9.85/4.55	YES
12.40/5.21	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.40/5.21	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.40/5.21	
12.40/5.21	
12.40/5.21	H-Termination with start terms of the given HASKELL could be proven:
12.40/5.21	
12.40/5.21	(0) HASKELL
12.40/5.21	(1) CR [EQUIVALENT, 0 ms]
12.40/5.21	(2) HASKELL
12.40/5.21	(3) BR [EQUIVALENT, 0 ms]
12.40/5.21	(4) HASKELL
12.40/5.21	(5) COR [EQUIVALENT, 19 ms]
12.40/5.21	(6) HASKELL
12.40/5.21	(7) LetRed [EQUIVALENT, 0 ms]
12.40/5.21	(8) HASKELL
12.40/5.21	(9) NumRed [SOUND, 0 ms]
12.40/5.21	(10) HASKELL
12.40/5.21	(11) Narrow [EQUIVALENT, 25 ms]
12.40/5.21	(12) YES
12.40/5.21	
12.40/5.21	
12.40/5.21	----------------------------------------
12.40/5.21	
12.40/5.21	(0)
12.40/5.21	Obligation:
12.40/5.21	mainModule Main 
12.40/5.21	module FiniteMap where {
12.40/5.21	import qualified Main;
12.40/5.21	import qualified Maybe;
12.40/5.21	import qualified Prelude;
12.40/5.21	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.40/5.21	
12.40/5.21	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
12.40/5.21	}
12.40/5.21	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
12.40/5.21	addToFM_C combiner EmptyFM key elt = unitFM key elt;
12.40/5.21	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
12.40/5.21	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
12.40/5.21	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
12.40/5.21	
12.40/5.21	emptyFM :: FiniteMap b a;
12.40/5.21	emptyFM = EmptyFM;
12.40/5.21	
12.40/5.21	findMax :: FiniteMap b a  ->  (b,a);
12.40/5.21	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
12.40/5.21	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
12.40/5.21	
12.40/5.21	findMin :: FiniteMap a b  ->  (a,b);
12.40/5.21	findMin (Branch key elt _ EmptyFM _) = (key,elt);
12.40/5.21	findMin (Branch key elt _ fm_l _) = findMin fm_l;
12.40/5.21	
12.40/5.21	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
12.40/5.21	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
12.40/5.21	 | size_r > sIZE_RATIO * size_l = case fm_R of { 
12.40/5.21	Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R
12.40/5.21	 | otherwise -> double_L fm_L fm_R; 
12.40/5.21	 } 
12.40/5.21	 | size_l > sIZE_RATIO * size_r = case fm_L of { 
12.40/5.21	Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R
12.40/5.21	 | otherwise -> double_R fm_L fm_R; 
12.40/5.21	 } 
12.40/5.21	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
12.40/5.21	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);
12.40/5.21	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);
12.40/5.21	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;
12.40/5.21	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);
12.40/5.21	size_l = sizeFM fm_L;
12.40/5.21	size_r = sizeFM fm_R;
12.40/5.21	 };
12.40/5.21	
12.40/5.21	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
12.40/5.21	mkBranch which key elt fm_l fm_r = let { 
12.40/5.21	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
12.40/5.21	} in result where { 
12.40/5.21	balance_ok = True;
12.40/5.21	left_ok = case fm_l of { 
12.40/5.21	EmptyFM-> True; 
12.40/5.21	Branch left_key _ _ _ _-> let { 
12.40/5.21	biggest_left_key = fst (findMax fm_l);
12.40/5.21	} in biggest_left_key < key; 
12.40/5.21	 } ;
12.40/5.21	left_size = sizeFM fm_l;
12.40/5.21	right_ok = case fm_r of { 
12.40/5.21	EmptyFM-> True; 
12.40/5.21	Branch right_key _ _ _ _-> let { 
12.40/5.21	smallest_right_key = fst (findMin fm_r);
12.40/5.21	} in key < smallest_right_key; 
12.40/5.21	 } ;
12.40/5.21	right_size = sizeFM fm_r;
12.40/5.21	unbox :: Int  ->  Int;
12.40/5.21	unbox x = x;
12.40/5.21	 };
12.40/5.21	
12.40/5.21	sIZE_RATIO :: Int;
12.40/5.21	sIZE_RATIO = 5;
12.40/5.21	
12.40/5.21	sizeFM :: FiniteMap b a  ->  Int;
12.40/5.21	sizeFM EmptyFM = 0;
12.40/5.21	sizeFM (Branch _ _ size _ _) = size;
12.40/5.21	
12.40/5.21	unitFM :: b  ->  a  ->  FiniteMap b a;
12.40/5.21	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
12.40/5.21	
12.40/5.21	}
12.40/5.21	module Maybe where {
12.40/5.21	import qualified FiniteMap;
12.40/5.21	import qualified Main;
12.40/5.21	import qualified Prelude;
12.40/5.21	}
12.40/5.21	module Main where {
12.40/5.21	import qualified FiniteMap;
12.40/5.21	import qualified Maybe;
12.40/5.21	import qualified Prelude;
12.40/5.21	}
12.40/5.21	
12.40/5.21	----------------------------------------
12.40/5.21	
12.40/5.21	(1) CR (EQUIVALENT)
12.40/5.21	Case Reductions:
12.40/5.21	The following Case expression
12.40/5.21	"case fm_r of {
12.40/5.21	EmptyFM  -> True;
12.40/5.21	Branch right_key _ _ _ _  -> let {
12.40/5.21	smallest_right_key  = fst (findMin fm_r);
12.40/5.21	} in key < smallest_right_key}
12.40/5.21	"
12.40/5.21	is transformed to
12.40/5.21	"right_ok0 fm_r key EmptyFM = True;
12.40/5.21	right_ok0 fm_r key (Branch right_key _ _ _ _) = let {
12.40/5.21	smallest_right_key  = fst (findMin fm_r);
12.40/5.21	} in key < smallest_right_key;
12.40/5.21	"
12.40/5.21	The following Case expression
12.40/5.21	"case fm_l of {
