9.97/4.95	YES
12.55/5.58	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.55/5.58	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.55/5.58	
12.55/5.58	
12.55/5.58	H-Termination with start terms of the given HASKELL could be proven:
12.55/5.58	
12.55/5.58	(0) HASKELL
12.55/5.58	(1) CR [EQUIVALENT, 0 ms]
12.55/5.58	(2) HASKELL
12.55/5.58	(3) BR [EQUIVALENT, 0 ms]
12.55/5.58	(4) HASKELL
12.55/5.58	(5) COR [EQUIVALENT, 0 ms]
12.55/5.58	(6) HASKELL
12.55/5.58	(7) Narrow [SOUND, 0 ms]
12.55/5.58	(8) QDP
12.55/5.58	(9) DependencyGraphProof [EQUIVALENT, 0 ms]
12.55/5.58	(10) AND
12.55/5.58	    (11) QDP
12.55/5.58	        (12) QDPSizeChangeProof [EQUIVALENT, 2 ms]
12.55/5.58	        (13) YES
12.55/5.58	    (14) QDP
12.55/5.58	        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.55/5.58	        (16) YES
12.55/5.58	    (17) QDP
12.55/5.58	        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.55/5.58	        (19) YES
12.55/5.58	
12.55/5.58	
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(0)
12.55/5.58	Obligation:
12.55/5.58	mainModule Main 
12.55/5.58	module FiniteMap where {
12.55/5.58	import qualified Main;
12.55/5.58	import qualified Maybe;
12.55/5.58	import qualified Prelude;
12.55/5.58	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.55/5.58	
12.55/5.58	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.55/5.58	}
12.55/5.58	lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
12.55/5.58	lookupFM EmptyFM key = Nothing;
12.55/5.58	lookupFM (Branch key elt _ fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
12.55/5.58	 | key_to_find > key = lookupFM fm_r key_to_find
12.55/5.58	 | otherwise = Just elt;
12.55/5.58	
12.55/5.58	lookupWithDefaultFM :: Ord a => FiniteMap a b  ->  b  ->  a  ->  b;
12.55/5.58	lookupWithDefaultFM fm deflt key = case lookupFM fm key of { 
12.55/5.58	Nothing-> deflt; 
12.55/5.58	Just elt-> elt; 
12.55/5.58	 } ;
12.55/5.58	
12.55/5.58	}
12.55/5.58	module Maybe where {
12.55/5.58	import qualified FiniteMap;
12.55/5.58	import qualified Main;
12.55/5.58	import qualified Prelude;
12.55/5.58	}
12.55/5.58	module Main where {
12.55/5.58	import qualified FiniteMap;
12.55/5.58	import qualified Maybe;
12.55/5.58	import qualified Prelude;
12.55/5.58	}
12.55/5.58	
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(1) CR (EQUIVALENT)
12.55/5.58	Case Reductions:
12.55/5.58	The following Case expression
12.55/5.58	"case lookupFM fm key of {
12.55/5.58	Nothing  -> deflt;
12.55/5.58	Just elt  -> elt}
12.55/5.58	"
12.55/5.58	is transformed to
12.55/5.58	"lookupWithDefaultFM0 deflt Nothing = deflt;
12.55/5.58	lookupWithDefaultFM0 deflt (Just elt) = elt;
12.55/5.58	"
12.55/5.58	
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(2)
12.55/5.58	Obligation:
12.55/5.58	mainModule Main 
12.55/5.58	module FiniteMap where {
12.55/5.58	import qualified Main;
12.55/5.58	import qualified Maybe;
12.55/5.58	import qualified Prelude;
12.55/5.58	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.55/5.58	
12.55/5.58	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.55/5.58	}
12.55/5.58	lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b;
12.55/5.58	lookupFM EmptyFM key = Nothing;
12.55/5.58	lookupFM (Branch key elt _ fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
12.55/5.58	 | key_to_find > key = lookupFM fm_r key_to_find
12.55/5.58	 | otherwise = Just elt;
12.55/5.58	
12.55/5.58	lookupWithDefaultFM :: Ord a => FiniteMap a b  ->  b  ->  a  ->  b;
12.55/5.58	lookupWithDefaultFM fm deflt key = lookupWithDefaultFM0 deflt (lookupFM fm key);
12.55/5.58	
12.55/5.58	lookupWithDefaultFM0 deflt Nothing = deflt;
12.55/5.58	lookupWithDefaultFM0 deflt (Just elt) = elt;
12.55/5.58	
12.55/5.58	}
12.55/5.58	module Maybe where {
12.55/5.58	import qualified FiniteMap;
12.55/5.58	import qualified Main;
12.55/5.58	import qualified Prelude;
12.55/5.58	}
12.55/5.58	module Main where {
12.55/5.58	import qualified FiniteMap;
12.55/5.58	import qualified Maybe;
12.55/5.58	import qualified Prelude;
12.55/5.58	}
12.55/5.58	
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(3) BR (EQUIVALENT)
12.55/5.58	Replaced joker patterns by fresh variables and removed binding patterns.
