10.29/4.59	YES
12.42/5.12	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.42/5.12	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.42/5.12	
12.42/5.12	
12.42/5.12	H-Termination with start terms of the given HASKELL could be proven:
12.42/5.12	
12.42/5.12	(0) HASKELL
12.42/5.12	(1) BR [EQUIVALENT, 0 ms]
12.42/5.12	(2) HASKELL
12.42/5.12	(3) COR [EQUIVALENT, 0 ms]
12.42/5.12	(4) HASKELL
12.42/5.12	(5) Narrow [SOUND, 0 ms]
12.42/5.12	(6) QDP
12.42/5.12	(7) DependencyGraphProof [EQUIVALENT, 0 ms]
12.42/5.12	(8) AND
12.42/5.12	    (9) QDP
12.42/5.12	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.42/5.12	        (11) YES
12.42/5.12	    (12) QDP
12.42/5.12	        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.42/5.12	        (14) YES
12.42/5.12	    (15) QDP
12.42/5.12	        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.42/5.12	        (17) YES
12.42/5.12	
12.42/5.12	
12.42/5.12	----------------------------------------
12.42/5.12	
12.42/5.12	(0)
12.42/5.12	Obligation:
12.42/5.12	mainModule Main 
12.42/5.12	module FiniteMap where {
12.42/5.12	import qualified Main;
12.42/5.12	import qualified Maybe;
12.42/5.12	import qualified Prelude;
12.42/5.12	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.42/5.12	
12.42/5.12	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
12.42/5.12	}
12.42/5.12	lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
12.42/5.12	lookupFM EmptyFM key = Nothing;
12.48/5.14	lookupFM (Branch key elt _ fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
12.48/5.14	 | key_to_find > key = lookupFM fm_r key_to_find
12.48/5.14	 | otherwise = Just elt;
12.48/5.14	
12.48/5.14	}
12.48/5.14	module Maybe where {
12.48/5.14	import qualified FiniteMap;
12.48/5.14	import qualified Main;
12.48/5.14	import qualified Prelude;
12.48/5.14	}
12.48/5.14	module Main where {
12.48/5.14	import qualified FiniteMap;
12.48/5.14	import qualified Maybe;
12.48/5.14	import qualified Prelude;
12.48/5.14	}
12.48/5.14	
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(1) BR (EQUIVALENT)
12.48/5.14	Replaced joker patterns by fresh variables and removed binding patterns.
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(2)
12.48/5.14	Obligation:
12.48/5.14	mainModule Main 
12.48/5.14	module FiniteMap where {
12.48/5.14	import qualified Main;
12.48/5.14	import qualified Maybe;
12.48/5.14	import qualified Prelude;
12.48/5.14	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.48/5.14	
12.48/5.14	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.48/5.14	}
12.48/5.14	lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
12.48/5.14	lookupFM EmptyFM key = Nothing;
12.48/5.14	lookupFM (Branch key elt vy fm_l fm_r) key_to_find  | key_to_find < key = lookupFM fm_l key_to_find
12.48/5.14	 | key_to_find > key = lookupFM fm_r key_to_find
12.48/5.14	 | otherwise = Just elt;
12.48/5.14	
12.48/5.14	}
12.48/5.14	module Maybe where {
12.48/5.14	import qualified FiniteMap;
12.48/5.14	import qualified Main;
12.48/5.14	import qualified Prelude;
12.48/5.14	}
12.48/5.14	module Main where {
12.48/5.14	import qualified FiniteMap;
12.48/5.14	import qualified Maybe;
12.48/5.14	import qualified Prelude;
12.48/5.14	}
12.48/5.14	
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(3) COR (EQUIVALENT)
12.48/5.14	Cond Reductions:
12.48/5.14	The following Function with conditions
12.48/5.14	"compare x y|x == yEQ|x <= yLT|otherwiseGT;
12.48/5.14	"
12.48/5.14	is transformed to
12.48/5.14	"compare x y = compare3 x y;
12.48/5.14	"
12.48/5.14	"compare1 x y True = LT;
12.48/5.14	compare1 x y False = compare0 x y otherwise;
12.48/5.14	"
12.48/5.14	"compare0 x y True = GT;
12.48/5.14	"
12.48/5.14	"compare2 x y True = EQ;
12.48/5.14	compare2 x y False = compare1 x y (x <= y);
12.48/5.14	"
12.48/5.14	"compare3 x y = compare2 x y (x == y);
12.48/5.14	"
12.48/5.14	The following Function with conditions
12.48/5.14	"undefined |Falseundefined;
12.48/5.14	"
12.48/5.14	is transformed to
12.48/5.14	"undefined  = undefined1;
12.48/5.14	"
12.48/5.14	"undefined0 True = undefined;
12.48/5.14	"
12.48/5.14	"undefined1  = undefined0 False;
12.48/5.14	"
12.48/5.14	The following Function with conditions
12.48/5.14	"lookupFM EmptyFM key = Nothing;
12.48/5.14	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;
12.48/5.14	"
12.48/5.14	is transformed to
12.48/5.14	"lookupFM EmptyFM key = lookupFM4 EmptyFM key;
12.48/5.14	lookupFM (Branch key elt vy fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find;
12.48/5.14	"
12.48/5.14	"lookupFM2 key elt vy fm_l fm_r key_to_find True = lookupFM fm_l key_to_find;
12.48/5.14	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);
12.48/5.14	"
12.48/5.14	"lookupFM1 key elt vy fm_l fm_r key_to_find True = lookupFM fm_r key_to_find;
12.48/5.14	lookupFM1 key elt vy fm_l fm_r key_to_find False = lookupFM0 key elt vy fm_l fm_r key_to_find otherwise;
12.48/5.14	"
12.48/5.14	"lookupFM0 key elt vy fm_l fm_r key_to_find True = Just elt;
12.48/5.14	"
12.48/5.14	"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);
12.48/5.14	"
12.48/5.14	"lookupFM4 EmptyFM key = Nothing;
12.48/5.14	lookupFM4 wv ww = lookupFM3 wv ww;
12.48/5.14	"
12.48/5.14	
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(4)
