10.13/4.59	YES
12.24/5.13	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.24/5.13	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.24/5.13	
12.24/5.13	
12.24/5.13	H-Termination with start terms of the given HASKELL could be proven:
12.24/5.13	
12.24/5.13	(0) HASKELL
12.24/5.13	(1) CR [EQUIVALENT, 0 ms]
12.24/5.13	(2) HASKELL
12.24/5.13	(3) BR [EQUIVALENT, 0 ms]
12.24/5.13	(4) HASKELL
12.24/5.13	(5) COR [EQUIVALENT, 0 ms]
12.24/5.13	(6) HASKELL
12.24/5.13	(7) Narrow [SOUND, 0 ms]
12.24/5.13	(8) QDP
12.24/5.13	(9) DependencyGraphProof [EQUIVALENT, 0 ms]
12.24/5.13	(10) AND
12.24/5.13	    (11) QDP
12.24/5.13	        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.24/5.13	        (13) YES
12.24/5.13	    (14) QDP
12.24/5.13	        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.24/5.13	        (16) YES
12.24/5.13	    (17) QDP
12.24/5.13	        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.24/5.13	        (19) YES
12.24/5.13	
12.24/5.13	
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(0)
12.24/5.13	Obligation:
12.24/5.13	mainModule Main 
12.24/5.13	module FiniteMap where {
12.24/5.13	import qualified Main;
12.24/5.13	import qualified Maybe;
12.24/5.13	import qualified Prelude;
12.24/5.13	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.24/5.13	
12.24/5.13	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
12.24/5.13	}
12.24/5.13	elemFM :: Ord b => b  ->  FiniteMap b a  ->  Bool;
12.24/5.13	elemFM key fm = case lookupFM fm key of { 
12.24/5.13	Nothing-> False; 
12.24/5.13	Just elt-> True; 
12.24/5.13	 } ;
12.24/5.13	
12.24/5.13	lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
12.24/5.13	lookupFM EmptyFM key = Nothing;
12.24/5.13	lookupFM (Branch key elt _ fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
12.24/5.13	 | key_to_find > key = lookupFM fm_r key_to_find
12.24/5.13	 | otherwise = Just elt;
12.24/5.13	
12.24/5.13	}
12.24/5.13	module Maybe where {
12.24/5.13	import qualified FiniteMap;
12.24/5.13	import qualified Main;
12.24/5.13	import qualified Prelude;
12.24/5.13	}
12.24/5.13	module Main where {
12.24/5.13	import qualified FiniteMap;
12.24/5.13	import qualified Maybe;
12.24/5.13	import qualified Prelude;
12.24/5.13	}
12.24/5.13	
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(1) CR (EQUIVALENT)
12.24/5.13	Case Reductions:
12.24/5.13	The following Case expression
12.24/5.13	"case lookupFM fm key of {
12.24/5.13	Nothing  -> False;
12.24/5.13	Just elt  -> True}
12.24/5.13	"
12.24/5.13	is transformed to
12.24/5.13	"elemFM0 Nothing = False;
12.24/5.13	elemFM0 (Just elt) = True;
12.24/5.13	"
12.24/5.13	
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(2)
12.24/5.13	Obligation:
12.24/5.13	mainModule Main 
12.24/5.13	module FiniteMap where {
12.24/5.13	import qualified Main;
12.24/5.13	import qualified Maybe;
12.24/5.13	import qualified Prelude;
12.24/5.13	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.24/5.13	
12.24/5.13	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.24/5.13	}
12.24/5.13	elemFM :: Ord b => b  ->  FiniteMap b a  ->  Bool;
12.24/5.13	elemFM key fm = elemFM0 (lookupFM fm key);
12.24/5.13	
12.24/5.13	elemFM0 Nothing = False;
12.24/5.13	elemFM0 (Just elt) = True;
12.24/5.13	
12.24/5.13	lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b;
12.24/5.13	lookupFM EmptyFM key = Nothing;
12.24/5.13	lookupFM (Branch key elt _ fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
12.24/5.13	 | key_to_find > key = lookupFM fm_r key_to_find
12.24/5.13	 | otherwise = Just elt;
12.24/5.13	
12.24/5.13	}
12.24/5.13	module Maybe where {
12.24/5.13	import qualified FiniteMap;
12.24/5.13	import qualified Main;
12.24/5.13	import qualified Prelude;
12.24/5.13	}
12.24/5.13	module Main where {
12.24/5.13	import qualified FiniteMap;
12.24/5.13	import qualified Maybe;
12.24/5.13	import qualified Prelude;
12.24/5.13	}
12.24/5.13	
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(3) BR (EQUIVALENT)
12.24/5.13	Replaced joker patterns by fresh variables and removed binding patterns.
