11.06/4.65	YES
12.91/5.23	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.91/5.23	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.91/5.23	
12.91/5.23	
12.91/5.23	H-Termination with start terms of the given HASKELL could be proven:
12.91/5.23	
12.91/5.23	(0) HASKELL
12.91/5.23	(1) LR [EQUIVALENT, 0 ms]
12.91/5.23	(2) HASKELL
12.91/5.23	(3) BR [EQUIVALENT, 0 ms]
12.91/5.23	(4) HASKELL
12.91/5.23	(5) COR [EQUIVALENT, 0 ms]
12.91/5.23	(6) HASKELL
12.91/5.23	(7) Narrow [SOUND, 0 ms]
12.91/5.23	(8) AND
12.91/5.23	    (9) QDP
12.91/5.23	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.91/5.23	        (11) YES
12.91/5.23	    (12) QDP
12.91/5.23	        (13) TransformationProof [EQUIVALENT, 0 ms]
12.91/5.23	        (14) QDP
12.91/5.23	        (15) TransformationProof [EQUIVALENT, 0 ms]
12.91/5.23	        (16) QDP
12.91/5.23	        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.91/5.23	        (18) YES
12.91/5.23	    (19) QDP
12.91/5.23	        (20) TransformationProof [EQUIVALENT, 0 ms]
12.91/5.23	        (21) QDP
12.91/5.23	        (22) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.91/5.23	        (23) YES
12.91/5.23	
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(0)
12.91/5.23	Obligation:
12.91/5.23	mainModule Main 
12.91/5.23	module FiniteMap where {
12.91/5.23	import qualified Main;
12.91/5.23	import qualified Maybe;
12.91/5.23	import qualified Prelude;
12.91/5.23	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.91/5.23	
12.91/5.23	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
12.91/5.23	}
12.91/5.23	eltsFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [b];
12.91/5.23	eltsFM_GE fm fr = foldFM_GE (\key elt rest ->elt : rest) [] fr fm;
12.91/5.23	
12.91/5.23	foldFM_GE :: Ord c => (c  ->  b  ->  a  ->  a)  ->  a  ->  c  ->  FiniteMap c b  ->  a;
12.91/5.23	foldFM_GE k z fr EmptyFM = z;
12.91/5.23	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
12.91/5.23	 | otherwise = foldFM_GE k z fr fm_r;
12.91/5.23	
12.91/5.23	}
12.91/5.23	module Maybe where {
12.91/5.23	import qualified FiniteMap;
12.91/5.23	import qualified Main;
12.91/5.23	import qualified Prelude;
12.91/5.23	}
12.91/5.23	module Main where {
12.91/5.23	import qualified FiniteMap;
12.91/5.23	import qualified Maybe;
12.91/5.23	import qualified Prelude;
12.91/5.23	}
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(1) LR (EQUIVALENT)
12.91/5.23	Lambda Reductions:
12.91/5.23	The following Lambda expression
12.91/5.23	"\keyeltrest->elt : rest"
12.91/5.23	is transformed to
12.91/5.23	"eltsFM_GE0 key elt rest = elt : rest;
12.91/5.23	"
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(2)
12.91/5.23	Obligation:
12.91/5.23	mainModule Main 
12.91/5.23	module FiniteMap where {
12.91/5.23	import qualified Main;
12.91/5.23	import qualified Maybe;
12.91/5.23	import qualified Prelude;
12.91/5.23	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.91/5.23	
12.91/5.23	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.91/5.23	}
12.91/5.23	eltsFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [b];
12.91/5.23	eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm;
12.91/5.23	
12.91/5.23	eltsFM_GE0 key elt rest = elt : rest;
12.91/5.23	
12.91/5.23	foldFM_GE :: Ord b => (b  ->  a  ->  c  ->  c)  ->  c  ->  b  ->  FiniteMap b a  ->  c;
12.91/5.23	foldFM_GE k z fr EmptyFM = z;
12.91/5.23	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
12.91/5.23	 | otherwise = foldFM_GE k z fr fm_r;
12.91/5.23	
12.91/5.23	}
12.91/5.23	module Maybe where {
12.91/5.23	import qualified FiniteMap;
12.91/5.23	import qualified Main;
12.91/5.23	import qualified Prelude;
12.91/5.23	}
12.91/5.23	module Main where {
12.91/5.23	import qualified FiniteMap;
12.91/5.23	import qualified Maybe;
12.91/5.23	import qualified Prelude;
12.91/5.23	}
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(3) BR (EQUIVALENT)
12.91/5.23	Replaced joker patterns by fresh variables and removed binding patterns.