12.40/5.21	EmptyFM  -> True;
12.40/5.21	Branch left_key _ _ _ _  -> let {
12.40/5.21	biggest_left_key  = fst (findMax fm_l);
12.40/5.21	} in biggest_left_key < key}
12.40/5.21	"
12.40/5.21	is transformed to
12.40/5.21	"left_ok0 fm_l key EmptyFM = True;
12.40/5.21	left_ok0 fm_l key (Branch left_key _ _ _ _) = let {
12.40/5.21	biggest_left_key  = fst (findMax fm_l);
12.40/5.21	} in biggest_left_key < key;
12.40/5.21	"
12.40/5.21	The following Case expression
12.40/5.21	"case fm_R of {
12.40/5.21	Branch _ _ _ fm_rl fm_rr |sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R}
12.40/5.21	"
12.40/5.21	is transformed to
12.40/5.21	"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;
12.40/5.21	"
12.40/5.21	The following Case expression
12.40/5.21	"case fm_L of {
12.40/5.21	Branch _ _ _ fm_ll fm_lr |sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R}
12.40/5.21	"
12.40/5.21	is transformed to
12.40/5.21	"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;
12.40/5.21	"
12.40/5.21	
12.40/5.21	----------------------------------------
12.40/5.21	
12.40/5.21	(2)
12.40/5.21	Obligation:
12.40/5.21	mainModule Main 
12.40/5.21	module FiniteMap where {
12.40/5.21	import qualified Main;
12.40/5.21	import qualified Maybe;
12.40/5.21	import qualified Prelude;
12.40/5.21	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.40/5.21	
12.40/5.21	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
12.40/5.21	}
12.40/5.21	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
12.40/5.21	addToFM_C combiner EmptyFM key elt = unitFM key elt;
12.40/5.21	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
12.40/5.21	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
12.40/5.21	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
12.40/5.21	
12.40/5.21	emptyFM :: FiniteMap a b;
12.40/5.21	emptyFM = EmptyFM;
12.40/5.21	
12.40/5.21	findMax :: FiniteMap b a  ->  (b,a);
12.40/5.21	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
12.40/5.21	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
12.40/5.21	
12.40/5.21	findMin :: FiniteMap a b  ->  (a,b);
12.40/5.21	findMin (Branch key elt _ EmptyFM _) = (key,elt);
12.40/5.21	findMin (Branch key elt _ fm_l _) = findMin fm_l;
12.40/5.21	
12.40/5.21	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
12.40/5.21	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
12.40/5.21	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
12.40/5.21	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
12.40/5.21	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
12.40/5.21	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);
12.40/5.21	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);
12.40/5.21	mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr)  | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R
12.40/5.21	 | otherwise = double_L fm_L fm_R;
12.40/5.21	mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr)  | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R
12.40/5.21	 | otherwise = double_R fm_L fm_R;
12.40/5.21	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;
12.40/5.21	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);
12.40/5.21	size_l = sizeFM fm_L;
12.40/5.21	size_r = sizeFM fm_R;
12.40/5.21	 };
12.40/5.21	
12.40/5.21	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
12.40/5.21	mkBranch which key elt fm_l fm_r = let { 
12.40/5.21	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
12.40/5.21	} in result where { 
12.40/5.21	balance_ok = True;
12.40/5.21	left_ok = left_ok0 fm_l key fm_l;
12.40/5.21	left_ok0 fm_l key EmptyFM = True;
12.40/5.21	left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 
12.40/5.21	biggest_left_key = fst (findMax fm_l);
12.40/5.21	} in biggest_left_key < key;
12.40/5.21	left_size = sizeFM fm_l;
12.40/5.21	right_ok = right_ok0 fm_r key fm_r;
12.40/5.21	right_ok0 fm_r key EmptyFM = True;
12.40/5.21	right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 
12.40/5.21	smallest_right_key = fst (findMin fm_r);
12.40/5.22	} in key < smallest_right_key;
12.40/5.22	right_size = sizeFM fm_r;
12.40/5.22	unbox :: Int  ->  Int;
12.40/5.22	unbox x = x;
12.40/5.22	 };
12.40/5.22	
12.40/5.22	sIZE_RATIO :: Int;
12.40/5.22	sIZE_RATIO = 5;
12.40/5.22	
12.40/5.22	sizeFM :: FiniteMap b a  ->  Int;
12.40/5.22	sizeFM EmptyFM = 0;
12.40/5.22	sizeFM (Branch _ _ size _ _) = size;
12.40/5.22	
12.40/5.22	unitFM :: a  ->  b  ->  FiniteMap a b;
12.40/5.22	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
12.40/5.22	
12.40/5.22	}
12.40/5.22	module Maybe where {
12.40/5.22	import qualified FiniteMap;
12.40/5.22	import qualified Main;
12.40/5.22	import qualified Prelude;
12.40/5.22	}
12.40/5.22	module Main where {
12.40/5.22	import qualified FiniteMap;
12.40/5.22	import qualified Maybe;
12.40/5.22	import qualified Prelude;
12.40/5.22	}
12.40/5.22	
12.40/5.22	----------------------------------------
12.40/5.22	
12.40/5.22	(3) BR (EQUIVALENT)
12.40/5.22	Replaced joker patterns by fresh variables and removed binding patterns.
