10.29/4.64	YES
12.57/5.22	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
12.57/5.22	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.57/5.22	
12.57/5.22	
12.57/5.22	H-Termination with start terms of the given HASKELL could be proven:
12.57/5.22	
12.57/5.22	(0) HASKELL
12.57/5.22	(1) LR [EQUIVALENT, 0 ms]
12.57/5.22	(2) HASKELL
12.57/5.22	(3) BR [EQUIVALENT, 0 ms]
12.57/5.22	(4) HASKELL
12.57/5.22	(5) COR [EQUIVALENT, 0 ms]
12.57/5.22	(6) HASKELL
12.57/5.22	(7) Narrow [SOUND, 0 ms]
12.57/5.22	(8) AND
12.57/5.22	    (9) QDP
12.57/5.22	        (10) TransformationProof [EQUIVALENT, 0 ms]
12.57/5.22	        (11) QDP
12.57/5.22	        (12) TransformationProof [EQUIVALENT, 0 ms]
12.57/5.22	        (13) QDP
12.57/5.22	        (14) TransformationProof [EQUIVALENT, 0 ms]
12.57/5.22	        (15) QDP
12.57/5.22	        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.57/5.22	        (17) YES
12.57/5.22	    (18) QDP
12.57/5.22	        (19) TransformationProof [EQUIVALENT, 0 ms]
12.57/5.22	        (20) QDP
12.57/5.22	        (21) TransformationProof [EQUIVALENT, 0 ms]
12.57/5.22	        (22) QDP
12.57/5.22	        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.57/5.22	        (24) YES
12.57/5.22	    (25) QDP
12.57/5.22	        (26) DependencyGraphProof [EQUIVALENT, 0 ms]
12.57/5.22	        (27) AND
12.57/5.22	            (28) QDP
12.57/5.22	                (29) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.57/5.22	                (30) YES
12.57/5.22	            (31) QDP
12.57/5.22	                (32) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.57/5.22	                (33) YES
12.57/5.22	            (34) QDP
12.57/5.22	                (35) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.57/5.22	                (36) YES
12.57/5.22	    (37) QDP
12.57/5.22	        (38) TransformationProof [EQUIVALENT, 0 ms]
12.57/5.22	        (39) QDP
12.57/5.22	        (40) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.57/5.22	        (41) YES
12.57/5.22	
12.57/5.22	
12.57/5.22	----------------------------------------
12.57/5.22	
12.57/5.22	(0)
12.57/5.22	Obligation:
12.57/5.22	mainModule Main 
12.57/5.22	module FiniteMap where {
12.57/5.22	import qualified Main;
12.57/5.22	import qualified Maybe;
12.57/5.22	import qualified Prelude;
12.57/5.22	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.57/5.22	
12.57/5.22	eltsFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [b];
12.57/5.22	eltsFM_LE fm fr = foldFM_LE (\key elt rest ->elt : rest) [] fr fm;
12.57/5.22	
12.57/5.22	foldFM_LE :: Ord c => (c  ->  a  ->  b  ->  b)  ->  b  ->  c  ->  FiniteMap c a  ->  b;
12.57/5.22	foldFM_LE k z fr EmptyFM = z;
12.57/5.22	foldFM_LE k z fr (Branch key elt _ fm_l fm_r)  | key <= fr = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r
12.57/5.22	 | otherwise = foldFM_LE k z fr fm_l;
12.57/5.22	
12.57/5.22	}
12.57/5.22	module Maybe where {
12.57/5.22	import qualified FiniteMap;
12.57/5.22	import qualified Main;
12.57/5.22	import qualified Prelude;
12.57/5.22	}
12.57/5.22	module Main where {
12.57/5.22	import qualified FiniteMap;
12.57/5.22	import qualified Maybe;
12.57/5.22	import qualified Prelude;
12.57/5.22	}
12.57/5.22	
12.57/5.22	----------------------------------------
12.57/5.22	
12.57/5.22	(1) LR (EQUIVALENT)
12.57/5.22	Lambda Reductions:
12.57/5.22	The following Lambda expression
12.57/5.22	"\keyeltrest->elt : rest"
12.57/5.22	is transformed to
12.57/5.22	"eltsFM_LE0 key elt rest = elt : rest;
12.57/5.22	"
12.57/5.22	
12.57/5.22	----------------------------------------
12.57/5.22	
12.57/5.22	(2)
12.57/5.22	Obligation:
12.57/5.22	mainModule Main 
12.57/5.22	module FiniteMap where {
12.57/5.22	import qualified Main;
12.57/5.22	import qualified Maybe;
12.57/5.22	import qualified Prelude;
12.57/5.22	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.57/5.22	
12.57/5.22	eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a];
12.57/5.22	eltsFM_LE fm fr = foldFM_LE eltsFM_LE0 [] fr fm;
12.57/5.22	
12.57/5.22	eltsFM_LE0 key elt rest = elt : rest;
12.57/5.22	
12.57/5.22	foldFM_LE :: Ord a => (a  ->  b  ->  c  ->  c)  ->  c  ->  a  ->  FiniteMap a b  ->  c;
12.57/5.22	foldFM_LE k z fr EmptyFM = z;
12.57/5.22	foldFM_LE k z fr (Branch key elt _ fm_l fm_r)  | key <= fr = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r
12.57/5.22	 | otherwise = foldFM_LE k z fr fm_l;
12.57/5.22	
12.57/5.22	}
12.57/5.22	module Maybe where {
12.57/5.22	import qualified FiniteMap;
12.57/5.22	import qualified Main;
12.57/5.22	import qualified Prelude;
12.57/5.22	}
12.57/5.22	module Main where {
12.57/5.22	import qualified FiniteMap;
12.57/5.22	import qualified Maybe;
12.57/5.22	import qualified Prelude;
12.57/5.22	}
12.57/5.22	
12.57/5.22	----------------------------------------
12.57/5.22	
12.57/5.22	(3) BR (EQUIVALENT)
12.57/5.22	Replaced joker patterns by fresh variables and removed binding patterns.
