10.42/4.61	YES
12.79/5.26	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.79/5.26	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.79/5.26	
12.79/5.26	
12.79/5.26	H-Termination with start terms of the given HASKELL could be proven:
12.79/5.26	
12.79/5.26	(0) HASKELL
12.79/5.26	(1) CR [EQUIVALENT, 0 ms]
12.79/5.26	(2) HASKELL
12.79/5.26	(3) BR [EQUIVALENT, 0 ms]
12.79/5.26	(4) HASKELL
12.79/5.26	(5) COR [EQUIVALENT, 19 ms]
12.79/5.26	(6) HASKELL
12.79/5.26	(7) LetRed [EQUIVALENT, 0 ms]
12.79/5.26	(8) HASKELL
12.79/5.26	(9) NumRed [SOUND, 0 ms]
12.79/5.26	(10) HASKELL
12.79/5.26	(11) Narrow [SOUND, 0 ms]
12.79/5.26	(12) QDP
12.79/5.26	(13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.79/5.26	(14) YES
12.79/5.26	
12.79/5.26	
12.79/5.26	----------------------------------------
12.79/5.26	
12.79/5.26	(0)
12.79/5.26	Obligation:
12.79/5.26	mainModule Main 
12.79/5.26	module FiniteMap where {
12.79/5.26	import qualified Main;
12.79/5.26	import qualified Maybe;
12.79/5.26	import qualified Prelude;
12.79/5.26	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.79/5.26	
12.79/5.26	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
12.79/5.26	}
12.79/5.26	addListToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
12.79/5.26	addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 
12.79/5.26	add fmap (key,elt) = addToFM_C combiner fmap key elt;
12.79/5.26	 };
12.79/5.26	
12.79/5.26	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
12.79/5.26	addToFM_C combiner EmptyFM key elt = unitFM key elt;
12.79/5.26	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
12.79/5.26	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
12.79/5.26	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
12.79/5.26	
12.79/5.26	emptyFM :: FiniteMap a b;
12.79/5.26	emptyFM = EmptyFM;
12.79/5.26	
12.79/5.26	findMax :: FiniteMap b a  ->  (b,a);
12.79/5.26	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
12.79/5.26	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
12.79/5.26	
12.79/5.26	findMin :: FiniteMap a b  ->  (a,b);
12.79/5.26	findMin (Branch key elt _ EmptyFM _) = (key,elt);
12.79/5.26	findMin (Branch key elt _ fm_l _) = findMin fm_l;
12.79/5.26	
12.79/5.26	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
12.79/5.26	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
12.79/5.26	 | size_r > sIZE_RATIO * size_l = case fm_R of { 
12.79/5.26	Branch _ _ _ fm_rl fm_rr | sizeFM fm_rl < 2 * sizeFM fm_rr -> single_L fm_L fm_R
12.79/5.26	 | otherwise -> double_L fm_L fm_R; 
12.79/5.26	 } 
12.79/5.26	 | size_l > sIZE_RATIO * size_r = case fm_L of { 
12.79/5.26	Branch _ _ _ fm_ll fm_lr | sizeFM fm_lr < 2 * sizeFM fm_ll -> single_R fm_L fm_R
12.79/5.26	 | otherwise -> double_R fm_L fm_R; 
12.79/5.26	 } 
12.79/5.26	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
12.79/5.26	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);
12.79/5.26	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);
12.79/5.26	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;
12.79/5.26	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);
12.79/5.26	size_l = sizeFM fm_L;
12.79/5.26	size_r = sizeFM fm_R;
12.79/5.26	 };
12.79/5.26	
12.79/5.26	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
12.79/5.26	mkBranch which key elt fm_l fm_r = let { 
12.79/5.26	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
12.79/5.26	} in result where { 
12.79/5.26	balance_ok = True;
12.79/5.26	left_ok = case fm_l of { 
12.79/5.26	EmptyFM-> True; 
12.79/5.26	Branch left_key _ _ _ _-> let { 
12.79/5.26	biggest_left_key = fst (findMax fm_l);
12.79/5.26	} in biggest_left_key < key; 
12.79/5.26	 } ;
12.79/5.26	left_size = sizeFM fm_l;
12.79/5.26	right_ok = case fm_r of { 
12.79/5.26	EmptyFM-> True; 
12.79/5.26	Branch right_key _ _ _ _-> let { 
12.79/5.26	smallest_right_key = fst (findMin fm_r);
12.79/5.26	} in key < smallest_right_key; 
12.79/5.26	 } ;
12.79/5.26	right_size = sizeFM fm_r;
12.79/5.26	unbox :: Int  ->  Int;
12.79/5.26	unbox x = x;
12.79/5.26	 };
12.79/5.26	
12.79/5.26	sIZE_RATIO :: Int;
12.79/5.26	sIZE_RATIO = 5;
12.79/5.26	
12.79/5.26	sizeFM :: FiniteMap b a  ->  Int;
12.79/5.26	sizeFM EmptyFM = 0;
12.79/5.26	sizeFM (Branch _ _ size _ _) = size;
12.79/5.26	
12.79/5.26	unitFM :: b  ->  a  ->  FiniteMap b a;
12.79/5.26	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
12.79/5.26	
12.79/5.26	}
12.79/5.26	module Maybe where {
12.79/5.26	import qualified FiniteMap;
12.79/5.26	import qualified Main;
12.79/5.26	import qualified Prelude;
12.79/5.26	}
12.79/5.26	module Main where {
12.79/5.26	import qualified FiniteMap;
12.79/5.26	import qualified Maybe;
12.79/5.26	import qualified Prelude;
12.79/5.26	}
12.79/5.26	
12.79/5.26	----------------------------------------
12.79/5.26	
12.79/5.26	(1) CR (EQUIVALENT)
12.79/5.26	Case Reductions:
12.79/5.26	The following Case expression
12.79/5.26	"case fm_r of {
12.79/5.26	EmptyFM  -> True;
12.79/5.26	Branch right_key _ _ _ _  -> let {
12.79/5.26	smallest_right_key  = fst (findMin fm_r);
12.79/5.26	} in key < smallest_right_key}
12.79/5.26	"
12.79/5.26	is transformed to
12.79/5.26	"right_ok0 fm_r key EmptyFM = True;
12.79/5.26	right_ok0 fm_r key (Branch right_key _ _ _ _) = let {
12.79/5.26	smallest_right_key  = fst (findMin fm_r);
12.79/5.26	} in key < smallest_right_key;
12.79/5.26	"
12.79/5.26	The following Case expression
12.79/5.26	"case fm_l of {
12.79/5.26	EmptyFM  -> True;
12.79/5.26	Branch left_key _ _ _ _  -> let {
12.79/5.26	biggest_left_key  = fst (findMax fm_l);
12.79/5.26	} in biggest_left_key < key}
12.79/5.26	"
12.79/5.26	is transformed to
12.79/5.26	"left_ok0 fm_l key EmptyFM = True;
12.79/5.26	left_ok0 fm_l key (Branch left_key _ _ _ _) = let {
12.79/5.26	biggest_left_key  = fst (findMax fm_l);
12.79/5.26	} in biggest_left_key < key;
12.79/5.26	"
12.79/5.26	The following Case expression
12.79/5.26	"case fm_R of {
12.79/5.26	Branch _ _ _ fm_rl fm_rr |sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R}
12.79/5.26	"
12.79/5.26	is transformed to
12.79/5.26	"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;
12.79/5.26	"
12.79/5.26	The following Case expression
12.79/5.26	"case fm_L of {
12.79/5.26	Branch _ _ _ fm_ll fm_lr |sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R}
12.79/5.26	"
12.79/5.26	is transformed to
12.79/5.26	"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;
12.79/5.26	"
12.79/5.26	
12.79/5.26	----------------------------------------
12.79/5.26	
12.79/5.26	(2)
12.79/5.26	Obligation:
12.79/5.26	mainModule Main 
12.79/5.26	module FiniteMap where {
12.79/5.26	import qualified Main;
12.79/5.26	import qualified Maybe;
12.79/5.26	import qualified Prelude;
12.79/5.26	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.79/5.26	
12.79/5.26	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.79/5.26	}
12.79/5.26	addListToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
12.79/5.26	addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 
12.79/5.26	add fmap (key,elt) = addToFM_C combiner fmap key elt;
12.79/5.26	 };
12.79/5.26	