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(4)
12.24/5.13	Obligation:
12.24/5.13	mainModule Main 
12.24/5.13	module FiniteMap where {
12.24/5.13	import qualified Main;
12.24/5.13	import qualified Maybe;
12.24/5.13	import qualified Prelude;
12.24/5.13	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.24/5.13	
12.24/5.13	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.24/5.13	}
12.24/5.13	elemFM :: Ord b => b  ->  FiniteMap b a  ->  Bool;
12.24/5.13	elemFM key fm = elemFM0 (lookupFM fm key);
12.24/5.13	
12.24/5.13	elemFM0 Nothing = False;
12.24/5.13	elemFM0 (Just elt) = True;
12.24/5.13	
12.24/5.13	lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
12.24/5.13	lookupFM EmptyFM key = Nothing;
12.24/5.13	lookupFM (Branch key elt vy fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
12.24/5.13	 | key_to_find > key = lookupFM fm_r key_to_find
12.24/5.13	 | otherwise = Just elt;
12.24/5.13	
12.24/5.13	}
12.24/5.13	module Maybe where {
12.24/5.13	import qualified FiniteMap;
12.24/5.13	import qualified Main;
12.24/5.13	import qualified Prelude;
12.24/5.13	}
12.24/5.13	module Main where {
12.24/5.13	import qualified FiniteMap;
12.24/5.13	import qualified Maybe;
12.24/5.13	import qualified Prelude;
12.24/5.13	}
12.24/5.13	
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(5) COR (EQUIVALENT)
12.24/5.13	Cond Reductions:
12.24/5.13	The following Function with conditions
12.24/5.13	"compare x y|x == yEQ|x <= yLT|otherwiseGT;
12.24/5.13	"
12.24/5.13	is transformed to
12.24/5.13	"compare x y = compare3 x y;
12.24/5.13	"
12.24/5.13	"compare2 x y True = EQ;
12.24/5.13	compare2 x y False = compare1 x y (x <= y);
12.24/5.13	"
12.24/5.13	"compare0 x y True = GT;
12.24/5.13	"
12.24/5.13	"compare1 x y True = LT;
12.24/5.13	compare1 x y False = compare0 x y otherwise;
12.24/5.13	"
12.24/5.13	"compare3 x y = compare2 x y (x == y);
12.24/5.13	"
12.24/5.13	The following Function with conditions
12.24/5.13	"undefined |Falseundefined;
12.24/5.13	"
12.24/5.13	is transformed to
12.24/5.13	"undefined  = undefined1;
12.24/5.13	"
12.24/5.13	"undefined0 True = undefined;
12.24/5.13	"
12.24/5.13	"undefined1  = undefined0 False;
12.24/5.13	"
12.24/5.13	The following Function with conditions
12.24/5.13	"lookupFM EmptyFM key = Nothing;
12.24/5.13	lookupFM (Branch key elt vy fm_l fm_r) key_to_find|key_to_find < keylookupFM fm_l key_to_find|key_to_find > keylookupFM fm_r key_to_find|otherwiseJust elt;
12.24/5.13	"
12.24/5.13	is transformed to
12.24/5.13	"lookupFM EmptyFM key = lookupFM4 EmptyFM key;
12.24/5.13	lookupFM (Branch key elt vy fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find;
12.24/5.13	"
12.24/5.13	"lookupFM0 key elt vy fm_l fm_r key_to_find True = Just elt;
12.24/5.13	"
12.24/5.13	"lookupFM2 key elt vy fm_l fm_r key_to_find True = lookupFM fm_l key_to_find;
12.24/5.13	lookupFM2 key elt vy fm_l fm_r key_to_find False = lookupFM1 key elt vy fm_l fm_r key_to_find (key_to_find > key);
12.24/5.13	"
12.24/5.13	"lookupFM1 key elt vy fm_l fm_r key_to_find True = lookupFM fm_r key_to_find;
12.24/5.13	lookupFM1 key elt vy fm_l fm_r key_to_find False = lookupFM0 key elt vy fm_l fm_r key_to_find otherwise;
12.24/5.13	"
12.24/5.13	"lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find = lookupFM2 key elt vy fm_l fm_r key_to_find (key_to_find < key);
12.24/5.13	"
12.24/5.13	"lookupFM4 EmptyFM key = Nothing;
12.24/5.13	lookupFM4 wv ww = lookupFM3 wv ww;
12.24/5.13	"
12.24/5.13	
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(6)
12.24/5.13	Obligation:
12.24/5.13	mainModule Main 
12.24/5.13	module FiniteMap where {
12.24/5.13	import qualified Main;
12.24/5.13	import qualified Maybe;
12.24/5.13	import qualified Prelude;
12.24/5.13	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.24/5.13	
12.24/5.13	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.24/5.13	}
12.24/5.13	elemFM :: Ord b => b  ->  FiniteMap b a  ->  Bool;
12.24/5.13	elemFM key fm = elemFM0 (lookupFM fm key);
12.24/5.13	
12.24/5.13	elemFM0 Nothing = False;
12.24/5.13	elemFM0 (Just elt) = True;
12.24/5.13	
12.24/5.13	lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b;
12.24/5.13	lookupFM EmptyFM key = lookupFM4 EmptyFM key;
12.24/5.13	lookupFM (Branch key elt vy fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find;
12.24/5.13	
12.24/5.13	lookupFM0 key elt vy fm_l fm_r key_to_find True = Just elt;
12.24/5.13	
12.24/5.13	lookupFM1 key elt vy fm_l fm_r key_to_find True = lookupFM fm_r key_to_find;
12.24/5.13	lookupFM1 key elt vy fm_l fm_r key_to_find False = lookupFM0 key elt vy fm_l fm_r key_to_find otherwise;
12.24/5.13	
12.24/5.13	lookupFM2 key elt vy fm_l fm_r key_to_find True = lookupFM fm_l key_to_find;
12.24/5.13	lookupFM2 key elt vy fm_l fm_r key_to_find False = lookupFM1 key elt vy fm_l fm_r key_to_find (key_to_find > key);
12.24/5.13	
12.24/5.13	lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find = lookupFM2 key elt vy fm_l fm_r key_to_find (key_to_find < key);
12.24/5.13	
12.24/5.13	lookupFM4 EmptyFM key = Nothing;
12.24/5.13	lookupFM4 wv ww = lookupFM3 wv ww;
12.24/5.13	
12.24/5.13	}
12.24/5.13	module Maybe where {
12.24/5.13	import qualified FiniteMap;
12.24/5.13	import qualified Main;
12.24/5.13	import qualified Prelude;
12.24/5.13	}
12.24/5.13	module Main where {
12.24/5.13	import qualified FiniteMap;
12.24/5.13	import qualified Maybe;
12.24/5.13	import qualified Prelude;
12.24/5.13	}
12.24/5.13	
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(7) Narrow (SOUND)
12.24/5.13	Haskell To QDPs
12.24/5.13	
12.24/5.13	digraph dp_graph {
12.24/5.13	node [outthreshold=100, inthreshold=100];1[label="FiniteMap.elemFM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
12.24/5.13	3[label="FiniteMap.elemFM wx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
12.24/5.13	4[label="FiniteMap.elemFM wx3 wx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
12.24/5.13	5[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx4 wx3)",fontsize=16,color="burlywood",shape="triangle"];155[label="wx4/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];5 -> 155[label="",style="solid", color="burlywood", weight=9];
