10.30/4.52	YES
12.04/5.02	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.04/5.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.04/5.02	
12.04/5.02	
12.04/5.02	H-Termination with start terms of the given HASKELL could be proven:
12.04/5.02	
12.04/5.02	(0) HASKELL
12.04/5.02	(1) BR [EQUIVALENT, 0 ms]
12.04/5.02	(2) HASKELL
12.04/5.02	(3) COR [EQUIVALENT, 0 ms]
12.04/5.02	(4) HASKELL
12.04/5.02	(5) Narrow [SOUND, 0 ms]
12.04/5.02	(6) QDP
12.04/5.02	(7) DependencyGraphProof [EQUIVALENT, 0 ms]
12.04/5.02	(8) AND
12.04/5.02	    (9) QDP
12.04/5.02	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.04/5.02	        (11) YES
12.04/5.02	    (12) QDP
12.04/5.02	        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.04/5.02	        (14) YES
12.04/5.02	    (15) QDP
12.04/5.02	        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.04/5.02	        (17) YES
12.04/5.02	
12.04/5.02	
12.04/5.02	----------------------------------------
12.04/5.02	
12.04/5.02	(0)
12.04/5.02	Obligation:
12.04/5.02	mainModule Main 
12.04/5.02	module FiniteMap where {
12.04/5.02	import qualified Main;
12.04/5.02	import qualified Maybe;
12.04/5.02	import qualified Prelude;
12.04/5.02	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.04/5.02	
12.04/5.02	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.04/5.02	}
12.04/5.02	foldFM_GE :: Ord b => (b  ->  c  ->  a  ->  a)  ->  a  ->  b  ->  FiniteMap b c  ->  a;
12.04/5.02	foldFM_GE k z fr EmptyFM = z;
12.04/5.02	foldFM_GE k z fr (Branch key elt _ fm_l fm_r)  | key >= fr = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l
12.04/5.02	 | otherwise = foldFM_GE k z fr fm_r;
12.04/5.02	
12.04/5.02	}
12.04/5.02	module Maybe where {
12.04/5.02	import qualified FiniteMap;
12.04/5.02	import qualified Main;
12.04/5.02	import qualified Prelude;
12.04/5.02	}
12.04/5.02	module Main where {
12.04/5.02	import qualified FiniteMap;
12.04/5.02	import qualified Maybe;
12.04/5.02	import qualified Prelude;
12.04/5.02	}
12.04/5.02	
12.04/5.02	----------------------------------------
12.04/5.02	
12.04/5.02	(1) BR (EQUIVALENT)
12.04/5.02	Replaced joker patterns by fresh variables and removed binding patterns.
12.04/5.02	----------------------------------------
12.04/5.02	
12.04/5.02	(2)
12.04/5.02	Obligation:
12.04/5.02	mainModule Main 
12.04/5.02	module FiniteMap where {
12.04/5.02	import qualified Main;
12.04/5.02	import qualified Maybe;
12.04/5.02	import qualified Prelude;
12.04/5.02	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.04/5.02	
12.04/5.02	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
12.04/5.02	}
12.04/5.02	foldFM_GE :: Ord b => (b  ->  a  ->  c  ->  c)  ->  c  ->  b  ->  FiniteMap b a  ->  c;
12.04/5.02	foldFM_GE k z fr EmptyFM = z;
12.04/5.02	foldFM_GE k z fr (Branch key elt vy fm_l fm_r)  | key >= fr = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l
12.04/5.02	 | otherwise = foldFM_GE k z fr fm_r;
12.04/5.02	
12.04/5.02	}
12.04/5.02	module Maybe where {
12.04/5.02	import qualified FiniteMap;
12.04/5.02	import qualified Main;
12.04/5.02	import qualified Prelude;
12.04/5.02	}
12.04/5.02	module Main where {
12.04/5.02	import qualified FiniteMap;
12.04/5.02	import qualified Maybe;
12.04/5.02	import qualified Prelude;
12.04/5.02	}
12.04/5.02	
12.04/5.02	----------------------------------------
12.04/5.02	
12.04/5.02	(3) COR (EQUIVALENT)
12.04/5.02	Cond Reductions:
12.04/5.02	The following Function with conditions
12.04/5.02	"compare x y|x == yEQ|x <= yLT|otherwiseGT;
12.04/5.02	"
12.04/5.02	is transformed to
12.04/5.02	"compare x y = compare3 x y;
12.04/5.02	"
12.04/5.02	"compare1 x y True = LT;
12.04/5.02	compare1 x y False = compare0 x y otherwise;
12.04/5.02	"
12.04/5.02	"compare2 x y True = EQ;
12.04/5.02	compare2 x y False = compare1 x y (x <= y);
12.04/5.02	"
12.04/5.02	"compare0 x y True = GT;
12.04/5.02	"
12.04/5.02	"compare3 x y = compare2 x y (x == y);
12.04/5.02	"
12.04/5.02	The following Function with conditions
12.04/5.02	"undefined |Falseundefined;
12.04/5.02	"
12.04/5.02	is transformed to
12.04/5.02	"undefined  = undefined1;
12.04/5.02	"
12.04/5.02	"undefined0 True = undefined;
12.04/5.02	"
12.04/5.02	"undefined1  = undefined0 False;
12.04/5.02	"
12.04/5.02	The following Function with conditions
12.04/5.02	"foldFM_GE k z fr EmptyFM = z;
12.04/5.02	foldFM_GE k z fr (Branch key elt vy fm_l fm_r)|key >= frfoldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l|otherwisefoldFM_GE k z fr fm_r;
12.04/5.02	"
12.04/5.02	is transformed to
12.04/5.02	"foldFM_GE k z fr EmptyFM = foldFM_GE3 k z fr EmptyFM;
12.04/5.02	foldFM_GE k z fr (Branch key elt vy fm_l fm_r) = foldFM_GE2 k z fr (Branch key elt vy fm_l fm_r);
12.04/5.02	"
12.04/5.02	"foldFM_GE1 k z fr key elt vy fm_l fm_r True = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l;
12.04/5.02	foldFM_GE1 k z fr key elt vy fm_l fm_r False = foldFM_GE0 k z fr key elt vy fm_l fm_r otherwise;
12.04/5.02	"
12.04/5.02	"foldFM_GE0 k z fr key elt vy fm_l fm_r True = foldFM_GE k z fr fm_r;
12.04/5.02	"
12.04/5.02	"foldFM_GE2 k z fr (Branch key elt vy fm_l fm_r) = foldFM_GE1 k z fr key elt vy fm_l fm_r (key >= fr);
12.04/5.02	"
12.04/5.02	"foldFM_GE3 k z fr EmptyFM = z;
12.04/5.02	foldFM_GE3 wv ww wx wy = foldFM_GE2 wv ww wx wy;
12.04/5.02	"
12.04/5.02	
12.04/5.02	----------------------------------------
12.04/5.02	
12.04/5.02	(4)