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(4)
12.55/5.58	Obligation:
12.55/5.58	mainModule Main 
12.55/5.58	module FiniteMap where {
12.55/5.58	import qualified Main;
12.55/5.58	import qualified Maybe;
12.55/5.58	import qualified Prelude;
12.55/5.58	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.55/5.58	
12.55/5.58	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.55/5.58	}
12.55/5.58	lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b;
12.55/5.58	lookupFM EmptyFM key = Nothing;
12.55/5.58	lookupFM (Branch key elt vy fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
12.55/5.58	 | key_to_find > key = lookupFM fm_r key_to_find
12.55/5.58	 | otherwise = Just elt;
12.55/5.58	
12.55/5.58	lookupWithDefaultFM :: Ord a => FiniteMap a b  ->  b  ->  a  ->  b;
12.55/5.58	lookupWithDefaultFM fm deflt key = lookupWithDefaultFM0 deflt (lookupFM fm key);
12.55/5.58	
12.55/5.58	lookupWithDefaultFM0 deflt Nothing = deflt;
12.55/5.58	lookupWithDefaultFM0 deflt (Just elt) = elt;
12.55/5.58	
12.55/5.58	}
12.55/5.58	module Maybe where {
12.55/5.58	import qualified FiniteMap;
12.55/5.58	import qualified Main;
12.55/5.58	import qualified Prelude;
12.55/5.58	}
12.55/5.58	module Main where {
12.55/5.58	import qualified FiniteMap;
12.55/5.58	import qualified Maybe;
12.55/5.58	import qualified Prelude;
12.55/5.58	}
12.55/5.58	
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(5) COR (EQUIVALENT)
12.55/5.58	Cond Reductions:
12.55/5.58	The following Function with conditions
12.55/5.58	"compare x y|x == yEQ|x <= yLT|otherwiseGT;
12.55/5.58	"
12.55/5.58	is transformed to
12.55/5.58	"compare x y = compare3 x y;
12.55/5.58	"
12.55/5.58	"compare2 x y True = EQ;
12.55/5.58	compare2 x y False = compare1 x y (x <= y);
12.55/5.58	"
12.55/5.58	"compare0 x y True = GT;
12.55/5.58	"
12.55/5.58	"compare1 x y True = LT;
12.55/5.58	compare1 x y False = compare0 x y otherwise;
12.55/5.58	"
12.55/5.58	"compare3 x y = compare2 x y (x == y);
12.55/5.58	"
12.55/5.58	The following Function with conditions
12.55/5.58	"undefined |Falseundefined;
12.55/5.58	"
12.55/5.58	is transformed to
12.55/5.58	"undefined  = undefined1;
12.55/5.58	"
12.55/5.58	"undefined0 True = undefined;
12.55/5.58	"
12.55/5.58	"undefined1  = undefined0 False;
12.55/5.58	"
12.55/5.58	The following Function with conditions
12.55/5.58	"lookupFM EmptyFM key = Nothing;
12.55/5.58	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;
12.55/5.58	"
12.55/5.58	is transformed to
12.55/5.58	"lookupFM EmptyFM key = lookupFM4 EmptyFM key;
12.55/5.58	lookupFM (Branch key elt vy fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find;
12.55/5.58	"
12.55/5.58	"lookupFM2 key elt vy fm_l fm_r key_to_find True = lookupFM fm_l key_to_find;
12.55/5.58	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);
12.55/5.58	"
12.55/5.58	"lookupFM0 key elt vy fm_l fm_r key_to_find True = Just elt;
12.55/5.58	"
12.55/5.58	"lookupFM1 key elt vy fm_l fm_r key_to_find True = lookupFM fm_r key_to_find;
12.55/5.58	lookupFM1 key elt vy fm_l fm_r key_to_find False = lookupFM0 key elt vy fm_l fm_r key_to_find otherwise;
12.55/5.58	"
12.55/5.58	"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);
12.55/5.58	"
12.55/5.58	"lookupFM4 EmptyFM key = Nothing;
12.55/5.58	lookupFM4 wv ww = lookupFM3 wv ww;
12.55/5.58	"
12.55/5.58	
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(6)
12.55/5.58	Obligation:
12.55/5.58	mainModule Main 
12.55/5.58	module FiniteMap where {
12.55/5.58	import qualified Main;
12.55/5.58	import qualified Maybe;
12.55/5.58	import qualified Prelude;
12.55/5.58	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.55/5.58	
12.55/5.58	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.55/5.58	}
12.55/5.58	lookupFM :: Ord a => FiniteMap a b  ->  a  ->  Maybe b;
12.55/5.58	lookupFM EmptyFM key = lookupFM4 EmptyFM key;
12.55/5.58	lookupFM (Branch key elt vy fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find;
12.55/5.58	
12.55/5.58	lookupFM0 key elt vy fm_l fm_r key_to_find True = Just elt;
12.55/5.58	
12.55/5.58	lookupFM1 key elt vy fm_l fm_r key_to_find True = lookupFM fm_r key_to_find;
12.55/5.58	lookupFM1 key elt vy fm_l fm_r key_to_find False = lookupFM0 key elt vy fm_l fm_r key_to_find otherwise;
12.55/5.58	
12.55/5.58	lookupFM2 key elt vy fm_l fm_r key_to_find True = lookupFM fm_l key_to_find;
12.55/5.58	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);
12.55/5.58	
12.55/5.58	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);
12.55/5.58	
12.55/5.58	lookupFM4 EmptyFM key = Nothing;
12.55/5.58	lookupFM4 wv ww = lookupFM3 wv ww;
12.55/5.58	
12.55/5.58	lookupWithDefaultFM :: Ord a => FiniteMap a b  ->  b  ->  a  ->  b;
12.55/5.58	lookupWithDefaultFM fm deflt key = lookupWithDefaultFM0 deflt (lookupFM fm key);
12.55/5.58	
12.55/5.58	lookupWithDefaultFM0 deflt Nothing = deflt;
12.55/5.58	lookupWithDefaultFM0 deflt (Just elt) = elt;
12.55/5.58	
12.55/5.58	}
12.55/5.58	module Maybe where {
12.55/5.58	import qualified FiniteMap;
12.55/5.58	import qualified Main;
12.55/5.58	import qualified Prelude;
12.55/5.58	}
12.55/5.58	module Main where {
12.55/5.58	import qualified FiniteMap;
12.55/5.58	import qualified Maybe;
12.55/5.58	import qualified Prelude;
12.55/5.58	}
12.55/5.58	
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(7) Narrow (SOUND)
12.55/5.58	Haskell To QDPs
12.55/5.58	
12.55/5.58	digraph dp_graph {
12.55/5.58	node [outthreshold=100, inthreshold=100];1[label="FiniteMap.lookupWithDefaultFM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
12.55/5.58	3[label="FiniteMap.lookupWithDefaultFM wx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
12.55/5.58	4[label="FiniteMap.lookupWithDefaultFM wx3 wx4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
12.55/5.58	5[label="FiniteMap.lookupWithDefaultFM wx3 wx4 wx5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3];
12.55/5.58	6[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM wx3 wx5)",fontsize=16,color="burlywood",shape="triangle"];156[label="wx3/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];6 -> 156[label="",style="solid", color="burlywood", weight=9];