12.40/5.22	----------------------------------------
12.40/5.22	
12.40/5.22	(4)
12.40/5.22	Obligation:
12.40/5.22	mainModule Main 
12.40/5.22	module FiniteMap where {
12.40/5.22	import qualified Main;
12.40/5.22	import qualified Maybe;
12.40/5.22	import qualified Prelude;
12.40/5.22	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.40/5.22	
12.40/5.22	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.40/5.22	}
12.40/5.22	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
12.40/5.22	addToFM_C combiner EmptyFM key elt = unitFM key elt;
12.40/5.22	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
12.40/5.22	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
12.40/5.22	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
12.40/5.22	
12.40/5.22	emptyFM :: FiniteMap b a;
12.40/5.22	emptyFM = EmptyFM;
12.40/5.22	
12.40/5.22	findMax :: FiniteMap b a  ->  (b,a);
12.40/5.22	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
12.40/5.22	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
12.40/5.22	
12.40/5.22	findMin :: FiniteMap a b  ->  (a,b);
12.40/5.22	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
12.40/5.22	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
12.40/5.22	
12.40/5.22	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
12.40/5.22	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
12.40/5.22	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
12.40/5.22	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
12.40/5.22	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
12.40/5.22	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);
12.40/5.22	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);
12.40/5.22	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
12.40/5.22	 | otherwise = double_L fm_L fm_R;
12.40/5.22	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
12.40/5.22	 | otherwise = double_R fm_L fm_R;
12.40/5.22	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;
12.40/5.22	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);
12.40/5.22	size_l = sizeFM fm_L;
12.40/5.22	size_r = sizeFM fm_R;
12.40/5.22	 };
12.40/5.22	
12.40/5.22	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
12.40/5.22	mkBranch which key elt fm_l fm_r = let { 
12.40/5.22	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
12.40/5.22	} in result where { 
12.40/5.22	balance_ok = True;
12.40/5.22	left_ok = left_ok0 fm_l key fm_l;
12.40/5.22	left_ok0 fm_l key EmptyFM = True;
12.40/5.22	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
12.40/5.22	biggest_left_key = fst (findMax fm_l);
12.40/5.22	} in biggest_left_key < key;
12.40/5.22	left_size = sizeFM fm_l;
12.40/5.22	right_ok = right_ok0 fm_r key fm_r;
12.40/5.22	right_ok0 fm_r key EmptyFM = True;
12.40/5.22	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
12.40/5.22	smallest_right_key = fst (findMin fm_r);
12.40/5.22	} in key < smallest_right_key;
12.40/5.22	right_size = sizeFM fm_r;
12.40/5.22	unbox :: Int  ->  Int;
12.40/5.22	unbox x = x;
12.40/5.22	 };
12.40/5.22	
12.40/5.22	sIZE_RATIO :: Int;
12.40/5.22	sIZE_RATIO = 5;
12.40/5.22	
12.40/5.22	sizeFM :: FiniteMap a b  ->  Int;
12.40/5.22	sizeFM EmptyFM = 0;
12.40/5.22	sizeFM (Branch vz wu size wv ww) = size;
12.40/5.22	
12.40/5.22	unitFM :: a  ->  b  ->  FiniteMap a b;
12.40/5.22	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
12.40/5.22	
12.40/5.22	}
12.40/5.22	module Maybe where {
12.40/5.22	import qualified FiniteMap;
12.40/5.22	import qualified Main;
12.40/5.22	import qualified Prelude;
12.40/5.22	}
12.40/5.22	module Main where {
12.40/5.22	import qualified FiniteMap;
12.40/5.22	import qualified Maybe;
12.40/5.22	import qualified Prelude;
12.40/5.22	}
12.40/5.22	
12.40/5.22	----------------------------------------
12.40/5.22	
12.40/5.22	(5) COR (EQUIVALENT)
12.40/5.22	Cond Reductions:
12.40/5.22	The following Function with conditions
12.40/5.22	"undefined |Falseundefined;
12.40/5.22	"
12.40/5.22	is transformed to
12.40/5.22	"undefined  = undefined1;
12.40/5.22	"
12.40/5.22	"undefined0 True = undefined;
12.40/5.22	"
12.40/5.22	"undefined1  = undefined0 False;
12.40/5.22	"
12.40/5.22	The following Function with conditions
12.40/5.22	"addToFM_C combiner EmptyFM key elt = unitFM key elt;
12.40/5.22	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;
12.40/5.22	"
12.40/5.22	is transformed to
12.40/5.22	"addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
12.40/5.22	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;
12.40/5.22	"
12.40/5.22	"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;
12.40/5.22	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);
12.40/5.22	"
12.40/5.22	"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);
12.40/5.22	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;
12.40/5.22	"
12.40/5.22	"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;
12.40/5.22	"
12.40/5.22	"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);
12.40/5.22	"
12.40/5.22	"addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
12.40/5.22	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
12.40/5.22	"
12.40/5.22	The following Function with conditions
12.40/5.22	"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;
12.40/5.22	"
12.40/5.22	is transformed to
12.40/5.22	"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);
12.40/5.22	"
12.40/5.22	"mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
12.40/5.22	"
12.40/5.22	"mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
12.40/5.22	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;
12.40/5.22	"
12.40/5.22	"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);
12.40/5.22	"
12.40/5.22	The following Function with conditions
12.40/5.22	"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;
12.40/5.22	"
12.40/5.22	is transformed to
12.40/5.22	"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);
12.40/5.22	"
12.40/5.22	"mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
12.40/5.22	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;
12.40/5.22	"
12.40/5.22	"mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
12.40/5.22	"
12.40/5.22	"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);
12.40/5.22	"
12.40/5.22	The following Function with conditions
12.40/5.22	"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 {