12.24/5.13	155 -> 6[label="",style="solid", color="burlywood", weight=3];
12.24/5.13	156[label="wx4/FiniteMap.Branch wx40 wx41 wx42 wx43 wx44",fontsize=10,color="white",style="solid",shape="box"];5 -> 156[label="",style="solid", color="burlywood", weight=9];
12.24/5.13	156 -> 7[label="",style="solid", color="burlywood", weight=3];
12.24/5.13	6[label="FiniteMap.elemFM0 (FiniteMap.lookupFM FiniteMap.EmptyFM wx3)",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
12.24/5.13	7[label="FiniteMap.elemFM0 (FiniteMap.lookupFM (FiniteMap.Branch wx40 wx41 wx42 wx43 wx44) wx3)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
12.24/5.13	8[label="FiniteMap.elemFM0 (FiniteMap.lookupFM4 FiniteMap.EmptyFM wx3)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
12.24/5.13	9[label="FiniteMap.elemFM0 (FiniteMap.lookupFM3 (FiniteMap.Branch wx40 wx41 wx42 wx43 wx44) wx3)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
12.24/5.13	10[label="FiniteMap.elemFM0 Nothing",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
12.24/5.13	11[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 wx3 (wx3 < wx40))",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
12.24/5.13	12[label="False",fontsize=16,color="green",shape="box"];13[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 wx3 (compare wx3 wx40 == LT))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
12.24/5.13	14[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 wx3 (compare3 wx3 wx40 == LT))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
12.24/5.13	15[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 wx3 (compare2 wx3 wx40 (wx3 == wx40) == LT))",fontsize=16,color="burlywood",shape="box"];157[label="wx3/LT",fontsize=10,color="white",style="solid",shape="box"];15 -> 157[label="",style="solid", color="burlywood", weight=9];
12.24/5.13	157 -> 16[label="",style="solid", color="burlywood", weight=3];
12.24/5.13	158[label="wx3/EQ",fontsize=10,color="white",style="solid",shape="box"];15 -> 158[label="",style="solid", color="burlywood", weight=9];
12.24/5.13	158 -> 17[label="",style="solid", color="burlywood", weight=3];
12.24/5.13	159[label="wx3/GT",fontsize=10,color="white",style="solid",shape="box"];15 -> 159[label="",style="solid", color="burlywood", weight=9];
12.24/5.13	159 -> 18[label="",style="solid", color="burlywood", weight=3];
12.24/5.13	16[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 LT (compare2 LT wx40 (LT == wx40) == LT))",fontsize=16,color="burlywood",shape="box"];160[label="wx40/LT",fontsize=10,color="white",style="solid",shape="box"];16 -> 160[label="",style="solid", color="burlywood", weight=9];
12.24/5.13	160 -> 19[label="",style="solid", color="burlywood", weight=3];
12.24/5.13	161[label="wx40/EQ",fontsize=10,color="white",style="solid",shape="box"];16 -> 161[label="",style="solid", color="burlywood", weight=9];
12.24/5.13	161 -> 20[label="",style="solid", color="burlywood", weight=3];
12.24/5.13	162[label="wx40/GT",fontsize=10,color="white",style="solid",shape="box"];16 -> 162[label="",style="solid", color="burlywood", weight=9];
12.24/5.13	162 -> 21[label="",style="solid", color="burlywood", weight=3];
12.24/5.13	17[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 EQ (compare2 EQ wx40 (EQ == wx40) == LT))",fontsize=16,color="burlywood",shape="box"];163[label="wx40/LT",fontsize=10,color="white",style="solid",shape="box"];17 -> 163[label="",style="solid", color="burlywood", weight=9];
12.24/5.13	163 -> 22[label="",style="solid", color="burlywood", weight=3];
12.24/5.13	164[label="wx40/EQ",fontsize=10,color="white",style="solid",shape="box"];17 -> 164[label="",style="solid", color="burlywood", weight=9];
12.24/5.13	164 -> 23[label="",style="solid", color="burlywood", weight=3];
12.24/5.13	165[label="wx40/GT",fontsize=10,color="white",style="solid",shape="box"];17 -> 165[label="",style="solid", color="burlywood", weight=9];
12.24/5.13	165 -> 24[label="",style="solid", color="burlywood", weight=3];
12.24/5.13	18[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 wx40 wx41 wx42 wx43 wx44 GT (compare2 GT wx40 (GT == wx40) == LT))",fontsize=16,color="burlywood",shape="box"];166[label="wx40/LT",fontsize=10,color="white",style="solid",shape="box"];18 -> 166[label="",style="solid", color="burlywood", weight=9];
12.24/5.13	166 -> 25[label="",style="solid", color="burlywood", weight=3];
12.24/5.13	167[label="wx40/EQ",fontsize=10,color="white",style="solid",shape="box"];18 -> 167[label="",style="solid", color="burlywood", weight=9];
12.24/5.13	167 -> 26[label="",style="solid", color="burlywood", weight=3];
12.24/5.13	168[label="wx40/GT",fontsize=10,color="white",style="solid",shape="box"];18 -> 168[label="",style="solid", color="burlywood", weight=9];
12.24/5.13	168 -> 27[label="",style="solid", color="burlywood", weight=3];
12.24/5.13	19[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 LT (compare2 LT LT (LT == LT) == LT))",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
12.24/5.13	20[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 LT (compare2 LT EQ (LT == EQ) == LT))",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
12.24/5.13	21[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 LT (compare2 LT GT (LT == GT) == LT))",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
12.24/5.13	22[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 EQ (compare2 EQ LT (EQ == LT) == LT))",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
12.24/5.13	23[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 EQ (compare2 EQ EQ (EQ == EQ) == LT))",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
12.24/5.13	24[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 EQ (compare2 EQ GT (EQ == GT) == LT))",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
12.24/5.13	25[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 GT (compare2 GT LT (GT == LT) == LT))",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
12.24/5.13	26[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 GT (compare2 GT EQ (GT == EQ) == LT))",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