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(4)
12.91/5.23	Obligation:
12.91/5.23	mainModule Main 
12.91/5.23	module FiniteMap where {
12.91/5.23	import qualified Main;
12.91/5.23	import qualified Maybe;
12.91/5.23	import qualified Prelude;
12.91/5.23	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.91/5.23	
12.91/5.23	instance (Eq a, Eq b) => Eq FiniteMap a b where { 
12.91/5.23	}
12.91/5.23	eltsFM_GE :: Ord a => FiniteMap a b  ->  a  ->  [b];
12.91/5.23	eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm;
12.91/5.23	
12.91/5.23	eltsFM_GE0 key elt rest = elt : rest;
12.91/5.23	
12.91/5.23	foldFM_GE :: Ord b => (b  ->  a  ->  c  ->  c)  ->  c  ->  b  ->  FiniteMap b a  ->  c;
12.91/5.23	foldFM_GE k z fr EmptyFM = z;
12.91/5.23	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
12.91/5.23	 | otherwise = foldFM_GE k z fr fm_r;
12.91/5.23	
12.91/5.23	}
12.91/5.23	module Maybe where {
12.91/5.23	import qualified FiniteMap;
12.91/5.23	import qualified Main;
12.91/5.23	import qualified Prelude;
12.91/5.23	}
12.91/5.23	module Main where {
12.91/5.23	import qualified FiniteMap;
12.91/5.23	import qualified Maybe;
12.91/5.23	import qualified Prelude;
12.91/5.23	}
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(5) COR (EQUIVALENT)
12.91/5.23	Cond Reductions:
12.91/5.23	The following Function with conditions
12.91/5.23	"compare x y|x == yEQ|x <= yLT|otherwiseGT;
12.91/5.23	"
12.91/5.23	is transformed to
12.91/5.23	"compare x y = compare3 x y;
12.91/5.23	"
12.91/5.23	"compare1 x y True = LT;
12.91/5.23	compare1 x y False = compare0 x y otherwise;
12.91/5.23	"
12.91/5.23	"compare2 x y True = EQ;
12.91/5.23	compare2 x y False = compare1 x y (x <= y);
12.91/5.23	"
12.91/5.23	"compare0 x y True = GT;
12.91/5.23	"
12.91/5.23	"compare3 x y = compare2 x y (x == y);
12.91/5.23	"
12.91/5.23	The following Function with conditions
12.91/5.23	"undefined |Falseundefined;
12.91/5.23	"
12.91/5.23	is transformed to
12.91/5.23	"undefined  = undefined1;
12.91/5.23	"
12.91/5.23	"undefined0 True = undefined;
12.91/5.23	"
12.91/5.23	"undefined1  = undefined0 False;
12.91/5.23	"
12.91/5.23	The following Function with conditions
12.91/5.23	"foldFM_GE k z fr EmptyFM = z;
12.91/5.23	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;
12.91/5.23	"
12.91/5.23	is transformed to
12.91/5.23	"foldFM_GE k z fr EmptyFM = foldFM_GE3 k z fr EmptyFM;
12.91/5.23	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);
12.91/5.23	"
12.91/5.23	"foldFM_GE0 k z fr key elt vy fm_l fm_r True = foldFM_GE k z fr fm_r;
12.91/5.23	"
12.91/5.23	"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;
12.91/5.23	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;
12.91/5.23	"
12.91/5.23	"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);
12.91/5.23	"
12.91/5.23	"foldFM_GE3 k z fr EmptyFM = z;
12.91/5.23	foldFM_GE3 wv ww wx wy = foldFM_GE2 wv ww wx wy;
12.91/5.23	"
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(6)
12.91/5.23	Obligation:
12.91/5.23	mainModule Main 
12.91/5.23	module FiniteMap where {
12.91/5.23	import qualified Main;
12.91/5.23	import qualified Maybe;
12.91/5.23	import qualified Prelude;
12.91/5.23	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.91/5.23	
12.91/5.23	instance (Eq a, Eq b) => Eq FiniteMap b a where { 
12.91/5.23	}
12.91/5.23	eltsFM_GE :: Ord b => FiniteMap b a  ->  b  ->  [a];
12.91/5.23	eltsFM_GE fm fr = foldFM_GE eltsFM_GE0 [] fr fm;
12.91/5.23	
12.91/5.23	eltsFM_GE0 key elt rest = elt : rest;
12.91/5.23	
12.91/5.23	foldFM_GE :: Ord a => (a  ->  b  ->  c  ->  c)  ->  c  ->  a  ->  FiniteMap a b  ->  c;
12.91/5.23	foldFM_GE k z fr EmptyFM = foldFM_GE3 k z fr EmptyFM;
12.91/5.23	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);
12.91/5.23	
12.91/5.23	foldFM_GE0 k z fr key elt vy fm_l fm_r True = foldFM_GE k z fr fm_r;
12.91/5.23	
12.91/5.23	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;
12.91/5.23	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;
12.91/5.23	
12.91/5.23	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);
12.91/5.23	
12.91/5.23	foldFM_GE3 k z fr EmptyFM = z;
12.91/5.23	foldFM_GE3 wv ww wx wy = foldFM_GE2 wv ww wx wy;
12.91/5.23	
12.91/5.23	}
12.91/5.23	module Maybe where {
12.91/5.23	import qualified FiniteMap;
12.91/5.23	import qualified Main;
12.91/5.23	import qualified Prelude;
12.91/5.23	}
12.91/5.23	module Main where {
12.91/5.23	import qualified FiniteMap;
12.91/5.23	import qualified Maybe;
12.91/5.23	import qualified Prelude;
12.91/5.23	}
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(7) Narrow (SOUND)
12.91/5.23	Haskell To QDPs
12.91/5.23	
12.91/5.23	digraph dp_graph {
12.91/5.23	node [outthreshold=100, inthreshold=100];1[label="FiniteMap.eltsFM_GE",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
12.91/5.23	3[label="FiniteMap.eltsFM_GE wz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
12.91/5.23	4[label="FiniteMap.eltsFM_GE wz3 wz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
12.91/5.23	5[label="FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 [] wz4 wz3",fontsize=16,color="burlywood",shape="triangle"];170[label="wz3/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];5 -> 170[label="",style="solid", color="burlywood", weight=9];
12.91/5.23	170 -> 6[label="",style="solid", color="burlywood", weight=3];
12.91/5.23	171[label="wz3/FiniteMap.Branch wz30 wz31 wz32 wz33 wz34",fontsize=10,color="white",style="solid",shape="box"];5 -> 171[label="",style="solid", color="burlywood", weight=9];
12.91/5.23	171 -> 7[label="",style="solid", color="burlywood", weight=3];
12.91/5.23	6[label="FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 [] wz4 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
12.91/5.23	7[label="FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 [] wz4 (FiniteMap.Branch wz30 wz31 wz32 wz33 wz34)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
12.91/5.23	8[label="FiniteMap.foldFM_GE3 FiniteMap.eltsFM_GE0 [] wz4 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
12.91/5.23	9[label="FiniteMap.foldFM_GE2 FiniteMap.eltsFM_GE0 [] wz4 (FiniteMap.Branch wz30 wz31 wz32 wz33 wz34)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