12.57/5.22	----------------------------------------
12.57/5.22	
12.57/5.22	(4)
12.57/5.22	Obligation:
12.57/5.22	mainModule Main 
12.57/5.22	module FiniteMap where {
12.57/5.22	import qualified Main;
12.57/5.22	import qualified Maybe;
12.57/5.22	import qualified Prelude;
12.57/5.22	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.57/5.22	
12.57/5.22	eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a];
12.57/5.22	eltsFM_LE fm fr = foldFM_LE eltsFM_LE0 [] fr fm;
12.57/5.22	
12.57/5.22	eltsFM_LE0 key elt rest = elt : rest;
12.57/5.22	
12.57/5.22	foldFM_LE :: Ord a => (a  ->  c  ->  b  ->  b)  ->  b  ->  a  ->  FiniteMap a c  ->  b;
12.57/5.22	foldFM_LE k z fr EmptyFM = z;
12.57/5.22	foldFM_LE k z fr (Branch key elt vy fm_l fm_r)  | key <= fr = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r
12.57/5.22	 | otherwise = foldFM_LE k z fr fm_l;
12.57/5.22	
12.57/5.22	}
12.57/5.22	module Maybe where {
12.57/5.22	import qualified FiniteMap;
12.57/5.22	import qualified Main;
12.57/5.22	import qualified Prelude;
12.57/5.22	}
12.57/5.22	module Main where {
12.57/5.22	import qualified FiniteMap;
12.57/5.22	import qualified Maybe;
12.57/5.22	import qualified Prelude;
12.57/5.22	}
12.57/5.22	
12.57/5.22	----------------------------------------
12.57/5.22	
12.57/5.22	(5) COR (EQUIVALENT)
12.57/5.22	Cond Reductions:
12.57/5.22	The following Function with conditions
12.57/5.22	"undefined |Falseundefined;
12.57/5.22	"
12.57/5.22	is transformed to
12.57/5.22	"undefined  = undefined1;
12.57/5.22	"
12.57/5.22	"undefined0 True = undefined;
12.57/5.22	"
12.57/5.22	"undefined1  = undefined0 False;
12.57/5.22	"
12.57/5.22	The following Function with conditions
12.57/5.22	"foldFM_LE k z fr EmptyFM = z;
12.57/5.22	foldFM_LE k z fr (Branch key elt vy fm_l fm_r)|key <= frfoldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r|otherwisefoldFM_LE k z fr fm_l;
12.57/5.22	"
12.57/5.22	is transformed to
12.57/5.22	"foldFM_LE k z fr EmptyFM = foldFM_LE3 k z fr EmptyFM;
12.57/5.22	foldFM_LE k z fr (Branch key elt vy fm_l fm_r) = foldFM_LE2 k z fr (Branch key elt vy fm_l fm_r);
12.57/5.22	"
12.57/5.22	"foldFM_LE0 k z fr key elt vy fm_l fm_r True = foldFM_LE k z fr fm_l;
12.57/5.22	"
12.57/5.22	"foldFM_LE1 k z fr key elt vy fm_l fm_r True = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r;
12.57/5.22	foldFM_LE1 k z fr key elt vy fm_l fm_r False = foldFM_LE0 k z fr key elt vy fm_l fm_r otherwise;
12.57/5.22	"
12.57/5.22	"foldFM_LE2 k z fr (Branch key elt vy fm_l fm_r) = foldFM_LE1 k z fr key elt vy fm_l fm_r (key <= fr);
12.57/5.22	"
12.57/5.22	"foldFM_LE3 k z fr EmptyFM = z;
12.57/5.22	foldFM_LE3 wv ww wx wy = foldFM_LE2 wv ww wx wy;
12.57/5.22	"
12.57/5.22	
12.57/5.22	----------------------------------------
12.57/5.22	
12.57/5.22	(6)
12.57/5.22	Obligation:
12.57/5.22	mainModule Main 
12.57/5.22	module FiniteMap where {
12.57/5.22	import qualified Main;
12.57/5.22	import qualified Maybe;
12.57/5.22	import qualified Prelude;
12.57/5.22	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.57/5.22	
12.57/5.22	eltsFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [a];
12.57/5.22	eltsFM_LE fm fr = foldFM_LE eltsFM_LE0 [] fr fm;
12.57/5.22	
12.57/5.22	eltsFM_LE0 key elt rest = elt : rest;
12.57/5.22	
12.57/5.22	foldFM_LE :: Ord b => (b  ->  c  ->  a  ->  a)  ->  a  ->  b  ->  FiniteMap b c  ->  a;
12.57/5.22	foldFM_LE k z fr EmptyFM = foldFM_LE3 k z fr EmptyFM;
12.57/5.22	foldFM_LE k z fr (Branch key elt vy fm_l fm_r) = foldFM_LE2 k z fr (Branch key elt vy fm_l fm_r);
12.57/5.22	
12.57/5.22	foldFM_LE0 k z fr key elt vy fm_l fm_r True = foldFM_LE k z fr fm_l;
12.57/5.22	
12.57/5.22	foldFM_LE1 k z fr key elt vy fm_l fm_r True = foldFM_LE k (k key elt (foldFM_LE k z fr fm_l)) fr fm_r;
12.57/5.22	foldFM_LE1 k z fr key elt vy fm_l fm_r False = foldFM_LE0 k z fr key elt vy fm_l fm_r otherwise;
12.57/5.22	
12.57/5.22	foldFM_LE2 k z fr (Branch key elt vy fm_l fm_r) = foldFM_LE1 k z fr key elt vy fm_l fm_r (key <= fr);
12.57/5.22	
12.57/5.22	foldFM_LE3 k z fr EmptyFM = z;
12.57/5.22	foldFM_LE3 wv ww wx wy = foldFM_LE2 wv ww wx wy;
12.57/5.22	
12.57/5.22	}
12.57/5.22	module Maybe where {
12.57/5.22	import qualified FiniteMap;
12.57/5.22	import qualified Main;
12.57/5.22	import qualified Prelude;
12.57/5.22	}
12.57/5.22	module Main where {
12.57/5.22	import qualified FiniteMap;
12.57/5.22	import qualified Maybe;
12.57/5.22	import qualified Prelude;
12.57/5.22	}
12.57/5.22	
12.57/5.22	----------------------------------------
12.57/5.22	
12.57/5.22	(7) Narrow (SOUND)
12.57/5.22	Haskell To QDPs
12.57/5.22	
12.57/5.22	digraph dp_graph {
12.57/5.22	node [outthreshold=100, inthreshold=100];1[label="FiniteMap.eltsFM_LE",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
12.57/5.22	3[label="FiniteMap.eltsFM_LE wz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
12.57/5.22	4[label="FiniteMap.eltsFM_LE wz3 wz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
12.57/5.22	5[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 [] wz4 wz3",fontsize=16,color="burlywood",shape="triangle"];216[label="wz3/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];5 -> 216[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	216 -> 6[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	217[label="wz3/FiniteMap.Branch wz30 wz31 wz32 wz33 wz34",fontsize=10,color="white",style="solid",shape="box"];5 -> 217[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	217 -> 7[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	6[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 [] wz4 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
12.57/5.22	7[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 [] wz4 (FiniteMap.Branch wz30 wz31 wz32 wz33 wz34)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
12.57/5.22	8[label="FiniteMap.foldFM_LE3 FiniteMap.eltsFM_LE0 [] wz4 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
12.57/5.22	9[label="FiniteMap.foldFM_LE2 FiniteMap.eltsFM_LE0 [] wz4 (FiniteMap.Branch wz30 wz31 wz32 wz33 wz34)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
12.57/5.22	10[label="[]",fontsize=16,color="green",shape="box"];11[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] wz4 wz30 wz31 wz32 wz33 wz34 (wz30 <= wz4)",fontsize=16,color="burlywood",shape="box"];218[label="wz30/LT",fontsize=10,color="white",style="solid",shape="box"];11 -> 218[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	218 -> 12[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	219[label="wz30/EQ",fontsize=10,color="white",style="solid",shape="box"];11 -> 219[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	219 -> 13[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	220[label="wz30/GT",fontsize=10,color="white",style="solid",shape="box"];11 -> 220[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	220 -> 14[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	12[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] wz4 LT wz31 wz32 wz33 wz34 (LT <= wz4)",fontsize=16,color="burlywood",shape="box"];221[label="wz4/LT",fontsize=10,color="white",style="solid",shape="box"];12 -> 221[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	221 -> 15[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	222[label="wz4/EQ",fontsize=10,color="white",style="solid",shape="box"];12 -> 222[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	222 -> 16[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	223[label="wz4/GT",fontsize=10,color="white",style="solid",shape="box"];12 -> 223[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	223 -> 17[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	13[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] wz4 EQ wz31 wz32 wz33 wz34 (EQ <= wz4)",fontsize=16,color="burlywood",shape="box"];224[label="wz4/LT",fontsize=10,color="white",style="solid",shape="box"];13 -> 224[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	224 -> 18[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	225[label="wz4/EQ",fontsize=10,color="white",style="solid",shape="box"];13 -> 225[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	225 -> 19[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	226[label="wz4/GT",fontsize=10,color="white",style="solid",shape="box"];13 -> 226[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	226 -> 20[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	14[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] wz4 GT wz31 wz32 wz33 wz34 (GT <= wz4)",fontsize=16,color="burlywood",shape="box"];227[label="wz4/LT",fontsize=10,color="white",style="solid",shape="box"];14 -> 227[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	227 -> 21[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	228[label="wz4/EQ",fontsize=10,color="white",style="solid",shape="box"];14 -> 228[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	228 -> 22[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	229[label="wz4/GT",fontsize=10,color="white",style="solid",shape="box"];14 -> 229[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	229 -> 23[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	15[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] LT LT wz31 wz32 wz33 wz34 (LT <= LT)",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