12.04/5.02	Obligation:
12.04/5.02	mainModule Main 
12.04/5.02	module FiniteMap where {
12.04/5.02	import qualified Main;
12.04/5.02	import qualified Maybe;
12.04/5.02	import qualified Prelude;
12.04/5.02	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.04/5.02	
12.04/5.02	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.04/5.03	}
12.04/5.03	foldFM_GE :: Ord a => (a  ->  c  ->  b  ->  b)  ->  b  ->  a  ->  FiniteMap a c  ->  b;
12.04/5.03	foldFM_GE k z fr EmptyFM = foldFM_GE3 k z fr EmptyFM;
12.04/5.03	foldFM_GE k z fr (Branch key elt vy fm_l fm_r) = foldFM_GE2 k z fr (Branch key elt vy fm_l fm_r);
12.04/5.03	
12.04/5.03	foldFM_GE0 k z fr key elt vy fm_l fm_r True = foldFM_GE k z fr fm_r;
12.04/5.03	
12.04/5.03	foldFM_GE1 k z fr key elt vy fm_l fm_r True = foldFM_GE k (k key elt (foldFM_GE k z fr fm_r)) fr fm_l;
12.04/5.03	foldFM_GE1 k z fr key elt vy fm_l fm_r False = foldFM_GE0 k z fr key elt vy fm_l fm_r otherwise;
12.04/5.03	
12.04/5.03	foldFM_GE2 k z fr (Branch key elt vy fm_l fm_r) = foldFM_GE1 k z fr key elt vy fm_l fm_r (key >= fr);
12.04/5.03	
12.04/5.03	foldFM_GE3 k z fr EmptyFM = z;
12.04/5.03	foldFM_GE3 wv ww wx wy = foldFM_GE2 wv ww wx wy;
12.04/5.03	
12.04/5.03	}
12.04/5.03	module Maybe where {
12.04/5.03	import qualified FiniteMap;
12.04/5.03	import qualified Main;
12.04/5.03	import qualified Prelude;
12.04/5.03	}
12.04/5.03	module Main where {
12.04/5.03	import qualified FiniteMap;
12.04/5.03	import qualified Maybe;
12.04/5.03	import qualified Prelude;
12.04/5.03	}
12.04/5.03	
12.04/5.03	----------------------------------------
12.04/5.03	
12.04/5.03	(5) Narrow (SOUND)
12.04/5.03	Haskell To QDPs
12.04/5.03	
12.04/5.03	digraph dp_graph {
12.04/5.03	node [outthreshold=100, inthreshold=100];1[label="FiniteMap.foldFM_GE",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
12.04/5.03	3[label="FiniteMap.foldFM_GE wz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
12.04/5.03	4[label="FiniteMap.foldFM_GE wz3 wz4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3];
12.04/5.03	5[label="FiniteMap.foldFM_GE wz3 wz4 wz5",fontsize=16,color="grey",shape="box"];5 -> 6[label="",style="dashed", color="grey", weight=3];
12.04/5.03	6[label="FiniteMap.foldFM_GE wz3 wz4 wz5 wz6",fontsize=16,color="burlywood",shape="triangle"];152[label="wz6/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];6 -> 152[label="",style="solid", color="burlywood", weight=9];
12.04/5.03	152 -> 7[label="",style="solid", color="burlywood", weight=3];
12.04/5.03	153[label="wz6/FiniteMap.Branch wz60 wz61 wz62 wz63 wz64",fontsize=10,color="white",style="solid",shape="box"];6 -> 153[label="",style="solid", color="burlywood", weight=9];
12.04/5.03	153 -> 8[label="",style="solid", color="burlywood", weight=3];
12.04/5.03	7[label="FiniteMap.foldFM_GE wz3 wz4 wz5 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
12.04/5.03	8[label="FiniteMap.foldFM_GE wz3 wz4 wz5 (FiniteMap.Branch wz60 wz61 wz62 wz63 wz64)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
12.04/5.03	9[label="FiniteMap.foldFM_GE3 wz3 wz4 wz5 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
12.04/5.03	10[label="FiniteMap.foldFM_GE2 wz3 wz4 wz5 (FiniteMap.Branch wz60 wz61 wz62 wz63 wz64)",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
12.04/5.03	11[label="wz4",fontsize=16,color="green",shape="box"];12[label="FiniteMap.foldFM_GE1 wz3 wz4 wz5 wz60 wz61 wz62 wz63 wz64 (wz60 >= wz5)",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
12.04/5.03	13[label="FiniteMap.foldFM_GE1 wz3 wz4 wz5 wz60 wz61 wz62 wz63 wz64 (compare wz60 wz5 /= LT)",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
12.04/5.03	14[label="FiniteMap.foldFM_GE1 wz3 wz4 wz5 wz60 wz61 wz62 wz63 wz64 (not (compare wz60 wz5 == LT))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
12.04/5.03	15[label="FiniteMap.foldFM_GE1 wz3 wz4 wz5 wz60 wz61 wz62 wz63 wz64 (not (compare3 wz60 wz5 == LT))",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3];
12.04/5.03	16[label="FiniteMap.foldFM_GE1 wz3 wz4 wz5 wz60 wz61 wz62 wz63 wz64 (not (compare2 wz60 wz5 (wz60 == wz5) == LT))",fontsize=16,color="burlywood",shape="box"];154[label="wz60/LT",fontsize=10,color="white",style="solid",shape="box"];16 -> 154[label="",style="solid", color="burlywood", weight=9];
12.04/5.03	154 -> 17[label="",style="solid", color="burlywood", weight=3];
12.04/5.03	155[label="wz60/EQ",fontsize=10,color="white",style="solid",shape="box"];16 -> 155[label="",style="solid", color="burlywood", weight=9];
12.04/5.03	155 -> 18[label="",style="solid", color="burlywood", weight=3];
12.04/5.03	156[label="wz60/GT",fontsize=10,color="white",style="solid",shape="box"];16 -> 156[label="",style="solid", color="burlywood", weight=9];
12.04/5.03	156 -> 19[label="",style="solid", color="burlywood", weight=3];
12.04/5.03	17[label="FiniteMap.foldFM_GE1 wz3 wz4 wz5 LT wz61 wz62 wz63 wz64 (not (compare2 LT wz5 (LT == wz5) == LT))",fontsize=16,color="burlywood",shape="box"];157[label="wz5/LT",fontsize=10,color="white",style="solid",shape="box"];17 -> 157[label="",style="solid", color="burlywood", weight=9];
12.04/5.03	157 -> 20[label="",style="solid", color="burlywood", weight=3];
12.04/5.03	158[label="wz5/EQ",fontsize=10,color="white",style="solid",shape="box"];17 -> 158[label="",style="solid", color="burlywood", weight=9];
12.04/5.03	158 -> 21[label="",style="solid", color="burlywood", weight=3];