12.40/5.22	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);
12.40/5.22	;
12.40/5.22	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);
12.40/5.22	;
12.40/5.22	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;
12.40/5.22	;
12.40/5.22	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;
12.40/5.22	;
12.40/5.22	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;
12.40/5.22	;
12.40/5.22	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);
12.40/5.22	;
12.40/5.22	size_l  = sizeFM fm_L;
12.40/5.22	;
12.40/5.22	size_r  = sizeFM fm_R;
12.40/5.22	} 
12.40/5.22	;
12.40/5.22	"
12.40/5.22	is transformed to
12.40/5.22	"mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
12.40/5.22	"
12.40/5.22	"mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
12.40/5.22	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);
12.40/5.22	;
12.40/5.22	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);
12.40/5.22	;
12.40/5.22	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);
12.40/5.22	;
12.40/5.22	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
12.40/5.22	;
12.40/5.22	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
12.40/5.22	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;
12.40/5.22	;
12.40/5.22	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);
12.40/5.22	;
12.40/5.22	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);
12.40/5.22	;
12.40/5.22	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
12.40/5.22	;
12.40/5.22	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
12.40/5.22	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;
12.40/5.22	;
12.40/5.22	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);
12.40/5.22	;
12.40/5.22	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
12.40/5.22	;
12.40/5.22	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
12.40/5.22	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
12.40/5.22	;
12.40/5.22	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
12.40/5.22	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
12.40/5.22	;
12.40/5.22	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
12.40/5.22	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
12.40/5.22	;
12.40/5.22	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;
12.40/5.22	;
12.40/5.22	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);
12.40/5.22	;
12.40/5.22	size_l  = sizeFM fm_L;
12.40/5.22	;
12.40/5.22	size_r  = sizeFM fm_R;
12.40/5.22	} 
12.40/5.22	;
12.40/5.22	"
12.40/5.22	
12.40/5.22	----------------------------------------
12.40/5.22	
12.40/5.22	(6)
12.40/5.22	Obligation:
12.40/5.22	mainModule Main 
12.40/5.22	module FiniteMap where {
12.40/5.23	import qualified Main;
12.40/5.23	import qualified Maybe;
12.40/5.23	import qualified Prelude;
12.40/5.23	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.40/5.23	
12.40/5.23	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.40/5.23	}
12.40/5.23	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
12.40/5.23	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
12.40/5.23	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;
12.40/5.23	
12.40/5.23	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;
12.40/5.23	
12.40/5.23	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);
12.40/5.23	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;
12.40/5.23	
12.40/5.23	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;
12.40/5.23	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);
12.40/5.23	
12.40/5.23	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);
12.40/5.23	
12.40/5.23	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
12.40/5.23	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
12.40/5.23	
12.40/5.23	emptyFM :: FiniteMap a b;
12.40/5.23	emptyFM = EmptyFM;
12.40/5.23	
12.40/5.23	findMax :: FiniteMap b a  ->  (b,a);
12.40/5.23	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
12.40/5.23	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
12.40/5.23	
12.40/5.23	findMin :: FiniteMap a b  ->  (a,b);
12.40/5.23	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
12.40/5.23	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
12.40/5.23	
12.40/5.23	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
12.40/5.23	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
12.40/5.23	
12.40/5.23	mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 
12.40/5.23	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);
12.40/5.23	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);
12.40/5.23	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);
12.40/5.23	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
12.40/5.23	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
12.40/5.23	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;
12.40/5.23	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);
12.40/5.23	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);
12.40/5.23	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
12.40/5.23	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
12.40/5.23	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;
12.40/5.23	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);
12.40/5.23	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
12.40/5.23	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
12.40/5.23	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
12.40/5.23	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
12.40/5.23	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
12.40/5.23	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
12.40/5.23	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
12.40/5.23	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;
12.40/5.23	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);
12.40/5.23	size_l = sizeFM fm_L;
12.40/5.23	size_r = sizeFM fm_R;
12.40/5.23	 };
12.40/5.23	
12.40/5.23	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
12.40/5.23	mkBranch which key elt fm_l fm_r = let { 
12.40/5.23	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
12.40/5.23	} in result where { 
12.40/5.23	balance_ok = True;
12.40/5.23	left_ok = left_ok0 fm_l key fm_l;
12.40/5.23	left_ok0 fm_l key EmptyFM = True;
12.40/5.23	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
12.40/5.23	biggest_left_key = fst (findMax fm_l);
12.40/5.23	} in biggest_left_key < key;