12.24/5.13	27[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 GT (compare2 GT GT (GT == GT) == LT))",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
12.24/5.13	28[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 LT (compare2 LT LT True == LT))",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3];
12.24/5.13	29[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 LT (compare2 LT EQ False == LT))",fontsize=16,color="black",shape="box"];29 -> 38[label="",style="solid", color="black", weight=3];
12.24/5.13	30[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 LT (compare2 LT GT False == LT))",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3];
12.24/5.13	31[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 EQ (compare2 EQ LT False == LT))",fontsize=16,color="black",shape="box"];31 -> 40[label="",style="solid", color="black", weight=3];
12.24/5.13	32[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 EQ (compare2 EQ EQ True == LT))",fontsize=16,color="black",shape="box"];32 -> 41[label="",style="solid", color="black", weight=3];
12.24/5.13	33[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 EQ (compare2 EQ GT False == LT))",fontsize=16,color="black",shape="box"];33 -> 42[label="",style="solid", color="black", weight=3];
12.24/5.13	34[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 GT (compare2 GT LT False == LT))",fontsize=16,color="black",shape="box"];34 -> 43[label="",style="solid", color="black", weight=3];
12.24/5.13	35[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 GT (compare2 GT EQ False == LT))",fontsize=16,color="black",shape="box"];35 -> 44[label="",style="solid", color="black", weight=3];
12.24/5.13	36[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 GT (compare2 GT GT True == LT))",fontsize=16,color="black",shape="box"];36 -> 45[label="",style="solid", color="black", weight=3];
12.24/5.13	37[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 LT (EQ == LT))",fontsize=16,color="black",shape="box"];37 -> 46[label="",style="solid", color="black", weight=3];
12.24/5.13	38[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 LT (compare1 LT EQ (LT <= EQ) == LT))",fontsize=16,color="black",shape="box"];38 -> 47[label="",style="solid", color="black", weight=3];
12.24/5.13	39[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 LT (compare1 LT GT (LT <= GT) == LT))",fontsize=16,color="black",shape="box"];39 -> 48[label="",style="solid", color="black", weight=3];
12.24/5.13	40[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 EQ (compare1 EQ LT (EQ <= LT) == LT))",fontsize=16,color="black",shape="box"];40 -> 49[label="",style="solid", color="black", weight=3];
12.24/5.13	41[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 EQ (EQ == LT))",fontsize=16,color="black",shape="box"];41 -> 50[label="",style="solid", color="black", weight=3];
12.24/5.13	42[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 EQ (compare1 EQ GT (EQ <= GT) == LT))",fontsize=16,color="black",shape="box"];42 -> 51[label="",style="solid", color="black", weight=3];
12.24/5.13	43[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 GT (compare1 GT LT (GT <= LT) == LT))",fontsize=16,color="black",shape="box"];43 -> 52[label="",style="solid", color="black", weight=3];
12.24/5.13	44[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 GT (compare1 GT EQ (GT <= EQ) == LT))",fontsize=16,color="black",shape="box"];44 -> 53[label="",style="solid", color="black", weight=3];
12.24/5.13	45[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 GT (EQ == LT))",fontsize=16,color="black",shape="box"];45 -> 54[label="",style="solid", color="black", weight=3];
12.24/5.13	46[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 LT False)",fontsize=16,color="black",shape="box"];46 -> 55[label="",style="solid", color="black", weight=3];
12.24/5.13	47[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 LT (compare1 LT EQ True == LT))",fontsize=16,color="black",shape="box"];47 -> 56[label="",style="solid", color="black", weight=3];
12.24/5.13	48[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 LT (compare1 LT GT True == LT))",fontsize=16,color="black",shape="box"];48 -> 57[label="",style="solid", color="black", weight=3];
12.24/5.13	49[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 EQ (compare1 EQ LT False == LT))",fontsize=16,color="black",shape="box"];49 -> 58[label="",style="solid", color="black", weight=3];
12.24/5.13	50[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 EQ False)",fontsize=16,color="black",shape="box"];50 -> 59[label="",style="solid", color="black", weight=3];
12.24/5.13	51[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 EQ (compare1 EQ GT True == LT))",fontsize=16,color="black",shape="box"];51 -> 60[label="",style="solid", color="black", weight=3];
12.24/5.13	52[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 GT (compare1 GT LT False == LT))",fontsize=16,color="black",shape="box"];52 -> 61[label="",style="solid", color="black", weight=3];
12.24/5.13	53[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 GT (compare1 GT EQ False == LT))",fontsize=16,color="black",shape="box"];53 -> 62[label="",style="solid", color="black", weight=3];
12.24/5.13	54[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 GT False)",fontsize=16,color="black",shape="box"];54 -> 63[label="",style="solid", color="black", weight=3];
12.24/5.13	55[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 LT (LT > LT))",fontsize=16,color="black",shape="box"];55 -> 64[label="",style="solid", color="black", weight=3];
12.24/5.13	56[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 LT (LT == LT))",fontsize=16,color="black",shape="box"];56 -> 65[label="",style="solid", color="black", weight=3];
12.24/5.13	57[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 LT (LT == LT))",fontsize=16,color="black",shape="box"];57 -> 66[label="",style="solid", color="black", weight=3];
12.24/5.13	58[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 EQ (compare0 EQ LT otherwise == LT))",fontsize=16,color="black",shape="box"];58 -> 67[label="",style="solid", color="black", weight=3];