12.04/5.03	159[label="wz5/GT",fontsize=10,color="white",style="solid",shape="box"];17 -> 159[label="",style="solid", color="burlywood", weight=9];
12.04/5.03	159 -> 22[label="",style="solid", color="burlywood", weight=3];
12.04/5.03	18[label="FiniteMap.foldFM_GE1 wz3 wz4 wz5 EQ wz61 wz62 wz63 wz64 (not (compare2 EQ wz5 (EQ == wz5) == LT))",fontsize=16,color="burlywood",shape="box"];160[label="wz5/LT",fontsize=10,color="white",style="solid",shape="box"];18 -> 160[label="",style="solid", color="burlywood", weight=9];
12.04/5.03	160 -> 23[label="",style="solid", color="burlywood", weight=3];
12.04/5.03	161[label="wz5/EQ",fontsize=10,color="white",style="solid",shape="box"];18 -> 161[label="",style="solid", color="burlywood", weight=9];
12.04/5.03	161 -> 24[label="",style="solid", color="burlywood", weight=3];
12.04/5.03	162[label="wz5/GT",fontsize=10,color="white",style="solid",shape="box"];18 -> 162[label="",style="solid", color="burlywood", weight=9];
12.04/5.03	162 -> 25[label="",style="solid", color="burlywood", weight=3];
12.04/5.03	19[label="FiniteMap.foldFM_GE1 wz3 wz4 wz5 GT wz61 wz62 wz63 wz64 (not (compare2 GT wz5 (GT == wz5) == LT))",fontsize=16,color="burlywood",shape="box"];163[label="wz5/LT",fontsize=10,color="white",style="solid",shape="box"];19 -> 163[label="",style="solid", color="burlywood", weight=9];
12.04/5.03	163 -> 26[label="",style="solid", color="burlywood", weight=3];
12.04/5.03	164[label="wz5/EQ",fontsize=10,color="white",style="solid",shape="box"];19 -> 164[label="",style="solid", color="burlywood", weight=9];
12.04/5.03	164 -> 27[label="",style="solid", color="burlywood", weight=3];
12.04/5.03	165[label="wz5/GT",fontsize=10,color="white",style="solid",shape="box"];19 -> 165[label="",style="solid", color="burlywood", weight=9];
12.04/5.03	165 -> 28[label="",style="solid", color="burlywood", weight=3];
12.04/5.03	20[label="FiniteMap.foldFM_GE1 wz3 wz4 LT LT wz61 wz62 wz63 wz64 (not (compare2 LT LT (LT == LT) == LT))",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
12.04/5.03	21[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 (not (compare2 LT EQ (LT == EQ) == LT))",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
12.04/5.03	22[label="FiniteMap.foldFM_GE1 wz3 wz4 GT LT wz61 wz62 wz63 wz64 (not (compare2 LT GT (LT == GT) == LT))",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
12.04/5.03	23[label="FiniteMap.foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not (compare2 EQ LT (EQ == LT) == LT))",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
12.04/5.03	24[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ EQ wz61 wz62 wz63 wz64 (not (compare2 EQ EQ (EQ == EQ) == LT))",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
12.04/5.03	25[label="FiniteMap.foldFM_GE1 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 (not (compare2 EQ GT (EQ == GT) == LT))",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
12.04/5.03	26[label="FiniteMap.foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not (compare2 GT LT (GT == LT) == LT))",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
12.04/5.03	27[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not (compare2 GT EQ (GT == EQ) == LT))",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
12.04/5.03	28[label="FiniteMap.foldFM_GE1 wz3 wz4 GT GT wz61 wz62 wz63 wz64 (not (compare2 GT GT (GT == GT) == LT))",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3];
12.04/5.03	29[label="FiniteMap.foldFM_GE1 wz3 wz4 LT LT wz61 wz62 wz63 wz64 (not (compare2 LT LT True == LT))",fontsize=16,color="black",shape="box"];29 -> 38[label="",style="solid", color="black", weight=3];
12.04/5.03	30[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 (not (compare2 LT EQ False == LT))",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3];
12.04/5.03	31[label="FiniteMap.foldFM_GE1 wz3 wz4 GT LT wz61 wz62 wz63 wz64 (not (compare2 LT GT False == LT))",fontsize=16,color="black",shape="box"];31 -> 40[label="",style="solid", color="black", weight=3];
12.04/5.03	32[label="FiniteMap.foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not (compare2 EQ LT False == LT))",fontsize=16,color="black",shape="box"];32 -> 41[label="",style="solid", color="black", weight=3];
12.04/5.03	33[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ EQ wz61 wz62 wz63 wz64 (not (compare2 EQ EQ True == LT))",fontsize=16,color="black",shape="box"];33 -> 42[label="",style="solid", color="black", weight=3];
12.04/5.03	34[label="FiniteMap.foldFM_GE1 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 (not (compare2 EQ GT False == LT))",fontsize=16,color="black",shape="box"];34 -> 43[label="",style="solid", color="black", weight=3];
12.04/5.03	35[label="FiniteMap.foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not (compare2 GT LT False == LT))",fontsize=16,color="black",shape="box"];35 -> 44[label="",style="solid", color="black", weight=3];
12.04/5.03	36[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not (compare2 GT EQ False == LT))",fontsize=16,color="black",shape="box"];36 -> 45[label="",style="solid", color="black", weight=3];
12.04/5.03	37[label="FiniteMap.foldFM_GE1 wz3 wz4 GT GT wz61 wz62 wz63 wz64 (not (compare2 GT GT True == LT))",fontsize=16,color="black",shape="box"];37 -> 46[label="",style="solid", color="black", weight=3];