12.55/5.58	156 -> 7[label="",style="solid", color="burlywood", weight=3];
12.55/5.58	157[label="wx3/FiniteMap.Branch wx30 wx31 wx32 wx33 wx34",fontsize=10,color="white",style="solid",shape="box"];6 -> 157[label="",style="solid", color="burlywood", weight=9];
12.55/5.58	157 -> 8[label="",style="solid", color="burlywood", weight=3];
12.55/5.58	7[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM FiniteMap.EmptyFM wx5)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
12.55/5.58	8[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM (FiniteMap.Branch wx30 wx31 wx32 wx33 wx34) wx5)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
12.55/5.58	9[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM4 FiniteMap.EmptyFM wx5)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
12.55/5.58	10[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM3 (FiniteMap.Branch wx30 wx31 wx32 wx33 wx34) wx5)",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
12.55/5.58	11[label="FiniteMap.lookupWithDefaultFM0 wx4 Nothing",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
12.55/5.58	12[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 wx5 (wx5 < wx30))",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
12.55/5.58	13[label="wx4",fontsize=16,color="green",shape="box"];14[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 wx5 (compare wx5 wx30 == LT))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
12.55/5.58	15[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 wx5 (compare3 wx5 wx30 == LT))",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3];
12.55/5.58	16[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 wx5 (compare2 wx5 wx30 (wx5 == wx30) == LT))",fontsize=16,color="burlywood",shape="box"];158[label="wx5/LT",fontsize=10,color="white",style="solid",shape="box"];16 -> 158[label="",style="solid", color="burlywood", weight=9];
12.55/5.58	158 -> 17[label="",style="solid", color="burlywood", weight=3];
12.55/5.58	159[label="wx5/EQ",fontsize=10,color="white",style="solid",shape="box"];16 -> 159[label="",style="solid", color="burlywood", weight=9];
12.55/5.58	159 -> 18[label="",style="solid", color="burlywood", weight=3];
12.55/5.58	160[label="wx5/GT",fontsize=10,color="white",style="solid",shape="box"];16 -> 160[label="",style="solid", color="burlywood", weight=9];
12.55/5.58	160 -> 19[label="",style="solid", color="burlywood", weight=3];
12.55/5.58	17[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 LT (compare2 LT wx30 (LT == wx30) == LT))",fontsize=16,color="burlywood",shape="box"];161[label="wx30/LT",fontsize=10,color="white",style="solid",shape="box"];17 -> 161[label="",style="solid", color="burlywood", weight=9];
12.55/5.58	161 -> 20[label="",style="solid", color="burlywood", weight=3];
12.55/5.58	162[label="wx30/EQ",fontsize=10,color="white",style="solid",shape="box"];17 -> 162[label="",style="solid", color="burlywood", weight=9];
12.55/5.58	162 -> 21[label="",style="solid", color="burlywood", weight=3];
12.55/5.58	163[label="wx30/GT",fontsize=10,color="white",style="solid",shape="box"];17 -> 163[label="",style="solid", color="burlywood", weight=9];
12.55/5.58	163 -> 22[label="",style="solid", color="burlywood", weight=3];
12.55/5.58	18[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 EQ (compare2 EQ wx30 (EQ == wx30) == LT))",fontsize=16,color="burlywood",shape="box"];164[label="wx30/LT",fontsize=10,color="white",style="solid",shape="box"];18 -> 164[label="",style="solid", color="burlywood", weight=9];
12.55/5.58	164 -> 23[label="",style="solid", color="burlywood", weight=3];
12.55/5.58	165[label="wx30/EQ",fontsize=10,color="white",style="solid",shape="box"];18 -> 165[label="",style="solid", color="burlywood", weight=9];
12.55/5.58	165 -> 24[label="",style="solid", color="burlywood", weight=3];
12.55/5.58	166[label="wx30/GT",fontsize=10,color="white",style="solid",shape="box"];18 -> 166[label="",style="solid", color="burlywood", weight=9];
12.55/5.58	166 -> 25[label="",style="solid", color="burlywood", weight=3];
12.55/5.58	19[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 GT (compare2 GT wx30 (GT == wx30) == LT))",fontsize=16,color="burlywood",shape="box"];167[label="wx30/LT",fontsize=10,color="white",style="solid",shape="box"];19 -> 167[label="",style="solid", color="burlywood", weight=9];
12.55/5.58	167 -> 26[label="",style="solid", color="burlywood", weight=3];
12.55/5.58	168[label="wx30/EQ",fontsize=10,color="white",style="solid",shape="box"];19 -> 168[label="",style="solid", color="burlywood", weight=9];
12.55/5.58	168 -> 27[label="",style="solid", color="burlywood", weight=3];
12.55/5.58	169[label="wx30/GT",fontsize=10,color="white",style="solid",shape="box"];19 -> 169[label="",style="solid", color="burlywood", weight=9];
12.55/5.58	169 -> 28[label="",style="solid", color="burlywood", weight=3];
12.55/5.58	20[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 LT (compare2 LT LT (LT == LT) == LT))",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
12.55/5.58	21[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 LT (compare2 LT EQ (LT == EQ) == LT))",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
12.55/5.58	22[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 LT (compare2 LT GT (LT == GT) == LT))",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
12.55/5.58	23[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ (compare2 EQ LT (EQ == LT) == LT))",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
12.55/5.58	24[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 EQ (compare2 EQ EQ (EQ == EQ) == LT))",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
12.55/5.58	25[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 EQ (compare2 EQ GT (EQ == GT) == LT))",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
12.55/5.58	26[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT (compare2 GT LT (GT == LT) == LT))",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
12.55/5.58	27[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT (compare2 GT EQ (GT == EQ) == LT))",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