12.48/5.14	Obligation:
12.48/5.14	mainModule Main 
12.48/5.14	module FiniteMap where {
12.48/5.14	import qualified Main;
12.48/5.14	import qualified Maybe;
12.48/5.14	import qualified Prelude;
12.48/5.14	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.48/5.14	
12.48/5.14	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
12.48/5.14	}
12.48/5.14	lookupFM :: Ord b => FiniteMap b a  ->  b  ->  Maybe a;
12.48/5.14	lookupFM EmptyFM key = lookupFM4 EmptyFM key;
12.48/5.14	lookupFM (Branch key elt vy fm_l fm_r) key_to_find = lookupFM3 (Branch key elt vy fm_l fm_r) key_to_find;
12.48/5.14	
12.48/5.14	lookupFM0 key elt vy fm_l fm_r key_to_find True = Just elt;
12.48/5.14	
12.48/5.14	lookupFM1 key elt vy fm_l fm_r key_to_find True = lookupFM fm_r key_to_find;
12.48/5.14	lookupFM1 key elt vy fm_l fm_r key_to_find False = lookupFM0 key elt vy fm_l fm_r key_to_find otherwise;
12.48/5.14	
12.48/5.14	lookupFM2 key elt vy fm_l fm_r key_to_find True = lookupFM fm_l key_to_find;
12.48/5.14	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);
12.48/5.14	
12.48/5.14	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);
12.48/5.14	
12.48/5.14	lookupFM4 EmptyFM key = Nothing;
12.48/5.14	lookupFM4 wv ww = lookupFM3 wv ww;
12.48/5.14	
12.48/5.14	}
12.48/5.14	module Maybe where {
12.48/5.14	import qualified FiniteMap;
12.48/5.14	import qualified Main;
12.48/5.14	import qualified Prelude;
12.48/5.14	}
12.48/5.14	module Main where {
12.48/5.14	import qualified FiniteMap;
12.48/5.14	import qualified Maybe;
12.48/5.14	import qualified Prelude;
12.48/5.14	}
12.48/5.14	
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(5) Narrow (SOUND)
12.48/5.14	Haskell To QDPs
12.48/5.14	
12.48/5.14	digraph dp_graph {
12.48/5.14	node [outthreshold=100, inthreshold=100];1[label="FiniteMap.lookupFM",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
12.48/5.14	3[label="FiniteMap.lookupFM wx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
12.48/5.14	4[label="FiniteMap.lookupFM wx3 wx4",fontsize=16,color="burlywood",shape="triangle"];152[label="wx3/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];4 -> 152[label="",style="solid", color="burlywood", weight=9];
12.48/5.14	152 -> 5[label="",style="solid", color="burlywood", weight=3];
12.48/5.14	153[label="wx3/FiniteMap.Branch wx30 wx31 wx32 wx33 wx34",fontsize=10,color="white",style="solid",shape="box"];4 -> 153[label="",style="solid", color="burlywood", weight=9];
12.48/5.14	153 -> 6[label="",style="solid", color="burlywood", weight=3];
12.48/5.14	5[label="FiniteMap.lookupFM FiniteMap.EmptyFM wx4",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
12.48/5.14	6[label="FiniteMap.lookupFM (FiniteMap.Branch wx30 wx31 wx32 wx33 wx34) wx4",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
12.48/5.14	7[label="FiniteMap.lookupFM4 FiniteMap.EmptyFM wx4",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
12.48/5.14	8[label="FiniteMap.lookupFM3 (FiniteMap.Branch wx30 wx31 wx32 wx33 wx34) wx4",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
12.48/5.14	9[label="Nothing",fontsize=16,color="green",shape="box"];10[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 wx4 (wx4 < wx30)",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
12.48/5.14	11[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 wx4 (compare wx4 wx30 == LT)",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12.48/5.14	12[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 wx4 (compare3 wx4 wx30 == LT)",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
12.48/5.14	13[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 wx4 (compare2 wx4 wx30 (wx4 == wx30) == LT)",fontsize=16,color="burlywood",shape="box"];154[label="wx4/LT",fontsize=10,color="white",style="solid",shape="box"];13 -> 154[label="",style="solid", color="burlywood", weight=9];
12.48/5.14	154 -> 14[label="",style="solid", color="burlywood", weight=3];
12.48/5.14	155[label="wx4/EQ",fontsize=10,color="white",style="solid",shape="box"];13 -> 155[label="",style="solid", color="burlywood", weight=9];
12.48/5.14	155 -> 15[label="",style="solid", color="burlywood", weight=3];
12.48/5.14	156[label="wx4/GT",fontsize=10,color="white",style="solid",shape="box"];13 -> 156[label="",style="solid", color="burlywood", weight=9];
12.48/5.14	156 -> 16[label="",style="solid", color="burlywood", weight=3];
12.48/5.14	14[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 LT (compare2 LT wx30 (LT == wx30) == LT)",fontsize=16,color="burlywood",shape="box"];157[label="wx30/LT",fontsize=10,color="white",style="solid",shape="box"];14 -> 157[label="",style="solid", color="burlywood", weight=9];
12.48/5.14	157 -> 17[label="",style="solid", color="burlywood", weight=3];
12.48/5.14	158[label="wx30/EQ",fontsize=10,color="white",style="solid",shape="box"];14 -> 158[label="",style="solid", color="burlywood", weight=9];
12.48/5.14	158 -> 18[label="",style="solid", color="burlywood", weight=3];
12.48/5.14	159[label="wx30/GT",fontsize=10,color="white",style="solid",shape="box"];14 -> 159[label="",style="solid", color="burlywood", weight=9];
12.48/5.14	159 -> 19[label="",style="solid", color="burlywood", weight=3];