12.91/5.23	10[label="[]",fontsize=16,color="green",shape="box"];11[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] wz4 wz30 wz31 wz32 wz33 wz34 (wz30 >= wz4)",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
12.91/5.23	12[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] wz4 wz30 wz31 wz32 wz33 wz34 (compare wz30 wz4 /= LT)",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
12.91/5.23	13[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] wz4 wz30 wz31 wz32 wz33 wz34 (not (compare wz30 wz4 == LT))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
12.91/5.23	14[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] wz4 wz30 wz31 wz32 wz33 wz34 (not (compare3 wz30 wz4 == LT))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
12.91/5.23	15[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] wz4 wz30 wz31 wz32 wz33 wz34 (not (compare2 wz30 wz4 (wz30 == wz4) == LT))",fontsize=16,color="burlywood",shape="box"];172[label="wz30/False",fontsize=10,color="white",style="solid",shape="box"];15 -> 172[label="",style="solid", color="burlywood", weight=9];
12.91/5.23	172 -> 16[label="",style="solid", color="burlywood", weight=3];
12.91/5.23	173[label="wz30/True",fontsize=10,color="white",style="solid",shape="box"];15 -> 173[label="",style="solid", color="burlywood", weight=9];
12.91/5.23	173 -> 17[label="",style="solid", color="burlywood", weight=3];
12.91/5.23	16[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] wz4 False wz31 wz32 wz33 wz34 (not (compare2 False wz4 (False == wz4) == LT))",fontsize=16,color="burlywood",shape="box"];174[label="wz4/False",fontsize=10,color="white",style="solid",shape="box"];16 -> 174[label="",style="solid", color="burlywood", weight=9];
12.91/5.23	174 -> 18[label="",style="solid", color="burlywood", weight=3];
12.91/5.23	175[label="wz4/True",fontsize=10,color="white",style="solid",shape="box"];16 -> 175[label="",style="solid", color="burlywood", weight=9];
12.91/5.23	175 -> 19[label="",style="solid", color="burlywood", weight=3];
12.91/5.23	17[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] wz4 True wz31 wz32 wz33 wz34 (not (compare2 True wz4 (True == wz4) == LT))",fontsize=16,color="burlywood",shape="box"];176[label="wz4/False",fontsize=10,color="white",style="solid",shape="box"];17 -> 176[label="",style="solid", color="burlywood", weight=9];
12.91/5.23	176 -> 20[label="",style="solid", color="burlywood", weight=3];
12.91/5.23	177[label="wz4/True",fontsize=10,color="white",style="solid",shape="box"];17 -> 177[label="",style="solid", color="burlywood", weight=9];
12.91/5.23	177 -> 21[label="",style="solid", color="burlywood", weight=3];
12.91/5.23	18[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] False False wz31 wz32 wz33 wz34 (not (compare2 False False (False == False) == LT))",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
12.91/5.23	19[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] True False wz31 wz32 wz33 wz34 (not (compare2 False True (False == True) == LT))",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
12.91/5.23	20[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] False True wz31 wz32 wz33 wz34 (not (compare2 True False (True == False) == LT))",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
12.91/5.23	21[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] True True wz31 wz32 wz33 wz34 (not (compare2 True True (True == True) == LT))",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
12.91/5.23	22[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] False False wz31 wz32 wz33 wz34 (not (compare2 False False True == LT))",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3];
12.91/5.23	23[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] True False wz31 wz32 wz33 wz34 (not (compare2 False True False == LT))",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3];
12.91/5.23	24[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] False True wz31 wz32 wz33 wz34 (not (compare2 True False False == LT))",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3];
12.91/5.23	25[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] True True wz31 wz32 wz33 wz34 (not (compare2 True True True == LT))",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3];
12.91/5.23	26[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] False False wz31 wz32 wz33 wz34 (not (EQ == LT))",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3];
12.91/5.23	27[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] True False wz31 wz32 wz33 wz34 (not (compare1 False True (False <= True) == LT))",fontsize=16,color="black",shape="box"];27 -> 31[label="",style="solid", color="black", weight=3];
12.91/5.23	28[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] False True wz31 wz32 wz33 wz34 (not (compare1 True False (True <= False) == LT))",fontsize=16,color="black",shape="box"];28 -> 32[label="",style="solid", color="black", weight=3];
12.91/5.23	29[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] True True wz31 wz32 wz33 wz34 (not (EQ == LT))",fontsize=16,color="black",shape="box"];29 -> 33[label="",style="solid", color="black", weight=3];
12.91/5.23	30[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] False False wz31 wz32 wz33 wz34 (not False)",fontsize=16,color="black",shape="box"];30 -> 34[label="",style="solid", color="black", weight=3];
12.91/5.23	31[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] True False wz31 wz32 wz33 wz34 (not (compare1 False True True == LT))",fontsize=16,color="black",shape="box"];31 -> 35[label="",style="solid", color="black", weight=3];
12.91/5.23	32[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] False True wz31 wz32 wz33 wz34 (not (compare1 True False False == LT))",fontsize=16,color="black",shape="box"];32 -> 36[label="",style="solid", color="black", weight=3];
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12.91/5.23	45[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] False True wz31 wz32 wz33 wz34 (not (GT == LT))",fontsize=16,color="black",shape="box"];45 -> 53[label="",style="solid", color="black", weight=3];