12.55/5.58	28[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 GT (compare2 GT GT (GT == GT) == LT))",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3];
12.55/5.58	29[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 LT (compare2 LT LT True == LT))",fontsize=16,color="black",shape="box"];29 -> 38[label="",style="solid", color="black", weight=3];
12.55/5.58	30[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 LT (compare2 LT EQ False == LT))",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3];
12.55/5.58	31[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 LT (compare2 LT GT False == LT))",fontsize=16,color="black",shape="box"];31 -> 40[label="",style="solid", color="black", weight=3];
12.55/5.58	32[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ (compare2 EQ LT False == LT))",fontsize=16,color="black",shape="box"];32 -> 41[label="",style="solid", color="black", weight=3];
12.55/5.58	33[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 EQ (compare2 EQ EQ True == LT))",fontsize=16,color="black",shape="box"];33 -> 42[label="",style="solid", color="black", weight=3];
12.55/5.58	34[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 EQ (compare2 EQ GT False == LT))",fontsize=16,color="black",shape="box"];34 -> 43[label="",style="solid", color="black", weight=3];
12.55/5.58	35[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT (compare2 GT LT False == LT))",fontsize=16,color="black",shape="box"];35 -> 44[label="",style="solid", color="black", weight=3];
12.55/5.58	36[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT (compare2 GT EQ False == LT))",fontsize=16,color="black",shape="box"];36 -> 45[label="",style="solid", color="black", weight=3];
12.55/5.58	37[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 GT (compare2 GT GT True == LT))",fontsize=16,color="black",shape="box"];37 -> 46[label="",style="solid", color="black", weight=3];
12.55/5.58	38[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 LT (EQ == LT))",fontsize=16,color="black",shape="box"];38 -> 47[label="",style="solid", color="black", weight=3];
12.55/5.58	39[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 LT (compare1 LT EQ (LT <= EQ) == LT))",fontsize=16,color="black",shape="box"];39 -> 48[label="",style="solid", color="black", weight=3];
12.55/5.58	40[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 LT (compare1 LT GT (LT <= GT) == LT))",fontsize=16,color="black",shape="box"];40 -> 49[label="",style="solid", color="black", weight=3];
12.55/5.58	41[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ (compare1 EQ LT (EQ <= LT) == LT))",fontsize=16,color="black",shape="box"];41 -> 50[label="",style="solid", color="black", weight=3];
12.55/5.58	42[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 EQ (EQ == LT))",fontsize=16,color="black",shape="box"];42 -> 51[label="",style="solid", color="black", weight=3];
12.55/5.58	43[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 EQ (compare1 EQ GT (EQ <= GT) == LT))",fontsize=16,color="black",shape="box"];43 -> 52[label="",style="solid", color="black", weight=3];
12.55/5.58	44[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT (compare1 GT LT (GT <= LT) == LT))",fontsize=16,color="black",shape="box"];44 -> 53[label="",style="solid", color="black", weight=3];
12.55/5.58	45[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT (compare1 GT EQ (GT <= EQ) == LT))",fontsize=16,color="black",shape="box"];45 -> 54[label="",style="solid", color="black", weight=3];
12.55/5.58	46[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 GT (EQ == LT))",fontsize=16,color="black",shape="box"];46 -> 55[label="",style="solid", color="black", weight=3];
12.55/5.58	47[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 LT False)",fontsize=16,color="black",shape="box"];47 -> 56[label="",style="solid", color="black", weight=3];
12.55/5.58	48[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 LT (compare1 LT EQ True == LT))",fontsize=16,color="black",shape="box"];48 -> 57[label="",style="solid", color="black", weight=3];
12.55/5.58	49[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 LT (compare1 LT GT True == LT))",fontsize=16,color="black",shape="box"];49 -> 58[label="",style="solid", color="black", weight=3];
12.55/5.58	50[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ (compare1 EQ LT False == LT))",fontsize=16,color="black",shape="box"];50 -> 59[label="",style="solid", color="black", weight=3];
12.55/5.58	51[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 EQ False)",fontsize=16,color="black",shape="box"];51 -> 60[label="",style="solid", color="black", weight=3];
12.55/5.58	52[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 EQ (compare1 EQ GT True == LT))",fontsize=16,color="black",shape="box"];52 -> 61[label="",style="solid", color="black", weight=3];
12.55/5.58	53[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT (compare1 GT LT False == LT))",fontsize=16,color="black",shape="box"];53 -> 62[label="",style="solid", color="black", weight=3];
12.55/5.58	54[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT (compare1 GT EQ False == LT))",fontsize=16,color="black",shape="box"];54 -> 63[label="",style="solid", color="black", weight=3];
12.55/5.58	55[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 GT False)",fontsize=16,color="black",shape="box"];55 -> 64[label="",style="solid", color="black", weight=3];
12.55/5.58	56[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 LT (LT > LT))",fontsize=16,color="black",shape="box"];56 -> 65[label="",style="solid", color="black", weight=3];
12.55/5.58	57[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 LT (LT == LT))",fontsize=16,color="black",shape="box"];57 -> 66[label="",style="solid", color="black", weight=3];
12.55/5.58	58[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 LT (LT == LT))",fontsize=16,color="black",shape="box"];58 -> 67[label="",style="solid", color="black", weight=3];
12.55/5.58	59[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ (compare0 EQ LT otherwise == LT))",fontsize=16,color="black",shape="box"];59 -> 68[label="",style="solid", color="black", weight=3];
