20/79.48	sIZE_RATIO :: Int;
111.20/79.48	sIZE_RATIO = 5;
111.20/79.48	
111.20/79.48	sizeFM :: FiniteMap b a  ->  Int;
111.20/79.48	sizeFM EmptyFM = 0;
111.20/79.48	sizeFM (Branch vz wu size wv ww) = size;
111.20/79.48	
111.20/79.48	unitFM :: a  ->  b  ->  FiniteMap a b;
111.20/79.48	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
111.20/79.48	
111.20/79.48	}
111.20/79.48	module Maybe where {
111.20/79.48	import qualified FiniteMap;
111.20/79.48	import qualified Main;
111.20/79.48	import qualified Prelude;
111.20/79.48	}
111.20/79.48	module Main where {
111.20/79.48	import qualified FiniteMap;
111.20/79.48	import qualified Maybe;
111.20/79.48	import qualified Prelude;
111.20/79.48	}
111.20/79.48	
111.20/79.48	----------------------------------------
111.20/79.48	
111.20/79.48	(9) NumRed (SOUND)
111.20/79.48	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
111.20/79.48	----------------------------------------
111.20/79.48	
111.20/79.48	(10)
111.20/79.48	Obligation:
111.20/79.48	mainModule Main 
111.20/79.48	module FiniteMap where {
111.20/79.48	import qualified Main;
111.20/79.48	import qualified Maybe;
111.20/79.48	import qualified Prelude;
111.20/79.48	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
111.20/79.48	
111.20/79.48	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
111.20/79.48	}
111.20/79.48	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
111.20/79.48	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
111.20/79.48	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt;
111.20/79.48	
111.20/79.48	addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r;
111.20/79.48	
111.20/79.48	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt);
111.20/79.48	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise;
111.20/79.48	
111.20/79.48	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r;
111.20/79.48	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key);
111.20/79.48	
111.20/79.48	addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key);
111.20/79.48	
111.20/79.48	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
111.20/79.48	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
111.20/79.48	
111.20/79.48	emptyFM :: FiniteMap a b;
111.20/79.48	emptyFM = EmptyFM;
111.20/79.48	
111.20/79.48	findMax :: FiniteMap b a  ->  (b,a);
111.20/79.48	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
111.20/79.48	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
111.20/79.48	
111.20/79.48	findMin :: FiniteMap a b  ->  (a,b);
111.20/79.48	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
111.20/79.48	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
111.20/79.48	
111.20/79.48	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
111.20/79.48	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
111.20/79.48	
111.20/79.48	mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 fm_R key elt fm_L key elt fm_L fm_R (mkBalBranch6Size_l fm_R key elt fm_L + mkBalBranch6Size_r fm_R key elt fm_L < Pos (Succ (Succ Zero)));
111.20/79.48	
111.20/79.48	mkBalBranch6Double_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) key_rl elt_rl (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) vwy vwz fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr);
111.20/79.48	
111.20/79.48	mkBalBranch6Double_R vwx vwy vwz vxu (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) key_lr elt_lr (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))) key_l elt_l fm_ll fm_lrl) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) vwy vwz fm_lrr fm_r);
111.20/79.48	
111.20/79.48	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);
111.20/79.48	
111.20/79.48	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;
111.20/79.48	
111.20/79.48	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;
111.20/79.48	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;
111.20/79.48	
111.20/79.48	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);
111.20/79.48	
111.20/79.48	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);
111.20/79.48	
111.20/79.48	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;
111.20/79.48	
111.20/79.48	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;
111.20/79.48	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;
111.20/79.48	
111.20/79.48	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);
111.20/79.48	
111.20/79.48	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R;
111.20/79.48	
111.20/79.48	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
111.20/79.48	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
111.20/79.48	
111.20/79.48	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
111.20/79.48	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);
111.20/79.48	
111.20/79.48	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R;
111.20/79.48	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);
111.20/79.48	
111.20/79.48	mkBalBranch6Single_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch (Pos (Succ (Succ (Succ Zero)))) key_r elt_r (mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) vwy vwz fm_l fm_rl) fm_rr;
111.20/79.48	
111.20/79.48	mkBalBranch6Single_R vwx vwy vwz vxu (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))) key_l elt_l fm_ll (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) vwy vwz fm_lr fm_r);
111.20/79.48	
111.20/79.48	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vxu;
111.20/79.48	
111.20/79.48	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vwx;
111.20/79.48	
111.20/79.48	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
111.20/79.48	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r;
111.20/79.48	
111.20/79.48	mkBranchBalance_ok vxv vxw vxx = True;
111.20/79.48	
111.20/79.48	mkBranchLeft_ok vxv vxw vxx = mkBranchLeft_ok0 vxv vxw vxx vxv vxw vxv;
111.20/79.48	
111.20/79.48	mkBranchLeft_ok0 vxv vxw vxx fm_l key EmptyFM = True;
111.20/79.48	mkBranchLeft_ok0 vxv vxw vxx fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
111.20/79.48	
111.20/79.48	mkBranchLeft_ok0Biggest_left_key vyx = fst (findMax vyx);
111.20/79.48	
111.20/79.48	mkBranchLeft_size vxv vxw vxx = sizeFM vxv;
111.20/79.48	
111.20/79.48	mkBranchResult vxy vxz vyu vyv = Branch vxy vxz (mkBranchUnbox vyu vxy vyv (Pos (Succ Zero) + mkBranchLeft_size vyu vxy vyv + mkBranchRight_size vyu vxy vyv)) vyu vyv;
111.20/79.48	
111.20/79.48	mkBranchRight_ok vxv vxw vxx = mkBranchRight_ok0 vxv vxw vxx vxx vxw vxx;
111.20/79.48	
111.20/79.48	mkBranchRight_ok0 vxv vxw vxx fm_r key EmptyFM = True;
111.20/79.48	mkBranchRight_ok0 vxv vxw vxx fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
111.20/79.48	
111.20/79.48	mkBranchRight_ok0Smallest_right_key vyw = fst (findMin vyw);
111.20/79.48	
111.20/79.48	mkBranchRight_size vxv vxw vxx = sizeFM vxx;
111.20/79.48	
111.20/79.48	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)));
111.20/79.48	mkBranchUnbox vxv vxw vxx x = x;
111.20/79.48	
111.20/79.48	sIZE_RATIO :: Int;
111.20/79.48	sIZE_RATIO = Pos (Succ (Succ (Succ (Succ (Succ Zero)))));
111.20/79.48	
111.20/79.48	sizeFM :: FiniteMap b a  ->  Int;
111.20/79.48	sizeFM EmptyFM = Pos Zero;
111.20/79.48	sizeFM (Branch vz wu size wv ww) = size;
111.20/79.48	
111.20/79.48	unitFM :: a  ->  b  ->  FiniteMap a b;
111.20/79.48	unitFM key elt = Branch key elt (Pos (Succ Zero)) emptyFM emptyFM;
111.20/79.48	
111.20/79.48	}
111.20/79.48	module Maybe where {
111.20/79.48	import qualified FiniteMap;
111.20/79.48	import qualified Main;
111.20/79.48	import qualified Prelude;
111.20/79.48	}
111.20/79.48	module Main where {
111.20/79.48	import qualified FiniteMap;
111.20/79.48	import qualified Maybe;
111.20/79.48	import qualified Prelude;
111.20/79.48	}
111.45/79.53	EOF