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12.91/5.23	95[label="FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 wz10 False (FiniteMap.Branch wz330 wz331 wz332 wz333 wz334)",fontsize=16,color="black",shape="box"];95 -> 102[label="",style="solid", color="black", weight=3];
12.91/5.23	52[label="FiniteMap.foldFM_GE0 FiniteMap.eltsFM_GE0 [] True False wz31 wz32 wz33 wz34 otherwise",fontsize=16,color="black",shape="box"];52 -> 60[label="",style="solid", color="black", weight=3];
12.91/5.23	53[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] False True wz31 wz32 wz33 wz34 (not False)",fontsize=16,color="black",shape="box"];53 -> 61[label="",style="solid", color="black", weight=3];
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12.91/5.23	57[label="FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 (FiniteMap.eltsFM_GE0 True wz31 wz6) True (FiniteMap.Branch wz330 wz331 wz332 wz333 wz334)",fontsize=16,color="black",shape="box"];57 -> 63[label="",style="solid", color="black", weight=3];
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12.91/5.23	102[label="FiniteMap.foldFM_GE2 FiniteMap.eltsFM_GE0 wz10 False (FiniteMap.Branch wz330 wz331 wz332 wz333 wz334)",fontsize=16,color="black",shape="box"];102 -> 107[label="",style="solid", color="black", weight=3];
12.91/5.23	60[label="FiniteMap.foldFM_GE0 FiniteMap.eltsFM_GE0 [] True False wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];60 -> 66[label="",style="solid", color="black", weight=3];
12.91/5.23	61[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 [] False True wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];61 -> 67[label="",style="solid", color="black", weight=3];
12.91/5.23	62[label="FiniteMap.foldFM_GE3 FiniteMap.eltsFM_GE0 (FiniteMap.eltsFM_GE0 True wz31 wz6) True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];62 -> 68[label="",style="solid", color="black", weight=3];
12.91/5.23	63[label="FiniteMap.foldFM_GE2 FiniteMap.eltsFM_GE0 (FiniteMap.eltsFM_GE0 True wz31 wz6) True (FiniteMap.Branch wz330 wz331 wz332 wz333 wz334)",fontsize=16,color="black",shape="box"];63 -> 69[label="",style="solid", color="black", weight=3];
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12.91/5.23	99 -> 104[label="",style="dashed", color="magenta", weight=3];
12.91/5.23	100[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True wz330 wz331 wz332 wz333 wz334 (compare wz330 True /= LT)",fontsize=16,color="black",shape="box"];100 -> 105[label="",style="solid", color="black", weight=3];
12.91/5.23	114[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz10 False wz330 wz331 wz332 wz333 wz334 (not (compare3 wz330 False == LT))",fontsize=16,color="black",shape="box"];114 -> 117[label="",style="solid", color="black", weight=3];
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12.91/5.23	117[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz10 False wz330 wz331 wz332 wz333 wz334 (not (compare2 wz330 False (wz330 == False) == LT))",fontsize=16,color="burlywood",shape="box"];182[label="wz330/False",fontsize=10,color="white",style="solid",shape="box"];117 -> 182[label="",style="solid", color="burlywood", weight=9];
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12.91/5.23	183[label="wz330/True",fontsize=10,color="white",style="solid",shape="box"];117 -> 183[label="",style="solid", color="burlywood", weight=9];
12.91/5.23	183 -> 121[label="",style="solid", color="burlywood", weight=3];
12.91/5.23	108[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True wz330 wz331 wz332 wz333 wz334 (not (compare3 wz330 True == LT))",fontsize=16,color="black",shape="box"];108 -> 110[label="",style="solid", color="black", weight=3];
12.91/5.23	120[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz10 False False wz331 wz332 wz333 wz334 (not (compare2 False False (False == False) == LT))",fontsize=16,color="black",shape="box"];120 -> 124[label="",style="solid", color="black", weight=3];
12.91/5.23	121[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz10 False True wz331 wz332 wz333 wz334 (not (compare2 True False (True == False) == LT))",fontsize=16,color="black",shape="box"];121 -> 125[label="",style="solid", color="black", weight=3];
12.91/5.23	110[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True wz330 wz331 wz332 wz333 wz334 (not (compare2 wz330 True (wz330 == True) == LT))",fontsize=16,color="burlywood",shape="box"];184[label="wz330/False",fontsize=10,color="white",style="solid",shape="box"];110 -> 184[label="",style="solid", color="burlywood", weight=9];
12.91/5.23	184 -> 112[label="",style="solid", color="burlywood", weight=3];
12.91/5.23	185[label="wz330/True",fontsize=10,color="white",style="solid",shape="box"];110 -> 185[label="",style="solid", color="burlywood", weight=9];
12.91/5.23	185 -> 113[label="",style="solid", color="burlywood", weight=3];
12.91/5.23	124[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz10 False False wz331 wz332 wz333 wz334 (not (compare2 False False True == LT))",fontsize=16,color="black",shape="box"];124 -> 128[label="",style="solid", color="black", weight=3];
12.91/5.23	125[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz10 False True wz331 wz332 wz333 wz334 (not (compare2 True False False == LT))",fontsize=16,color="black",shape="box"];125 -> 129[label="",style="solid", color="black", weight=3];
12.91/5.23	112[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True False wz331 wz332 wz333 wz334 (not (compare2 False True (False == True) == LT))",fontsize=16,color="black",shape="box"];112 -> 115[label="",style="solid", color="black", weight=3];
12.91/5.23	113[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True True wz331 wz332 wz333 wz334 (not (compare2 True True (True == True) == LT))",fontsize=16,color="black",shape="box"];113 -> 116[label="",style="solid", color="black", weight=3];
12.91/5.23	128[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz10 False False wz331 wz332 wz333 wz334 (not (EQ == LT))",fontsize=16,color="black",shape="box"];128 -> 132[label="",style="solid", color="black", weight=3];
12.91/5.23	129[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz10 False True wz331 wz332 wz333 wz334 (not (compare1 True False (True <= False) == LT))",fontsize=16,color="black",shape="box"];129 -> 133[label="",style="solid", color="black", weight=3];