12.57/5.22	16[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] EQ LT wz31 wz32 wz33 wz34 (LT <= EQ)",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
12.57/5.22	17[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] GT LT wz31 wz32 wz33 wz34 (LT <= GT)",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
12.57/5.22	18[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] LT EQ wz31 wz32 wz33 wz34 (EQ <= LT)",fontsize=16,color="black",shape="box"];18 -> 27[label="",style="solid", color="black", weight=3];
12.57/5.22	19[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] EQ EQ wz31 wz32 wz33 wz34 (EQ <= EQ)",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
12.57/5.22	20[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] GT EQ wz31 wz32 wz33 wz34 (EQ <= GT)",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
12.57/5.22	21[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] LT GT wz31 wz32 wz33 wz34 (GT <= LT)",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
12.57/5.22	22[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] EQ GT wz31 wz32 wz33 wz34 (GT <= EQ)",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
12.57/5.22	23[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] GT GT wz31 wz32 wz33 wz34 (GT <= GT)",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
12.57/5.22	24[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] LT LT wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
12.57/5.22	25[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] EQ LT wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
12.57/5.22	26[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] GT LT wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
12.57/5.22	27[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] LT EQ wz31 wz32 wz33 wz34 False",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
12.57/5.22	28[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] EQ EQ wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3];
12.57/5.22	29[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 [] GT EQ wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];29 -> 38[label="",style="solid", color="black", weight=3];
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12.57/5.22	111 -> 122[label="",style="dashed", color="red", weight=0];
12.57/5.22	111[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 EQ wz31 wz9) GT wz340 wz341 wz342 wz343 wz344 (wz340 <= GT)",fontsize=16,color="magenta"];111 -> 124[label="",style="dashed", color="magenta", weight=3];
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12.57/5.22	113 -> 122[label="",style="dashed", color="red", weight=0];
12.57/5.22	113[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 GT wz31 wz10) GT wz340 wz341 wz342 wz343 wz344 (wz340 <= GT)",fontsize=16,color="magenta"];113 -> 125[label="",style="dashed", color="magenta", weight=3];
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12.57/5.22	116[label="FiniteMap.eltsFM_LE0 LT wz31 wz5",fontsize=16,color="magenta"];115[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz11 LT wz340 wz341 wz342 wz343 wz344 (wz340 <= LT)",fontsize=16,color="burlywood",shape="triangle"];242[label="wz340/LT",fontsize=10,color="white",style="solid",shape="box"];115 -> 242[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	242 -> 129[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	243[label="wz340/EQ",fontsize=10,color="white",style="solid",shape="box"];115 -> 243[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	243 -> 130[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	244[label="wz340/GT",fontsize=10,color="white",style="solid",shape="box"];115 -> 244[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	244 -> 131[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	117[label="wz6",fontsize=16,color="green",shape="box"];119 -> 102[label="",style="dashed", color="red", weight=0];
12.57/5.22	119[label="FiniteMap.eltsFM_LE0 LT wz31 wz6",fontsize=16,color="magenta"];119 -> 132[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	118[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz12 EQ wz340 wz341 wz342 wz343 wz344 (wz340 <= EQ)",fontsize=16,color="burlywood",shape="triangle"];245[label="wz340/LT",fontsize=10,color="white",style="solid",shape="box"];118 -> 245[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	245 -> 133[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	246[label="wz340/EQ",fontsize=10,color="white",style="solid",shape="box"];118 -> 246[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	246 -> 134[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	247[label="wz340/GT",fontsize=10,color="white",style="solid",shape="box"];118 -> 247[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	247 -> 135[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	121[label="wz7",fontsize=16,color="green",shape="box"];123 -> 102[label="",style="dashed", color="red", weight=0];
12.57/5.22	123[label="FiniteMap.eltsFM_LE0 LT wz31 wz7",fontsize=16,color="magenta"];123 -> 136[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	122[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz13 GT wz340 wz341 wz342 wz343 wz344 (wz340 <= GT)",fontsize=16,color="burlywood",shape="triangle"];248[label="wz340/LT",fontsize=10,color="white",style="solid",shape="box"];122 -> 248[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	248 -> 137[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	249[label="wz340/EQ",fontsize=10,color="white",style="solid",shape="box"];122 -> 249[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	249 -> 138[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	250[label="wz340/GT",fontsize=10,color="white",style="solid",shape="box"];122 -> 250[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	250 -> 139[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	126[label="wz31 : wz8",fontsize=16,color="green",shape="box"];120 -> 108[label="",style="dashed", color="red", weight=0];
12.57/5.22	120[label="FiniteMap.eltsFM_LE0 EQ wz31 wz8",fontsize=16,color="magenta"];127[label="wz9",fontsize=16,color="green",shape="box"];124 -> 108[label="",style="dashed", color="red", weight=0];
12.57/5.22	124[label="FiniteMap.eltsFM_LE0 EQ wz31 wz9",fontsize=16,color="magenta"];124 -> 140[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	128[label="wz31 : wz10",fontsize=16,color="green",shape="box"];125 -> 112[label="",style="dashed", color="red", weight=0];
12.57/5.22	125[label="FiniteMap.eltsFM_LE0 GT wz31 wz10",fontsize=16,color="magenta"];129[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz11 LT LT wz341 wz342 wz343 wz344 (LT <= LT)",fontsize=16,color="black",shape="box"];129 -> 141[label="",style="solid", color="black", weight=3];
12.57/5.22	130[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz11 LT EQ wz341 wz342 wz343 wz344 (EQ <= LT)",fontsize=16,color="black",shape="box"];130 -> 142[label="",style="solid", color="black", weight=3];
12.57/5.22	131[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz11 LT GT wz341 wz342 wz343 wz344 (GT <= LT)",fontsize=16,color="black",shape="box"];131 -> 143[label="",style="solid", color="black", weight=3];
12.57/5.22	132[label="wz6",fontsize=16,color="green",shape="box"];133[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz12 EQ LT wz341 wz342 wz343 wz344 (LT <= EQ)",fontsize=16,color="black",shape="box"];133 -> 144[label="",style="solid", color="black", weight=3];
12.57/5.22	134[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz12 EQ EQ wz341 wz342 wz343 wz344 (EQ <= EQ)",fontsize=16,color="black",shape="box"];134 -> 145[label="",style="solid", color="black", weight=3];
12.57/5.22	135[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz12 EQ GT wz341 wz342 wz343 wz344 (GT <= EQ)",fontsize=16,color="black",shape="box"];135 -> 146[label="",style="solid", color="black", weight=3];
12.57/5.22	136[label="wz7",fontsize=16,color="green",shape="box"];137[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz13 GT LT wz341 wz342 wz343 wz344 (LT <= GT)",fontsize=16,color="black",shape="box"];137 -> 147[label="",style="solid", color="black", weight=3];
12.57/5.22	138[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz13 GT EQ wz341 wz342 wz343 wz344 (EQ <= GT)",fontsize=16,color="black",shape="box"];138 -> 148[label="",style="solid", color="black", weight=3];