12.04/5.03	38[label="FiniteMap.foldFM_GE1 wz3 wz4 LT LT wz61 wz62 wz63 wz64 (not (EQ == LT))",fontsize=16,color="black",shape="box"];38 -> 47[label="",style="solid", color="black", weight=3];
12.04/5.03	39[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 (not (compare1 LT EQ (LT <= EQ) == LT))",fontsize=16,color="black",shape="box"];39 -> 48[label="",style="solid", color="black", weight=3];
12.04/5.03	40[label="FiniteMap.foldFM_GE1 wz3 wz4 GT LT wz61 wz62 wz63 wz64 (not (compare1 LT GT (LT <= GT) == LT))",fontsize=16,color="black",shape="box"];40 -> 49[label="",style="solid", color="black", weight=3];
12.04/5.03	41[label="FiniteMap.foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not (compare1 EQ LT (EQ <= LT) == LT))",fontsize=16,color="black",shape="box"];41 -> 50[label="",style="solid", color="black", weight=3];
12.04/5.03	42[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ EQ wz61 wz62 wz63 wz64 (not (EQ == LT))",fontsize=16,color="black",shape="box"];42 -> 51[label="",style="solid", color="black", weight=3];
12.04/5.03	43[label="FiniteMap.foldFM_GE1 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 (not (compare1 EQ GT (EQ <= GT) == LT))",fontsize=16,color="black",shape="box"];43 -> 52[label="",style="solid", color="black", weight=3];
12.04/5.03	44[label="FiniteMap.foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not (compare1 GT LT (GT <= LT) == LT))",fontsize=16,color="black",shape="box"];44 -> 53[label="",style="solid", color="black", weight=3];
12.04/5.03	45[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not (compare1 GT EQ (GT <= EQ) == LT))",fontsize=16,color="black",shape="box"];45 -> 54[label="",style="solid", color="black", weight=3];
12.04/5.03	46[label="FiniteMap.foldFM_GE1 wz3 wz4 GT GT wz61 wz62 wz63 wz64 (not (EQ == LT))",fontsize=16,color="black",shape="box"];46 -> 55[label="",style="solid", color="black", weight=3];
12.04/5.03	47[label="FiniteMap.foldFM_GE1 wz3 wz4 LT LT wz61 wz62 wz63 wz64 (not False)",fontsize=16,color="black",shape="box"];47 -> 56[label="",style="solid", color="black", weight=3];
12.04/5.03	48[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 (not (compare1 LT EQ True == LT))",fontsize=16,color="black",shape="box"];48 -> 57[label="",style="solid", color="black", weight=3];
12.04/5.03	49[label="FiniteMap.foldFM_GE1 wz3 wz4 GT LT wz61 wz62 wz63 wz64 (not (compare1 LT GT True == LT))",fontsize=16,color="black",shape="box"];49 -> 58[label="",style="solid", color="black", weight=3];
12.04/5.03	50[label="FiniteMap.foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not (compare1 EQ LT False == LT))",fontsize=16,color="black",shape="box"];50 -> 59[label="",style="solid", color="black", weight=3];
12.04/5.03	51[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ EQ wz61 wz62 wz63 wz64 (not False)",fontsize=16,color="black",shape="box"];51 -> 60[label="",style="solid", color="black", weight=3];
12.04/5.03	52[label="FiniteMap.foldFM_GE1 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 (not (compare1 EQ GT True == LT))",fontsize=16,color="black",shape="box"];52 -> 61[label="",style="solid", color="black", weight=3];
12.04/5.03	53[label="FiniteMap.foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not (compare1 GT LT False == LT))",fontsize=16,color="black",shape="box"];53 -> 62[label="",style="solid", color="black", weight=3];
12.04/5.03	54[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not (compare1 GT EQ False == LT))",fontsize=16,color="black",shape="box"];54 -> 63[label="",style="solid", color="black", weight=3];
12.04/5.03	55[label="FiniteMap.foldFM_GE1 wz3 wz4 GT GT wz61 wz62 wz63 wz64 (not False)",fontsize=16,color="black",shape="box"];55 -> 64[label="",style="solid", color="black", weight=3];
12.04/5.03	56[label="FiniteMap.foldFM_GE1 wz3 wz4 LT LT wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];56 -> 65[label="",style="solid", color="black", weight=3];
12.04/5.03	57[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 (not (LT == LT))",fontsize=16,color="black",shape="box"];57 -> 66[label="",style="solid", color="black", weight=3];
12.04/5.03	58[label="FiniteMap.foldFM_GE1 wz3 wz4 GT LT wz61 wz62 wz63 wz64 (not (LT == LT))",fontsize=16,color="black",shape="box"];58 -> 67[label="",style="solid", color="black", weight=3];
12.04/5.03	59[label="FiniteMap.foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not (compare0 EQ LT otherwise == LT))",fontsize=16,color="black",shape="box"];59 -> 68[label="",style="solid", color="black", weight=3];
12.04/5.03	60[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ EQ wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];60 -> 69[label="",style="solid", color="black", weight=3];
12.04/5.03	61[label="FiniteMap.foldFM_GE1 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 (not (LT == LT))",fontsize=16,color="black",shape="box"];61 -> 70[label="",style="solid", color="black", weight=3];
12.04/5.03	62[label="FiniteMap.foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not (compare0 GT LT otherwise == LT))",fontsize=16,color="black",shape="box"];62 -> 71[label="",style="solid", color="black", weight=3];
12.04/5.03	63[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not (compare0 GT EQ otherwise == LT))",fontsize=16,color="black",shape="box"];63 -> 72[label="",style="solid", color="black", weight=3];