12.40/5.23	left_size = sizeFM fm_l;
12.40/5.23	right_ok = right_ok0 fm_r key fm_r;
12.40/5.23	right_ok0 fm_r key EmptyFM = True;
12.40/5.23	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
12.40/5.23	smallest_right_key = fst (findMin fm_r);
12.40/5.23	} in key < smallest_right_key;
12.40/5.23	right_size = sizeFM fm_r;
12.40/5.23	unbox :: Int  ->  Int;
12.40/5.23	unbox x = x;
12.40/5.23	 };
12.40/5.23	
12.40/5.23	sIZE_RATIO :: Int;
12.40/5.23	sIZE_RATIO = 5;
12.40/5.23	
12.40/5.23	sizeFM :: FiniteMap a b  ->  Int;
12.40/5.23	sizeFM EmptyFM = 0;
12.40/5.23	sizeFM (Branch vz wu size wv ww) = size;
12.94/5.38	
12.94/5.38	unitFM :: a  ->  b  ->  FiniteMap a b;
12.94/5.38	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
12.94/5.38	
12.94/5.38	}
12.94/5.38	module Maybe where {
12.94/5.38	import qualified FiniteMap;
12.94/5.38	import qualified Main;
12.94/5.38	import qualified Prelude;
12.94/5.38	}
12.94/5.38	module Main where {
12.94/5.38	import qualified FiniteMap;
12.94/5.38	import qualified Maybe;
12.94/5.38	import qualified Prelude;
12.94/5.38	}
12.94/5.38	
12.94/5.38	----------------------------------------
12.94/5.38	
12.94/5.38	(7) LetRed (EQUIVALENT)
12.94/5.38	Let/Where Reductions:
12.94/5.38	The bindings of the following Let/Where expression
12.94/5.38	"mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
12.94/5.38	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);
12.94/5.38	;
12.94/5.38	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);
12.94/5.38	;
12.94/5.38	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);
12.94/5.38	;
12.94/5.38	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
12.94/5.38	;
12.94/5.38	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
12.94/5.38	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;
12.94/5.38	;
12.94/5.38	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);
12.94/5.38	;
12.94/5.38	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);
12.94/5.38	;
12.94/5.38	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
12.94/5.38	;
12.94/5.38	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
12.94/5.38	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;
12.94/5.38	;
12.94/5.38	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);
12.94/5.38	;
12.94/5.38	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
12.94/5.38	;
12.94/5.38	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
12.94/5.38	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
12.94/5.38	;
12.94/5.38	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
12.94/5.38	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
12.94/5.38	;
12.94/5.38	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
12.94/5.38	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
12.94/5.38	;
12.94/5.38	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;
12.94/5.38	;
12.94/5.38	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);
12.94/5.38	;
12.94/5.38	size_l  = sizeFM fm_L;
12.94/5.38	;
12.94/5.38	size_r  = sizeFM fm_R;
12.94/5.38	} 
12.94/5.38	"
12.94/5.38	are unpacked to the following functions on top level
12.94/5.38	"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;
12.94/5.38	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;
12.94/5.38	"
12.94/5.38	"mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
12.94/5.38	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);
12.94/5.38	"
12.94/5.38	"mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
12.94/5.38	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
12.94/5.38	"
12.94/5.38	"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;
12.94/5.38	"
12.94/5.38	"mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vwz;
12.94/5.38	"
12.94/5.38	"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;
12.94/5.38	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;
12.94/5.38	"
12.94/5.38	"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);
12.94/5.38	"
12.94/5.38	"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);
12.94/5.38	"
12.94/5.38	"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);
12.94/5.38	"
12.94/5.38	"mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
12.94/5.38	"
12.94/5.38	"mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vxu;
12.94/5.38	"
12.94/5.38	"mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
12.94/5.38	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);
12.94/5.38	"
12.94/5.38	"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);
12.94/5.38	"
12.94/5.38	"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;
12.94/5.38	"
12.94/5.38	"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);
12.94/5.38	"
12.94/5.38	"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);
12.94/5.38	"
12.94/5.38	"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;
12.94/5.38	"
12.94/5.38	"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);
12.94/5.38	"
12.94/5.38	The bindings of the following Let/Where expression
12.94/5.38	"let {
12.94/5.38	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
12.94/5.38	} in result where {
12.94/5.38	balance_ok  = True;
12.94/5.38	;
12.94/5.38	left_ok  = left_ok0 fm_l key fm_l;
12.94/5.38	;
12.94/5.38	left_ok0 fm_l key EmptyFM = True;
12.94/5.38	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let {
12.94/5.38	biggest_left_key  = fst (findMax fm_l);
12.94/5.38	} in biggest_left_key < key;
12.94/5.38	;
12.94/5.38	left_size  = sizeFM fm_l;
12.94/5.38	;
12.94/5.38	right_ok  = right_ok0 fm_r key fm_r;
12.94/5.38	;
12.94/5.38	right_ok0 fm_r key EmptyFM = True;
12.94/5.38	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let {
12.94/5.38	smallest_right_key  = fst (findMin fm_r);
12.94/5.38	} in key < smallest_right_key;
12.94/5.38	;
12.94/5.38	right_size  = sizeFM fm_r;
12.94/5.38	;
12.94/5.38	unbox x = x;
12.94/5.38	} 
12.94/5.38	"
12.94/5.38	are unpacked to the following functions on top level
12.94/5.38	"mkBranchLeft_ok0 vxv vxw vxx fm_l key EmptyFM = True;
12.94/5.38	mkBranchLeft_ok0 vxv vxw vxx fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
12.94/5.38	"
12.94/5.38	"mkBranchLeft_size vxv vxw vxx = sizeFM vxv;
12.94/5.38	"
12.94/5.38	"mkBranchBalance_ok vxv vxw vxx = True;
12.94/5.38	"
12.94/5.38	"mkBranchUnbox vxv vxw vxx x = x;
12.94/5.38	"
12.94/5.38	"mkBranchRight_ok vxv vxw vxx = mkBranchRight_ok0 vxv vxw vxx vxw vxx vxw;