12.24/5.13	59[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 EQ (EQ > EQ))",fontsize=16,color="black",shape="box"];59 -> 68[label="",style="solid", color="black", weight=3];
12.24/5.13	60[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 EQ (LT == LT))",fontsize=16,color="black",shape="box"];60 -> 69[label="",style="solid", color="black", weight=3];
12.24/5.13	61[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 GT (compare0 GT LT otherwise == LT))",fontsize=16,color="black",shape="box"];61 -> 70[label="",style="solid", color="black", weight=3];
12.24/5.13	62[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 GT (compare0 GT EQ otherwise == LT))",fontsize=16,color="black",shape="box"];62 -> 71[label="",style="solid", color="black", weight=3];
12.24/5.13	63[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 GT wx41 wx42 wx43 wx44 GT (GT > GT))",fontsize=16,color="black",shape="box"];63 -> 72[label="",style="solid", color="black", weight=3];
12.24/5.13	64[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 LT (compare LT LT == GT))",fontsize=16,color="black",shape="box"];64 -> 73[label="",style="solid", color="black", weight=3];
12.24/5.13	65[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 LT True)",fontsize=16,color="black",shape="box"];65 -> 74[label="",style="solid", color="black", weight=3];
12.24/5.13	66[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 LT True)",fontsize=16,color="black",shape="box"];66 -> 75[label="",style="solid", color="black", weight=3];
12.24/5.13	67[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 EQ (compare0 EQ LT True == LT))",fontsize=16,color="black",shape="box"];67 -> 76[label="",style="solid", color="black", weight=3];
12.24/5.13	68[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 EQ (compare EQ EQ == GT))",fontsize=16,color="black",shape="box"];68 -> 77[label="",style="solid", color="black", weight=3];
12.24/5.13	69[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 GT wx41 wx42 wx43 wx44 EQ True)",fontsize=16,color="black",shape="box"];69 -> 78[label="",style="solid", color="black", weight=3];
12.24/5.13	70[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 GT (compare0 GT LT True == LT))",fontsize=16,color="black",shape="box"];70 -> 79[label="",style="solid", color="black", weight=3];
12.24/5.13	71[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 GT (compare0 GT EQ True == LT))",fontsize=16,color="black",shape="box"];71 -> 80[label="",style="solid", color="black", weight=3];
12.24/5.13	72[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 GT wx41 wx42 wx43 wx44 GT (compare GT GT == GT))",fontsize=16,color="black",shape="box"];72 -> 81[label="",style="solid", color="black", weight=3];
12.24/5.13	73[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 LT (compare3 LT LT == GT))",fontsize=16,color="black",shape="box"];73 -> 82[label="",style="solid", color="black", weight=3];
12.24/5.13	74 -> 5[label="",style="dashed", color="red", weight=0];
12.24/5.13	74[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx43 LT)",fontsize=16,color="magenta"];74 -> 83[label="",style="dashed", color="magenta", weight=3];
12.24/5.13	74 -> 84[label="",style="dashed", color="magenta", weight=3];
12.24/5.13	75 -> 5[label="",style="dashed", color="red", weight=0];
12.24/5.13	75[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx43 LT)",fontsize=16,color="magenta"];75 -> 85[label="",style="dashed", color="magenta", weight=3];
12.24/5.13	75 -> 86[label="",style="dashed", color="magenta", weight=3];
12.24/5.13	76[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 EQ (GT == LT))",fontsize=16,color="black",shape="box"];76 -> 87[label="",style="solid", color="black", weight=3];
12.24/5.13	77[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 EQ (compare3 EQ EQ == GT))",fontsize=16,color="black",shape="box"];77 -> 88[label="",style="solid", color="black", weight=3];
12.24/5.13	78 -> 5[label="",style="dashed", color="red", weight=0];
12.24/5.13	78[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx43 EQ)",fontsize=16,color="magenta"];78 -> 89[label="",style="dashed", color="magenta", weight=3];
12.24/5.13	78 -> 90[label="",style="dashed", color="magenta", weight=3];
12.24/5.13	79[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 GT (GT == LT))",fontsize=16,color="black",shape="box"];79 -> 91[label="",style="solid", color="black", weight=3];
12.24/5.13	80[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 GT (GT == LT))",fontsize=16,color="black",shape="box"];80 -> 92[label="",style="solid", color="black", weight=3];
12.24/5.13	81[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 GT wx41 wx42 wx43 wx44 GT (compare3 GT GT == GT))",fontsize=16,color="black",shape="box"];81 -> 93[label="",style="solid", color="black", weight=3];
12.24/5.13	82[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 LT (compare2 LT LT (LT == LT) == GT))",fontsize=16,color="black",shape="box"];82 -> 94[label="",style="solid", color="black", weight=3];
12.24/5.13	83[label="wx43",fontsize=16,color="green",shape="box"];84[label="LT",fontsize=16,color="green",shape="box"];85[label="wx43",fontsize=16,color="green",shape="box"];86[label="LT",fontsize=16,color="green",shape="box"];87[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 EQ False)",fontsize=16,color="black",shape="box"];87 -> 95[label="",style="solid", color="black", weight=3];
12.24/5.13	88[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 EQ (compare2 EQ EQ (EQ == EQ) == GT))",fontsize=16,color="black",shape="box"];88 -> 96[label="",style="solid", color="black", weight=3];
12.24/5.13	89[label="wx43",fontsize=16,color="green",shape="box"];90[label="EQ",fontsize=16,color="green",shape="box"];91[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 LT wx41 wx42 wx43 wx44 GT False)",fontsize=16,color="black",shape="box"];91 -> 97[label="",style="solid", color="black", weight=3];