12.79/5.26	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
12.79/5.26	addToFM_C combiner EmptyFM key elt = unitFM key elt;
12.79/5.26	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
12.79/5.26	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
12.79/5.26	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
12.79/5.26	
12.79/5.26	emptyFM :: FiniteMap b a;
12.79/5.26	emptyFM = EmptyFM;
12.79/5.26	
12.79/5.26	findMax :: FiniteMap b a  ->  (b,a);
12.79/5.26	findMax (Branch key elt _ _ EmptyFM) = (key,elt);
12.79/5.26	findMax (Branch key elt _ _ fm_r) = findMax fm_r;
12.79/5.26	
12.79/5.26	findMin :: FiniteMap b a  ->  (b,a);
12.79/5.26	findMin (Branch key elt _ EmptyFM _) = (key,elt);
12.79/5.26	findMin (Branch key elt _ fm_l _) = findMin fm_l;
12.79/5.26	
12.79/5.26	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
12.79/5.26	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
12.79/5.26	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
12.79/5.26	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
12.79/5.26	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
12.79/5.26	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);
12.79/5.26	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);
12.79/5.26	mkBalBranch0 fm_L fm_R (Branch _ _ _ fm_rl fm_rr)  | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R
12.79/5.26	 | otherwise = double_L fm_L fm_R;
12.79/5.26	mkBalBranch1 fm_L fm_R (Branch _ _ _ fm_ll fm_lr)  | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R
12.79/5.26	 | otherwise = double_R fm_L fm_R;
12.79/5.26	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;
12.79/5.26	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);
12.79/5.26	size_l = sizeFM fm_L;
12.79/5.26	size_r = sizeFM fm_R;
12.79/5.26	 };
12.79/5.26	
12.79/5.26	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
13.11/5.32	mkBranch which key elt fm_l fm_r = let { 
13.11/5.32	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
13.11/5.32	} in result where { 
13.11/5.32	balance_ok = True;
13.11/5.32	left_ok = left_ok0 fm_l key fm_l;
13.11/5.32	left_ok0 fm_l key EmptyFM = True;
13.11/5.32	left_ok0 fm_l key (Branch left_key _ _ _ _) = let { 
13.11/5.32	biggest_left_key = fst (findMax fm_l);
13.11/5.32	} in biggest_left_key < key;
13.11/5.32	left_size = sizeFM fm_l;
13.11/5.32	right_ok = right_ok0 fm_r key fm_r;
13.11/5.32	right_ok0 fm_r key EmptyFM = True;
13.11/5.32	right_ok0 fm_r key (Branch right_key _ _ _ _) = let { 
13.11/5.32	smallest_right_key = fst (findMin fm_r);
13.11/5.32	} in key < smallest_right_key;
13.11/5.32	right_size = sizeFM fm_r;
13.11/5.32	unbox :: Int  ->  Int;
13.11/5.32	unbox x = x;
13.11/5.32	 };
13.11/5.32	
13.11/5.32	sIZE_RATIO :: Int;
13.11/5.32	sIZE_RATIO = 5;
13.11/5.32	
13.11/5.32	sizeFM :: FiniteMap a b  ->  Int;
13.11/5.32	sizeFM EmptyFM = 0;
13.11/5.32	sizeFM (Branch _ _ size _ _) = size;
13.11/5.32	
13.11/5.32	unitFM :: b  ->  a  ->  FiniteMap b a;
13.11/5.32	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
13.11/5.32	
13.11/5.32	}
13.11/5.32	module Maybe where {
13.11/5.32	import qualified FiniteMap;
13.11/5.32	import qualified Main;
13.11/5.32	import qualified Prelude;
13.11/5.32	}
13.11/5.32	module Main where {
13.11/5.32	import qualified FiniteMap;
13.11/5.32	import qualified Maybe;
13.11/5.32	import qualified Prelude;
13.11/5.32	}
13.11/5.32	
13.11/5.32	----------------------------------------
13.11/5.32	
13.11/5.32	(3) BR (EQUIVALENT)
13.11/5.32	Replaced joker patterns by fresh variables and removed binding patterns.
13.11/5.32	----------------------------------------
13.11/5.32	
13.11/5.32	(4)
13.11/5.32	Obligation:
13.11/5.32	mainModule Main 
13.11/5.32	module FiniteMap where {
13.11/5.32	import qualified Main;
13.11/5.32	import qualified Maybe;
13.11/5.32	import qualified Prelude;
13.11/5.32	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
13.11/5.32	
13.11/5.32	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
13.11/5.32	}
13.11/5.32	addListToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
13.11/5.32	addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 
13.11/5.32	add fmap (key,elt) = addToFM_C combiner fmap key elt;
13.11/5.32	 };
13.11/5.32	
13.11/5.32	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
13.11/5.32	addToFM_C combiner EmptyFM key elt = unitFM key elt;
13.11/5.32	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt  | new_key < key = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
13.11/5.32	 | new_key > key = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
13.11/5.32	 | otherwise = Branch new_key (combiner elt new_elt) size fm_l fm_r;
13.11/5.32	
13.11/5.32	emptyFM :: FiniteMap a b;
13.11/5.32	emptyFM = EmptyFM;
13.11/5.32	
13.11/5.32	findMax :: FiniteMap b a  ->  (b,a);
13.11/5.32	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
13.11/5.32	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
13.11/5.32	
13.11/5.32	findMin :: FiniteMap a b  ->  (a,b);
13.11/5.32	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
13.11/5.32	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
13.11/5.32	
13.11/5.32	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
13.11/5.32	mkBalBranch key elt fm_L fm_R  | size_l + size_r < 2 = mkBranch 1 key elt fm_L fm_R
13.11/5.32	 | size_r > sIZE_RATIO * size_l = mkBalBranch0 fm_L fm_R fm_R
13.11/5.32	 | size_l > sIZE_RATIO * size_r = mkBalBranch1 fm_L fm_R fm_L
13.11/5.32	 | otherwise = mkBranch 2 key elt fm_L fm_R where { 
13.11/5.32	double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
13.11/5.32	double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
13.11/5.32	mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr)  | sizeFM fm_rl < 2 * sizeFM fm_rr = single_L fm_L fm_R
13.11/5.32	 | otherwise = double_L fm_L fm_R;
13.11/5.32	mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr)  | sizeFM fm_lr < 2 * sizeFM fm_ll = single_R fm_L fm_R
13.11/5.32	 | otherwise = double_R fm_L fm_R;
13.11/5.32	single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
13.11/5.32	single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
13.11/5.32	size_l = sizeFM fm_L;
13.11/5.32	size_r = sizeFM fm_R;
13.11/5.32	 };
13.11/5.32	
13.11/5.32	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
13.11/5.32	mkBranch which key elt fm_l fm_r = let { 
13.11/5.32	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
13.11/5.32	} in result where { 
13.11/5.32	balance_ok = True;
13.11/5.32	left_ok = left_ok0 fm_l key fm_l;
13.11/5.32	left_ok0 fm_l key EmptyFM = True;
13.11/5.32	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
13.11/5.32	biggest_left_key = fst (findMax fm_l);
13.11/5.32	} in biggest_left_key < key;
13.11/5.32	left_size = sizeFM fm_l;
13.11/5.32	right_ok = right_ok0 fm_r key fm_r;
13.11/5.32	right_ok0 fm_r key EmptyFM = True;
13.11/5.32	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
13.11/5.32	smallest_right_key = fst (findMin fm_r);
13.11/5.32	} in key < smallest_right_key;
13.11/5.32	right_size = sizeFM fm_r;
13.11/5.32	unbox :: Int  ->  Int;
13.11/5.32	unbox x = x;