12.57/5.22	139[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz13 GT GT wz341 wz342 wz343 wz344 (GT <= GT)",fontsize=16,color="black",shape="box"];139 -> 149[label="",style="solid", color="black", weight=3];
12.57/5.22	140[label="wz9",fontsize=16,color="green",shape="box"];141[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz11 LT LT wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];141 -> 150[label="",style="solid", color="black", weight=3];
12.57/5.22	142[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz11 LT EQ wz341 wz342 wz343 wz344 False",fontsize=16,color="black",shape="box"];142 -> 151[label="",style="solid", color="black", weight=3];
12.57/5.22	143[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz11 LT GT wz341 wz342 wz343 wz344 False",fontsize=16,color="black",shape="box"];143 -> 152[label="",style="solid", color="black", weight=3];
12.57/5.22	144[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz12 EQ LT wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];144 -> 153[label="",style="solid", color="black", weight=3];
12.57/5.22	145[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz12 EQ EQ wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];145 -> 154[label="",style="solid", color="black", weight=3];
12.57/5.22	146[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz12 EQ GT wz341 wz342 wz343 wz344 False",fontsize=16,color="black",shape="box"];146 -> 155[label="",style="solid", color="black", weight=3];
12.57/5.22	147[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz13 GT LT wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];147 -> 156[label="",style="solid", color="black", weight=3];
12.57/5.22	148[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz13 GT EQ wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];148 -> 157[label="",style="solid", color="black", weight=3];
12.57/5.22	149[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz13 GT GT wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];149 -> 158[label="",style="solid", color="black", weight=3];
12.57/5.22	150 -> 42[label="",style="dashed", color="red", weight=0];
12.57/5.22	150[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 LT wz341 (FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz11 LT wz343)) LT wz344",fontsize=16,color="magenta"];150 -> 159[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	150 -> 160[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	150 -> 161[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	151[label="FiniteMap.foldFM_LE0 FiniteMap.eltsFM_LE0 wz11 LT EQ wz341 wz342 wz343 wz344 otherwise",fontsize=16,color="black",shape="box"];151 -> 162[label="",style="solid", color="black", weight=3];
12.57/5.22	152[label="FiniteMap.foldFM_LE0 FiniteMap.eltsFM_LE0 wz11 LT GT wz341 wz342 wz343 wz344 otherwise",fontsize=16,color="black",shape="box"];152 -> 163[label="",style="solid", color="black", weight=3];
12.57/5.22	153 -> 44[label="",style="dashed", color="red", weight=0];
12.57/5.22	153[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 LT wz341 (FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz12 EQ wz343)) EQ wz344",fontsize=16,color="magenta"];153 -> 164[label="",style="dashed", color="magenta", weight=3];
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12.57/5.22	154[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 EQ wz341 (FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz12 EQ wz343)) EQ wz344",fontsize=16,color="magenta"];154 -> 167[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	154 -> 168[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	154 -> 169[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	155[label="FiniteMap.foldFM_LE0 FiniteMap.eltsFM_LE0 wz12 EQ GT wz341 wz342 wz343 wz344 otherwise",fontsize=16,color="black",shape="box"];155 -> 170[label="",style="solid", color="black", weight=3];
12.57/5.22	156 -> 46[label="",style="dashed", color="red", weight=0];
12.57/5.22	156[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 LT wz341 (FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz13 GT wz343)) GT wz344",fontsize=16,color="magenta"];156 -> 171[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	156 -> 172[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	156 -> 173[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	157 -> 51[label="",style="dashed", color="red", weight=0];
12.57/5.22	157[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 EQ wz341 (FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz13 GT wz343)) GT wz344",fontsize=16,color="magenta"];157 -> 174[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	157 -> 175[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	157 -> 176[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	158 -> 55[label="",style="dashed", color="red", weight=0];
12.57/5.22	158[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 (FiniteMap.eltsFM_LE0 GT wz341 (FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz13 GT wz343)) GT wz344",fontsize=16,color="magenta"];158 -> 177[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	158 -> 178[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	158 -> 179[label="",style="dashed", color="magenta", weight=3];
12.57/5.22	159[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz11 LT wz343",fontsize=16,color="burlywood",shape="triangle"];251[label="wz343/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];159 -> 251[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	251 -> 180[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	252[label="wz343/FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434",fontsize=10,color="white",style="solid",shape="box"];159 -> 252[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	252 -> 181[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	160[label="wz344",fontsize=16,color="green",shape="box"];161[label="wz341",fontsize=16,color="green",shape="box"];162[label="FiniteMap.foldFM_LE0 FiniteMap.eltsFM_LE0 wz11 LT EQ wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];162 -> 182[label="",style="solid", color="black", weight=3];
12.57/5.22	163[label="FiniteMap.foldFM_LE0 FiniteMap.eltsFM_LE0 wz11 LT GT wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];163 -> 183[label="",style="solid", color="black", weight=3];
12.57/5.22	164[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz12 EQ wz343",fontsize=16,color="burlywood",shape="triangle"];253[label="wz343/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];164 -> 253[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	253 -> 184[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	254[label="wz343/FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434",fontsize=10,color="white",style="solid",shape="box"];164 -> 254[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	254 -> 185[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	165[label="wz344",fontsize=16,color="green",shape="box"];166[label="wz341",fontsize=16,color="green",shape="box"];167[label="wz344",fontsize=16,color="green",shape="box"];168[label="wz341",fontsize=16,color="green",shape="box"];169 -> 164[label="",style="dashed", color="red", weight=0];
12.57/5.22	169[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz12 EQ wz343",fontsize=16,color="magenta"];170[label="FiniteMap.foldFM_LE0 FiniteMap.eltsFM_LE0 wz12 EQ GT wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];170 -> 186[label="",style="solid", color="black", weight=3];
12.57/5.22	171[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz13 GT wz343",fontsize=16,color="burlywood",shape="triangle"];255[label="wz343/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];171 -> 255[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	255 -> 187[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	256[label="wz343/FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434",fontsize=10,color="white",style="solid",shape="box"];171 -> 256[label="",style="solid", color="burlywood", weight=9];
12.57/5.22	256 -> 188[label="",style="solid", color="burlywood", weight=3];
12.57/5.22	172[label="wz344",fontsize=16,color="green",shape="box"];173[label="wz341",fontsize=16,color="green",shape="box"];174[label="wz344",fontsize=16,color="green",shape="box"];175 -> 171[label="",style="dashed", color="red", weight=0];
12.57/5.22	175[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz13 GT wz343",fontsize=16,color="magenta"];176[label="wz341",fontsize=16,color="green",shape="box"];177 -> 171[label="",style="dashed", color="red", weight=0];
12.57/5.22	177[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz13 GT wz343",fontsize=16,color="magenta"];178[label="wz344",fontsize=16,color="green",shape="box"];179[label="wz341",fontsize=16,color="green",shape="box"];180[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz11 LT FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];180 -> 189[label="",style="solid", color="black", weight=3];