12.48/5.14	15[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 EQ (compare2 EQ wx30 (EQ == wx30) == LT)",fontsize=16,color="burlywood",shape="box"];160[label="wx30/LT",fontsize=10,color="white",style="solid",shape="box"];15 -> 160[label="",style="solid", color="burlywood", weight=9];
12.48/5.14	160 -> 20[label="",style="solid", color="burlywood", weight=3];
12.48/5.14	161[label="wx30/EQ",fontsize=10,color="white",style="solid",shape="box"];15 -> 161[label="",style="solid", color="burlywood", weight=9];
12.48/5.14	161 -> 21[label="",style="solid", color="burlywood", weight=3];
12.48/5.14	162[label="wx30/GT",fontsize=10,color="white",style="solid",shape="box"];15 -> 162[label="",style="solid", color="burlywood", weight=9];
12.48/5.14	162 -> 22[label="",style="solid", color="burlywood", weight=3];
12.48/5.14	16[label="FiniteMap.lookupFM2 wx30 wx31 wx32 wx33 wx34 GT (compare2 GT wx30 (GT == wx30) == LT)",fontsize=16,color="burlywood",shape="box"];163[label="wx30/LT",fontsize=10,color="white",style="solid",shape="box"];16 -> 163[label="",style="solid", color="burlywood", weight=9];
12.48/5.14	163 -> 23[label="",style="solid", color="burlywood", weight=3];
12.48/5.14	164[label="wx30/EQ",fontsize=10,color="white",style="solid",shape="box"];16 -> 164[label="",style="solid", color="burlywood", weight=9];
12.48/5.14	164 -> 24[label="",style="solid", color="burlywood", weight=3];
12.48/5.14	165[label="wx30/GT",fontsize=10,color="white",style="solid",shape="box"];16 -> 165[label="",style="solid", color="burlywood", weight=9];
12.48/5.14	165 -> 25[label="",style="solid", color="burlywood", weight=3];
12.48/5.14	17[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 LT (compare2 LT LT (LT == LT) == LT)",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
12.48/5.14	18[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 LT (compare2 LT EQ (LT == EQ) == LT)",fontsize=16,color="black",shape="box"];18 -> 27[label="",style="solid", color="black", weight=3];
12.48/5.14	19[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 LT (compare2 LT GT (LT == GT) == LT)",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
12.48/5.14	20[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ (compare2 EQ LT (EQ == LT) == LT)",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
12.48/5.14	21[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 EQ (compare2 EQ EQ (EQ == EQ) == LT)",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
12.48/5.14	22[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 EQ (compare2 EQ GT (EQ == GT) == LT)",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
12.48/5.14	23[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT (compare2 GT LT (GT == LT) == LT)",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
12.48/5.14	24[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT (compare2 GT EQ (GT == EQ) == LT)",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
12.48/5.14	25[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 GT (compare2 GT GT (GT == GT) == LT)",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
12.48/5.14	26[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 LT (compare2 LT LT True == LT)",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
12.48/5.14	27[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 LT (compare2 LT EQ False == LT)",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
12.48/5.14	28[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 LT (compare2 LT GT False == LT)",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3];
12.48/5.14	29[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ (compare2 EQ LT False == LT)",fontsize=16,color="black",shape="box"];29 -> 38[label="",style="solid", color="black", weight=3];
12.48/5.14	30[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 EQ (compare2 EQ EQ True == LT)",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3];
12.48/5.14	31[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 EQ (compare2 EQ GT False == LT)",fontsize=16,color="black",shape="box"];31 -> 40[label="",style="solid", color="black", weight=3];
12.48/5.14	32[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT (compare2 GT LT False == LT)",fontsize=16,color="black",shape="box"];32 -> 41[label="",style="solid", color="black", weight=3];
12.48/5.14	33[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT (compare2 GT EQ False == LT)",fontsize=16,color="black",shape="box"];33 -> 42[label="",style="solid", color="black", weight=3];
12.48/5.14	34[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 GT (compare2 GT GT True == LT)",fontsize=16,color="black",shape="box"];34 -> 43[label="",style="solid", color="black", weight=3];
12.48/5.14	35[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 LT (EQ == LT)",fontsize=16,color="black",shape="box"];35 -> 44[label="",style="solid", color="black", weight=3];
12.48/5.14	36[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 LT (compare1 LT EQ (LT <= EQ) == LT)",fontsize=16,color="black",shape="box"];36 -> 45[label="",style="solid", color="black", weight=3];
12.48/5.14	37[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 LT (compare1 LT GT (LT <= GT) == LT)",fontsize=16,color="black",shape="box"];37 -> 46[label="",style="solid", color="black", weight=3];