12.91/5.23	115[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True False wz331 wz332 wz333 wz334 (not (compare2 False True False == LT))",fontsize=16,color="black",shape="box"];115 -> 118[label="",style="solid", color="black", weight=3];
12.91/5.23	116[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True True wz331 wz332 wz333 wz334 (not (compare2 True True True == LT))",fontsize=16,color="black",shape="box"];116 -> 119[label="",style="solid", color="black", weight=3];
12.91/5.23	132[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz10 False False wz331 wz332 wz333 wz334 (not False)",fontsize=16,color="black",shape="box"];132 -> 138[label="",style="solid", color="black", weight=3];
12.91/5.23	133[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz10 False True wz331 wz332 wz333 wz334 (not (compare1 True False False == LT))",fontsize=16,color="black",shape="box"];133 -> 139[label="",style="solid", color="black", weight=3];
12.91/5.23	118[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True False wz331 wz332 wz333 wz334 (not (compare1 False True (False <= True) == LT))",fontsize=16,color="black",shape="box"];118 -> 122[label="",style="solid", color="black", weight=3];
12.91/5.23	119[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True True wz331 wz332 wz333 wz334 (not (EQ == LT))",fontsize=16,color="black",shape="box"];119 -> 123[label="",style="solid", color="black", weight=3];
12.91/5.23	138[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz10 False False wz331 wz332 wz333 wz334 True",fontsize=16,color="black",shape="box"];138 -> 143[label="",style="solid", color="black", weight=3];
12.91/5.23	139[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz10 False True wz331 wz332 wz333 wz334 (not (compare0 True False otherwise == LT))",fontsize=16,color="black",shape="box"];139 -> 144[label="",style="solid", color="black", weight=3];
12.91/5.23	122[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True False wz331 wz332 wz333 wz334 (not (compare1 False True True == LT))",fontsize=16,color="black",shape="box"];122 -> 126[label="",style="solid", color="black", weight=3];
12.91/5.23	123[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True True wz331 wz332 wz333 wz334 (not False)",fontsize=16,color="black",shape="box"];123 -> 127[label="",style="solid", color="black", weight=3];
12.91/5.23	143 -> 83[label="",style="dashed", color="red", weight=0];
12.91/5.23	143[label="FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 (FiniteMap.eltsFM_GE0 False wz331 (FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 wz10 False wz334)) False wz333",fontsize=16,color="magenta"];143 -> 148[label="",style="dashed", color="magenta", weight=3];
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12.91/5.23	144[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz10 False True wz331 wz332 wz333 wz334 (not (compare0 True False True == LT))",fontsize=16,color="black",shape="box"];144 -> 150[label="",style="solid", color="black", weight=3];
12.91/5.23	126[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True False wz331 wz332 wz333 wz334 (not (LT == LT))",fontsize=16,color="black",shape="box"];126 -> 130[label="",style="solid", color="black", weight=3];
12.91/5.23	127[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True True wz331 wz332 wz333 wz334 True",fontsize=16,color="black",shape="box"];127 -> 131[label="",style="solid", color="black", weight=3];
12.91/5.23	148 -> 92[label="",style="dashed", color="red", weight=0];
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12.91/5.23	130[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True False wz331 wz332 wz333 wz334 (not True)",fontsize=16,color="black",shape="box"];130 -> 134[label="",style="solid", color="black", weight=3];
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12.91/5.23	131 -> 136[label="",style="dashed", color="magenta", weight=3];
12.91/5.23	131 -> 137[label="",style="dashed", color="magenta", weight=3];
12.91/5.23	154[label="wz331",fontsize=16,color="green",shape="box"];155 -> 83[label="",style="dashed", color="red", weight=0];
12.91/5.23	155[label="FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 wz10 False wz334",fontsize=16,color="magenta"];155 -> 162[label="",style="dashed", color="magenta", weight=3];
12.91/5.23	156[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz10 False True wz331 wz332 wz333 wz334 (not False)",fontsize=16,color="black",shape="box"];156 -> 163[label="",style="solid", color="black", weight=3];
12.91/5.23	134[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True False wz331 wz332 wz333 wz334 False",fontsize=16,color="black",shape="box"];134 -> 140[label="",style="solid", color="black", weight=3];
12.91/5.23	135[label="wz331",fontsize=16,color="green",shape="box"];136[label="FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 wz9 True wz334",fontsize=16,color="burlywood",shape="triangle"];186[label="wz334/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];136 -> 186[label="",style="solid", color="burlywood", weight=9];
12.91/5.23	186 -> 141[label="",style="solid", color="burlywood", weight=3];
12.91/5.23	187[label="wz334/FiniteMap.Branch wz3340 wz3341 wz3342 wz3343 wz3344",fontsize=10,color="white",style="solid",shape="box"];136 -> 187[label="",style="solid", color="burlywood", weight=9];
12.91/5.23	187 -> 142[label="",style="solid", color="burlywood", weight=3];
12.91/5.23	137[label="wz333",fontsize=16,color="green",shape="box"];162[label="wz334",fontsize=16,color="green",shape="box"];163[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz10 False True wz331 wz332 wz333 wz334 True",fontsize=16,color="black",shape="box"];163 -> 164[label="",style="solid", color="black", weight=3];
12.91/5.23	140[label="FiniteMap.foldFM_GE0 FiniteMap.eltsFM_GE0 wz9 True False wz331 wz332 wz333 wz334 otherwise",fontsize=16,color="black",shape="box"];140 -> 145[label="",style="solid", color="black", weight=3];
12.91/5.23	141[label="FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 wz9 True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];141 -> 146[label="",style="solid", color="black", weight=3];