13.11/5.32	 };
13.11/5.32	
13.11/5.32	sIZE_RATIO :: Int;
13.11/5.32	sIZE_RATIO = 5;
13.11/5.32	
13.11/5.32	sizeFM :: FiniteMap b a  ->  Int;
13.11/5.32	sizeFM EmptyFM = 0;
13.11/5.32	sizeFM (Branch vz wu size wv ww) = size;
13.11/5.32	
13.11/5.32	unitFM :: a  ->  b  ->  FiniteMap a b;
13.11/5.32	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
13.11/5.32	
13.11/5.32	}
13.11/5.32	module Maybe where {
13.11/5.32	import qualified FiniteMap;
13.11/5.32	import qualified Main;
13.11/5.32	import qualified Prelude;
13.11/5.32	}
13.11/5.32	module Main where {
13.11/5.32	import qualified FiniteMap;
13.11/5.32	import qualified Maybe;
13.11/5.32	import qualified Prelude;
13.11/5.32	}
13.11/5.32	
13.11/5.32	----------------------------------------
13.11/5.32	
13.11/5.32	(5) COR (EQUIVALENT)
13.11/5.32	Cond Reductions:
13.11/5.32	The following Function with conditions
13.11/5.32	"undefined |Falseundefined;
13.11/5.33	"
13.11/5.33	is transformed to
13.11/5.33	"undefined  = undefined1;
13.11/5.33	"
13.11/5.33	"undefined0 True = undefined;
13.11/5.33	"
13.11/5.33	"undefined1  = undefined0 False;
13.11/5.33	"
13.11/5.33	The following Function with conditions
13.11/5.33	"addToFM_C combiner EmptyFM key elt = unitFM key elt;
13.11/5.33	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt|new_key < keymkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r|new_key > keymkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)|otherwiseBranch new_key (combiner elt new_elt) size fm_l fm_r;
13.11/5.33	"
13.11/5.33	is transformed to
13.11/5.33	"addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
13.11/5.33	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt;
13.11/5.33	"
13.11/5.33	"addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r;
13.11/5.33	"
13.11/5.33	"addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt);
13.11/5.33	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise;
13.11/5.33	"
13.11/5.33	"addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r;
13.11/5.33	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key);
13.11/5.33	"
13.11/5.33	"addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key);
13.11/5.33	"
13.11/5.33	"addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
13.11/5.33	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
13.11/5.33	"
13.11/5.33	The following Function with conditions
13.11/5.33	"mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R;
13.11/5.33	"
13.11/5.33	is transformed to
13.11/5.33	"mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
13.11/5.33	"
13.11/5.33	"mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
13.11/5.33	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
13.11/5.33	"
13.11/5.33	"mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
13.11/5.33	"
13.11/5.33	"mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
13.11/5.33	"
13.11/5.33	The following Function with conditions
13.11/5.33	"mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R;
13.11/5.33	"
13.11/5.33	is transformed to
13.11/5.33	"mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
13.11/5.33	"
13.11/5.33	"mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
13.11/5.33	"
13.11/5.33	"mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
13.11/5.33	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
13.11/5.33	"
13.11/5.33	"mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
13.11/5.33	"
13.11/5.33	The following Function with conditions
13.11/5.33	"mkBalBranch key elt fm_L fm_R|size_l + size_r < 2mkBranch 1 key elt fm_L fm_R|size_r > sIZE_RATIO * size_lmkBalBranch0 fm_L fm_R fm_R|size_l > sIZE_RATIO * size_rmkBalBranch1 fm_L fm_R fm_L|otherwisemkBranch 2 key elt fm_L fm_R where {
13.11/5.33	double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
13.11/5.33	;
13.11/5.33	double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
13.11/5.33	;
13.11/5.33	mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr)|sizeFM fm_rl < 2 * sizeFM fm_rrsingle_L fm_L fm_R|otherwisedouble_L fm_L fm_R;
13.11/5.33	;
13.11/5.33	mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr)|sizeFM fm_lr < 2 * sizeFM fm_llsingle_R fm_L fm_R|otherwisedouble_R fm_L fm_R;
13.11/5.33	;
13.11/5.33	single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
13.11/5.33	;
13.11/5.33	single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
13.11/5.33	;
13.11/5.33	size_l  = sizeFM fm_L;
13.11/5.33	;
13.11/5.33	size_r  = sizeFM fm_R;
13.11/5.33	} 
13.11/5.33	;
13.11/5.33	"
13.11/5.33	is transformed to
13.11/5.33	"mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
13.11/5.33	"
13.11/5.33	"mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
13.11/5.33	double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
13.11/5.33	;
13.11/5.33	double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
13.11/5.33	;
13.11/5.33	mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
13.11/5.33	;
13.11/5.33	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
13.11/5.33	;
13.11/5.33	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
13.11/5.33	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
13.11/5.33	;
13.11/5.33	mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
13.11/5.33	;
13.11/5.33	mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
13.11/5.33	;
13.11/5.33	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
13.11/5.33	;
13.11/5.33	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
13.11/5.33	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
13.11/5.33	;
13.11/5.33	mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
13.11/5.33	;
13.11/5.33	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
13.11/5.33	;
13.11/5.33	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
13.11/5.33	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
13.11/5.33	;
13.11/5.33	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
13.11/5.33	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
13.11/5.33	;
13.11/5.33	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
13.11/5.33	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
13.11/5.33	;
13.11/5.33	single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
13.11/5.33	;
13.11/5.33	single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
13.11/5.33	;
13.11/5.33	size_l  = sizeFM fm_L;
13.11/5.33	;
13.11/5.33	size_r  = sizeFM fm_R;
13.11/5.33	} 
13.11/5.33	;
13.11/5.33	"
13.11/5.33	
13.11/5.33	----------------------------------------
13.11/5.33	
13.11/5.33	(6)
13.11/5.33	Obligation:
13.11/5.33	mainModule Main 
13.11/5.33	module FiniteMap where {
13.11/5.33	import qualified Main;
13.11/5.33	import qualified Maybe;
13.11/5.33	import qualified Prelude;
13.11/5.33	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
13.11/5.33	
13.11/5.33	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
13.11/5.33	}
13.11/5.33	addListToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
13.11/5.33	addListToFM_C combiner fm key_elt_pairs = foldl add fm key_elt_pairs where { 
13.11/5.33	add fmap (key,elt) = addToFM_C combiner fmap key elt;