12.04/5.03	64[label="FiniteMap.foldFM_GE1 wz3 wz4 GT GT wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];64 -> 73[label="",style="solid", color="black", weight=3];
12.04/5.03	65 -> 6[label="",style="dashed", color="red", weight=0];
12.04/5.03	65[label="FiniteMap.foldFM_GE wz3 (wz3 LT wz61 (FiniteMap.foldFM_GE wz3 wz4 LT wz64)) LT wz63",fontsize=16,color="magenta"];65 -> 74[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	65 -> 75[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	65 -> 76[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	66[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 (not True)",fontsize=16,color="black",shape="box"];66 -> 77[label="",style="solid", color="black", weight=3];
12.04/5.03	67[label="FiniteMap.foldFM_GE1 wz3 wz4 GT LT wz61 wz62 wz63 wz64 (not True)",fontsize=16,color="black",shape="box"];67 -> 78[label="",style="solid", color="black", weight=3];
12.04/5.03	68[label="FiniteMap.foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not (compare0 EQ LT True == LT))",fontsize=16,color="black",shape="box"];68 -> 79[label="",style="solid", color="black", weight=3];
12.04/5.03	69 -> 6[label="",style="dashed", color="red", weight=0];
12.04/5.03	69[label="FiniteMap.foldFM_GE wz3 (wz3 EQ wz61 (FiniteMap.foldFM_GE wz3 wz4 EQ wz64)) EQ wz63",fontsize=16,color="magenta"];69 -> 80[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	69 -> 81[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	69 -> 82[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	70[label="FiniteMap.foldFM_GE1 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 (not True)",fontsize=16,color="black",shape="box"];70 -> 83[label="",style="solid", color="black", weight=3];
12.04/5.03	71[label="FiniteMap.foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not (compare0 GT LT True == LT))",fontsize=16,color="black",shape="box"];71 -> 84[label="",style="solid", color="black", weight=3];
12.04/5.03	72[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not (compare0 GT EQ True == LT))",fontsize=16,color="black",shape="box"];72 -> 85[label="",style="solid", color="black", weight=3];
12.04/5.03	73 -> 6[label="",style="dashed", color="red", weight=0];
12.04/5.03	73[label="FiniteMap.foldFM_GE wz3 (wz3 GT wz61 (FiniteMap.foldFM_GE wz3 wz4 GT wz64)) GT wz63",fontsize=16,color="magenta"];73 -> 86[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	73 -> 87[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	73 -> 88[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	74[label="LT",fontsize=16,color="green",shape="box"];75[label="wz3 LT wz61 (FiniteMap.foldFM_GE wz3 wz4 LT wz64)",fontsize=16,color="green",shape="box"];75 -> 89[label="",style="dashed", color="green", weight=3];
12.04/5.03	75 -> 90[label="",style="dashed", color="green", weight=3];
12.04/5.03	75 -> 91[label="",style="dashed", color="green", weight=3];
12.04/5.03	76[label="wz63",fontsize=16,color="green",shape="box"];77[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 False",fontsize=16,color="black",shape="box"];77 -> 92[label="",style="solid", color="black", weight=3];
12.04/5.03	78[label="FiniteMap.foldFM_GE1 wz3 wz4 GT LT wz61 wz62 wz63 wz64 False",fontsize=16,color="black",shape="box"];78 -> 93[label="",style="solid", color="black", weight=3];
12.04/5.03	79[label="FiniteMap.foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not (GT == LT))",fontsize=16,color="black",shape="box"];79 -> 94[label="",style="solid", color="black", weight=3];
12.04/5.03	80[label="EQ",fontsize=16,color="green",shape="box"];81[label="wz3 EQ wz61 (FiniteMap.foldFM_GE wz3 wz4 EQ wz64)",fontsize=16,color="green",shape="box"];81 -> 95[label="",style="dashed", color="green", weight=3];
12.04/5.03	81 -> 96[label="",style="dashed", color="green", weight=3];
12.04/5.03	81 -> 97[label="",style="dashed", color="green", weight=3];
12.04/5.03	82[label="wz63",fontsize=16,color="green",shape="box"];83[label="FiniteMap.foldFM_GE1 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 False",fontsize=16,color="black",shape="box"];83 -> 98[label="",style="solid", color="black", weight=3];
12.04/5.03	84[label="FiniteMap.foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not (GT == LT))",fontsize=16,color="black",shape="box"];84 -> 99[label="",style="solid", color="black", weight=3];
12.04/5.03	85[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not (GT == LT))",fontsize=16,color="black",shape="box"];85 -> 100[label="",style="solid", color="black", weight=3];
12.04/5.03	86[label="GT",fontsize=16,color="green",shape="box"];87[label="wz3 GT wz61 (FiniteMap.foldFM_GE wz3 wz4 GT wz64)",fontsize=16,color="green",shape="box"];87 -> 101[label="",style="dashed", color="green", weight=3];
12.04/5.03	87 -> 102[label="",style="dashed", color="green", weight=3];
12.04/5.03	87 -> 103[label="",style="dashed", color="green", weight=3];
12.04/5.03	88[label="wz63",fontsize=16,color="green",shape="box"];89[label="LT",fontsize=16,color="green",shape="box"];90[label="wz61",fontsize=16,color="green",shape="box"];91 -> 6[label="",style="dashed", color="red", weight=0];
12.04/5.03	91[label="FiniteMap.foldFM_GE wz3 wz4 LT wz64",fontsize=16,color="magenta"];91 -> 104[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	91 -> 105[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	92[label="FiniteMap.foldFM_GE0 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 otherwise",fontsize=16,color="black",shape="box"];92 -> 106[label="",style="solid", color="black", weight=3];