12.55/5.58	60[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 EQ (EQ > EQ))",fontsize=16,color="black",shape="box"];60 -> 69[label="",style="solid", color="black", weight=3];
12.55/5.58	61[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 EQ (LT == LT))",fontsize=16,color="black",shape="box"];61 -> 70[label="",style="solid", color="black", weight=3];
12.55/5.58	62[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT (compare0 GT LT otherwise == LT))",fontsize=16,color="black",shape="box"];62 -> 71[label="",style="solid", color="black", weight=3];
12.55/5.58	63[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT (compare0 GT EQ otherwise == LT))",fontsize=16,color="black",shape="box"];63 -> 72[label="",style="solid", color="black", weight=3];
12.55/5.58	64[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 GT wx31 wx32 wx33 wx34 GT (GT > GT))",fontsize=16,color="black",shape="box"];64 -> 73[label="",style="solid", color="black", weight=3];
12.55/5.58	65[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 LT (compare LT LT == GT))",fontsize=16,color="black",shape="box"];65 -> 74[label="",style="solid", color="black", weight=3];
12.55/5.58	66[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 LT True)",fontsize=16,color="black",shape="box"];66 -> 75[label="",style="solid", color="black", weight=3];
12.55/5.58	67[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 LT True)",fontsize=16,color="black",shape="box"];67 -> 76[label="",style="solid", color="black", weight=3];
12.55/5.58	68[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ (compare0 EQ LT True == LT))",fontsize=16,color="black",shape="box"];68 -> 77[label="",style="solid", color="black", weight=3];
12.55/5.58	69[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 EQ (compare EQ EQ == GT))",fontsize=16,color="black",shape="box"];69 -> 78[label="",style="solid", color="black", weight=3];
12.55/5.58	70[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 EQ True)",fontsize=16,color="black",shape="box"];70 -> 79[label="",style="solid", color="black", weight=3];
12.55/5.58	71[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT (compare0 GT LT True == LT))",fontsize=16,color="black",shape="box"];71 -> 80[label="",style="solid", color="black", weight=3];
12.55/5.58	72[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT (compare0 GT EQ True == LT))",fontsize=16,color="black",shape="box"];72 -> 81[label="",style="solid", color="black", weight=3];
12.55/5.58	73[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 GT wx31 wx32 wx33 wx34 GT (compare GT GT == GT))",fontsize=16,color="black",shape="box"];73 -> 82[label="",style="solid", color="black", weight=3];
12.55/5.58	74[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 LT (compare3 LT LT == GT))",fontsize=16,color="black",shape="box"];74 -> 83[label="",style="solid", color="black", weight=3];
12.55/5.58	75 -> 6[label="",style="dashed", color="red", weight=0];
12.55/5.58	75[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM wx33 LT)",fontsize=16,color="magenta"];75 -> 84[label="",style="dashed", color="magenta", weight=3];
12.55/5.58	75 -> 85[label="",style="dashed", color="magenta", weight=3];
12.55/5.58	76 -> 6[label="",style="dashed", color="red", weight=0];
12.55/5.58	76[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM wx33 LT)",fontsize=16,color="magenta"];76 -> 86[label="",style="dashed", color="magenta", weight=3];
12.55/5.58	76 -> 87[label="",style="dashed", color="magenta", weight=3];
12.55/5.58	77[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ (GT == LT))",fontsize=16,color="black",shape="box"];77 -> 88[label="",style="solid", color="black", weight=3];
12.55/5.58	78[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 EQ (compare3 EQ EQ == GT))",fontsize=16,color="black",shape="box"];78 -> 89[label="",style="solid", color="black", weight=3];
12.55/5.58	79 -> 6[label="",style="dashed", color="red", weight=0];
12.55/5.58	79[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM wx33 EQ)",fontsize=16,color="magenta"];79 -> 90[label="",style="dashed", color="magenta", weight=3];
12.55/5.58	79 -> 91[label="",style="dashed", color="magenta", weight=3];
12.55/5.58	80[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT (GT == LT))",fontsize=16,color="black",shape="box"];80 -> 92[label="",style="solid", color="black", weight=3];
12.55/5.58	81[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT (GT == LT))",fontsize=16,color="black",shape="box"];81 -> 93[label="",style="solid", color="black", weight=3];
12.55/5.58	82[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 GT wx31 wx32 wx33 wx34 GT (compare3 GT GT == GT))",fontsize=16,color="black",shape="box"];82 -> 94[label="",style="solid", color="black", weight=3];
12.55/5.58	83[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 LT (compare2 LT LT (LT == LT) == GT))",fontsize=16,color="black",shape="box"];83 -> 95[label="",style="solid", color="black", weight=3];
12.55/5.58	84[label="LT",fontsize=16,color="green",shape="box"];85[label="wx33",fontsize=16,color="green",shape="box"];86[label="LT",fontsize=16,color="green",shape="box"];87[label="wx33",fontsize=16,color="green",shape="box"];88[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ False)",fontsize=16,color="black",shape="box"];88 -> 96[label="",style="solid", color="black", weight=3];
12.55/5.58	89[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 EQ (compare2 EQ EQ (EQ == EQ) == GT))",fontsize=16,color="black",shape="box"];89 -> 97[label="",style="solid", color="black", weight=3];
12.55/5.58	90[label="EQ",fontsize=16,color="green",shape="box"];91[label="wx33",fontsize=16,color="green",shape="box"];92[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT False)",fontsize=16,color="black",shape="box"];92 -> 98[label="",style="solid", color="black", weight=3];
12.55/5.58	93[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT False)",fontsize=16,color="black",shape="box"];93 -> 99[label="",style="solid", color="black", weight=3];