12.24/5.13	92[label="FiniteMap.elemFM0 (FiniteMap.lookupFM2 EQ wx41 wx42 wx43 wx44 GT False)",fontsize=16,color="black",shape="box"];92 -> 98[label="",style="solid", color="black", weight=3];
12.24/5.13	93[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 GT wx41 wx42 wx43 wx44 GT (compare2 GT GT (GT == GT) == GT))",fontsize=16,color="black",shape="box"];93 -> 99[label="",style="solid", color="black", weight=3];
12.24/5.13	94[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 LT (compare2 LT LT True == GT))",fontsize=16,color="black",shape="box"];94 -> 100[label="",style="solid", color="black", weight=3];
12.24/5.13	95[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 EQ (EQ > LT))",fontsize=16,color="black",shape="box"];95 -> 101[label="",style="solid", color="black", weight=3];
12.24/5.13	96[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 EQ (compare2 EQ EQ True == GT))",fontsize=16,color="black",shape="box"];96 -> 102[label="",style="solid", color="black", weight=3];
12.24/5.13	97[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 GT (GT > LT))",fontsize=16,color="black",shape="box"];97 -> 103[label="",style="solid", color="black", weight=3];
12.24/5.13	98[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 GT (GT > EQ))",fontsize=16,color="black",shape="box"];98 -> 104[label="",style="solid", color="black", weight=3];
12.24/5.13	99[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 GT wx41 wx42 wx43 wx44 GT (compare2 GT GT True == GT))",fontsize=16,color="black",shape="box"];99 -> 105[label="",style="solid", color="black", weight=3];
12.24/5.13	100[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 LT (EQ == GT))",fontsize=16,color="black",shape="box"];100 -> 106[label="",style="solid", color="black", weight=3];
12.24/5.13	101[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 EQ (compare EQ LT == GT))",fontsize=16,color="black",shape="box"];101 -> 107[label="",style="solid", color="black", weight=3];
12.24/5.13	102[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 EQ (EQ == GT))",fontsize=16,color="black",shape="box"];102 -> 108[label="",style="solid", color="black", weight=3];
12.24/5.13	103[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 GT (compare GT LT == GT))",fontsize=16,color="black",shape="box"];103 -> 109[label="",style="solid", color="black", weight=3];
12.24/5.13	104[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 GT (compare GT EQ == GT))",fontsize=16,color="black",shape="box"];104 -> 110[label="",style="solid", color="black", weight=3];
12.24/5.13	105[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 GT wx41 wx42 wx43 wx44 GT (EQ == GT))",fontsize=16,color="black",shape="box"];105 -> 111[label="",style="solid", color="black", weight=3];
12.24/5.13	106[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 LT False)",fontsize=16,color="black",shape="box"];106 -> 112[label="",style="solid", color="black", weight=3];
12.24/5.13	107[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 EQ (compare3 EQ LT == GT))",fontsize=16,color="black",shape="box"];107 -> 113[label="",style="solid", color="black", weight=3];
12.24/5.13	108[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 EQ False)",fontsize=16,color="black",shape="box"];108 -> 114[label="",style="solid", color="black", weight=3];
12.24/5.13	109[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 GT (compare3 GT LT == GT))",fontsize=16,color="black",shape="box"];109 -> 115[label="",style="solid", color="black", weight=3];
12.24/5.13	110[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 GT (compare3 GT EQ == GT))",fontsize=16,color="black",shape="box"];110 -> 116[label="",style="solid", color="black", weight=3];
12.24/5.13	111[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 GT wx41 wx42 wx43 wx44 GT False)",fontsize=16,color="black",shape="box"];111 -> 117[label="",style="solid", color="black", weight=3];
12.24/5.13	112[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 LT wx41 wx42 wx43 wx44 LT otherwise)",fontsize=16,color="black",shape="box"];112 -> 118[label="",style="solid", color="black", weight=3];
12.24/5.13	113[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 EQ (compare2 EQ LT (EQ == LT) == GT))",fontsize=16,color="black",shape="box"];113 -> 119[label="",style="solid", color="black", weight=3];
12.24/5.13	114[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 EQ wx41 wx42 wx43 wx44 EQ otherwise)",fontsize=16,color="black",shape="box"];114 -> 120[label="",style="solid", color="black", weight=3];
12.24/5.13	115[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 GT (compare2 GT LT (GT == LT) == GT))",fontsize=16,color="black",shape="box"];115 -> 121[label="",style="solid", color="black", weight=3];
12.24/5.13	116[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 GT (compare2 GT EQ (GT == EQ) == GT))",fontsize=16,color="black",shape="box"];116 -> 122[label="",style="solid", color="black", weight=3];
12.24/5.13	117[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 GT wx41 wx42 wx43 wx44 GT otherwise)",fontsize=16,color="black",shape="box"];117 -> 123[label="",style="solid", color="black", weight=3];
12.24/5.13	118[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 LT wx41 wx42 wx43 wx44 LT True)",fontsize=16,color="black",shape="box"];118 -> 124[label="",style="solid", color="black", weight=3];
12.24/5.13	119[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 EQ (compare2 EQ LT False == GT))",fontsize=16,color="black",shape="box"];119 -> 125[label="",style="solid", color="black", weight=3];
12.24/5.13	120[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 EQ wx41 wx42 wx43 wx44 EQ True)",fontsize=16,color="black",shape="box"];120 -> 126[label="",style="solid", color="black", weight=3];
12.24/5.13	121[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 GT (compare2 GT LT False == GT))",fontsize=16,color="black",shape="box"];121 -> 127[label="",style="solid", color="black", weight=3];
12.24/5.13	122[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 GT (compare2 GT EQ False == GT))",fontsize=16,color="black",shape="box"];122 -> 128[label="",style="solid", color="black", weight=3];