12.04/5.03	93[label="FiniteMap.foldFM_GE0 wz3 wz4 GT LT wz61 wz62 wz63 wz64 otherwise",fontsize=16,color="black",shape="box"];93 -> 107[label="",style="solid", color="black", weight=3];
12.04/5.03	94[label="FiniteMap.foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 (not False)",fontsize=16,color="black",shape="box"];94 -> 108[label="",style="solid", color="black", weight=3];
12.04/5.03	95[label="EQ",fontsize=16,color="green",shape="box"];96[label="wz61",fontsize=16,color="green",shape="box"];97 -> 6[label="",style="dashed", color="red", weight=0];
12.04/5.03	97[label="FiniteMap.foldFM_GE wz3 wz4 EQ wz64",fontsize=16,color="magenta"];97 -> 109[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	97 -> 110[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	98[label="FiniteMap.foldFM_GE0 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 otherwise",fontsize=16,color="black",shape="box"];98 -> 111[label="",style="solid", color="black", weight=3];
12.04/5.03	99[label="FiniteMap.foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 (not False)",fontsize=16,color="black",shape="box"];99 -> 112[label="",style="solid", color="black", weight=3];
12.04/5.03	100[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 (not False)",fontsize=16,color="black",shape="box"];100 -> 113[label="",style="solid", color="black", weight=3];
12.04/5.03	101[label="GT",fontsize=16,color="green",shape="box"];102[label="wz61",fontsize=16,color="green",shape="box"];103 -> 6[label="",style="dashed", color="red", weight=0];
12.04/5.03	103[label="FiniteMap.foldFM_GE wz3 wz4 GT wz64",fontsize=16,color="magenta"];103 -> 114[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	103 -> 115[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	104[label="LT",fontsize=16,color="green",shape="box"];105[label="wz64",fontsize=16,color="green",shape="box"];106[label="FiniteMap.foldFM_GE0 wz3 wz4 EQ LT wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];106 -> 116[label="",style="solid", color="black", weight=3];
12.04/5.03	107[label="FiniteMap.foldFM_GE0 wz3 wz4 GT LT wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];107 -> 117[label="",style="solid", color="black", weight=3];
12.04/5.03	108[label="FiniteMap.foldFM_GE1 wz3 wz4 LT EQ wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];108 -> 118[label="",style="solid", color="black", weight=3];
12.04/5.03	109[label="EQ",fontsize=16,color="green",shape="box"];110[label="wz64",fontsize=16,color="green",shape="box"];111[label="FiniteMap.foldFM_GE0 wz3 wz4 GT EQ wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];111 -> 119[label="",style="solid", color="black", weight=3];
12.04/5.03	112[label="FiniteMap.foldFM_GE1 wz3 wz4 LT GT wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];112 -> 120[label="",style="solid", color="black", weight=3];
12.04/5.03	113[label="FiniteMap.foldFM_GE1 wz3 wz4 EQ GT wz61 wz62 wz63 wz64 True",fontsize=16,color="black",shape="box"];113 -> 121[label="",style="solid", color="black", weight=3];
12.04/5.03	114[label="GT",fontsize=16,color="green",shape="box"];115[label="wz64",fontsize=16,color="green",shape="box"];116 -> 6[label="",style="dashed", color="red", weight=0];
12.04/5.03	116[label="FiniteMap.foldFM_GE wz3 wz4 EQ wz64",fontsize=16,color="magenta"];116 -> 122[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	116 -> 123[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	117 -> 6[label="",style="dashed", color="red", weight=0];
12.04/5.03	117[label="FiniteMap.foldFM_GE wz3 wz4 GT wz64",fontsize=16,color="magenta"];117 -> 124[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	117 -> 125[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	118 -> 6[label="",style="dashed", color="red", weight=0];
12.04/5.03	118[label="FiniteMap.foldFM_GE wz3 (wz3 EQ wz61 (FiniteMap.foldFM_GE wz3 wz4 LT wz64)) LT wz63",fontsize=16,color="magenta"];118 -> 126[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	118 -> 127[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	118 -> 128[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	119 -> 6[label="",style="dashed", color="red", weight=0];
12.04/5.03	119[label="FiniteMap.foldFM_GE wz3 wz4 GT wz64",fontsize=16,color="magenta"];119 -> 129[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	119 -> 130[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	120 -> 6[label="",style="dashed", color="red", weight=0];
12.04/5.03	120[label="FiniteMap.foldFM_GE wz3 (wz3 GT wz61 (FiniteMap.foldFM_GE wz3 wz4 LT wz64)) LT wz63",fontsize=16,color="magenta"];120 -> 131[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	120 -> 132[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	120 -> 133[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	121 -> 6[label="",style="dashed", color="red", weight=0];