12.91/5.23	142[label="FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 wz9 True (FiniteMap.Branch wz3340 wz3341 wz3342 wz3343 wz3344)",fontsize=16,color="black",shape="box"];142 -> 147[label="",style="solid", color="black", weight=3];
12.91/5.23	164 -> 83[label="",style="dashed", color="red", weight=0];
12.91/5.23	164[label="FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 (FiniteMap.eltsFM_GE0 True wz331 (FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 wz10 False wz334)) False wz333",fontsize=16,color="magenta"];164 -> 165[label="",style="dashed", color="magenta", weight=3];
12.91/5.23	164 -> 166[label="",style="dashed", color="magenta", weight=3];
12.91/5.23	145[label="FiniteMap.foldFM_GE0 FiniteMap.eltsFM_GE0 wz9 True False wz331 wz332 wz333 wz334 True",fontsize=16,color="black",shape="box"];145 -> 151[label="",style="solid", color="black", weight=3];
12.91/5.23	146[label="FiniteMap.foldFM_GE3 FiniteMap.eltsFM_GE0 wz9 True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];146 -> 152[label="",style="solid", color="black", weight=3];
12.91/5.23	147[label="FiniteMap.foldFM_GE2 FiniteMap.eltsFM_GE0 wz9 True (FiniteMap.Branch wz3340 wz3341 wz3342 wz3343 wz3344)",fontsize=16,color="black",shape="box"];147 -> 153[label="",style="solid", color="black", weight=3];
12.91/5.23	165 -> 68[label="",style="dashed", color="red", weight=0];
12.91/5.23	165[label="FiniteMap.eltsFM_GE0 True wz331 (FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 wz10 False wz334)",fontsize=16,color="magenta"];165 -> 167[label="",style="dashed", color="magenta", weight=3];
12.91/5.23	165 -> 168[label="",style="dashed", color="magenta", weight=3];
12.91/5.23	166[label="wz333",fontsize=16,color="green",shape="box"];151 -> 136[label="",style="dashed", color="red", weight=0];
12.91/5.23	151[label="FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 wz9 True wz334",fontsize=16,color="magenta"];152[label="wz9",fontsize=16,color="green",shape="box"];153 -> 78[label="",style="dashed", color="red", weight=0];
12.91/5.23	153[label="FiniteMap.foldFM_GE1 FiniteMap.eltsFM_GE0 wz9 True wz3340 wz3341 wz3342 wz3343 wz3344 (wz3340 >= True)",fontsize=16,color="magenta"];153 -> 157[label="",style="dashed", color="magenta", weight=3];
12.91/5.23	153 -> 158[label="",style="dashed", color="magenta", weight=3];
12.91/5.23	153 -> 159[label="",style="dashed", color="magenta", weight=3];
12.91/5.23	153 -> 160[label="",style="dashed", color="magenta", weight=3];
12.91/5.23	153 -> 161[label="",style="dashed", color="magenta", weight=3];
12.91/5.23	167[label="wz331",fontsize=16,color="green",shape="box"];168 -> 83[label="",style="dashed", color="red", weight=0];
12.91/5.23	168[label="FiniteMap.foldFM_GE FiniteMap.eltsFM_GE0 wz10 False wz334",fontsize=16,color="magenta"];168 -> 169[label="",style="dashed", color="magenta", weight=3];
12.91/5.23	157[label="wz3341",fontsize=16,color="green",shape="box"];158[label="wz3343",fontsize=16,color="green",shape="box"];159[label="wz3344",fontsize=16,color="green",shape="box"];160[label="wz3340",fontsize=16,color="green",shape="box"];161[label="wz3342",fontsize=16,color="green",shape="box"];169[label="wz334",fontsize=16,color="green",shape="box"];}
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(8)
12.91/5.23	Complex Obligation (AND)
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(9)
12.91/5.23	Obligation:
12.91/5.23	Q DP problem:
12.91/5.23	The TRS P consists of the following rules:
12.91/5.23	
12.91/5.23	   new_foldFM_GE6(True, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_GE6(True, wz34, h)
12.91/5.23	   new_foldFM_GE6(True, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_GE6(True, wz34, h)
12.91/5.23	
12.91/5.23	R is empty.
12.91/5.23	Q is empty.
12.91/5.23	We have to consider all minimal (P,Q,R)-chains.
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(10) QDPSizeChangeProof (EQUIVALENT)
12.91/5.23	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. 
12.91/5.23	
12.91/5.23	From the DPs we obtained the following set of size-change graphs:
12.91/5.23	*new_foldFM_GE6(True, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_GE6(True, wz34, h)
12.91/5.23	The graph contains the following edges 1 >= 1, 2 > 1, 2 > 2, 3 >= 3
12.91/5.23	
12.91/5.23	
12.91/5.23	*new_foldFM_GE6(True, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_GE6(True, wz34, h)
12.91/5.23	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.91/5.23	
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(11)
12.91/5.23	YES
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(12)
12.91/5.23	Obligation:
12.91/5.23	Q DP problem:
12.91/5.23	The TRS P consists of the following rules:
12.91/5.23	
12.91/5.23	   new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(new_eltsFM_GE0(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h)
12.91/5.23	   new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h)
12.91/5.23	   new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h)
12.91/5.23	   new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(new_eltsFM_GE00(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h)
12.91/5.23	
12.91/5.23	The TRS R consists of the following rules:
12.91/5.23	
12.91/5.23	   new_foldFM_GE5(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE5(new_eltsFM_GE00(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h)
12.91/5.23	   new_eltsFM_GE00(wz31, wz11, h) -> :(wz31, wz11)
12.91/5.23	   new_eltsFM_GE0(wz31, wz6, h) -> :(wz31, wz6)
12.91/5.23	   new_foldFM_GE5(wz10, EmptyFM, h) -> wz10
12.91/5.23	   new_foldFM_GE5(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE5(new_eltsFM_GE0(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h)
12.91/5.23	
12.91/5.23	The set Q consists of the following terms:
12.91/5.23	
12.91/5.23	   new_foldFM_GE5(x0, Branch(False, x1, x2, x3, x4), x5)
12.91/5.23	   new_foldFM_GE5(x0, Branch(True, x1, x2, x3, x4), x5)
12.91/5.23	   new_eltsFM_GE0(x0, x1, x2)
12.91/5.23	   new_eltsFM_GE00(x0, x1, x2)
12.91/5.23	   new_foldFM_GE5(x0, EmptyFM, x1)
12.91/5.23	
12.91/5.23	We have to consider all minimal (P,Q,R)-chains.