12.24/5.13	123[label="FiniteMap.elemFM0 (FiniteMap.lookupFM0 GT wx41 wx42 wx43 wx44 GT True)",fontsize=16,color="black",shape="box"];123 -> 129[label="",style="solid", color="black", weight=3];
12.24/5.13	124[label="FiniteMap.elemFM0 (Just wx41)",fontsize=16,color="black",shape="triangle"];124 -> 130[label="",style="solid", color="black", weight=3];
12.24/5.13	125[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 EQ (compare1 EQ LT (EQ <= LT) == GT))",fontsize=16,color="black",shape="box"];125 -> 131[label="",style="solid", color="black", weight=3];
12.24/5.13	126 -> 124[label="",style="dashed", color="red", weight=0];
12.24/5.13	126[label="FiniteMap.elemFM0 (Just wx41)",fontsize=16,color="magenta"];127[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 GT (compare1 GT LT (GT <= LT) == GT))",fontsize=16,color="black",shape="box"];127 -> 132[label="",style="solid", color="black", weight=3];
12.24/5.13	128[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 GT (compare1 GT EQ (GT <= EQ) == GT))",fontsize=16,color="black",shape="box"];128 -> 133[label="",style="solid", color="black", weight=3];
12.24/5.13	129 -> 124[label="",style="dashed", color="red", weight=0];
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12.24/5.13	132[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 GT (compare1 GT LT False == GT))",fontsize=16,color="black",shape="box"];132 -> 135[label="",style="solid", color="black", weight=3];
12.24/5.13	133[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 GT (compare1 GT EQ False == GT))",fontsize=16,color="black",shape="box"];133 -> 136[label="",style="solid", color="black", weight=3];
12.24/5.13	134[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 EQ (compare0 EQ LT otherwise == GT))",fontsize=16,color="black",shape="box"];134 -> 137[label="",style="solid", color="black", weight=3];
12.24/5.13	135[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 GT (compare0 GT LT otherwise == GT))",fontsize=16,color="black",shape="box"];135 -> 138[label="",style="solid", color="black", weight=3];
12.24/5.13	136[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 GT (compare0 GT EQ otherwise == GT))",fontsize=16,color="black",shape="box"];136 -> 139[label="",style="solid", color="black", weight=3];
12.24/5.13	137[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 EQ (compare0 EQ LT True == GT))",fontsize=16,color="black",shape="box"];137 -> 140[label="",style="solid", color="black", weight=3];
12.24/5.13	138[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 GT (compare0 GT LT True == GT))",fontsize=16,color="black",shape="box"];138 -> 141[label="",style="solid", color="black", weight=3];
12.24/5.13	139[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 GT (compare0 GT EQ True == GT))",fontsize=16,color="black",shape="box"];139 -> 142[label="",style="solid", color="black", weight=3];
12.24/5.13	140[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 EQ (GT == GT))",fontsize=16,color="black",shape="box"];140 -> 143[label="",style="solid", color="black", weight=3];
12.24/5.13	141[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 GT (GT == GT))",fontsize=16,color="black",shape="box"];141 -> 144[label="",style="solid", color="black", weight=3];
12.24/5.13	142[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 GT (GT == GT))",fontsize=16,color="black",shape="box"];142 -> 145[label="",style="solid", color="black", weight=3];
12.24/5.13	143[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 EQ True)",fontsize=16,color="black",shape="box"];143 -> 146[label="",style="solid", color="black", weight=3];
12.24/5.13	144[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 LT wx41 wx42 wx43 wx44 GT True)",fontsize=16,color="black",shape="box"];144 -> 147[label="",style="solid", color="black", weight=3];
12.24/5.13	145[label="FiniteMap.elemFM0 (FiniteMap.lookupFM1 EQ wx41 wx42 wx43 wx44 GT True)",fontsize=16,color="black",shape="box"];145 -> 148[label="",style="solid", color="black", weight=3];
12.24/5.13	146 -> 5[label="",style="dashed", color="red", weight=0];
12.24/5.13	146[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx44 EQ)",fontsize=16,color="magenta"];146 -> 149[label="",style="dashed", color="magenta", weight=3];
12.24/5.13	146 -> 150[label="",style="dashed", color="magenta", weight=3];
12.24/5.13	147 -> 5[label="",style="dashed", color="red", weight=0];
12.24/5.13	147[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx44 GT)",fontsize=16,color="magenta"];147 -> 151[label="",style="dashed", color="magenta", weight=3];
12.24/5.13	147 -> 152[label="",style="dashed", color="magenta", weight=3];
12.24/5.13	148 -> 5[label="",style="dashed", color="red", weight=0];
12.24/5.13	148[label="FiniteMap.elemFM0 (FiniteMap.lookupFM wx44 GT)",fontsize=16,color="magenta"];148 -> 153[label="",style="dashed", color="magenta", weight=3];
12.24/5.13	148 -> 154[label="",style="dashed", color="magenta", weight=3];
12.24/5.13	149[label="wx44",fontsize=16,color="green",shape="box"];150[label="EQ",fontsize=16,color="green",shape="box"];151[label="wx44",fontsize=16,color="green",shape="box"];152[label="GT",fontsize=16,color="green",shape="box"];153[label="wx44",fontsize=16,color="green",shape="box"];154[label="GT",fontsize=16,color="green",shape="box"];}
12.24/5.13	
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(8)
12.24/5.13	Obligation:
12.24/5.13	Q DP problem:
12.24/5.13	The TRS P consists of the following rules:
12.24/5.13	
12.24/5.13	   new_elemFM0(Branch(LT, wx41, wx42, wx43, wx44), EQ, h) -> new_elemFM0(wx44, EQ, h)
12.24/5.13	   new_elemFM0(Branch(EQ, wx41, wx42, wx43, wx44), GT, h) -> new_elemFM0(wx44, GT, h)
12.24/5.13	   new_elemFM0(Branch(EQ, wx41, wx42, wx43, wx44), LT, h) -> new_elemFM0(wx43, LT, h)
12.24/5.13	   new_elemFM0(Branch(GT, wx41, wx42, wx43, wx44), LT, h) -> new_elemFM0(wx43, LT, h)
12.24/5.13	   new_elemFM0(Branch(LT, wx41, wx42, wx43, wx44), GT, h) -> new_elemFM0(wx44, GT, h)
12.24/5.13	   new_elemFM0(Branch(GT, wx41, wx42, wx43, wx44), EQ, h) -> new_elemFM0(wx43, EQ, h)
12.24/5.13	
12.24/5.13	R is empty.