12.48/5.14	38[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ (compare1 EQ LT (EQ <= LT) == LT)",fontsize=16,color="black",shape="box"];38 -> 47[label="",style="solid", color="black", weight=3];
12.48/5.14	39[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 EQ (EQ == LT)",fontsize=16,color="black",shape="box"];39 -> 48[label="",style="solid", color="black", weight=3];
12.48/5.14	40[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 EQ (compare1 EQ GT (EQ <= GT) == LT)",fontsize=16,color="black",shape="box"];40 -> 49[label="",style="solid", color="black", weight=3];
12.48/5.14	41[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT (compare1 GT LT (GT <= LT) == LT)",fontsize=16,color="black",shape="box"];41 -> 50[label="",style="solid", color="black", weight=3];
12.48/5.14	42[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT (compare1 GT EQ (GT <= EQ) == LT)",fontsize=16,color="black",shape="box"];42 -> 51[label="",style="solid", color="black", weight=3];
12.48/5.14	43[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 GT (EQ == LT)",fontsize=16,color="black",shape="box"];43 -> 52[label="",style="solid", color="black", weight=3];
12.48/5.14	44[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 LT False",fontsize=16,color="black",shape="box"];44 -> 53[label="",style="solid", color="black", weight=3];
12.48/5.14	45[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 LT (compare1 LT EQ True == LT)",fontsize=16,color="black",shape="box"];45 -> 54[label="",style="solid", color="black", weight=3];
12.48/5.14	46[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 LT (compare1 LT GT True == LT)",fontsize=16,color="black",shape="box"];46 -> 55[label="",style="solid", color="black", weight=3];
12.48/5.14	47[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ (compare1 EQ LT False == LT)",fontsize=16,color="black",shape="box"];47 -> 56[label="",style="solid", color="black", weight=3];
12.48/5.14	48[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 EQ False",fontsize=16,color="black",shape="box"];48 -> 57[label="",style="solid", color="black", weight=3];
12.48/5.14	49[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 EQ (compare1 EQ GT True == LT)",fontsize=16,color="black",shape="box"];49 -> 58[label="",style="solid", color="black", weight=3];
12.48/5.14	50[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT (compare1 GT LT False == LT)",fontsize=16,color="black",shape="box"];50 -> 59[label="",style="solid", color="black", weight=3];
12.48/5.14	51[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT (compare1 GT EQ False == LT)",fontsize=16,color="black",shape="box"];51 -> 60[label="",style="solid", color="black", weight=3];
12.48/5.14	52[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 GT False",fontsize=16,color="black",shape="box"];52 -> 61[label="",style="solid", color="black", weight=3];
12.48/5.14	53[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 LT (LT > LT)",fontsize=16,color="black",shape="box"];53 -> 62[label="",style="solid", color="black", weight=3];
12.48/5.14	54[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 LT (LT == LT)",fontsize=16,color="black",shape="box"];54 -> 63[label="",style="solid", color="black", weight=3];
12.48/5.14	55[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 LT (LT == LT)",fontsize=16,color="black",shape="box"];55 -> 64[label="",style="solid", color="black", weight=3];
12.48/5.14	56[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ (compare0 EQ LT otherwise == LT)",fontsize=16,color="black",shape="box"];56 -> 65[label="",style="solid", color="black", weight=3];
12.48/5.14	57[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 EQ (EQ > EQ)",fontsize=16,color="black",shape="box"];57 -> 66[label="",style="solid", color="black", weight=3];
12.48/5.14	58[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 EQ (LT == LT)",fontsize=16,color="black",shape="box"];58 -> 67[label="",style="solid", color="black", weight=3];
12.48/5.14	59[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT (compare0 GT LT otherwise == LT)",fontsize=16,color="black",shape="box"];59 -> 68[label="",style="solid", color="black", weight=3];
12.48/5.14	60[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT (compare0 GT EQ otherwise == LT)",fontsize=16,color="black",shape="box"];60 -> 69[label="",style="solid", color="black", weight=3];
12.48/5.14	61[label="FiniteMap.lookupFM1 GT wx31 wx32 wx33 wx34 GT (GT > GT)",fontsize=16,color="black",shape="box"];61 -> 70[label="",style="solid", color="black", weight=3];
12.48/5.14	62[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 LT (compare LT LT == GT)",fontsize=16,color="black",shape="box"];62 -> 71[label="",style="solid", color="black", weight=3];
12.48/5.14	63[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 LT True",fontsize=16,color="black",shape="box"];63 -> 72[label="",style="solid", color="black", weight=3];
12.48/5.14	64[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 LT True",fontsize=16,color="black",shape="box"];64 -> 73[label="",style="solid", color="black", weight=3];