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(13) TransformationProof (EQUIVALENT)
12.91/5.23	By rewriting [LPAR04] the rule new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(new_eltsFM_GE0(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h) at position [0] we obtained the following new rules [LPAR04]:
12.91/5.23	
12.91/5.23	   (new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(wz331, new_foldFM_GE5(wz10, wz334, h)), wz333, h),new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(wz331, new_foldFM_GE5(wz10, wz334, h)), wz333, h))
12.91/5.23	
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(14)
12.91/5.23	Obligation:
12.91/5.23	Q DP problem:
12.91/5.23	The TRS P consists of the following rules:
12.91/5.23	
12.91/5.23	   new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h)
12.91/5.23	   new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h)
12.91/5.23	   new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(new_eltsFM_GE00(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h)
12.91/5.23	   new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(wz331, new_foldFM_GE5(wz10, wz334, h)), wz333, h)
12.91/5.23	
12.91/5.23	The TRS R consists of the following rules:
12.91/5.23	
12.91/5.23	   new_foldFM_GE5(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE5(new_eltsFM_GE00(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h)
12.91/5.23	   new_eltsFM_GE00(wz31, wz11, h) -> :(wz31, wz11)
12.91/5.23	   new_eltsFM_GE0(wz31, wz6, h) -> :(wz31, wz6)
12.91/5.23	   new_foldFM_GE5(wz10, EmptyFM, h) -> wz10
12.91/5.23	   new_foldFM_GE5(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE5(new_eltsFM_GE0(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h)
12.91/5.23	
12.91/5.23	The set Q consists of the following terms:
12.91/5.23	
12.91/5.23	   new_foldFM_GE5(x0, Branch(False, x1, x2, x3, x4), x5)
12.91/5.23	   new_foldFM_GE5(x0, Branch(True, x1, x2, x3, x4), x5)
12.91/5.23	   new_eltsFM_GE0(x0, x1, x2)
12.91/5.23	   new_eltsFM_GE00(x0, x1, x2)
12.91/5.23	   new_foldFM_GE5(x0, EmptyFM, x1)
12.91/5.23	
12.91/5.23	We have to consider all minimal (P,Q,R)-chains.
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(15) TransformationProof (EQUIVALENT)
12.91/5.23	By rewriting [LPAR04] the rule new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(new_eltsFM_GE00(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h) at position [0] we obtained the following new rules [LPAR04]:
12.91/5.23	
12.91/5.23	   (new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(wz331, new_foldFM_GE5(wz10, wz334, h)), wz333, h),new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(wz331, new_foldFM_GE5(wz10, wz334, h)), wz333, h))
12.91/5.23	
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(16)
12.91/5.23	Obligation:
12.91/5.23	Q DP problem:
12.91/5.23	The TRS P consists of the following rules:
12.91/5.23	
12.91/5.23	   new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h)
12.91/5.23	   new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h)
12.91/5.23	   new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(wz331, new_foldFM_GE5(wz10, wz334, h)), wz333, h)
12.91/5.23	   new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(wz331, new_foldFM_GE5(wz10, wz334, h)), wz333, h)
12.91/5.23	
12.91/5.23	The TRS R consists of the following rules:
12.91/5.23	
12.91/5.23	   new_foldFM_GE5(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE5(new_eltsFM_GE00(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h)
12.91/5.23	   new_eltsFM_GE00(wz31, wz11, h) -> :(wz31, wz11)
12.91/5.23	   new_eltsFM_GE0(wz31, wz6, h) -> :(wz31, wz6)
12.91/5.23	   new_foldFM_GE5(wz10, EmptyFM, h) -> wz10
12.91/5.23	   new_foldFM_GE5(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE5(new_eltsFM_GE0(wz331, new_foldFM_GE5(wz10, wz334, h), h), wz333, h)
12.91/5.23	
12.91/5.23	The set Q consists of the following terms:
12.91/5.23	
12.91/5.23	   new_foldFM_GE5(x0, Branch(False, x1, x2, x3, x4), x5)
12.91/5.23	   new_foldFM_GE5(x0, Branch(True, x1, x2, x3, x4), x5)
12.91/5.23	   new_eltsFM_GE0(x0, x1, x2)
12.91/5.23	   new_eltsFM_GE00(x0, x1, x2)
12.91/5.23	   new_foldFM_GE5(x0, EmptyFM, x1)
12.91/5.23	
12.91/5.23	We have to consider all minimal (P,Q,R)-chains.
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(17) QDPSizeChangeProof (EQUIVALENT)
12.91/5.23	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. 
12.91/5.23	
12.91/5.23	From the DPs we obtained the following set of size-change graphs:
12.91/5.23	*new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h)
12.91/5.23	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.91/5.23	
12.91/5.23	
12.91/5.23	*new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(wz10, wz334, h)
12.91/5.23	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.91/5.23	
12.91/5.23	
12.91/5.23	*new_foldFM_GE4(wz10, Branch(True, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(wz331, new_foldFM_GE5(wz10, wz334, h)), wz333, h)
12.91/5.23	The graph contains the following edges 2 > 2, 3 >= 3
12.91/5.23	
12.91/5.23	
12.91/5.23	*new_foldFM_GE4(wz10, Branch(False, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE4(:(wz331, new_foldFM_GE5(wz10, wz334, h)), wz333, h)
12.91/5.23	The graph contains the following edges 2 > 2, 3 >= 3
12.91/5.23	
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(18)
12.91/5.23	YES
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(19)
12.91/5.23	Obligation:
12.91/5.23	Q DP problem:
12.91/5.23	The TRS P consists of the following rules:
12.91/5.23	
12.91/5.23	   new_foldFM_GE1(wz9, True, wz331, wz332, wz333, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE1(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h)
12.91/5.23	   new_foldFM_GE(wz9, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE1(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h)
12.91/5.23	   new_foldFM_GE1(wz9, False, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE(wz9, wz334, h)
12.91/5.23	   new_foldFM_GE0(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE1(new_eltsFM_GE0(wz31, wz6, h), wz330, wz331, wz332, wz333, wz334, h)
12.91/5.23	   new_foldFM_GE1(wz9, True, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE0(wz331, new_foldFM_GE2(wz9, wz334, h), wz333, h)
12.91/5.23	
12.91/5.23	The TRS R consists of the following rules:
12.91/5.23	
12.91/5.23	   new_foldFM_GE2(wz9, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE10(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h)
12.91/5.23	   new_eltsFM_GE0(wz31, wz6, h) -> :(wz31, wz6)
12.91/5.23	   new_foldFM_GE10(wz9, True, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE3(wz331, new_foldFM_GE2(wz9, wz334, h), wz333, h)
12.91/5.23	   new_foldFM_GE10(wz9, False, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE2(wz9, wz334, h)
12.91/5.23	   new_foldFM_GE2(wz9, EmptyFM, h) -> wz9
12.91/5.23	   new_foldFM_GE3(wz31, wz6, EmptyFM, h) -> new_eltsFM_GE0(wz31, wz6, h)
12.91/5.23	   new_foldFM_GE3(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE10(new_eltsFM_GE0(wz31, wz6, h), wz330, wz331, wz332, wz333, wz334, h)
12.91/5.23	
12.91/5.23	The set Q consists of the following terms:
12.91/5.23	
12.91/5.23	   new_foldFM_GE10(x0, True, x1, x2, x3, x4, x5)
12.91/5.23	   new_foldFM_GE2(x0, Branch(x1, x2, x3, x4, x5), x6)
12.91/5.23	   new_eltsFM_GE0(x0, x1, x2)
12.91/5.23	   new_foldFM_GE10(x0, False, x1, x2, x3, x4, x5)
12.91/5.23	   new_foldFM_GE3(x0, x1, EmptyFM, x2)
12.91/5.23	   new_foldFM_GE2(x0, EmptyFM, x1)
12.91/5.23	   new_foldFM_GE3(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.91/5.23	
12.91/5.23	We have to consider all minimal (P,Q,R)-chains.