12.55/5.58	94[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 GT wx31 wx32 wx33 wx34 GT (compare2 GT GT (GT == GT) == GT))",fontsize=16,color="black",shape="box"];94 -> 100[label="",style="solid", color="black", weight=3];
12.55/5.58	95[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 LT (compare2 LT LT True == GT))",fontsize=16,color="black",shape="box"];95 -> 101[label="",style="solid", color="black", weight=3];
12.55/5.58	96[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (EQ > LT))",fontsize=16,color="black",shape="box"];96 -> 102[label="",style="solid", color="black", weight=3];
12.55/5.58	97[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 EQ (compare2 EQ EQ True == GT))",fontsize=16,color="black",shape="box"];97 -> 103[label="",style="solid", color="black", weight=3];
12.55/5.58	98[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (GT > LT))",fontsize=16,color="black",shape="box"];98 -> 104[label="",style="solid", color="black", weight=3];
12.55/5.58	99[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (GT > EQ))",fontsize=16,color="black",shape="box"];99 -> 105[label="",style="solid", color="black", weight=3];
12.55/5.58	100[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 GT wx31 wx32 wx33 wx34 GT (compare2 GT GT True == GT))",fontsize=16,color="black",shape="box"];100 -> 106[label="",style="solid", color="black", weight=3];
12.55/5.58	101[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 LT (EQ == GT))",fontsize=16,color="black",shape="box"];101 -> 107[label="",style="solid", color="black", weight=3];
12.55/5.58	102[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare EQ LT == GT))",fontsize=16,color="black",shape="box"];102 -> 108[label="",style="solid", color="black", weight=3];
12.55/5.58	103[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 EQ (EQ == GT))",fontsize=16,color="black",shape="box"];103 -> 109[label="",style="solid", color="black", weight=3];
12.55/5.58	104[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare GT LT == GT))",fontsize=16,color="black",shape="box"];104 -> 110[label="",style="solid", color="black", weight=3];
12.55/5.58	105[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare GT EQ == GT))",fontsize=16,color="black",shape="box"];105 -> 111[label="",style="solid", color="black", weight=3];
12.55/5.58	106[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 GT wx31 wx32 wx33 wx34 GT (EQ == GT))",fontsize=16,color="black",shape="box"];106 -> 112[label="",style="solid", color="black", weight=3];
12.55/5.58	107[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 LT False)",fontsize=16,color="black",shape="box"];107 -> 113[label="",style="solid", color="black", weight=3];
12.55/5.58	108[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare3 EQ LT == GT))",fontsize=16,color="black",shape="box"];108 -> 114[label="",style="solid", color="black", weight=3];
12.55/5.58	109[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 EQ False)",fontsize=16,color="black",shape="box"];109 -> 115[label="",style="solid", color="black", weight=3];
12.55/5.58	110[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare3 GT LT == GT))",fontsize=16,color="black",shape="box"];110 -> 116[label="",style="solid", color="black", weight=3];
12.55/5.58	111[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare3 GT EQ == GT))",fontsize=16,color="black",shape="box"];111 -> 117[label="",style="solid", color="black", weight=3];
12.55/5.58	112[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 GT wx31 wx32 wx33 wx34 GT False)",fontsize=16,color="black",shape="box"];112 -> 118[label="",style="solid", color="black", weight=3];
12.55/5.58	113[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM0 LT wx31 wx32 wx33 wx34 LT otherwise)",fontsize=16,color="black",shape="box"];113 -> 119[label="",style="solid", color="black", weight=3];
12.55/5.58	114[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare2 EQ LT (EQ == LT) == GT))",fontsize=16,color="black",shape="box"];114 -> 120[label="",style="solid", color="black", weight=3];
12.55/5.58	115[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM0 EQ wx31 wx32 wx33 wx34 EQ otherwise)",fontsize=16,color="black",shape="box"];115 -> 121[label="",style="solid", color="black", weight=3];
12.55/5.58	116[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare2 GT LT (GT == LT) == GT))",fontsize=16,color="black",shape="box"];116 -> 122[label="",style="solid", color="black", weight=3];
12.55/5.58	117[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare2 GT EQ (GT == EQ) == GT))",fontsize=16,color="black",shape="box"];117 -> 123[label="",style="solid", color="black", weight=3];
12.55/5.58	118[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM0 GT wx31 wx32 wx33 wx34 GT otherwise)",fontsize=16,color="black",shape="box"];118 -> 124[label="",style="solid", color="black", weight=3];
12.55/5.58	119[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM0 LT wx31 wx32 wx33 wx34 LT True)",fontsize=16,color="black",shape="box"];119 -> 125[label="",style="solid", color="black", weight=3];
12.55/5.58	120[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare2 EQ LT False == GT))",fontsize=16,color="black",shape="box"];120 -> 126[label="",style="solid", color="black", weight=3];
12.55/5.58	121[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM0 EQ wx31 wx32 wx33 wx34 EQ True)",fontsize=16,color="black",shape="box"];121 -> 127[label="",style="solid", color="black", weight=3];
12.55/5.58	122[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare2 GT LT False == GT))",fontsize=16,color="black",shape="box"];122 -> 128[label="",style="solid", color="black", weight=3];
12.55/5.58	123[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare2 GT EQ False == GT))",fontsize=16,color="black",shape="box"];123 -> 129[label="",style="solid", color="black", weight=3];
12.55/5.58	124[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM0 GT wx31 wx32 wx33 wx34 GT True)",fontsize=16,color="black",shape="box"];124 -> 130[label="",style="solid", color="black", weight=3];
12.55/5.58	125[label="FiniteMap.lookupWithDefaultFM0 wx4 (Just wx31)",fontsize=16,color="black",shape="triangle"];125 -> 131[label="",style="solid", color="black", weight=3];