12.04/5.03	121[label="FiniteMap.foldFM_GE wz3 (wz3 GT wz61 (FiniteMap.foldFM_GE wz3 wz4 EQ wz64)) EQ wz63",fontsize=16,color="magenta"];121 -> 134[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	121 -> 135[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	121 -> 136[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	122[label="EQ",fontsize=16,color="green",shape="box"];123[label="wz64",fontsize=16,color="green",shape="box"];124[label="GT",fontsize=16,color="green",shape="box"];125[label="wz64",fontsize=16,color="green",shape="box"];126[label="LT",fontsize=16,color="green",shape="box"];127[label="wz3 EQ wz61 (FiniteMap.foldFM_GE wz3 wz4 LT wz64)",fontsize=16,color="green",shape="box"];127 -> 137[label="",style="dashed", color="green", weight=3];
12.04/5.03	127 -> 138[label="",style="dashed", color="green", weight=3];
12.04/5.03	127 -> 139[label="",style="dashed", color="green", weight=3];
12.04/5.03	128[label="wz63",fontsize=16,color="green",shape="box"];129[label="GT",fontsize=16,color="green",shape="box"];130[label="wz64",fontsize=16,color="green",shape="box"];131[label="LT",fontsize=16,color="green",shape="box"];132[label="wz3 GT wz61 (FiniteMap.foldFM_GE wz3 wz4 LT wz64)",fontsize=16,color="green",shape="box"];132 -> 140[label="",style="dashed", color="green", weight=3];
12.04/5.03	132 -> 141[label="",style="dashed", color="green", weight=3];
12.04/5.03	132 -> 142[label="",style="dashed", color="green", weight=3];
12.04/5.03	133[label="wz63",fontsize=16,color="green",shape="box"];134[label="EQ",fontsize=16,color="green",shape="box"];135[label="wz3 GT wz61 (FiniteMap.foldFM_GE wz3 wz4 EQ wz64)",fontsize=16,color="green",shape="box"];135 -> 143[label="",style="dashed", color="green", weight=3];
12.04/5.03	135 -> 144[label="",style="dashed", color="green", weight=3];
12.04/5.03	135 -> 145[label="",style="dashed", color="green", weight=3];
12.04/5.03	136[label="wz63",fontsize=16,color="green",shape="box"];137[label="EQ",fontsize=16,color="green",shape="box"];138[label="wz61",fontsize=16,color="green",shape="box"];139 -> 6[label="",style="dashed", color="red", weight=0];
12.04/5.03	139[label="FiniteMap.foldFM_GE wz3 wz4 LT wz64",fontsize=16,color="magenta"];139 -> 146[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	139 -> 147[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	140[label="GT",fontsize=16,color="green",shape="box"];141[label="wz61",fontsize=16,color="green",shape="box"];142 -> 6[label="",style="dashed", color="red", weight=0];
12.04/5.03	142[label="FiniteMap.foldFM_GE wz3 wz4 LT wz64",fontsize=16,color="magenta"];142 -> 148[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	142 -> 149[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	143[label="GT",fontsize=16,color="green",shape="box"];144[label="wz61",fontsize=16,color="green",shape="box"];145 -> 6[label="",style="dashed", color="red", weight=0];
12.04/5.03	145[label="FiniteMap.foldFM_GE wz3 wz4 EQ wz64",fontsize=16,color="magenta"];145 -> 150[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	145 -> 151[label="",style="dashed", color="magenta", weight=3];
12.04/5.03	146[label="LT",fontsize=16,color="green",shape="box"];147[label="wz64",fontsize=16,color="green",shape="box"];148[label="LT",fontsize=16,color="green",shape="box"];149[label="wz64",fontsize=16,color="green",shape="box"];150[label="EQ",fontsize=16,color="green",shape="box"];151[label="wz64",fontsize=16,color="green",shape="box"];}
12.04/5.03	
12.04/5.03	----------------------------------------
12.04/5.03	
12.04/5.03	(6)
12.04/5.03	Obligation:
12.04/5.03	Q DP problem:
12.04/5.03	The TRS P consists of the following rules:
12.04/5.03	
12.04/5.03	   new_foldFM_GE(wz3, EQ, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, EQ, wz63, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, LT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz63, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, EQ, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, EQ, wz64, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, EQ, Branch(LT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, EQ, wz64, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, GT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, GT, wz63, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, LT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz63, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, LT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz63, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, LT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz64, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, EQ, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, EQ, wz63, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, GT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, GT, wz64, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, LT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz64, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, GT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, GT, wz64, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, LT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz64, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, GT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, GT, wz64, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, EQ, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, EQ, wz64, h, ba)
12.04/5.03	
12.04/5.03	R is empty.
12.04/5.03	Q is empty.
12.04/5.03	We have to consider all minimal (P,Q,R)-chains.
12.04/5.03	----------------------------------------
12.04/5.03	
12.04/5.03	(7) DependencyGraphProof (EQUIVALENT)
12.04/5.03	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs.