13.11/5.33	 };
13.11/5.33	
13.11/5.33	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
13.11/5.33	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
13.11/5.33	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt;
13.11/5.33	
13.11/5.33	addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r;
13.11/5.33	
13.11/5.33	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt);
13.11/5.33	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise;
13.11/5.33	
13.11/5.33	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r;
13.11/5.33	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key);
13.11/5.33	
13.11/5.33	addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key);
13.11/5.33	
13.11/5.33	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
13.11/5.33	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
13.11/5.33	
13.11/5.33	emptyFM :: FiniteMap a b;
13.11/5.33	emptyFM = EmptyFM;
13.11/5.33	
13.11/5.33	findMax :: FiniteMap a b  ->  (a,b);
13.11/5.33	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
13.11/5.33	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
13.11/5.33	
13.11/5.33	findMin :: FiniteMap b a  ->  (b,a);
13.11/5.33	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
13.11/5.33	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
13.11/5.33	
13.11/5.33	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
13.11/5.33	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
13.11/5.33	
13.11/5.33	mkBalBranch6 key elt fm_L fm_R = mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where { 
13.11/5.33	double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
13.11/5.33	double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
13.11/5.33	mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
13.11/5.33	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
13.11/5.33	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
13.11/5.33	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
13.11/5.33	mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
13.11/5.33	mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
13.11/5.33	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
13.11/5.33	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
13.11/5.33	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
13.11/5.33	mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
13.11/5.33	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
13.11/5.33	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
13.11/5.33	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
13.11/5.33	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
13.11/5.33	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
13.11/5.33	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
13.11/5.33	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
13.11/5.33	single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
13.11/5.33	single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
13.41/5.41	size_l = sizeFM fm_L;
13.41/5.41	size_r = sizeFM fm_R;
13.41/5.41	 };
13.41/5.41	
13.41/5.41	mkBranch :: Ord a => Int  ->  a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
13.41/5.41	mkBranch which key elt fm_l fm_r = let { 
13.41/5.41	result = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
13.41/5.41	} in result where { 
13.41/5.41	balance_ok = True;
13.41/5.41	left_ok = left_ok0 fm_l key fm_l;
13.41/5.41	left_ok0 fm_l key EmptyFM = True;
13.41/5.41	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let { 
13.41/5.41	biggest_left_key = fst (findMax fm_l);
13.41/5.41	} in biggest_left_key < key;
13.41/5.41	left_size = sizeFM fm_l;
13.41/5.41	right_ok = right_ok0 fm_r key fm_r;
13.41/5.41	right_ok0 fm_r key EmptyFM = True;
13.41/5.41	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let { 
13.41/5.41	smallest_right_key = fst (findMin fm_r);
13.41/5.41	} in key < smallest_right_key;
13.41/5.41	right_size = sizeFM fm_r;
13.41/5.41	unbox :: Int  ->  Int;
13.41/5.41	unbox x = x;
13.41/5.41	 };
13.41/5.41	
13.41/5.41	sIZE_RATIO :: Int;
13.41/5.41	sIZE_RATIO = 5;
13.41/5.41	
13.41/5.41	sizeFM :: FiniteMap b a  ->  Int;
13.41/5.41	sizeFM EmptyFM = 0;
13.41/5.41	sizeFM (Branch vz wu size wv ww) = size;
13.41/5.41	
13.41/5.41	unitFM :: a  ->  b  ->  FiniteMap a b;
13.41/5.41	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
13.41/5.41	
13.41/5.41	}
13.41/5.41	module Maybe where {
13.41/5.41	import qualified FiniteMap;
13.41/5.41	import qualified Main;
13.41/5.41	import qualified Prelude;
13.41/5.41	}
13.41/5.41	module Main where {
13.41/5.41	import qualified FiniteMap;
13.41/5.41	import qualified Maybe;
13.41/5.41	import qualified Prelude;
13.41/5.41	}
13.41/5.41	
13.41/5.41	----------------------------------------
13.41/5.41	
13.41/5.41	(7) LetRed (EQUIVALENT)
13.41/5.41	Let/Where Reductions:
13.41/5.41	The bindings of the following Let/Where expression
13.41/5.41	"mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where {
13.41/5.41	double_L fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
13.41/5.41	;
13.41/5.41	double_R (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r);
13.41/5.41	;
13.41/5.41	mkBalBranch0 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
13.41/5.41	;
13.41/5.41	mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr True = double_L fm_L fm_R;
13.41/5.41	;
13.41/5.41	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr True = single_L fm_L fm_R;
13.41/5.41	mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
13.41/5.41	;
13.41/5.41	mkBalBranch02 fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
13.41/5.41	;
13.41/5.41	mkBalBranch1 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
13.41/5.41	;
13.41/5.41	mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr True = double_R fm_L fm_R;
13.41/5.41	;
13.41/5.41	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr True = single_R fm_L fm_R;
13.41/5.41	mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch10 fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
13.41/5.41	;
13.41/5.41	mkBalBranch12 fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch11 fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
13.41/5.41	;
13.41/5.41	mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
13.41/5.41	;
13.41/5.41	mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L;
13.41/5.41	mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise;
13.41/5.41	;
13.41/5.41	mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R;
13.41/5.41	mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r);
13.41/5.41	;
13.41/5.41	mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
13.41/5.41	mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l);
13.41/5.41	;
13.41/5.41	single_L fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr;
13.41/5.41	;
13.41/5.41	single_R (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r);
13.41/5.41	;
13.41/5.41	size_l  = sizeFM fm_L;
13.41/5.41	;
13.41/5.41	size_r  = sizeFM fm_R;
13.41/5.41	} 
13.41/5.41	"
13.41/5.41	are unpacked to the following functions on top level