12.57/5.23	181[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz11 LT (FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434)",fontsize=16,color="black",shape="box"];181 -> 190[label="",style="solid", color="black", weight=3];
12.57/5.23	182 -> 159[label="",style="dashed", color="red", weight=0];
12.57/5.23	182[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz11 LT wz343",fontsize=16,color="magenta"];183 -> 159[label="",style="dashed", color="red", weight=0];
12.57/5.23	183[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz11 LT wz343",fontsize=16,color="magenta"];184[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz12 EQ FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];184 -> 191[label="",style="solid", color="black", weight=3];
12.57/5.23	185[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz12 EQ (FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434)",fontsize=16,color="black",shape="box"];185 -> 192[label="",style="solid", color="black", weight=3];
12.57/5.23	186 -> 164[label="",style="dashed", color="red", weight=0];
12.57/5.23	186[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz12 EQ wz343",fontsize=16,color="magenta"];187[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz13 GT FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];187 -> 193[label="",style="solid", color="black", weight=3];
12.57/5.23	188[label="FiniteMap.foldFM_LE FiniteMap.eltsFM_LE0 wz13 GT (FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434)",fontsize=16,color="black",shape="box"];188 -> 194[label="",style="solid", color="black", weight=3];
12.57/5.23	189[label="FiniteMap.foldFM_LE3 FiniteMap.eltsFM_LE0 wz11 LT FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];189 -> 195[label="",style="solid", color="black", weight=3];
12.57/5.23	190[label="FiniteMap.foldFM_LE2 FiniteMap.eltsFM_LE0 wz11 LT (FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434)",fontsize=16,color="black",shape="box"];190 -> 196[label="",style="solid", color="black", weight=3];
12.57/5.23	191[label="FiniteMap.foldFM_LE3 FiniteMap.eltsFM_LE0 wz12 EQ FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];191 -> 197[label="",style="solid", color="black", weight=3];
12.57/5.23	192[label="FiniteMap.foldFM_LE2 FiniteMap.eltsFM_LE0 wz12 EQ (FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434)",fontsize=16,color="black",shape="box"];192 -> 198[label="",style="solid", color="black", weight=3];
12.57/5.23	193[label="FiniteMap.foldFM_LE3 FiniteMap.eltsFM_LE0 wz13 GT FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];193 -> 199[label="",style="solid", color="black", weight=3];
12.57/5.23	194[label="FiniteMap.foldFM_LE2 FiniteMap.eltsFM_LE0 wz13 GT (FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434)",fontsize=16,color="black",shape="box"];194 -> 200[label="",style="solid", color="black", weight=3];
12.57/5.23	195[label="wz11",fontsize=16,color="green",shape="box"];196 -> 115[label="",style="dashed", color="red", weight=0];
12.57/5.23	196[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz11 LT wz3430 wz3431 wz3432 wz3433 wz3434 (wz3430 <= LT)",fontsize=16,color="magenta"];196 -> 201[label="",style="dashed", color="magenta", weight=3];
12.57/5.23	196 -> 202[label="",style="dashed", color="magenta", weight=3];
12.57/5.23	196 -> 203[label="",style="dashed", color="magenta", weight=3];
12.57/5.23	196 -> 204[label="",style="dashed", color="magenta", weight=3];
12.57/5.23	196 -> 205[label="",style="dashed", color="magenta", weight=3];
12.57/5.23	197[label="wz12",fontsize=16,color="green",shape="box"];198 -> 118[label="",style="dashed", color="red", weight=0];
12.57/5.23	198[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz12 EQ wz3430 wz3431 wz3432 wz3433 wz3434 (wz3430 <= EQ)",fontsize=16,color="magenta"];198 -> 206[label="",style="dashed", color="magenta", weight=3];
12.57/5.23	198 -> 207[label="",style="dashed", color="magenta", weight=3];
12.57/5.23	198 -> 208[label="",style="dashed", color="magenta", weight=3];
12.57/5.23	198 -> 209[label="",style="dashed", color="magenta", weight=3];
12.57/5.23	198 -> 210[label="",style="dashed", color="magenta", weight=3];
12.57/5.23	199[label="wz13",fontsize=16,color="green",shape="box"];200 -> 122[label="",style="dashed", color="red", weight=0];
12.57/5.23	200[label="FiniteMap.foldFM_LE1 FiniteMap.eltsFM_LE0 wz13 GT wz3430 wz3431 wz3432 wz3433 wz3434 (wz3430 <= GT)",fontsize=16,color="magenta"];200 -> 211[label="",style="dashed", color="magenta", weight=3];
12.57/5.23	200 -> 212[label="",style="dashed", color="magenta", weight=3];
12.57/5.23	200 -> 213[label="",style="dashed", color="magenta", weight=3];
12.57/5.23	200 -> 214[label="",style="dashed", color="magenta", weight=3];
12.57/5.23	200 -> 215[label="",style="dashed", color="magenta", weight=3];
12.57/5.23	201[label="wz3432",fontsize=16,color="green",shape="box"];202[label="wz3434",fontsize=16,color="green",shape="box"];203[label="wz3431",fontsize=16,color="green",shape="box"];204[label="wz3430",fontsize=16,color="green",shape="box"];205[label="wz3433",fontsize=16,color="green",shape="box"];206[label="wz3432",fontsize=16,color="green",shape="box"];207[label="wz3434",fontsize=16,color="green",shape="box"];208[label="wz3431",fontsize=16,color="green",shape="box"];209[label="wz3430",fontsize=16,color="green",shape="box"];210[label="wz3433",fontsize=16,color="green",shape="box"];211[label="wz3432",fontsize=16,color="green",shape="box"];212[label="wz3434",fontsize=16,color="green",shape="box"];213[label="wz3431",fontsize=16,color="green",shape="box"];214[label="wz3430",fontsize=16,color="green",shape="box"];215[label="wz3433",fontsize=16,color="green",shape="box"];}
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(8)
12.57/5.23	Complex Obligation (AND)
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(9)
12.57/5.23	Obligation:
12.57/5.23	Q DP problem:
12.57/5.23	The TRS P consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE1(wz13, LT, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE1(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.57/5.23	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.57/5.23	   new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_eltsFM_LE01(wz31, wz10, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_eltsFM_LE0(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE3(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_eltsFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE1(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	
12.57/5.23	The TRS R consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE7(wz31, wz7, EmptyFM, h) -> new_eltsFM_LE0(wz31, wz7, h)
12.57/5.23	   new_foldFM_LE5(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE10(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE6(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_eltsFM_LE01(wz31, wz10, h) -> :(wz31, wz10)
12.57/5.23	   new_eltsFM_LE00(wz31, wz8, h) -> :(wz31, wz8)
12.57/5.23	   new_eltsFM_LE0(wz31, wz5, h) -> :(wz31, wz5)
12.57/5.23	   new_foldFM_LE10(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE5(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE0(wz13, EmptyFM, h) -> wz13
12.57/5.23	   new_foldFM_LE7(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE0(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE5(wz31, wz9, EmptyFM, h) -> new_eltsFM_LE00(wz31, wz9, h)
12.57/5.23	   new_foldFM_LE6(wz31, wz10, EmptyFM, h) -> new_eltsFM_LE01(wz31, wz10, h)
12.57/5.23	   new_foldFM_LE10(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE7(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE6(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE01(wz31, wz10, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE0(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE10(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	
12.57/5.23	The set Q consists of the following terms:
12.57/5.23	
12.57/5.23	   new_foldFM_LE7(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE7(x0, x1, EmptyFM, x2)
12.57/5.23	   new_eltsFM_LE01(x0, x1, x2)
12.57/5.23	   new_foldFM_LE10(x0, LT, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE0(x0, Branch(x1, x2, x3, x4, x5), x6)
12.57/5.23	   new_eltsFM_LE0(x0, x1, x2)
12.57/5.23	   new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE10(x0, EQ, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE6(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE5(x0, x1, EmptyFM, x2)
12.57/5.23	   new_eltsFM_LE00(x0, x1, x2)
12.57/5.23	   new_foldFM_LE6(x0, x1, EmptyFM, x2)
12.57/5.23	   new_foldFM_LE0(x0, EmptyFM, x1)
12.57/5.23	   new_foldFM_LE10(x0, GT, x1, x2, x3, x4, x5)
12.57/5.23	
12.57/5.23	We have to consider all minimal (P,Q,R)-chains.