12.48/5.14	65[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ (compare0 EQ LT True == LT)",fontsize=16,color="black",shape="box"];65 -> 74[label="",style="solid", color="black", weight=3];
12.48/5.14	66[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 EQ (compare EQ EQ == GT)",fontsize=16,color="black",shape="box"];66 -> 75[label="",style="solid", color="black", weight=3];
12.48/5.14	67[label="FiniteMap.lookupFM2 GT wx31 wx32 wx33 wx34 EQ True",fontsize=16,color="black",shape="box"];67 -> 76[label="",style="solid", color="black", weight=3];
12.48/5.14	68[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT (compare0 GT LT True == LT)",fontsize=16,color="black",shape="box"];68 -> 77[label="",style="solid", color="black", weight=3];
12.48/5.14	69[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT (compare0 GT EQ True == LT)",fontsize=16,color="black",shape="box"];69 -> 78[label="",style="solid", color="black", weight=3];
12.48/5.14	70[label="FiniteMap.lookupFM1 GT wx31 wx32 wx33 wx34 GT (compare GT GT == GT)",fontsize=16,color="black",shape="box"];70 -> 79[label="",style="solid", color="black", weight=3];
12.48/5.14	71[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 LT (compare3 LT LT == GT)",fontsize=16,color="black",shape="box"];71 -> 80[label="",style="solid", color="black", weight=3];
12.48/5.14	72 -> 4[label="",style="dashed", color="red", weight=0];
12.48/5.14	72[label="FiniteMap.lookupFM wx33 LT",fontsize=16,color="magenta"];72 -> 81[label="",style="dashed", color="magenta", weight=3];
12.48/5.14	72 -> 82[label="",style="dashed", color="magenta", weight=3];
12.48/5.14	73 -> 4[label="",style="dashed", color="red", weight=0];
12.48/5.14	73[label="FiniteMap.lookupFM wx33 LT",fontsize=16,color="magenta"];73 -> 83[label="",style="dashed", color="magenta", weight=3];
12.48/5.14	73 -> 84[label="",style="dashed", color="magenta", weight=3];
12.48/5.14	74[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ (GT == LT)",fontsize=16,color="black",shape="box"];74 -> 85[label="",style="solid", color="black", weight=3];
12.48/5.14	75[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 EQ (compare3 EQ EQ == GT)",fontsize=16,color="black",shape="box"];75 -> 86[label="",style="solid", color="black", weight=3];
12.48/5.14	76 -> 4[label="",style="dashed", color="red", weight=0];
12.48/5.14	76[label="FiniteMap.lookupFM wx33 EQ",fontsize=16,color="magenta"];76 -> 87[label="",style="dashed", color="magenta", weight=3];
12.48/5.14	76 -> 88[label="",style="dashed", color="magenta", weight=3];
12.48/5.14	77[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT (GT == LT)",fontsize=16,color="black",shape="box"];77 -> 89[label="",style="solid", color="black", weight=3];
12.48/5.14	78[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT (GT == LT)",fontsize=16,color="black",shape="box"];78 -> 90[label="",style="solid", color="black", weight=3];
12.48/5.14	79[label="FiniteMap.lookupFM1 GT wx31 wx32 wx33 wx34 GT (compare3 GT GT == GT)",fontsize=16,color="black",shape="box"];79 -> 91[label="",style="solid", color="black", weight=3];
12.48/5.14	80[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 LT (compare2 LT LT (LT == LT) == GT)",fontsize=16,color="black",shape="box"];80 -> 92[label="",style="solid", color="black", weight=3];
12.48/5.14	81[label="wx33",fontsize=16,color="green",shape="box"];82[label="LT",fontsize=16,color="green",shape="box"];83[label="wx33",fontsize=16,color="green",shape="box"];84[label="LT",fontsize=16,color="green",shape="box"];85[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 EQ False",fontsize=16,color="black",shape="box"];85 -> 93[label="",style="solid", color="black", weight=3];
12.48/5.14	86[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 EQ (compare2 EQ EQ (EQ == EQ) == GT)",fontsize=16,color="black",shape="box"];86 -> 94[label="",style="solid", color="black", weight=3];
12.48/5.14	87[label="wx33",fontsize=16,color="green",shape="box"];88[label="EQ",fontsize=16,color="green",shape="box"];89[label="FiniteMap.lookupFM2 LT wx31 wx32 wx33 wx34 GT False",fontsize=16,color="black",shape="box"];89 -> 95[label="",style="solid", color="black", weight=3];
12.48/5.14	90[label="FiniteMap.lookupFM2 EQ wx31 wx32 wx33 wx34 GT False",fontsize=16,color="black",shape="box"];90 -> 96[label="",style="solid", color="black", weight=3];
12.48/5.14	91[label="FiniteMap.lookupFM1 GT wx31 wx32 wx33 wx34 GT (compare2 GT GT (GT == GT) == GT)",fontsize=16,color="black",shape="box"];91 -> 97[label="",style="solid", color="black", weight=3];
12.48/5.14	92[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 LT (compare2 LT LT True == GT)",fontsize=16,color="black",shape="box"];92 -> 98[label="",style="solid", color="black", weight=3];
12.48/5.14	93[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (EQ > LT)",fontsize=16,color="black",shape="box"];93 -> 99[label="",style="solid", color="black", weight=3];
12.48/5.14	94[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 EQ (compare2 EQ EQ True == GT)",fontsize=16,color="black",shape="box"];94 -> 100[label="",style="solid", color="black", weight=3];
12.48/5.14	95[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (GT > LT)",fontsize=16,color="black",shape="box"];95 -> 101[label="",style="solid", color="black", weight=3];