13.41/5.41	"mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
13.41/5.41	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
13.41/5.41	"
13.41/5.41	"mkBalBranch6Single_R vwx vwy vwz vxu (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 vwx vwy fm_lr fm_r);
13.41/5.41	"
13.41/5.41	"mkBalBranch6Double_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 vwx vwy fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
13.41/5.41	"
13.41/5.41	"mkBalBranch6Double_R vwx vwy vwz vxu (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 vwx vwy fm_lrr fm_r);
13.41/5.41	"
13.41/5.41	"mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
13.41/5.41	"
13.41/5.41	"mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
13.41/5.41	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_l vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_r vwx vwy vwz vxu);
13.41/5.41	"
13.41/5.41	"mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
13.41/5.41	"
13.41/5.41	"mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Single_L vwx vwy vwz vxu fm_L fm_R;
13.41/5.41	mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
13.41/5.41	"
13.41/5.41	"mkBalBranch6Single_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 vwx vwy fm_l fm_rl) fm_rr;
13.41/5.41	"
13.41/5.41	"mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Double_L vwx vwy vwz vxu fm_L fm_R;
13.41/5.41	"
13.41/5.41	"mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Double_R vwx vwy vwz vxu fm_L fm_R;
13.41/5.41	"
13.41/5.41	"mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
13.41/5.41	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_r vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_l vwx vwy vwz vxu);
13.41/5.41	"
13.41/5.41	"mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vwz;
13.41/5.41	"
13.41/5.41	"mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vxu;
13.41/5.41	"
13.41/5.41	"mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
13.41/5.41	"
13.41/5.41	"mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
13.41/5.41	"
13.41/5.41	"mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
13.41/5.41	"
13.41/5.41	"mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Single_R vwx vwy vwz vxu fm_L fm_R;
13.41/5.41	mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
13.41/5.41	"
13.41/5.41	The bindings of the following Let/Where expression
13.41/5.41	"foldl add fm key_elt_pairs where {
13.41/5.41	add fmap (key,elt) = addToFM_C combiner fmap key elt;
13.41/5.41	} 
13.41/5.41	"
13.41/5.41	are unpacked to the following functions on top level
13.41/5.41	"addListToFM_CAdd vxv fmap (key,elt) = addToFM_C vxv fmap key elt;
13.41/5.41	"
13.41/5.41	The bindings of the following Let/Where expression
13.41/5.41	"let {
13.41/5.41	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
13.41/5.41	} in result where {
13.41/5.41	balance_ok  = True;
13.41/5.41	;
13.41/5.41	left_ok  = left_ok0 fm_l key fm_l;
13.41/5.41	;
13.41/5.41	left_ok0 fm_l key EmptyFM = True;
13.41/5.41	left_ok0 fm_l key (Branch left_key xv xw xx xy) = let {
13.41/5.41	biggest_left_key  = fst (findMax fm_l);
13.41/5.41	} in biggest_left_key < key;
13.41/5.41	;
13.41/5.41	left_size  = sizeFM fm_l;
13.41/5.41	;
13.41/5.41	right_ok  = right_ok0 fm_r key fm_r;
13.41/5.41	;
13.41/5.41	right_ok0 fm_r key EmptyFM = True;
13.41/5.41	right_ok0 fm_r key (Branch right_key xz yu yv yw) = let {
13.41/5.41	smallest_right_key  = fst (findMin fm_r);
13.41/5.41	} in key < smallest_right_key;
13.41/5.41	;
13.41/5.41	right_size  = sizeFM fm_r;
13.41/5.41	;
13.41/5.41	unbox x = x;
13.41/5.41	} 
13.41/5.41	"
13.41/5.41	are unpacked to the following functions on top level
13.41/5.46	"mkBranchUnbox vxw vxx vxy x = x;
13.41/5.46	"
13.41/5.46	"mkBranchRight_size vxw vxx vxy = sizeFM vxw;
13.41/5.46	"
13.41/5.46	"mkBranchBalance_ok vxw vxx vxy = True;
13.41/5.46	"
13.41/5.46	"mkBranchLeft_size vxw vxx vxy = sizeFM vxx;
13.41/5.46	"
13.41/5.46	"mkBranchRight_ok vxw vxx vxy = mkBranchRight_ok0 vxw vxx vxy vxw vxy vxw;
13.41/5.46	"
13.41/5.46	"mkBranchRight_ok0 vxw vxx vxy fm_r key EmptyFM = True;
13.41/5.46	mkBranchRight_ok0 vxw vxx vxy fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
13.41/5.46	"
13.41/5.46	"mkBranchLeft_ok vxw vxx vxy = mkBranchLeft_ok0 vxw vxx vxy vxx vxy vxx;
13.41/5.46	"
13.41/5.46	"mkBranchLeft_ok0 vxw vxx vxy fm_l key EmptyFM = True;
13.41/5.46	mkBranchLeft_ok0 vxw vxx vxy fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
13.41/5.46	"
13.41/5.46	The bindings of the following Let/Where expression
13.41/5.46	"let {
13.41/5.46	result  = Branch key elt (unbox (1 + left_size + right_size)) fm_l fm_r;
13.41/5.46	} in result"
13.41/5.46	are unpacked to the following functions on top level
13.41/5.46	"mkBranchResult vxz vyu vyv vyw = Branch vxz vyu (mkBranchUnbox vyv vyw vxz (1 + mkBranchLeft_size vyv vyw vxz + mkBranchRight_size vyv vyw vxz)) vyw vyv;
13.41/5.46	"
13.41/5.46	The bindings of the following Let/Where expression
13.41/5.46	"let {
13.41/5.46	smallest_right_key  = fst (findMin fm_r);
13.41/5.46	} in key < smallest_right_key"
13.41/5.46	are unpacked to the following functions on top level
13.41/5.46	"mkBranchRight_ok0Smallest_right_key vyx = fst (findMin vyx);
13.41/5.46	"
13.41/5.46	The bindings of the following Let/Where expression
13.41/5.46	"let {
13.41/5.46	biggest_left_key  = fst (findMax fm_l);
13.41/5.46	} in biggest_left_key < key"
13.41/5.46	are unpacked to the following functions on top level
13.41/5.46	"mkBranchLeft_ok0Biggest_left_key vyy = fst (findMax vyy);
13.41/5.46	"
13.41/5.46	
13.41/5.46	----------------------------------------
13.41/5.46	
13.41/5.46	(8)
13.41/5.46	Obligation:
13.41/5.46	mainModule Main 
13.41/5.46	module FiniteMap where {
13.41/5.46	import qualified Main;
13.41/5.46	import qualified Maybe;
13.41/5.46	import qualified Prelude;
13.41/5.46	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
13.41/5.46	
13.41/5.46	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
13.41/5.46	}
13.41/5.46	addListToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
13.41/5.46	addListToFM_C combiner fm key_elt_pairs = foldl (addListToFM_CAdd combiner) fm key_elt_pairs;
13.41/5.46	
13.41/5.46	addListToFM_CAdd vxv fmap (key,elt) = addToFM_C vxv fmap key elt;
13.41/5.46	
13.41/5.46	addToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b;
13.41/5.46	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
13.41/5.46	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt;
13.41/5.46	
13.41/5.46	addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r;
13.41/5.46	
13.41/5.46	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt);
13.41/5.46	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise;
13.41/5.46	
13.41/5.46	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r;
13.41/5.46	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key);
13.41/5.46	
13.41/5.46	addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key);
13.41/5.46	
13.41/5.46	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
13.41/5.46	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