12.94/5.38	"
12.94/5.38	"mkBranchLeft_ok vxv vxw vxx = mkBranchLeft_ok0 vxv vxw vxx vxv vxx vxv;
12.94/5.38	"
12.94/5.38	"mkBranchRight_ok0 vxv vxw vxx fm_r key EmptyFM = True;
12.94/5.38	mkBranchRight_ok0 vxv vxw vxx fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
12.94/5.38	"
12.94/5.38	"mkBranchRight_size vxv vxw vxx = sizeFM vxw;
12.94/5.38	"
12.94/5.38	The bindings of the following Let/Where expression
12.94/5.38	"let {
12.94/5.38	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
12.94/5.38	} in result"
12.94/5.38	are unpacked to the following functions on top level
12.94/5.38	"mkBranchResult vxy vxz vyu vyv = Branch vxy vxz (mkBranchUnbox vyu vyv vxy (1 + mkBranchLeft_size vyu vyv vxy + mkBranchRight_size vyu vyv vxy)) vyu vyv;
12.94/5.38	"
12.94/5.38	The bindings of the following Let/Where expression
12.94/5.38	"let {
12.94/5.38	biggest_left_key  = fst (findMax fm_l);
12.94/5.38	} in biggest_left_key < key"
12.94/5.38	are unpacked to the following functions on top level
12.94/5.38	"mkBranchLeft_ok0Biggest_left_key vyw = fst (findMax vyw);
12.94/5.38	"
12.94/5.38	The bindings of the following Let/Where expression
12.94/5.38	"let {
12.94/5.38	smallest_right_key  = fst (findMin fm_r);
12.94/5.38	} in key < smallest_right_key"
12.94/5.38	are unpacked to the following functions on top level
12.94/5.38	"mkBranchRight_ok0Smallest_right_key vyx = fst (findMin vyx);
12.94/5.38	"
12.94/5.38	
12.94/5.38	----------------------------------------
12.94/5.38	
12.94/5.38	(8)
12.94/5.38	Obligation:
12.94/5.38	mainModule Main 
12.94/5.38	module FiniteMap where {
12.94/5.38	import qualified Main;
12.94/5.38	import qualified Maybe;
12.94/5.38	import qualified Prelude;
12.94/5.38	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.94/5.38	
12.94/5.38	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
12.94/5.38	}
12.94/5.38	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
12.94/5.38	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
12.94/5.38	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;
12.94/5.38	
12.94/5.38	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;
12.94/5.38	
12.94/5.38	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);
12.94/5.38	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;
12.94/5.38	
12.94/5.38	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;
12.94/5.38	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);
12.94/5.38	
12.94/5.38	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);
12.94/5.38	
12.94/5.38	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
12.94/5.38	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
12.94/5.38	
12.94/5.38	emptyFM :: FiniteMap a b;
12.94/5.38	emptyFM = EmptyFM;
12.94/5.38	
12.94/5.38	findMax :: FiniteMap a b  ->  (a,b);
12.94/5.38	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
12.94/5.38	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
12.94/5.38	
12.94/5.38	findMin :: FiniteMap a b  ->  (a,b);
12.94/5.38	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
12.94/5.38	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
12.94/5.38	
12.94/5.38	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
12.94/5.38	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
12.94/5.38	
12.94/5.38	mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 key elt fm_R fm_L key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_R fm_L + mkBalBranch6Size_r key elt fm_R fm_L < 2);
12.94/5.38	
12.94/5.38	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);
12.94/5.38	
12.94/5.38	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);
12.94/5.38	
12.94/5.38	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);
12.94/5.38	
12.94/5.38	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;
12.94/5.38	
12.94/5.38	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;
12.94/5.38	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;
12.94/5.38	
12.94/5.38	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);
12.94/5.38	
12.94/5.38	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);
12.94/5.38	
12.94/5.38	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;
12.94/5.38	
12.94/5.38	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;
12.94/5.38	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;
12.94/5.38	
12.94/5.38	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);
12.94/5.38	
12.94/5.38	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
12.94/5.38	
12.94/5.38	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
12.94/5.38	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
12.94/5.38	
12.94/5.38	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
12.94/5.38	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);
12.94/5.38	
12.94/5.38	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
12.94/5.38	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);
12.94/5.38	
12.94/5.38	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;
12.94/5.38	
12.94/5.38	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);
12.94/5.38	
12.94/5.38	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vxu;
12.94/5.38	
12.94/5.38	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vwz;
12.94/5.38	
12.94/5.38	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
12.94/5.38	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r;
12.94/5.38	
12.94/5.38	mkBranchBalance_ok vxv vxw vxx = True;
12.94/5.38	
12.94/5.38	mkBranchLeft_ok vxv vxw vxx = mkBranchLeft_ok0 vxv vxw vxx vxv vxx vxv;
12.94/5.38	
12.94/5.38	mkBranchLeft_ok0 vxv vxw vxx fm_l key EmptyFM = True;
12.94/5.38	mkBranchLeft_ok0 vxv vxw vxx fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
12.94/5.38	
12.94/5.38	mkBranchLeft_ok0Biggest_left_key vyw = fst (findMax vyw);
12.94/5.38	
12.94/5.38	mkBranchLeft_size vxv vxw vxx = sizeFM vxv;
12.94/5.38	
12.94/5.38	mkBranchResult vxy vxz vyu vyv = Branch vxy vxz (mkBranchUnbox vyu vyv vxy (1 + mkBranchLeft_size vyu vyv vxy + mkBranchRight_size vyu vyv vxy)) vyu vyv;
12.94/5.38	
12.94/5.38	mkBranchRight_ok vxv vxw vxx = mkBranchRight_ok0 vxv vxw vxx vxw vxx vxw;
12.94/5.38	
12.94/5.38	mkBranchRight_ok0 vxv vxw vxx fm_r key EmptyFM = True;
12.94/5.38	mkBranchRight_ok0 vxv vxw vxx fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
12.94/5.38	