12.48/5.14	96[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (GT > EQ)",fontsize=16,color="black",shape="box"];96 -> 102[label="",style="solid", color="black", weight=3];
12.48/5.14	97[label="FiniteMap.lookupFM1 GT wx31 wx32 wx33 wx34 GT (compare2 GT GT True == GT)",fontsize=16,color="black",shape="box"];97 -> 103[label="",style="solid", color="black", weight=3];
12.48/5.14	98[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 LT (EQ == GT)",fontsize=16,color="black",shape="box"];98 -> 104[label="",style="solid", color="black", weight=3];
12.48/5.14	99[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare EQ LT == GT)",fontsize=16,color="black",shape="box"];99 -> 105[label="",style="solid", color="black", weight=3];
12.48/5.14	100[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 EQ (EQ == GT)",fontsize=16,color="black",shape="box"];100 -> 106[label="",style="solid", color="black", weight=3];
12.48/5.14	101[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare GT LT == GT)",fontsize=16,color="black",shape="box"];101 -> 107[label="",style="solid", color="black", weight=3];
12.48/5.14	102[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare GT EQ == GT)",fontsize=16,color="black",shape="box"];102 -> 108[label="",style="solid", color="black", weight=3];
12.48/5.14	103[label="FiniteMap.lookupFM1 GT wx31 wx32 wx33 wx34 GT (EQ == GT)",fontsize=16,color="black",shape="box"];103 -> 109[label="",style="solid", color="black", weight=3];
12.48/5.14	104[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 LT False",fontsize=16,color="black",shape="box"];104 -> 110[label="",style="solid", color="black", weight=3];
12.48/5.14	105[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare3 EQ LT == GT)",fontsize=16,color="black",shape="box"];105 -> 111[label="",style="solid", color="black", weight=3];
12.48/5.14	106[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 EQ False",fontsize=16,color="black",shape="box"];106 -> 112[label="",style="solid", color="black", weight=3];
12.48/5.14	107[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare3 GT LT == GT)",fontsize=16,color="black",shape="box"];107 -> 113[label="",style="solid", color="black", weight=3];
12.48/5.14	108[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare3 GT EQ == GT)",fontsize=16,color="black",shape="box"];108 -> 114[label="",style="solid", color="black", weight=3];
12.48/5.14	109[label="FiniteMap.lookupFM1 GT wx31 wx32 wx33 wx34 GT False",fontsize=16,color="black",shape="box"];109 -> 115[label="",style="solid", color="black", weight=3];
12.48/5.14	110[label="FiniteMap.lookupFM0 LT wx31 wx32 wx33 wx34 LT otherwise",fontsize=16,color="black",shape="box"];110 -> 116[label="",style="solid", color="black", weight=3];
12.48/5.14	111[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare2 EQ LT (EQ == LT) == GT)",fontsize=16,color="black",shape="box"];111 -> 117[label="",style="solid", color="black", weight=3];
12.48/5.14	112[label="FiniteMap.lookupFM0 EQ wx31 wx32 wx33 wx34 EQ otherwise",fontsize=16,color="black",shape="box"];112 -> 118[label="",style="solid", color="black", weight=3];
12.48/5.14	113[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare2 GT LT (GT == LT) == GT)",fontsize=16,color="black",shape="box"];113 -> 119[label="",style="solid", color="black", weight=3];
12.48/5.14	114[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare2 GT EQ (GT == EQ) == GT)",fontsize=16,color="black",shape="box"];114 -> 120[label="",style="solid", color="black", weight=3];
12.48/5.14	115[label="FiniteMap.lookupFM0 GT wx31 wx32 wx33 wx34 GT otherwise",fontsize=16,color="black",shape="box"];115 -> 121[label="",style="solid", color="black", weight=3];
12.48/5.14	116[label="FiniteMap.lookupFM0 LT wx31 wx32 wx33 wx34 LT True",fontsize=16,color="black",shape="box"];116 -> 122[label="",style="solid", color="black", weight=3];
12.48/5.14	117[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare2 EQ LT False == GT)",fontsize=16,color="black",shape="box"];117 -> 123[label="",style="solid", color="black", weight=3];
12.48/5.14	118[label="FiniteMap.lookupFM0 EQ wx31 wx32 wx33 wx34 EQ True",fontsize=16,color="black",shape="box"];118 -> 124[label="",style="solid", color="black", weight=3];
12.48/5.14	119[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare2 GT LT False == GT)",fontsize=16,color="black",shape="box"];119 -> 125[label="",style="solid", color="black", weight=3];
12.48/5.14	120[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare2 GT EQ False == GT)",fontsize=16,color="black",shape="box"];120 -> 126[label="",style="solid", color="black", weight=3];
12.48/5.14	121[label="FiniteMap.lookupFM0 GT wx31 wx32 wx33 wx34 GT True",fontsize=16,color="black",shape="box"];121 -> 127[label="",style="solid", color="black", weight=3];
12.48/5.14	122[label="Just wx31",fontsize=16,color="green",shape="box"];123[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare1 EQ LT (EQ <= LT) == GT)",fontsize=16,color="black",shape="box"];123 -> 128[label="",style="solid", color="black", weight=3];
12.48/5.14	124[label="Just wx31",fontsize=16,color="green",shape="box"];125[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare1 GT LT (GT <= LT) == GT)",fontsize=16,color="black",shape="box"];125 -> 129[label="",style="solid", color="black", weight=3];