12.24/5.13	Q is empty.
12.24/5.13	We have to consider all minimal (P,Q,R)-chains.
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(9) DependencyGraphProof (EQUIVALENT)
12.24/5.13	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs.
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(10)
12.24/5.13	Complex Obligation (AND)
12.24/5.13	
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(11)
12.24/5.13	Obligation:
12.24/5.13	Q DP problem:
12.24/5.13	The TRS P consists of the following rules:
12.24/5.13	
12.24/5.13	   new_elemFM0(Branch(GT, wx41, wx42, wx43, wx44), LT, h) -> new_elemFM0(wx43, LT, h)
12.24/5.13	   new_elemFM0(Branch(EQ, wx41, wx42, wx43, wx44), LT, h) -> new_elemFM0(wx43, LT, h)
12.24/5.13	
12.24/5.13	R is empty.
12.24/5.13	Q is empty.
12.24/5.13	We have to consider all minimal (P,Q,R)-chains.
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(12) QDPSizeChangeProof (EQUIVALENT)
12.24/5.13	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. 
12.24/5.13	
12.24/5.13	From the DPs we obtained the following set of size-change graphs:
12.24/5.13	*new_elemFM0(Branch(GT, wx41, wx42, wx43, wx44), LT, h) -> new_elemFM0(wx43, LT, h)
12.24/5.13	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
12.24/5.13	
12.24/5.13	
12.24/5.13	*new_elemFM0(Branch(EQ, wx41, wx42, wx43, wx44), LT, h) -> new_elemFM0(wx43, LT, h)
12.24/5.13	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
12.24/5.13	
12.24/5.13	
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(13)
12.24/5.13	YES
12.24/5.13	
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(14)
12.24/5.13	Obligation:
12.24/5.13	Q DP problem:
12.24/5.13	The TRS P consists of the following rules:
12.24/5.13	
12.24/5.13	   new_elemFM0(Branch(LT, wx41, wx42, wx43, wx44), GT, h) -> new_elemFM0(wx44, GT, h)
12.24/5.13	   new_elemFM0(Branch(EQ, wx41, wx42, wx43, wx44), GT, h) -> new_elemFM0(wx44, GT, h)
12.24/5.13	
12.24/5.13	R is empty.
12.24/5.13	Q is empty.
12.24/5.13	We have to consider all minimal (P,Q,R)-chains.
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(15) QDPSizeChangeProof (EQUIVALENT)
12.24/5.13	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. 
12.24/5.13	
12.24/5.13	From the DPs we obtained the following set of size-change graphs:
12.24/5.13	*new_elemFM0(Branch(LT, wx41, wx42, wx43, wx44), GT, h) -> new_elemFM0(wx44, GT, h)
12.24/5.13	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
12.24/5.13	
12.24/5.13	
12.24/5.13	*new_elemFM0(Branch(EQ, wx41, wx42, wx43, wx44), GT, h) -> new_elemFM0(wx44, GT, h)
12.24/5.13	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
12.24/5.13	
12.24/5.13	
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(16)
12.24/5.13	YES
12.24/5.13	
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(17)
12.24/5.13	Obligation:
12.24/5.13	Q DP problem:
12.24/5.13	The TRS P consists of the following rules:
12.24/5.13	
12.24/5.13	   new_elemFM0(Branch(GT, wx41, wx42, wx43, wx44), EQ, h) -> new_elemFM0(wx43, EQ, h)
12.24/5.13	   new_elemFM0(Branch(LT, wx41, wx42, wx43, wx44), EQ, h) -> new_elemFM0(wx44, EQ, h)
12.24/5.13	
12.24/5.13	R is empty.
12.24/5.13	Q is empty.
12.24/5.13	We have to consider all minimal (P,Q,R)-chains.
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(18) QDPSizeChangeProof (EQUIVALENT)
12.24/5.13	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. 
12.24/5.13	
12.24/5.13	From the DPs we obtained the following set of size-change graphs:
12.24/5.13	*new_elemFM0(Branch(GT, wx41, wx42, wx43, wx44), EQ, h) -> new_elemFM0(wx43, EQ, h)
12.24/5.13	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
12.24/5.13	
12.24/5.13	
12.24/5.13	*new_elemFM0(Branch(LT, wx41, wx42, wx43, wx44), EQ, h) -> new_elemFM0(wx44, EQ, h)
12.24/5.13	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
12.24/5.13	
12.24/5.13	
12.24/5.13	----------------------------------------
12.24/5.13	
12.24/5.13	(19)
12.24/5.13	YES
12.31/9.16	EOF