12.94/5.38	mkBranchRight_ok0Smallest_right_key vyx = fst (findMin vyx);
12.94/5.38	
12.94/5.38	mkBranchRight_size vxv vxw vxx = sizeFM vxw;
12.94/5.38	
12.94/5.38	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)));
12.94/5.38	mkBranchUnbox vxv vxw vxx x = x;
12.94/5.38	
12.94/5.38	sIZE_RATIO :: Int;
12.94/5.38	sIZE_RATIO = 5;
12.94/5.38	
12.94/5.38	sizeFM :: FiniteMap b a  ->  Int;
12.94/5.38	sizeFM EmptyFM = 0;
12.94/5.38	sizeFM (Branch vz wu size wv ww) = size;
12.94/5.38	
12.94/5.38	unitFM :: a  ->  b  ->  FiniteMap a b;
12.94/5.38	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
12.94/5.38	
12.94/5.38	}
12.94/5.38	module Maybe where {
12.94/5.38	import qualified FiniteMap;
12.94/5.38	import qualified Main;
12.94/5.38	import qualified Prelude;
12.94/5.38	}
12.94/5.38	module Main where {
12.94/5.38	import qualified FiniteMap;
12.94/5.38	import qualified Maybe;
12.94/5.38	import qualified Prelude;
12.94/5.38	}
12.94/5.38	
12.94/5.38	----------------------------------------
12.94/5.38	
12.94/5.38	(9) NumRed (SOUND)
12.94/5.38	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
12.94/5.38	----------------------------------------
12.94/5.38	
12.94/5.38	(10)
12.94/5.38	Obligation:
12.94/5.38	mainModule Main 
12.94/5.38	module FiniteMap where {
12.94/5.38	import qualified Main;
12.94/5.38	import qualified Maybe;
12.94/5.38	import qualified Prelude;
12.94/5.38	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.94/5.38	
12.94/5.38	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
12.94/5.38	}
12.94/5.38	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
12.94/5.38	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
12.94/5.38	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;
12.94/5.38	
12.94/5.38	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;
12.94/5.38	
12.94/5.38	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);
12.94/5.38	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;
12.94/5.38	
12.94/5.38	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;
12.94/5.38	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);
12.94/5.38	
12.94/5.38	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);
12.94/5.38	
12.94/5.38	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
12.94/5.38	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
12.94/5.38	
12.94/5.38	emptyFM :: FiniteMap b a;
12.94/5.38	emptyFM = EmptyFM;
12.94/5.38	
12.94/5.38	findMax :: FiniteMap b a  ->  (b,a);
12.94/5.38	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
12.94/5.38	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
12.94/5.38	
12.94/5.38	findMin :: FiniteMap b a  ->  (b,a);
12.94/5.38	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
12.94/5.38	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
12.94/5.38	
12.94/5.38	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
12.94/5.38	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
12.94/5.38	
12.94/5.38	mkBalBranch6 key elt fm_L fm_R = mkBalBranch6MkBalBranch5 key elt fm_R fm_L key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_R fm_L + mkBalBranch6Size_r key elt fm_R fm_L < Pos (Succ (Succ Zero)));
12.94/5.38	
12.94/5.38	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);
12.94/5.39	
12.94/5.39	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);
12.94/5.39	
12.94/5.39	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);
12.94/5.39	
12.94/5.39	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;
12.94/5.39	
12.94/5.39	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;
12.94/5.39	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;
12.94/5.39	
12.94/5.39	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);
12.94/5.39	
12.94/5.39	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);
12.94/5.39	
12.94/5.39	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;
12.94/5.39	
12.94/5.39	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;
12.94/5.39	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;
12.94/5.39	
12.94/5.39	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);
12.94/5.39	
12.94/5.39	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R;
12.94/5.39	
12.94/5.39	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
12.94/5.39	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
12.94/5.39	
12.94/5.39	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
12.94/5.39	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);
12.94/5.39	
12.94/5.39	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R;
12.94/5.39	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);
12.94/5.39	
12.94/5.39	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;
12.94/5.39	
12.94/5.39	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);
12.94/5.39	
12.94/5.39	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vxu;
12.94/5.39	
12.94/5.39	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vwz;
12.94/5.39	
12.94/5.39	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
12.94/5.39	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_l fm_r;
12.94/5.39	
12.94/5.39	mkBranchBalance_ok vxv vxw vxx = True;
12.94/5.39	
12.94/5.39	mkBranchLeft_ok vxv vxw vxx = mkBranchLeft_ok0 vxv vxw vxx vxv vxx vxv;
12.94/5.39	
12.94/5.39	mkBranchLeft_ok0 vxv vxw vxx fm_l key EmptyFM = True;
12.94/5.39	mkBranchLeft_ok0 vxv vxw vxx fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
12.94/5.39	
12.94/5.39	mkBranchLeft_ok0Biggest_left_key vyw = fst (findMax vyw);
12.94/5.39	
12.94/5.39	mkBranchLeft_size vxv vxw vxx = sizeFM vxv;
12.94/5.39	
12.94/5.39	mkBranchResult vxy vxz vyu vyv = Branch vxy vxz (mkBranchUnbox vyu vyv vxy (Pos (Succ Zero) + mkBranchLeft_size vyu vyv vxy + mkBranchRight_size vyu vyv vxy)) vyu vyv;
12.94/5.39	
12.94/5.39	mkBranchRight_ok vxv vxw vxx = mkBranchRight_ok0 vxv vxw vxx vxw vxx vxw;
12.94/5.39	
12.94/5.39	mkBranchRight_ok0 vxv vxw vxx fm_r key EmptyFM = True;
12.94/5.39	mkBranchRight_ok0 vxv vxw vxx fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
12.94/5.39	
12.94/5.39	mkBranchRight_ok0Smallest_right_key vyx = fst (findMin vyx);
12.94/5.39	
12.94/5.39	mkBranchRight_size vxv vxw vxx = sizeFM vxw;
12.94/5.39	
12.94/5.39	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)));
12.94/5.39	mkBranchUnbox vxv vxw vxx x = x;
12.94/5.39	
12.94/5.39	sIZE_RATIO :: Int;
12.94/5.39	sIZE_RATIO = Pos (Succ (Succ (Succ (Succ (Succ Zero)))));