12.48/5.14	126[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare1 GT EQ (GT <= EQ) == GT)",fontsize=16,color="black",shape="box"];126 -> 130[label="",style="solid", color="black", weight=3];
12.48/5.14	127[label="Just wx31",fontsize=16,color="green",shape="box"];128[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare1 EQ LT False == GT)",fontsize=16,color="black",shape="box"];128 -> 131[label="",style="solid", color="black", weight=3];
12.48/5.14	129[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare1 GT LT False == GT)",fontsize=16,color="black",shape="box"];129 -> 132[label="",style="solid", color="black", weight=3];
12.48/5.14	130[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare1 GT EQ False == GT)",fontsize=16,color="black",shape="box"];130 -> 133[label="",style="solid", color="black", weight=3];
12.48/5.14	131[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare0 EQ LT otherwise == GT)",fontsize=16,color="black",shape="box"];131 -> 134[label="",style="solid", color="black", weight=3];
12.48/5.14	132[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare0 GT LT otherwise == GT)",fontsize=16,color="black",shape="box"];132 -> 135[label="",style="solid", color="black", weight=3];
12.48/5.14	133[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare0 GT EQ otherwise == GT)",fontsize=16,color="black",shape="box"];133 -> 136[label="",style="solid", color="black", weight=3];
12.48/5.14	134[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (compare0 EQ LT True == GT)",fontsize=16,color="black",shape="box"];134 -> 137[label="",style="solid", color="black", weight=3];
12.48/5.14	135[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (compare0 GT LT True == GT)",fontsize=16,color="black",shape="box"];135 -> 138[label="",style="solid", color="black", weight=3];
12.48/5.14	136[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (compare0 GT EQ True == GT)",fontsize=16,color="black",shape="box"];136 -> 139[label="",style="solid", color="black", weight=3];
12.48/5.14	137[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ (GT == GT)",fontsize=16,color="black",shape="box"];137 -> 140[label="",style="solid", color="black", weight=3];
12.48/5.14	138[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT (GT == GT)",fontsize=16,color="black",shape="box"];138 -> 141[label="",style="solid", color="black", weight=3];
12.48/5.14	139[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT (GT == GT)",fontsize=16,color="black",shape="box"];139 -> 142[label="",style="solid", color="black", weight=3];
12.48/5.14	140[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 EQ True",fontsize=16,color="black",shape="box"];140 -> 143[label="",style="solid", color="black", weight=3];
12.48/5.14	141[label="FiniteMap.lookupFM1 LT wx31 wx32 wx33 wx34 GT True",fontsize=16,color="black",shape="box"];141 -> 144[label="",style="solid", color="black", weight=3];
12.48/5.14	142[label="FiniteMap.lookupFM1 EQ wx31 wx32 wx33 wx34 GT True",fontsize=16,color="black",shape="box"];142 -> 145[label="",style="solid", color="black", weight=3];
12.48/5.14	143 -> 4[label="",style="dashed", color="red", weight=0];
12.48/5.14	143[label="FiniteMap.lookupFM wx34 EQ",fontsize=16,color="magenta"];143 -> 146[label="",style="dashed", color="magenta", weight=3];
12.48/5.14	143 -> 147[label="",style="dashed", color="magenta", weight=3];
12.48/5.14	144 -> 4[label="",style="dashed", color="red", weight=0];
12.48/5.14	144[label="FiniteMap.lookupFM wx34 GT",fontsize=16,color="magenta"];144 -> 148[label="",style="dashed", color="magenta", weight=3];
12.48/5.14	144 -> 149[label="",style="dashed", color="magenta", weight=3];
12.48/5.14	145 -> 4[label="",style="dashed", color="red", weight=0];
12.48/5.14	145[label="FiniteMap.lookupFM wx34 GT",fontsize=16,color="magenta"];145 -> 150[label="",style="dashed", color="magenta", weight=3];
12.48/5.14	145 -> 151[label="",style="dashed", color="magenta", weight=3];
12.48/5.14	146[label="wx34",fontsize=16,color="green",shape="box"];147[label="EQ",fontsize=16,color="green",shape="box"];148[label="wx34",fontsize=16,color="green",shape="box"];149[label="GT",fontsize=16,color="green",shape="box"];150[label="wx34",fontsize=16,color="green",shape="box"];151[label="GT",fontsize=16,color="green",shape="box"];}
12.48/5.14	
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(6)
12.48/5.14	Obligation:
12.48/5.14	Q DP problem:
12.48/5.14	The TRS P consists of the following rules:
12.48/5.14	
12.48/5.14	   new_lookupFM(Branch(EQ, wx31, wx32, wx33, wx34), LT, h) -> new_lookupFM(wx33, LT, h)
12.48/5.14	   new_lookupFM(Branch(GT, wx31, wx32, wx33, wx34), EQ, h) -> new_lookupFM(wx33, EQ, h)
12.48/5.14	   new_lookupFM(Branch(GT, wx31, wx32, wx33, wx34), LT, h) -> new_lookupFM(wx33, LT, h)
12.48/5.14	   new_lookupFM(Branch(LT, wx31, wx32, wx33, wx34), GT, h) -> new_lookupFM(wx34, GT, h)
12.48/5.14	   new_lookupFM(Branch(EQ, wx31, wx32, wx33, wx34), GT, h) -> new_lookupFM(wx34, GT, h)
12.48/5.14	   new_lookupFM(Branch(LT, wx31, wx32, wx33, wx34), EQ, h) -> new_lookupFM(wx34, EQ, h)
12.48/5.14	
12.48/5.14	R is empty.