12.55/5.58	126[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare1 EQ LT (EQ <= LT) == GT))",fontsize=16,color="black",shape="box"];126 -> 132[label="",style="solid", color="black", weight=3];
12.55/5.58	127 -> 125[label="",style="dashed", color="red", weight=0];
12.55/5.58	127[label="FiniteMap.lookupWithDefaultFM0 wx4 (Just wx31)",fontsize=16,color="magenta"];128[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare1 GT LT (GT <= LT) == GT))",fontsize=16,color="black",shape="box"];128 -> 133[label="",style="solid", color="black", weight=3];
12.55/5.58	129[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare1 GT EQ (GT <= EQ) == GT))",fontsize=16,color="black",shape="box"];129 -> 134[label="",style="solid", color="black", weight=3];
12.55/5.58	130 -> 125[label="",style="dashed", color="red", weight=0];
12.55/5.58	130[label="FiniteMap.lookupWithDefaultFM0 wx4 (Just wx31)",fontsize=16,color="magenta"];131[label="wx31",fontsize=16,color="green",shape="box"];132[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare1 EQ LT False == GT))",fontsize=16,color="black",shape="box"];132 -> 135[label="",style="solid", color="black", weight=3];
12.55/5.58	133[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare1 GT LT False == GT))",fontsize=16,color="black",shape="box"];133 -> 136[label="",style="solid", color="black", weight=3];
12.55/5.58	134[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare1 GT EQ False == GT))",fontsize=16,color="black",shape="box"];134 -> 137[label="",style="solid", color="black", weight=3];
12.55/5.58	135[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare0 EQ LT otherwise == GT))",fontsize=16,color="black",shape="box"];135 -> 138[label="",style="solid", color="black", weight=3];
12.55/5.58	136[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare0 GT LT otherwise == GT))",fontsize=16,color="black",shape="box"];136 -> 139[label="",style="solid", color="black", weight=3];
12.55/5.58	137[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare0 GT EQ otherwise == GT))",fontsize=16,color="black",shape="box"];137 -> 140[label="",style="solid", color="black", weight=3];
12.55/5.58	138[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare0 EQ LT True == GT))",fontsize=16,color="black",shape="box"];138 -> 141[label="",style="solid", color="black", weight=3];
12.55/5.58	139[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare0 GT LT True == GT))",fontsize=16,color="black",shape="box"];139 -> 142[label="",style="solid", color="black", weight=3];
12.55/5.58	140[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare0 GT EQ True == GT))",fontsize=16,color="black",shape="box"];140 -> 143[label="",style="solid", color="black", weight=3];
12.55/5.58	141[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (GT == GT))",fontsize=16,color="black",shape="box"];141 -> 144[label="",style="solid", color="black", weight=3];
12.55/5.58	142[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (GT == GT))",fontsize=16,color="black",shape="box"];142 -> 145[label="",style="solid", color="black", weight=3];
12.55/5.58	143[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (GT == GT))",fontsize=16,color="black",shape="box"];143 -> 146[label="",style="solid", color="black", weight=3];
12.55/5.58	144[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ True)",fontsize=16,color="black",shape="box"];144 -> 147[label="",style="solid", color="black", weight=3];
12.55/5.58	145[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT True)",fontsize=16,color="black",shape="box"];145 -> 148[label="",style="solid", color="black", weight=3];
12.55/5.58	146[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT True)",fontsize=16,color="black",shape="box"];146 -> 149[label="",style="solid", color="black", weight=3];
12.55/5.58	147 -> 6[label="",style="dashed", color="red", weight=0];
12.55/5.58	147[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM wx34 EQ)",fontsize=16,color="magenta"];147 -> 150[label="",style="dashed", color="magenta", weight=3];
12.55/5.58	147 -> 151[label="",style="dashed", color="magenta", weight=3];
12.55/5.58	148 -> 6[label="",style="dashed", color="red", weight=0];
12.55/5.58	148[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM wx34 GT)",fontsize=16,color="magenta"];148 -> 152[label="",style="dashed", color="magenta", weight=3];
12.55/5.58	148 -> 153[label="",style="dashed", color="magenta", weight=3];
12.55/5.58	149 -> 6[label="",style="dashed", color="red", weight=0];
12.55/5.58	149[label="FiniteMap.lookupWithDefaultFM0 wx4 (FiniteMap.lookupFM wx34 GT)",fontsize=16,color="magenta"];149 -> 154[label="",style="dashed", color="magenta", weight=3];
12.55/5.58	149 -> 155[label="",style="dashed", color="magenta", weight=3];
12.55/5.58	150[label="EQ",fontsize=16,color="green",shape="box"];151[label="wx34",fontsize=16,color="green",shape="box"];152[label="GT",fontsize=16,color="green",shape="box"];153[label="wx34",fontsize=16,color="green",shape="box"];154[label="GT",fontsize=16,color="green",shape="box"];155[label="wx34",fontsize=16,color="green",shape="box"];}
12.55/5.58	
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(8)
12.55/5.58	Obligation:
12.55/5.58	Q DP problem:
12.55/5.58	The TRS P consists of the following rules:
12.55/5.58	
12.55/5.58	   new_lookupWithDefaultFM0(wx4, Branch(GT, wx31, wx32, wx33, wx34), EQ, h) -> new_lookupWithDefaultFM0(wx4, wx33, EQ, h)
12.55/5.58	   new_lookupWithDefaultFM0(wx4, Branch(GT, wx31, wx32, wx33, wx34), LT, h) -> new_lookupWithDefaultFM0(wx4, wx33, LT, h)
12.55/5.58	   new_lookupWithDefaultFM0(wx4, Branch(LT, wx31, wx32, wx33, wx34), GT, h) -> new_lookupWithDefaultFM0(wx4, wx34, GT, h)
12.55/5.58	   new_lookupWithDefaultFM0(wx4, Branch(LT, wx31, wx32, wx33, wx34), EQ, h) -> new_lookupWithDefaultFM0(wx4, wx34, EQ, h)
12.55/5.58	   new_lookupWithDefaultFM0(wx4, Branch(EQ, wx31, wx32, wx33, wx34), LT, h) -> new_lookupWithDefaultFM0(wx4, wx33, LT, h)
12.55/5.58	   new_lookupWithDefaultFM0(wx4, Branch(EQ, wx31, wx32, wx33, wx34), GT, h) -> new_lookupWithDefaultFM0(wx4, wx34, GT, h)
12.55/5.58	
12.55/5.58	R is empty.