13.41/5.46	
13.41/5.46	emptyFM :: FiniteMap b a;
13.41/5.46	emptyFM = EmptyFM;
13.41/5.46	
13.41/5.46	findMax :: FiniteMap a b  ->  (a,b);
13.41/5.46	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
13.41/5.46	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
13.41/5.46	
13.41/5.46	findMin :: FiniteMap b a  ->  (b,a);
13.41/5.46	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
13.41/5.46	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
13.41/5.46	
13.41/5.46	mkBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
13.41/5.46	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
13.41/5.46	
13.41/5.46	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);
13.41/5.46	
13.41/5.46	mkBalBranch6Double_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 vwx vwy fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr);
13.41/5.46	
13.41/5.46	mkBalBranch6Double_R vwx vwy vwz vxu (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 vwx vwy fm_lrr fm_r);
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Double_L vwx vwy vwz vxu fm_L fm_R;
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Single_L vwx vwy vwz vxu fm_L fm_R;
13.41/5.46	mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr);
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Double_R vwx vwy vwz vxu fm_L fm_R;
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Single_R vwx vwy vwz vxu fm_L fm_R;
13.41/5.46	mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll);
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R;
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
13.41/5.46	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
13.41/5.46	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_l vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_r vwx vwy vwz vxu);
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R;
13.41/5.46	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_r vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_l vwx vwy vwz vxu);
13.41/5.46	
13.41/5.46	mkBalBranch6Single_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 vwx vwy fm_l fm_rl) fm_rr;
13.41/5.46	
13.41/5.46	mkBalBranch6Single_R vwx vwy vwz vxu (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 vwx vwy fm_lr fm_r);
13.41/5.46	
13.41/5.46	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vxu;
13.41/5.46	
13.41/5.46	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vwz;
13.41/5.46	
13.41/5.46	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
13.41/5.46	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_r fm_l;
13.41/5.46	
13.41/5.46	mkBranchBalance_ok vxw vxx vxy = True;
13.41/5.46	
13.41/5.46	mkBranchLeft_ok vxw vxx vxy = mkBranchLeft_ok0 vxw vxx vxy vxx vxy vxx;
13.41/5.46	
13.41/5.46	mkBranchLeft_ok0 vxw vxx vxy fm_l key EmptyFM = True;
13.41/5.46	mkBranchLeft_ok0 vxw vxx vxy fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
13.41/5.46	
13.41/5.46	mkBranchLeft_ok0Biggest_left_key vyy = fst (findMax vyy);
13.41/5.46	
13.41/5.46	mkBranchLeft_size vxw vxx vxy = sizeFM vxx;
13.41/5.46	
13.41/5.46	mkBranchResult vxz vyu vyv vyw = Branch vxz vyu (mkBranchUnbox vyv vyw vxz (1 + mkBranchLeft_size vyv vyw vxz + mkBranchRight_size vyv vyw vxz)) vyw vyv;
13.41/5.46	
13.41/5.46	mkBranchRight_ok vxw vxx vxy = mkBranchRight_ok0 vxw vxx vxy vxw vxy vxw;
13.41/5.46	
13.41/5.46	mkBranchRight_ok0 vxw vxx vxy fm_r key EmptyFM = True;
13.41/5.46	mkBranchRight_ok0 vxw vxx vxy fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
13.41/5.46	
13.41/5.46	mkBranchRight_ok0Smallest_right_key vyx = fst (findMin vyx);
13.41/5.46	
13.41/5.46	mkBranchRight_size vxw vxx vxy = sizeFM vxw;
13.41/5.46	
13.41/5.46	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)));
13.41/5.46	mkBranchUnbox vxw vxx vxy x = x;
13.41/5.46	
13.41/5.46	sIZE_RATIO :: Int;
13.41/5.46	sIZE_RATIO = 5;
13.41/5.46	
13.41/5.46	sizeFM :: FiniteMap b a  ->  Int;
13.41/5.46	sizeFM EmptyFM = 0;
13.41/5.46	sizeFM (Branch vz wu size wv ww) = size;
13.41/5.46	
13.41/5.46	unitFM :: b  ->  a  ->  FiniteMap b a;
13.41/5.46	unitFM key elt = Branch key elt 1 emptyFM emptyFM;
13.41/5.46	
13.41/5.46	}
13.41/5.46	module Maybe where {
13.41/5.46	import qualified FiniteMap;
13.41/5.46	import qualified Main;
13.41/5.46	import qualified Prelude;
13.41/5.46	}
13.41/5.46	module Main where {
13.41/5.46	import qualified FiniteMap;
13.41/5.46	import qualified Maybe;
13.41/5.46	import qualified Prelude;
13.41/5.46	}
13.41/5.46	
13.41/5.46	----------------------------------------
13.41/5.46	
13.41/5.46	(9) NumRed (SOUND)
13.41/5.46	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
13.41/5.46	----------------------------------------
13.41/5.46	
13.41/5.46	(10)
13.41/5.46	Obligation:
13.41/5.46	mainModule Main 
13.41/5.46	module FiniteMap where {
13.41/5.46	import qualified Main;
13.41/5.46	import qualified Maybe;
13.41/5.46	import qualified Prelude;
13.41/5.46	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
13.41/5.46	
13.41/5.46	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
13.41/5.46	}
13.41/5.46	addListToFM_C :: Ord a => (b  ->  b  ->  b)  ->  FiniteMap a b  ->  [(a,b)]  ->  FiniteMap a b;
13.41/5.46	addListToFM_C combiner fm key_elt_pairs = foldl (addListToFM_CAdd combiner) fm key_elt_pairs;
13.41/5.46	
13.41/5.46	addListToFM_CAdd vxv fmap (key,elt) = addToFM_C vxv fmap key elt;
13.41/5.46	
13.41/5.46	addToFM_C :: Ord b => (a  ->  a  ->  a)  ->  FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a;
13.41/5.46	addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt;
13.41/5.46	addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt;
13.41/5.46	
13.41/5.46	addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt True = Branch new_key (combiner elt new_elt) size fm_l fm_r;
13.41/5.46	
13.41/5.46	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt);
13.41/5.46	addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise;
13.41/5.46	
13.41/5.46	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r;
13.41/5.46	addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt (new_key > key);
13.41/5.46	
13.41/5.46	addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C2 combiner key elt size fm_l fm_r new_key new_elt (new_key < key);
13.41/5.46	
13.41/5.46	addToFM_C4 combiner EmptyFM key elt = unitFM key elt;
13.41/5.46	addToFM_C4 vvx vvy vvz vwu = addToFM_C3 vvx vvy vvz vwu;
13.41/5.46	
13.41/5.46	emptyFM :: FiniteMap b a;
13.41/5.46	emptyFM = EmptyFM;
13.41/5.46	
13.41/5.46	findMax :: FiniteMap b a  ->  (b,a);
13.41/5.46	findMax (Branch key elt yx yy EmptyFM) = (key,elt);
13.41/5.46	findMax (Branch key elt yz zu fm_r) = findMax fm_r;
13.41/5.46	
13.41/5.46	findMin :: FiniteMap b a  ->  (b,a);
13.41/5.46	findMin (Branch key elt wx EmptyFM wy) = (key,elt);
13.41/5.46	findMin (Branch key elt wz fm_l xu) = findMin fm_l;
13.41/5.46	
13.41/5.46	mkBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b;
13.41/5.46	mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R;
13.41/5.46	
13.41/5.46	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)));