12.48/5.14	Q is empty.
12.48/5.14	We have to consider all minimal (P,Q,R)-chains.
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(7) DependencyGraphProof (EQUIVALENT)
12.48/5.14	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs.
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(8)
12.48/5.14	Complex Obligation (AND)
12.48/5.14	
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(9)
12.48/5.14	Obligation:
12.48/5.14	Q DP problem:
12.48/5.14	The TRS P consists of the following rules:
12.48/5.14	
12.48/5.14	   new_lookupFM(Branch(EQ, wx31, wx32, wx33, wx34), GT, h) -> new_lookupFM(wx34, GT, h)
12.48/5.14	   new_lookupFM(Branch(LT, wx31, wx32, wx33, wx34), GT, h) -> new_lookupFM(wx34, GT, h)
12.48/5.14	
12.48/5.14	R is empty.
12.48/5.14	Q is empty.
12.48/5.14	We have to consider all minimal (P,Q,R)-chains.
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(10) QDPSizeChangeProof (EQUIVALENT)
12.48/5.14	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. 
12.48/5.14	
12.48/5.14	From the DPs we obtained the following set of size-change graphs:
12.48/5.14	*new_lookupFM(Branch(EQ, wx31, wx32, wx33, wx34), GT, h) -> new_lookupFM(wx34, GT, h)
12.48/5.14	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
12.48/5.14	
12.48/5.14	
12.48/5.14	*new_lookupFM(Branch(LT, wx31, wx32, wx33, wx34), GT, h) -> new_lookupFM(wx34, GT, h)
12.48/5.14	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
12.48/5.14	
12.48/5.14	
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(11)
12.48/5.14	YES
12.48/5.14	
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(12)
12.48/5.14	Obligation:
12.48/5.14	Q DP problem:
12.48/5.14	The TRS P consists of the following rules:
12.48/5.14	
12.48/5.14	   new_lookupFM(Branch(LT, wx31, wx32, wx33, wx34), EQ, h) -> new_lookupFM(wx34, EQ, h)
12.48/5.14	   new_lookupFM(Branch(GT, wx31, wx32, wx33, wx34), EQ, h) -> new_lookupFM(wx33, EQ, h)
12.48/5.14	
12.48/5.14	R is empty.
12.48/5.14	Q is empty.
12.48/5.14	We have to consider all minimal (P,Q,R)-chains.
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(13) QDPSizeChangeProof (EQUIVALENT)
12.48/5.14	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. 
12.48/5.14	
12.48/5.14	From the DPs we obtained the following set of size-change graphs:
12.48/5.14	*new_lookupFM(Branch(LT, wx31, wx32, wx33, wx34), EQ, h) -> new_lookupFM(wx34, EQ, h)
12.48/5.14	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
12.48/5.14	
12.48/5.14	
12.48/5.14	*new_lookupFM(Branch(GT, wx31, wx32, wx33, wx34), EQ, h) -> new_lookupFM(wx33, EQ, h)
12.48/5.14	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
12.48/5.14	
12.48/5.14	
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(14)
12.48/5.14	YES
12.48/5.14	
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(15)
12.48/5.14	Obligation:
12.48/5.14	Q DP problem:
12.48/5.14	The TRS P consists of the following rules:
12.48/5.14	
12.48/5.14	   new_lookupFM(Branch(GT, wx31, wx32, wx33, wx34), LT, h) -> new_lookupFM(wx33, LT, h)
12.48/5.14	   new_lookupFM(Branch(EQ, wx31, wx32, wx33, wx34), LT, h) -> new_lookupFM(wx33, LT, h)
12.48/5.14	
12.48/5.14	R is empty.
12.48/5.14	Q is empty.
12.48/5.14	We have to consider all minimal (P,Q,R)-chains.
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(16) QDPSizeChangeProof (EQUIVALENT)
12.48/5.14	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. 
12.48/5.14	
12.48/5.14	From the DPs we obtained the following set of size-change graphs:
12.48/5.14	*new_lookupFM(Branch(GT, wx31, wx32, wx33, wx34), LT, h) -> new_lookupFM(wx33, LT, h)
12.48/5.14	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
12.48/5.14	
12.48/5.14	
12.48/5.14	*new_lookupFM(Branch(EQ, wx31, wx32, wx33, wx34), LT, h) -> new_lookupFM(wx33, LT, h)
12.48/5.14	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3
12.48/5.14	
12.48/5.14	
12.48/5.14	----------------------------------------
12.48/5.14	
12.48/5.14	(17)
12.48/5.14	YES
12.48/5.20	EOF