12.55/5.58	Q is empty.
12.55/5.58	We have to consider all minimal (P,Q,R)-chains.
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(9) DependencyGraphProof (EQUIVALENT)
12.55/5.58	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs.
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(10)
12.55/5.58	Complex Obligation (AND)
12.55/5.58	
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(11)
12.55/5.58	Obligation:
12.55/5.58	Q DP problem:
12.55/5.58	The TRS P consists of the following rules:
12.55/5.58	
12.55/5.58	   new_lookupWithDefaultFM0(wx4, Branch(EQ, wx31, wx32, wx33, wx34), GT, h) -> new_lookupWithDefaultFM0(wx4, wx34, GT, h)
12.55/5.58	   new_lookupWithDefaultFM0(wx4, Branch(LT, wx31, wx32, wx33, wx34), GT, h) -> new_lookupWithDefaultFM0(wx4, wx34, GT, h)
12.55/5.58	
12.55/5.58	R is empty.
12.55/5.58	Q is empty.
12.55/5.58	We have to consider all minimal (P,Q,R)-chains.
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(12) QDPSizeChangeProof (EQUIVALENT)
12.55/5.58	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. 
12.55/5.58	
12.55/5.58	From the DPs we obtained the following set of size-change graphs:
12.55/5.58	*new_lookupWithDefaultFM0(wx4, Branch(EQ, wx31, wx32, wx33, wx34), GT, h) -> new_lookupWithDefaultFM0(wx4, wx34, GT, h)
12.55/5.58	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
12.55/5.58	
12.55/5.58	
12.55/5.58	*new_lookupWithDefaultFM0(wx4, Branch(LT, wx31, wx32, wx33, wx34), GT, h) -> new_lookupWithDefaultFM0(wx4, wx34, GT, h)
12.55/5.58	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
12.55/5.58	
12.55/5.58	
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(13)
12.55/5.58	YES
12.55/5.58	
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(14)
12.55/5.58	Obligation:
12.55/5.58	Q DP problem:
12.55/5.58	The TRS P consists of the following rules:
12.55/5.58	
12.55/5.58	   new_lookupWithDefaultFM0(wx4, Branch(EQ, wx31, wx32, wx33, wx34), LT, h) -> new_lookupWithDefaultFM0(wx4, wx33, LT, h)
12.55/5.58	   new_lookupWithDefaultFM0(wx4, Branch(GT, wx31, wx32, wx33, wx34), LT, h) -> new_lookupWithDefaultFM0(wx4, wx33, LT, h)
12.55/5.58	
12.55/5.58	R is empty.
12.55/5.58	Q is empty.
12.55/5.58	We have to consider all minimal (P,Q,R)-chains.
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(15) QDPSizeChangeProof (EQUIVALENT)
12.55/5.58	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. 
12.55/5.58	
12.55/5.58	From the DPs we obtained the following set of size-change graphs:
12.55/5.58	*new_lookupWithDefaultFM0(wx4, Branch(EQ, wx31, wx32, wx33, wx34), LT, h) -> new_lookupWithDefaultFM0(wx4, wx33, LT, h)
12.55/5.58	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
12.55/5.58	
12.55/5.58	
12.55/5.58	*new_lookupWithDefaultFM0(wx4, Branch(GT, wx31, wx32, wx33, wx34), LT, h) -> new_lookupWithDefaultFM0(wx4, wx33, LT, h)
12.55/5.58	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
12.55/5.58	
12.55/5.58	
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(16)
12.55/5.58	YES
12.55/5.58	
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(17)
12.55/5.58	Obligation:
12.55/5.58	Q DP problem:
12.55/5.58	The TRS P consists of the following rules:
12.55/5.58	
12.55/5.58	   new_lookupWithDefaultFM0(wx4, Branch(LT, wx31, wx32, wx33, wx34), EQ, h) -> new_lookupWithDefaultFM0(wx4, wx34, EQ, h)
12.55/5.58	   new_lookupWithDefaultFM0(wx4, Branch(GT, wx31, wx32, wx33, wx34), EQ, h) -> new_lookupWithDefaultFM0(wx4, wx33, EQ, h)
12.55/5.58	
12.55/5.58	R is empty.
12.55/5.58	Q is empty.
12.55/5.58	We have to consider all minimal (P,Q,R)-chains.
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(18) QDPSizeChangeProof (EQUIVALENT)
12.55/5.58	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. 
12.55/5.58	
12.55/5.58	From the DPs we obtained the following set of size-change graphs:
12.55/5.58	*new_lookupWithDefaultFM0(wx4, Branch(LT, wx31, wx32, wx33, wx34), EQ, h) -> new_lookupWithDefaultFM0(wx4, wx34, EQ, h)
12.55/5.58	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
12.55/5.58	
12.55/5.58	
12.55/5.58	*new_lookupWithDefaultFM0(wx4, Branch(GT, wx31, wx32, wx33, wx34), EQ, h) -> new_lookupWithDefaultFM0(wx4, wx33, EQ, h)
12.55/5.58	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4
12.55/5.58	
12.55/5.58	
12.55/5.58	----------------------------------------
12.55/5.58	
12.55/5.58	(19)
12.55/5.58	YES
12.71/5.63	EOF