12.94/5.39	
12.94/5.39	sizeFM :: FiniteMap b a  ->  Int;
12.94/5.39	sizeFM EmptyFM = Pos Zero;
12.94/5.39	sizeFM (Branch vz wu size wv ww) = size;
12.94/5.39	
12.94/5.39	unitFM :: b  ->  a  ->  FiniteMap b a;
12.94/5.39	unitFM key elt = Branch key elt (Pos (Succ Zero)) emptyFM emptyFM;
12.94/5.39	
12.94/5.39	}
12.94/5.39	module Maybe where {
12.94/5.39	import qualified FiniteMap;
12.94/5.39	import qualified Main;
12.94/5.39	import qualified Prelude;
12.94/5.39	}
12.94/5.39	module Main where {
12.94/5.39	import qualified FiniteMap;
12.94/5.39	import qualified Maybe;
12.94/5.39	import qualified Prelude;
12.94/5.39	}
12.94/5.39	
12.94/5.39	----------------------------------------
12.94/5.39	
12.94/5.39	(11) Narrow (EQUIVALENT)
12.94/5.39	Haskell To QDPs
12.94/5.39	
12.94/5.39	digraph dp_graph {
12.94/5.39	node [outthreshold=100, inthreshold=100];1[label="FiniteMap.addToFM_C",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
12.94/5.39	3[label="FiniteMap.addToFM_C vyy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
12.94/5.39	4[label="FiniteMap.addToFM_C vyy3 vyy4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
12.94/5.39	5[label="FiniteMap.addToFM_C vyy3 vyy4 vyy5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3];
12.94/5.39	6[label="FiniteMap.addToFM_C vyy3 vyy4 vyy5 vyy6",fontsize=16,color="burlywood",shape="triangle"];32[label="vyy4/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];6 -> 32[label="",style="solid", color="burlywood", weight=9];
12.94/5.39	32 -> 7[label="",style="solid", color="burlywood", weight=3];
12.94/5.39	33[label="vyy4/FiniteMap.Branch vyy40 vyy41 vyy42 vyy43 vyy44",fontsize=10,color="white",style="solid",shape="box"];6 -> 33[label="",style="solid", color="burlywood", weight=9];
12.94/5.39	33 -> 8[label="",style="solid", color="burlywood", weight=3];
12.94/5.39	7[label="FiniteMap.addToFM_C vyy3 FiniteMap.EmptyFM vyy5 vyy6",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
12.94/5.39	8[label="FiniteMap.addToFM_C vyy3 (FiniteMap.Branch vyy40 vyy41 vyy42 vyy43 vyy44) vyy5 vyy6",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
12.94/5.39	9[label="FiniteMap.addToFM_C4 vyy3 FiniteMap.EmptyFM vyy5 vyy6",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
12.94/5.39	10[label="FiniteMap.addToFM_C3 vyy3 (FiniteMap.Branch vyy40 vyy41 vyy42 vyy43 vyy44) vyy5 vyy6",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
12.94/5.39	11[label="FiniteMap.unitFM vyy5 vyy6",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
12.94/5.39	12[label="FiniteMap.addToFM_C2 vyy3 vyy40 vyy41 vyy42 vyy43 vyy44 vyy5 vyy6 (vyy5 < vyy40)",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
12.94/5.39	13[label="FiniteMap.Branch vyy5 vyy6 (Pos (Succ Zero)) FiniteMap.emptyFM FiniteMap.emptyFM",fontsize=16,color="green",shape="box"];13 -> 15[label="",style="dashed", color="green", weight=3];
12.94/5.39	13 -> 16[label="",style="dashed", color="green", weight=3];
12.94/5.39	14[label="FiniteMap.addToFM_C2 vyy3 vyy40 vyy41 vyy42 vyy43 vyy44 vyy5 vyy6 (compare vyy5 vyy40 == LT)",fontsize=16,color="burlywood",shape="box"];34[label="vyy5/()",fontsize=10,color="white",style="solid",shape="box"];14 -> 34[label="",style="solid", color="burlywood", weight=9];
12.94/5.39	34 -> 17[label="",style="solid", color="burlywood", weight=3];
12.94/5.39	15[label="FiniteMap.emptyFM",fontsize=16,color="black",shape="triangle"];15 -> 18[label="",style="solid", color="black", weight=3];
12.94/5.39	16 -> 15[label="",style="dashed", color="red", weight=0];
12.94/5.39	16[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];17[label="FiniteMap.addToFM_C2 vyy3 vyy40 vyy41 vyy42 vyy43 vyy44 () vyy6 (compare () vyy40 == LT)",fontsize=16,color="burlywood",shape="box"];35[label="vyy40/()",fontsize=10,color="white",style="solid",shape="box"];17 -> 35[label="",style="solid", color="burlywood", weight=9];
12.94/5.39	35 -> 19[label="",style="solid", color="burlywood", weight=3];
12.94/5.39	18[label="FiniteMap.EmptyFM",fontsize=16,color="green",shape="box"];19[label="FiniteMap.addToFM_C2 vyy3 () vyy41 vyy42 vyy43 vyy44 () vyy6 (compare () () == LT)",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3];
12.94/5.39	20[label="FiniteMap.addToFM_C2 vyy3 () vyy41 vyy42 vyy43 vyy44 () vyy6 (EQ == LT)",fontsize=16,color="black",shape="box"];20 -> 21[label="",style="solid", color="black", weight=3];
12.94/5.39	21[label="FiniteMap.addToFM_C2 vyy3 () vyy41 vyy42 vyy43 vyy44 () vyy6 False",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3];
12.94/5.39	22[label="FiniteMap.addToFM_C1 vyy3 () vyy41 vyy42 vyy43 vyy44 () vyy6 (() > ())",fontsize=16,color="black",shape="box"];22 -> 23[label="",style="solid", color="black", weight=3];
12.94/5.39	23[label="FiniteMap.addToFM_C1 vyy3 () vyy41 vyy42 vyy43 vyy44 () vyy6 (compare () () == GT)",fontsize=16,color="black",shape="box"];23 -> 24[label="",style="solid", color="black", weight=3];
12.94/5.39	24[label="FiniteMap.addToFM_C1 vyy3 () vyy41 vyy42 vyy43 vyy44 () vyy6 (EQ == GT)",fontsize=16,color="black",shape="box"];24 -> 25[label="",style="solid", color="black", weight=3];
12.94/5.39	25[label="FiniteMap.addToFM_C1 vyy3 () vyy41 vyy42 vyy43 vyy44 () vyy6 False",fontsize=16,color="black",shape="box"];25 -> 26[label="",style="solid", color="black", weight=3];
12.94/5.39	26[label="FiniteMap.addToFM_C0 vyy3 () vyy41 vyy42 vyy43 vyy44 () vyy6 otherwise",fontsize=16,color="black",shape="box"];26 -> 27[label="",style="solid", color="black", weight=3];
12.94/5.39	27[label="FiniteMap.addToFM_C0 vyy3 () vyy41 vyy42 vyy43 vyy44 () vyy6 True",fontsize=16,color="black",shape="box"];27 -> 28[label="",style="solid", color="black", weight=3];
12.94/5.39	28[label="FiniteMap.Branch () (vyy3 vyy41 vyy6) vyy42 vyy43 vyy44",fontsize=16,color="green",shape="box"];28 -> 29[label="",style="dashed", color="green", weight=3];
12.94/5.39	29[label="vyy3 vyy41 vyy6",fontsize=16,color="green",shape="box"];29 -> 30[label="",style="dashed", color="green", weight=3];
12.94/5.39	29 -> 31[label="",style="dashed", color="green", weight=3];
12.94/5.39	30[label="vyy41",fontsize=16,color="green",shape="box"];31[label="vyy6",fontsize=16,color="green",shape="box"];}
12.94/5.39	
12.94/5.39	----------------------------------------
12.94/5.39	
12.94/5.39	(12)
12.94/5.39	YES
13.20/6.46	EOF