13.41/5.46	
13.41/5.46	mkBalBranch6Double_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vuv (Branch key_rl elt_rl vuw fm_rll fm_rlr) fm_rr) = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ Zero)))))) key_rl elt_rl (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) vwx vwy fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr);
13.41/5.46	
13.41/5.46	mkBalBranch6Double_R vwx vwy vwz vxu (Branch key_l elt_l zw fm_ll (Branch key_lr elt_lr zx fm_lrl fm_lrr)) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) key_lr elt_lr (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))) key_l elt_l fm_ll fm_lrl) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) vwx vwy fm_lrr fm_r);
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr);
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Double_L vwx vwy vwz vxu fm_L fm_R;
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr True = mkBalBranch6Single_L vwx vwy vwz vxu fm_L fm_R;
13.41/5.46	mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr False = mkBalBranch6MkBalBranch00 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr otherwise;
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch02 vwx vwy vwz vxu fm_L fm_R (Branch vux vuy vuz fm_rl fm_rr) = mkBalBranch6MkBalBranch01 vwx vwy vwz vxu fm_L fm_R vux vuy vuz fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr);
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr);
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Double_R vwx vwy vwz vxu fm_L fm_R;
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr True = mkBalBranch6Single_R vwx vwy vwz vxu fm_L fm_R;
13.41/5.46	mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr False = mkBalBranch6MkBalBranch10 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr otherwise;
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch12 vwx vwy vwz vxu fm_L fm_R (Branch zy zz vuu fm_ll fm_lr) = mkBalBranch6MkBalBranch11 vwx vwy vwz vxu fm_L fm_R zy zz vuu fm_ll fm_lr (sizeFM fm_lr < Pos (Succ (Succ Zero)) * sizeFM fm_ll);
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R;
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 vwx vwy vwz vxu fm_L fm_R fm_L;
13.41/5.46	mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 vwx vwy vwz vxu key elt fm_L fm_R otherwise;
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 vwx vwy vwz vxu fm_L fm_R fm_R;
13.41/5.46	mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_l vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_r vwx vwy vwz vxu);
13.41/5.46	
13.41/5.46	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R;
13.41/5.46	mkBalBranch6MkBalBranch5 vwx vwy vwz vxu key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 vwx vwy vwz vxu key elt fm_L fm_R (mkBalBranch6Size_r vwx vwy vwz vxu > sIZE_RATIO * mkBalBranch6Size_l vwx vwy vwz vxu);
13.41/5.46	
13.41/5.46	mkBalBranch6Single_L vwx vwy vwz vxu fm_l (Branch key_r elt_r vvu fm_rl fm_rr) = mkBranch (Pos (Succ (Succ (Succ Zero)))) key_r elt_r (mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) vwx vwy fm_l fm_rl) fm_rr;
13.41/5.46	
13.41/5.46	mkBalBranch6Single_R vwx vwy vwz vxu (Branch key_l elt_l zv fm_ll fm_lr) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))) key_l elt_l fm_ll (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) vwx vwy fm_lr fm_r);
13.41/5.46	
13.41/5.46	mkBalBranch6Size_l vwx vwy vwz vxu = sizeFM vxu;
13.41/5.46	
13.41/5.46	mkBalBranch6Size_r vwx vwy vwz vxu = sizeFM vwz;
13.41/5.46	
13.41/5.46	mkBranch :: Ord b => Int  ->  b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a;
13.41/5.46	mkBranch which key elt fm_l fm_r = mkBranchResult key elt fm_r fm_l;
13.41/5.46	
13.41/5.46	mkBranchBalance_ok vxw vxx vxy = True;
13.41/5.46	
13.41/5.46	mkBranchLeft_ok vxw vxx vxy = mkBranchLeft_ok0 vxw vxx vxy vxx vxy vxx;
13.41/5.46	
13.41/5.46	mkBranchLeft_ok0 vxw vxx vxy fm_l key EmptyFM = True;
13.41/5.46	mkBranchLeft_ok0 vxw vxx vxy fm_l key (Branch left_key xv xw xx xy) = mkBranchLeft_ok0Biggest_left_key fm_l < key;
13.41/5.46	
13.41/5.46	mkBranchLeft_ok0Biggest_left_key vyy = fst (findMax vyy);
13.41/5.46	
13.41/5.46	mkBranchLeft_size vxw vxx vxy = sizeFM vxx;
13.41/5.46	
13.41/5.46	mkBranchResult vxz vyu vyv vyw = Branch vxz vyu (mkBranchUnbox vyv vyw vxz (Pos (Succ Zero) + mkBranchLeft_size vyv vyw vxz + mkBranchRight_size vyv vyw vxz)) vyw vyv;
13.41/5.46	
13.41/5.46	mkBranchRight_ok vxw vxx vxy = mkBranchRight_ok0 vxw vxx vxy vxw vxy vxw;
13.41/5.46	
13.41/5.46	mkBranchRight_ok0 vxw vxx vxy fm_r key EmptyFM = True;
13.41/5.46	mkBranchRight_ok0 vxw vxx vxy fm_r key (Branch right_key xz yu yv yw) = key < mkBranchRight_ok0Smallest_right_key fm_r;
13.41/5.46	
13.41/5.46	mkBranchRight_ok0Smallest_right_key vyx = fst (findMin vyx);
13.41/5.46	
13.41/5.46	mkBranchRight_size vxw vxx vxy = sizeFM vxw;
13.41/5.46	
13.41/5.46	mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  (FiniteMap a b) ( ->  a (Int  ->  Int)));
13.41/5.46	mkBranchUnbox vxw vxx vxy x = x;
13.41/5.46	
13.41/5.46	sIZE_RATIO :: Int;
13.41/5.46	sIZE_RATIO = Pos (Succ (Succ (Succ (Succ (Succ Zero)))));
13.41/5.46	
13.41/5.46	sizeFM :: FiniteMap a b  ->  Int;
13.41/5.46	sizeFM EmptyFM = Pos Zero;
13.41/5.46	sizeFM (Branch vz wu size wv ww) = size;
13.41/5.46	
13.41/5.46	unitFM :: b  ->  a  ->  FiniteMap b a;
13.41/5.46	unitFM key elt = Branch key elt (Pos (Succ Zero)) emptyFM emptyFM;
13.41/5.46	
13.41/5.46	}
13.41/5.46	module Maybe where {
13.41/5.46	import qualified FiniteMap;
13.41/5.46	import qualified Main;
13.41/5.46	import qualified Prelude;
13.41/5.46	}
13.41/5.46	module Main where {
13.41/5.46	import qualified FiniteMap;
13.41/5.46	import qualified Maybe;
13.41/5.46	import qualified Prelude;
13.41/5.46	}
13.41/5.46	
13.41/5.46	----------------------------------------
13.41/5.46	
13.41/5.46	(11) Narrow (SOUND)
13.41/5.46	Haskell To QDPs
13.41/5.46	
13.41/5.46	digraph dp_graph {
13.41/5.46	node [outthreshold=100, inthreshold=100];1[label="FiniteMap.addListToFM_C",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
13.41/5.46	3[label="FiniteMap.addListToFM_C vyz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
13.41/5.46	4[label="FiniteMap.addListToFM_C vyz3 vyz4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
13.41/5.46	5[label="FiniteMap.addListToFM_C vyz3 vyz4 vyz5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3];
13.41/5.46	6[label="foldl (FiniteMap.addListToFM_CAdd vyz3) vyz4 vyz5",fontsize=16,color="burlywood",shape="triangle"];40[label="vyz5/vyz50 : vyz51",fontsize=10,color="white",style="solid",shape="box"];6 -> 40[label="",style="solid", color="burlywood", weight=9];
13.41/5.46	40 -> 7[label="",style="solid", color="burlywood", weight=3];
13.41/5.46	41[label="vyz5/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 41[label="",style="solid", color="burlywood", weight=9];
13.41/5.46	41 -> 8[label="",style="solid", color="burlywood", weight=3];
13.41/5.46	7[label="foldl (FiniteMap.addListToFM_CAdd vyz3) vyz4 (vyz50 : vyz51)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