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(10) TransformationProof (EQUIVALENT)
12.57/5.23	By rewriting [LPAR04] the rule new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_eltsFM_LE01(wz31, wz10, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]:
12.57/5.23	
12.57/5.23	   (new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz10), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz10), wz340, wz341, wz342, wz343, wz344, h))
12.57/5.23	
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(11)
12.57/5.23	Obligation:
12.57/5.23	Q DP problem:
12.57/5.23	The TRS P consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE1(wz13, LT, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE1(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.57/5.23	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.57/5.23	   new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_eltsFM_LE0(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE3(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_eltsFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE1(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz10), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	
12.57/5.23	The TRS R consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE7(wz31, wz7, EmptyFM, h) -> new_eltsFM_LE0(wz31, wz7, h)
12.57/5.23	   new_foldFM_LE5(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE10(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE6(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_eltsFM_LE01(wz31, wz10, h) -> :(wz31, wz10)
12.57/5.23	   new_eltsFM_LE00(wz31, wz8, h) -> :(wz31, wz8)
12.57/5.23	   new_eltsFM_LE0(wz31, wz5, h) -> :(wz31, wz5)
12.57/5.23	   new_foldFM_LE10(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE5(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE0(wz13, EmptyFM, h) -> wz13
12.57/5.23	   new_foldFM_LE7(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE0(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE5(wz31, wz9, EmptyFM, h) -> new_eltsFM_LE00(wz31, wz9, h)
12.57/5.23	   new_foldFM_LE6(wz31, wz10, EmptyFM, h) -> new_eltsFM_LE01(wz31, wz10, h)
12.57/5.23	   new_foldFM_LE10(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE7(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE6(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE01(wz31, wz10, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE0(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE10(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	
12.57/5.23	The set Q consists of the following terms:
12.57/5.23	
12.57/5.23	   new_foldFM_LE7(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE7(x0, x1, EmptyFM, x2)
12.57/5.23	   new_eltsFM_LE01(x0, x1, x2)
12.57/5.23	   new_foldFM_LE10(x0, LT, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE0(x0, Branch(x1, x2, x3, x4, x5), x6)
12.57/5.23	   new_eltsFM_LE0(x0, x1, x2)
12.57/5.23	   new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE10(x0, EQ, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE6(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE5(x0, x1, EmptyFM, x2)
12.57/5.23	   new_eltsFM_LE00(x0, x1, x2)
12.57/5.23	   new_foldFM_LE6(x0, x1, EmptyFM, x2)
12.57/5.23	   new_foldFM_LE0(x0, EmptyFM, x1)
12.57/5.23	   new_foldFM_LE10(x0, GT, x1, x2, x3, x4, x5)
12.57/5.23	
12.57/5.23	We have to consider all minimal (P,Q,R)-chains.
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(12) TransformationProof (EQUIVALENT)
12.57/5.23	By rewriting [LPAR04] the rule new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_eltsFM_LE0(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]:
12.57/5.23	
12.57/5.23	   (new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz7), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz7), wz340, wz341, wz342, wz343, wz344, h))
12.57/5.23	
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(13)
12.57/5.23	Obligation:
12.57/5.23	Q DP problem:
12.57/5.23	The TRS P consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE1(wz13, LT, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE1(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.57/5.23	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.57/5.23	   new_foldFM_LE3(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_eltsFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE1(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz10), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz7), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	
12.57/5.23	The TRS R consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE7(wz31, wz7, EmptyFM, h) -> new_eltsFM_LE0(wz31, wz7, h)
12.57/5.23	   new_foldFM_LE5(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE10(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE6(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_eltsFM_LE01(wz31, wz10, h) -> :(wz31, wz10)
12.57/5.23	   new_eltsFM_LE00(wz31, wz8, h) -> :(wz31, wz8)
12.57/5.23	   new_eltsFM_LE0(wz31, wz5, h) -> :(wz31, wz5)
12.57/5.23	   new_foldFM_LE10(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE5(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE0(wz13, EmptyFM, h) -> wz13
12.57/5.23	   new_foldFM_LE7(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE0(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE5(wz31, wz9, EmptyFM, h) -> new_eltsFM_LE00(wz31, wz9, h)
12.57/5.23	   new_foldFM_LE6(wz31, wz10, EmptyFM, h) -> new_eltsFM_LE01(wz31, wz10, h)
12.57/5.23	   new_foldFM_LE10(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE7(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE6(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE01(wz31, wz10, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE0(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE10(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	
12.57/5.23	The set Q consists of the following terms:
12.57/5.23	
12.57/5.23	   new_foldFM_LE7(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE7(x0, x1, EmptyFM, x2)
12.57/5.23	   new_eltsFM_LE01(x0, x1, x2)
12.57/5.23	   new_foldFM_LE10(x0, LT, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE0(x0, Branch(x1, x2, x3, x4, x5), x6)
12.57/5.23	   new_eltsFM_LE0(x0, x1, x2)
12.57/5.23	   new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE10(x0, EQ, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE6(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE5(x0, x1, EmptyFM, x2)
12.57/5.23	   new_eltsFM_LE00(x0, x1, x2)
12.57/5.23	   new_foldFM_LE6(x0, x1, EmptyFM, x2)
12.57/5.23	   new_foldFM_LE0(x0, EmptyFM, x1)
12.57/5.23	   new_foldFM_LE10(x0, GT, x1, x2, x3, x4, x5)
12.57/5.23	
12.57/5.23	We have to consider all minimal (P,Q,R)-chains.