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(20) TransformationProof (EQUIVALENT)
12.91/5.23	By rewriting [LPAR04] the rule new_foldFM_GE0(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE1(new_eltsFM_GE0(wz31, wz6, h), wz330, wz331, wz332, wz333, wz334, h) at position [0] we obtained the following new rules [LPAR04]:
12.91/5.23	
12.91/5.23	   (new_foldFM_GE0(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE1(:(wz31, wz6), wz330, wz331, wz332, wz333, wz334, h),new_foldFM_GE0(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE1(:(wz31, wz6), wz330, wz331, wz332, wz333, wz334, h))
12.91/5.23	
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(21)
12.91/5.23	Obligation:
12.91/5.23	Q DP problem:
12.91/5.23	The TRS P consists of the following rules:
12.91/5.23	
12.91/5.23	   new_foldFM_GE1(wz9, True, wz331, wz332, wz333, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE1(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h)
12.91/5.23	   new_foldFM_GE(wz9, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE1(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h)
12.91/5.23	   new_foldFM_GE1(wz9, False, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE(wz9, wz334, h)
12.91/5.23	   new_foldFM_GE1(wz9, True, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE0(wz331, new_foldFM_GE2(wz9, wz334, h), wz333, h)
12.91/5.23	   new_foldFM_GE0(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE1(:(wz31, wz6), wz330, wz331, wz332, wz333, wz334, h)
12.91/5.23	
12.91/5.23	The TRS R consists of the following rules:
12.91/5.23	
12.91/5.23	   new_foldFM_GE2(wz9, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE10(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h)
12.91/5.23	   new_eltsFM_GE0(wz31, wz6, h) -> :(wz31, wz6)
12.91/5.23	   new_foldFM_GE10(wz9, True, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE3(wz331, new_foldFM_GE2(wz9, wz334, h), wz333, h)
12.91/5.23	   new_foldFM_GE10(wz9, False, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE2(wz9, wz334, h)
12.91/5.23	   new_foldFM_GE2(wz9, EmptyFM, h) -> wz9
12.91/5.23	   new_foldFM_GE3(wz31, wz6, EmptyFM, h) -> new_eltsFM_GE0(wz31, wz6, h)
12.91/5.23	   new_foldFM_GE3(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE10(new_eltsFM_GE0(wz31, wz6, h), wz330, wz331, wz332, wz333, wz334, h)
12.91/5.23	
12.91/5.23	The set Q consists of the following terms:
12.91/5.23	
12.91/5.23	   new_foldFM_GE10(x0, True, x1, x2, x3, x4, x5)
12.91/5.23	   new_foldFM_GE2(x0, Branch(x1, x2, x3, x4, x5), x6)
12.91/5.23	   new_eltsFM_GE0(x0, x1, x2)
12.91/5.23	   new_foldFM_GE10(x0, False, x1, x2, x3, x4, x5)
12.91/5.23	   new_foldFM_GE3(x0, x1, EmptyFM, x2)
12.91/5.23	   new_foldFM_GE2(x0, EmptyFM, x1)
12.91/5.23	   new_foldFM_GE3(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.91/5.23	
12.91/5.23	We have to consider all minimal (P,Q,R)-chains.
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(22) QDPSizeChangeProof (EQUIVALENT)
12.91/5.23	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. 
12.91/5.23	
12.91/5.23	From the DPs we obtained the following set of size-change graphs:
12.91/5.23	*new_foldFM_GE1(wz9, True, wz331, wz332, wz333, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE1(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h)
12.91/5.23	The graph contains the following edges 1 >= 1, 6 > 2, 6 > 3, 6 > 4, 6 > 5, 6 > 6, 7 >= 7
12.91/5.23	
12.91/5.23	
12.91/5.23	*new_foldFM_GE1(wz9, False, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE(wz9, wz334, h)
12.91/5.23	The graph contains the following edges 1 >= 1, 6 >= 2, 7 >= 3
12.91/5.23	
12.91/5.23	
12.91/5.23	*new_foldFM_GE1(wz9, True, wz331, wz332, wz333, wz334, h) -> new_foldFM_GE0(wz331, new_foldFM_GE2(wz9, wz334, h), wz333, h)
12.91/5.23	The graph contains the following edges 3 >= 1, 5 >= 3, 7 >= 4
12.91/5.23	
12.91/5.23	
12.91/5.23	*new_foldFM_GE(wz9, Branch(wz3340, wz3341, wz3342, wz3343, wz3344), h) -> new_foldFM_GE1(wz9, wz3340, wz3341, wz3342, wz3343, wz3344, h)
12.91/5.23	The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 7
12.91/5.23	
12.91/5.23	
12.91/5.23	*new_foldFM_GE0(wz31, wz6, Branch(wz330, wz331, wz332, wz333, wz334), h) -> new_foldFM_GE1(:(wz31, wz6), wz330, wz331, wz332, wz333, wz334, h)
12.91/5.23	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.91/5.23	
12.91/5.23	
12.91/5.23	----------------------------------------
12.91/5.23	
12.91/5.23	(23)
12.91/5.23	YES
13.20/5.28	EOF