12.04/5.03	----------------------------------------
12.04/5.03	
12.04/5.03	(8)
12.04/5.03	Complex Obligation (AND)
12.04/5.03	
12.04/5.03	----------------------------------------
12.04/5.03	
12.04/5.03	(9)
12.04/5.03	Obligation:
12.04/5.03	Q DP problem:
12.04/5.03	The TRS P consists of the following rules:
12.04/5.03	
12.04/5.03	   new_foldFM_GE(wz3, GT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, GT, wz64, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, GT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, GT, wz63, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, GT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, GT, wz64, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, GT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, GT, wz64, h, ba)
12.04/5.03	
12.04/5.03	R is empty.
12.04/5.03	Q is empty.
12.04/5.03	We have to consider all minimal (P,Q,R)-chains.
12.04/5.03	----------------------------------------
12.04/5.03	
12.04/5.03	(10) QDPSizeChangeProof (EQUIVALENT)
12.04/5.03	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. 
12.04/5.03	
12.04/5.03	From the DPs we obtained the following set of size-change graphs:
12.04/5.03	*new_foldFM_GE(wz3, GT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, GT, wz64, h, ba)
12.04/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
12.04/5.03	
12.04/5.03	
12.04/5.03	*new_foldFM_GE(wz3, GT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, GT, wz63, h, ba)
12.04/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5
12.04/5.03	
12.04/5.03	
12.04/5.03	*new_foldFM_GE(wz3, GT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, GT, wz64, h, ba)
12.04/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5
12.04/5.03	
12.04/5.03	
12.04/5.03	*new_foldFM_GE(wz3, GT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, GT, wz64, h, ba)
12.04/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
12.04/5.03	
12.04/5.03	
12.04/5.03	----------------------------------------
12.04/5.03	
12.04/5.03	(11)
12.04/5.03	YES
12.04/5.03	
12.04/5.03	----------------------------------------
12.04/5.03	
12.04/5.03	(12)
12.04/5.03	Obligation:
12.04/5.03	Q DP problem:
12.04/5.03	The TRS P consists of the following rules:
12.04/5.03	
12.04/5.03	   new_foldFM_GE(wz3, LT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz63, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, LT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz63, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, LT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz63, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, LT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz64, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, LT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz64, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, LT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz64, h, ba)
12.04/5.03	
12.04/5.03	R is empty.
12.04/5.03	Q is empty.
12.04/5.03	We have to consider all minimal (P,Q,R)-chains.
12.04/5.03	----------------------------------------
12.04/5.03	
12.04/5.03	(13) QDPSizeChangeProof (EQUIVALENT)
12.04/5.03	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. 
12.04/5.03	
12.04/5.03	From the DPs we obtained the following set of size-change graphs:
12.04/5.03	*new_foldFM_GE(wz3, LT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz63, h, ba)
12.04/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5
12.04/5.03	
12.04/5.03	
12.04/5.03	*new_foldFM_GE(wz3, LT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz63, h, ba)
12.04/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
12.04/5.03	
12.04/5.03	
12.04/5.03	*new_foldFM_GE(wz3, LT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz63, h, ba)
12.04/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
12.04/5.03	
12.04/5.03	
12.04/5.03	*new_foldFM_GE(wz3, LT, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz64, h, ba)
12.04/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
12.04/5.03	
12.04/5.03	
12.04/5.03	*new_foldFM_GE(wz3, LT, Branch(LT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz64, h, ba)
12.04/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5
12.04/5.03	
12.04/5.03	
12.04/5.03	*new_foldFM_GE(wz3, LT, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, LT, wz64, h, ba)
12.04/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
12.04/5.03	
12.04/5.03	
12.04/5.03	----------------------------------------
12.04/5.03	
12.04/5.03	(14)
12.04/5.03	YES
12.04/5.03	
12.04/5.03	----------------------------------------
12.04/5.03	
12.04/5.03	(15)
12.04/5.03	Obligation:
12.04/5.03	Q DP problem:
12.04/5.03	The TRS P consists of the following rules:
12.04/5.03	
12.04/5.03	   new_foldFM_GE(wz3, EQ, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, EQ, wz64, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, EQ, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, EQ, wz63, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, EQ, Branch(LT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, EQ, wz64, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, EQ, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, EQ, wz63, h, ba)
12.04/5.03	   new_foldFM_GE(wz3, EQ, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, EQ, wz64, h, ba)
12.04/5.03	
12.04/5.03	R is empty.
12.04/5.03	Q is empty.
12.04/5.03	We have to consider all minimal (P,Q,R)-chains.
12.04/5.03	----------------------------------------
12.04/5.03	
12.04/5.03	(16) QDPSizeChangeProof (EQUIVALENT)
12.04/5.03	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. 
12.04/5.03	
12.04/5.03	From the DPs we obtained the following set of size-change graphs:
12.04/5.03	*new_foldFM_GE(wz3, EQ, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, EQ, wz64, h, ba)
12.04/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
12.04/5.03	
12.04/5.03	
12.04/5.03	*new_foldFM_GE(wz3, EQ, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, EQ, wz63, h, ba)
12.04/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5
12.04/5.03	
12.04/5.03	
12.04/5.03	*new_foldFM_GE(wz3, EQ, Branch(LT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, EQ, wz64, h, ba)
12.04/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
12.04/5.03	
12.04/5.03	
12.04/5.03	*new_foldFM_GE(wz3, EQ, Branch(GT, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, EQ, wz63, h, ba)
12.04/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5
12.04/5.03	
12.04/5.03	
12.04/5.03	*new_foldFM_GE(wz3, EQ, Branch(EQ, wz61, wz62, wz63, wz64), h, ba) -> new_foldFM_GE(wz3, EQ, wz64, h, ba)
12.04/5.03	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5
12.04/5.03	
12.04/5.03	
12.04/5.03	----------------------------------------
12.04/5.03	
12.04/5.03	(17)
12.04/5.03	YES
12.24/7.82	EOF