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(14) TransformationProof (EQUIVALENT)
12.57/5.23	By rewriting [LPAR04] the rule new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_eltsFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]:
12.57/5.23	
12.57/5.23	   (new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz9), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz9), wz340, wz341, wz342, wz343, wz344, h))
12.57/5.23	
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(15)
12.57/5.23	Obligation:
12.57/5.23	Q DP problem:
12.57/5.23	The TRS P consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE1(wz13, LT, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE1(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.57/5.23	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.57/5.23	   new_foldFM_LE3(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE1(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz10), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz7), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz9), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	
12.57/5.23	The TRS R consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE7(wz31, wz7, EmptyFM, h) -> new_eltsFM_LE0(wz31, wz7, h)
12.57/5.23	   new_foldFM_LE5(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE10(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE6(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_eltsFM_LE01(wz31, wz10, h) -> :(wz31, wz10)
12.57/5.23	   new_eltsFM_LE00(wz31, wz8, h) -> :(wz31, wz8)
12.57/5.23	   new_eltsFM_LE0(wz31, wz5, h) -> :(wz31, wz5)
12.57/5.23	   new_foldFM_LE10(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE5(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE0(wz13, EmptyFM, h) -> wz13
12.57/5.23	   new_foldFM_LE7(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE0(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE5(wz31, wz9, EmptyFM, h) -> new_eltsFM_LE00(wz31, wz9, h)
12.57/5.23	   new_foldFM_LE6(wz31, wz10, EmptyFM, h) -> new_eltsFM_LE01(wz31, wz10, h)
12.57/5.23	   new_foldFM_LE10(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE7(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE6(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_eltsFM_LE01(wz31, wz10, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE0(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE10(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	
12.57/5.23	The set Q consists of the following terms:
12.57/5.23	
12.57/5.23	   new_foldFM_LE7(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE7(x0, x1, EmptyFM, x2)
12.57/5.23	   new_eltsFM_LE01(x0, x1, x2)
12.57/5.23	   new_foldFM_LE10(x0, LT, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE0(x0, Branch(x1, x2, x3, x4, x5), x6)
12.57/5.23	   new_eltsFM_LE0(x0, x1, x2)
12.57/5.23	   new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE10(x0, EQ, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE6(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE5(x0, x1, EmptyFM, x2)
12.57/5.23	   new_eltsFM_LE00(x0, x1, x2)
12.57/5.23	   new_foldFM_LE6(x0, x1, EmptyFM, x2)
12.57/5.23	   new_foldFM_LE0(x0, EmptyFM, x1)
12.57/5.23	   new_foldFM_LE10(x0, GT, x1, x2, x3, x4, x5)
12.57/5.23	
12.57/5.23	We have to consider all minimal (P,Q,R)-chains.
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(16) QDPSizeChangeProof (EQUIVALENT)
12.57/5.23	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. 
12.57/5.23	
12.57/5.23	From the DPs we obtained the following set of size-change graphs:
12.57/5.23	*new_foldFM_LE1(wz13, LT, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE1(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 5 > 6, 7 >= 7
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE3(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 7
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz9), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz10), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(wz31, wz7), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE1(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.57/5.23	The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3
12.57/5.23	
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(17)
12.57/5.23	YES
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(18)
12.57/5.23	Obligation:
12.57/5.23	Q DP problem:
12.57/5.23	The TRS P consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE8(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(new_eltsFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.57/5.23	   new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE12(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE11(wz12, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.57/5.23	   new_foldFM_LE13(wz12, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE11(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE11(wz12, LT, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE11(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE11(wz12, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE8(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE12(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(new_eltsFM_LE00(wz31, wz8, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	
12.57/5.23	The TRS R consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE14(wz12, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE9(wz12, wz343, h)
12.57/5.23	   new_eltsFM_LE0(wz31, wz5, h) -> :(wz31, wz5)
12.57/5.23	   new_foldFM_LE9(wz12, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE14(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE15(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE14(new_eltsFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE16(wz31, wz8, EmptyFM, h) -> new_eltsFM_LE00(wz31, wz8, h)
12.57/5.23	   new_foldFM_LE15(wz31, wz6, EmptyFM, h) -> new_eltsFM_LE0(wz31, wz6, h)
12.57/5.23	   new_foldFM_LE16(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE14(new_eltsFM_LE00(wz31, wz8, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE14(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE16(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.57/5.23	   new_eltsFM_LE00(wz31, wz8, h) -> :(wz31, wz8)
12.57/5.23	   new_foldFM_LE14(wz12, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE15(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE9(wz12, EmptyFM, h) -> wz12
12.57/5.23	
12.57/5.23	The set Q consists of the following terms:
12.57/5.23	
12.57/5.23	   new_foldFM_LE9(x0, Branch(x1, x2, x3, x4, x5), x6)
12.57/5.23	   new_foldFM_LE16(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE14(x0, GT, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE14(x0, EQ, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE16(x0, x1, EmptyFM, x2)
12.57/5.23	   new_eltsFM_LE00(x0, x1, x2)
12.57/5.23	   new_foldFM_LE14(x0, LT, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE15(x0, x1, EmptyFM, x2)
12.57/5.23	   new_foldFM_LE9(x0, EmptyFM, x1)
12.57/5.23	   new_eltsFM_LE0(x0, x1, x2)
12.57/5.23	   new_foldFM_LE15(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	
12.57/5.23	We have to consider all minimal (P,Q,R)-chains.
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(19) TransformationProof (EQUIVALENT)
12.57/5.23	By rewriting [LPAR04] the rule new_foldFM_LE8(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(new_eltsFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]:
12.57/5.23	
12.57/5.23	   (new_foldFM_LE8(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(wz31, wz6), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE8(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(wz31, wz6), wz340, wz341, wz342, wz343, wz344, h))
12.57/5.23	
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(20)
12.57/5.23	Obligation:
12.57/5.23	Q DP problem:
12.57/5.23	The TRS P consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.57/5.23	   new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE12(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE11(wz12, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.57/5.23	   new_foldFM_LE13(wz12, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE11(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE11(wz12, LT, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE11(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE11(wz12, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE8(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE12(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(new_eltsFM_LE00(wz31, wz8, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE8(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(wz31, wz6), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	
12.57/5.23	The TRS R consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE14(wz12, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE9(wz12, wz343, h)
12.57/5.23	   new_eltsFM_LE0(wz31, wz5, h) -> :(wz31, wz5)
12.57/5.23	   new_foldFM_LE9(wz12, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE14(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE15(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE14(new_eltsFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE16(wz31, wz8, EmptyFM, h) -> new_eltsFM_LE00(wz31, wz8, h)
12.57/5.23	   new_foldFM_LE15(wz31, wz6, EmptyFM, h) -> new_eltsFM_LE0(wz31, wz6, h)
12.57/5.23	   new_foldFM_LE16(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE14(new_eltsFM_LE00(wz31, wz8, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE14(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE16(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.57/5.23	   new_eltsFM_LE00(wz31, wz8, h) -> :(wz31, wz8)
12.57/5.23	   new_foldFM_LE14(wz12, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE15(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE9(wz12, EmptyFM, h) -> wz12
12.57/5.23	
12.57/5.23	The set Q consists of the following terms:
12.57/5.23	
12.57/5.23	   new_foldFM_LE9(x0, Branch(x1, x2, x3, x4, x5), x6)
12.57/5.23	   new_foldFM_LE16(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE14(x0, GT, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE14(x0, EQ, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE16(x0, x1, EmptyFM, x2)
12.57/5.23	   new_eltsFM_LE00(x0, x1, x2)
12.57/5.23	   new_foldFM_LE14(x0, LT, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE15(x0, x1, EmptyFM, x2)
12.57/5.23	   new_foldFM_LE9(x0, EmptyFM, x1)
12.57/5.23	   new_eltsFM_LE0(x0, x1, x2)
12.57/5.23	   new_foldFM_LE15(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	
12.57/5.23	We have to consider all minimal (P,Q,R)-chains.