13.41/5.46	8[label="foldl (FiniteMap.addListToFM_CAdd vyz3) vyz4 []",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
13.41/5.46	9 -> 6[label="",style="dashed", color="red", weight=0];
13.41/5.46	9[label="foldl (FiniteMap.addListToFM_CAdd vyz3) (FiniteMap.addListToFM_CAdd vyz3 vyz4 vyz50) vyz51",fontsize=16,color="magenta"];9 -> 11[label="",style="dashed", color="magenta", weight=3];
13.41/5.46	9 -> 12[label="",style="dashed", color="magenta", weight=3];
13.41/5.46	10[label="vyz4",fontsize=16,color="green",shape="box"];11[label="FiniteMap.addListToFM_CAdd vyz3 vyz4 vyz50",fontsize=16,color="burlywood",shape="box"];42[label="vyz50/(vyz500,vyz501)",fontsize=10,color="white",style="solid",shape="box"];11 -> 42[label="",style="solid", color="burlywood", weight=9];
13.41/5.46	42 -> 13[label="",style="solid", color="burlywood", weight=3];
13.41/5.46	12[label="vyz51",fontsize=16,color="green",shape="box"];13[label="FiniteMap.addListToFM_CAdd vyz3 vyz4 (vyz500,vyz501)",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
13.41/5.46	14[label="FiniteMap.addToFM_C vyz3 vyz4 vyz500 vyz501",fontsize=16,color="burlywood",shape="box"];43[label="vyz4/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];14 -> 43[label="",style="solid", color="burlywood", weight=9];
13.41/5.46	43 -> 15[label="",style="solid", color="burlywood", weight=3];
13.41/5.46	44[label="vyz4/FiniteMap.Branch vyz40 vyz41 vyz42 vyz43 vyz44",fontsize=10,color="white",style="solid",shape="box"];14 -> 44[label="",style="solid", color="burlywood", weight=9];
13.41/5.46	44 -> 16[label="",style="solid", color="burlywood", weight=3];
13.41/5.46	15[label="FiniteMap.addToFM_C vyz3 FiniteMap.EmptyFM vyz500 vyz501",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
13.41/5.46	16[label="FiniteMap.addToFM_C vyz3 (FiniteMap.Branch vyz40 vyz41 vyz42 vyz43 vyz44) vyz500 vyz501",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3];
13.41/5.46	17[label="FiniteMap.addToFM_C4 vyz3 FiniteMap.EmptyFM vyz500 vyz501",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3];
13.41/5.46	18[label="FiniteMap.addToFM_C3 vyz3 (FiniteMap.Branch vyz40 vyz41 vyz42 vyz43 vyz44) vyz500 vyz501",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3];
13.41/5.46	19[label="FiniteMap.unitFM vyz500 vyz501",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3];
13.41/5.46	20[label="FiniteMap.addToFM_C2 vyz3 vyz40 vyz41 vyz42 vyz43 vyz44 vyz500 vyz501 (vyz500 < vyz40)",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3];
13.41/5.46	21[label="FiniteMap.Branch vyz500 vyz501 (Pos (Succ Zero)) FiniteMap.emptyFM FiniteMap.emptyFM",fontsize=16,color="green",shape="box"];21 -> 23[label="",style="dashed", color="green", weight=3];
13.41/5.46	21 -> 24[label="",style="dashed", color="green", weight=3];
13.41/5.46	22[label="FiniteMap.addToFM_C2 vyz3 vyz40 vyz41 vyz42 vyz43 vyz44 vyz500 vyz501 (compare vyz500 vyz40 == LT)",fontsize=16,color="burlywood",shape="box"];45[label="vyz500/()",fontsize=10,color="white",style="solid",shape="box"];22 -> 45[label="",style="solid", color="burlywood", weight=9];
13.41/5.46	45 -> 25[label="",style="solid", color="burlywood", weight=3];
13.41/5.46	23[label="FiniteMap.emptyFM",fontsize=16,color="black",shape="triangle"];23 -> 26[label="",style="solid", color="black", weight=3];
13.41/5.46	24 -> 23[label="",style="dashed", color="red", weight=0];
13.41/5.46	24[label="FiniteMap.emptyFM",fontsize=16,color="magenta"];25[label="FiniteMap.addToFM_C2 vyz3 vyz40 vyz41 vyz42 vyz43 vyz44 () vyz501 (compare () vyz40 == LT)",fontsize=16,color="burlywood",shape="box"];46[label="vyz40/()",fontsize=10,color="white",style="solid",shape="box"];25 -> 46[label="",style="solid", color="burlywood", weight=9];
13.41/5.46	46 -> 27[label="",style="solid", color="burlywood", weight=3];
13.41/5.46	26[label="FiniteMap.EmptyFM",fontsize=16,color="green",shape="box"];27[label="FiniteMap.addToFM_C2 vyz3 () vyz41 vyz42 vyz43 vyz44 () vyz501 (compare () () == LT)",fontsize=16,color="black",shape="box"];27 -> 28[label="",style="solid", color="black", weight=3];
13.41/5.46	28[label="FiniteMap.addToFM_C2 vyz3 () vyz41 vyz42 vyz43 vyz44 () vyz501 (EQ == LT)",fontsize=16,color="black",shape="box"];28 -> 29[label="",style="solid", color="black", weight=3];
13.41/5.46	29[label="FiniteMap.addToFM_C2 vyz3 () vyz41 vyz42 vyz43 vyz44 () vyz501 False",fontsize=16,color="black",shape="box"];29 -> 30[label="",style="solid", color="black", weight=3];
13.41/5.46	30[label="FiniteMap.addToFM_C1 vyz3 () vyz41 vyz42 vyz43 vyz44 () vyz501 (() > ())",fontsize=16,color="black",shape="box"];30 -> 31[label="",style="solid", color="black", weight=3];
13.41/5.46	31[label="FiniteMap.addToFM_C1 vyz3 () vyz41 vyz42 vyz43 vyz44 () vyz501 (compare () () == GT)",fontsize=16,color="black",shape="box"];31 -> 32[label="",style="solid", color="black", weight=3];
13.41/5.46	32[label="FiniteMap.addToFM_C1 vyz3 () vyz41 vyz42 vyz43 vyz44 () vyz501 (EQ == GT)",fontsize=16,color="black",shape="box"];32 -> 33[label="",style="solid", color="black", weight=3];
13.41/5.46	33[label="FiniteMap.addToFM_C1 vyz3 () vyz41 vyz42 vyz43 vyz44 () vyz501 False",fontsize=16,color="black",shape="box"];33 -> 34[label="",style="solid", color="black", weight=3];
13.41/5.46	34[label="FiniteMap.addToFM_C0 vyz3 () vyz41 vyz42 vyz43 vyz44 () vyz501 otherwise",fontsize=16,color="black",shape="box"];34 -> 35[label="",style="solid", color="black", weight=3];
13.41/5.46	35[label="FiniteMap.addToFM_C0 vyz3 () vyz41 vyz42 vyz43 vyz44 () vyz501 True",fontsize=16,color="black",shape="box"];35 -> 36[label="",style="solid", color="black", weight=3];
13.41/5.46	36[label="FiniteMap.Branch () (vyz3 vyz41 vyz501) vyz42 vyz43 vyz44",fontsize=16,color="green",shape="box"];36 -> 37[label="",style="dashed", color="green", weight=3];
13.41/5.46	37[label="vyz3 vyz41 vyz501",fontsize=16,color="green",shape="box"];37 -> 38[label="",style="dashed", color="green", weight=3];
13.41/5.46	37 -> 39[label="",style="dashed", color="green", weight=3];
13.41/5.46	38[label="vyz41",fontsize=16,color="green",shape="box"];39[label="vyz501",fontsize=16,color="green",shape="box"];}
13.41/5.46	
13.41/5.46	----------------------------------------
13.41/5.46	
13.41/5.46	(12)
13.41/5.46	Obligation:
13.41/5.46	Q DP problem:
13.41/5.46	The TRS P consists of the following rules:
13.41/5.46	
13.41/5.46	   new_foldl(vyz3, :(vyz50, vyz51), h) -> new_foldl(vyz3, vyz51, h)
13.41/5.46	
13.41/5.46	R is empty.
13.41/5.46	Q is empty.
13.41/5.46	We have to consider all minimal (P,Q,R)-chains.
13.41/5.46	----------------------------------------
13.41/5.46	
13.41/5.46	(13) QDPSizeChangeProof (EQUIVALENT)
13.41/5.46	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
13.41/5.46	
13.41/5.46	From the DPs we obtained the following set of size-change graphs:
13.41/5.46	*new_foldl(vyz3, :(vyz50, vyz51), h) -> new_foldl(vyz3, vyz51, h)
13.41/5.46	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
13.41/5.46	
13.41/5.46	
13.41/5.46	----------------------------------------
13.41/5.46	
13.41/5.46	(14)
13.41/5.46	YES
13.72/5.51	EOF