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(21) TransformationProof (EQUIVALENT)
12.57/5.23	By rewriting [LPAR04] the rule new_foldFM_LE12(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(new_eltsFM_LE00(wz31, wz8, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]:
12.57/5.23	
12.57/5.23	   (new_foldFM_LE12(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(wz31, wz8), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE12(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(wz31, wz8), wz340, wz341, wz342, wz343, wz344, h))
12.57/5.23	
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(22)
12.57/5.23	Obligation:
12.57/5.23	Q DP problem:
12.57/5.23	The TRS P consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.57/5.23	   new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE12(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE11(wz12, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.57/5.23	   new_foldFM_LE13(wz12, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE11(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE11(wz12, LT, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE11(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE11(wz12, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE8(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE8(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(wz31, wz6), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE12(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(wz31, wz8), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	
12.57/5.23	The TRS R consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE14(wz12, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE9(wz12, wz343, h)
12.57/5.23	   new_eltsFM_LE0(wz31, wz5, h) -> :(wz31, wz5)
12.57/5.23	   new_foldFM_LE9(wz12, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE14(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE15(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE14(new_eltsFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE16(wz31, wz8, EmptyFM, h) -> new_eltsFM_LE00(wz31, wz8, h)
12.57/5.23	   new_foldFM_LE15(wz31, wz6, EmptyFM, h) -> new_eltsFM_LE0(wz31, wz6, h)
12.57/5.23	   new_foldFM_LE16(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE14(new_eltsFM_LE00(wz31, wz8, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE14(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE16(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.57/5.23	   new_eltsFM_LE00(wz31, wz8, h) -> :(wz31, wz8)
12.57/5.23	   new_foldFM_LE14(wz12, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE15(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE9(wz12, EmptyFM, h) -> wz12
12.57/5.23	
12.57/5.23	The set Q consists of the following terms:
12.57/5.23	
12.57/5.23	   new_foldFM_LE9(x0, Branch(x1, x2, x3, x4, x5), x6)
12.57/5.23	   new_foldFM_LE16(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE14(x0, GT, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE14(x0, EQ, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE16(x0, x1, EmptyFM, x2)
12.57/5.23	   new_eltsFM_LE00(x0, x1, x2)
12.57/5.23	   new_foldFM_LE14(x0, LT, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE15(x0, x1, EmptyFM, x2)
12.57/5.23	   new_foldFM_LE9(x0, EmptyFM, x1)
12.57/5.23	   new_eltsFM_LE0(x0, x1, x2)
12.57/5.23	   new_foldFM_LE15(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	
12.57/5.23	We have to consider all minimal (P,Q,R)-chains.
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(23) QDPSizeChangeProof (EQUIVALENT)
12.57/5.23	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. 
12.57/5.23	
12.57/5.23	From the DPs we obtained the following set of size-change graphs:
12.57/5.23	*new_foldFM_LE13(wz12, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE11(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 7
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE12(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(wz31, wz8), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE11(wz12, LT, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE11(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 5 > 6, 7 >= 7
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE8(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(wz31, wz6), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE11(wz12, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE8(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.57/5.23	The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE12(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.57/5.23	The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE11(wz12, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3
12.57/5.23	
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(24)
12.57/5.23	YES
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(25)
12.57/5.23	Obligation:
12.57/5.23	Q DP problem:
12.57/5.23	The TRS P consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE22(EQ, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.57/5.23	   new_foldFM_LE22(EQ, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.57/5.23	   new_foldFM_LE22(LT, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.57/5.23	   new_foldFM_LE22(LT, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.57/5.23	   new_foldFM_LE22(GT, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.57/5.23	   new_foldFM_LE22(GT, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.57/5.23	   new_foldFM_LE22(EQ, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.57/5.23	   new_foldFM_LE22(LT, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.57/5.23	   new_foldFM_LE22(GT, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.57/5.23	
12.57/5.23	R is empty.
12.57/5.23	Q is empty.
12.57/5.23	We have to consider all minimal (P,Q,R)-chains.
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(26) DependencyGraphProof (EQUIVALENT)
12.57/5.23	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs.
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(27)
12.57/5.23	Complex Obligation (AND)
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(28)
12.57/5.23	Obligation:
12.57/5.23	Q DP problem:
12.57/5.23	The TRS P consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE22(GT, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.57/5.23	   new_foldFM_LE22(GT, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.57/5.23	   new_foldFM_LE22(GT, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.57/5.23	
12.57/5.23	R is empty.
12.57/5.23	Q is empty.
12.57/5.23	We have to consider all minimal (P,Q,R)-chains.
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(29) QDPSizeChangeProof (EQUIVALENT)
12.57/5.23	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. 
12.57/5.23	
12.57/5.23	From the DPs we obtained the following set of size-change graphs:
12.57/5.23	*new_foldFM_LE22(GT, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE22(GT, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 2 > 1, 2 > 2, 3 >= 3
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE22(GT, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.57/5.23	
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(30)
12.57/5.23	YES
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(31)
12.57/5.23	Obligation:
12.57/5.23	Q DP problem:
12.57/5.23	The TRS P consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE22(LT, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.57/5.23	   new_foldFM_LE22(LT, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.57/5.23	   new_foldFM_LE22(LT, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.57/5.23	
12.57/5.23	R is empty.
12.57/5.23	Q is empty.
12.57/5.23	We have to consider all minimal (P,Q,R)-chains.
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(32) QDPSizeChangeProof (EQUIVALENT)
12.57/5.23	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. 
12.57/5.23	
12.57/5.23	From the DPs we obtained the following set of size-change graphs:
12.57/5.23	*new_foldFM_LE22(LT, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE22(LT, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 2 > 1, 2 > 2, 3 >= 3
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE22(LT, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.57/5.23	
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(33)
12.57/5.23	YES
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(34)
12.57/5.23	Obligation:
12.57/5.23	Q DP problem:
12.57/5.23	The TRS P consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE22(EQ, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.57/5.23	   new_foldFM_LE22(EQ, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.57/5.23	   new_foldFM_LE22(EQ, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.57/5.23	
12.57/5.23	R is empty.
12.57/5.23	Q is empty.
12.57/5.23	We have to consider all minimal (P,Q,R)-chains.
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(35) QDPSizeChangeProof (EQUIVALENT)
12.57/5.23	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. 
12.57/5.23	
12.57/5.23	From the DPs we obtained the following set of size-change graphs:
12.57/5.23	*new_foldFM_LE22(EQ, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE22(EQ, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE22(EQ, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 2 > 1, 2 > 2, 3 >= 3
12.57/5.23	
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(36)
12.57/5.23	YES
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(37)
12.57/5.23	Obligation:
12.57/5.23	Q DP problem:
12.57/5.23	The TRS P consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE18(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE17(new_eltsFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE17(wz11, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE20(wz11, wz343, h)
12.57/5.23	   new_foldFM_LE17(wz11, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE18(wz341, new_foldFM_LE19(wz11, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE20(wz11, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE17(wz11, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE17(wz11, LT, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE17(wz11, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE17(wz11, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE20(wz11, wz343, h)
12.57/5.23	
12.57/5.23	The TRS R consists of the following rules:
12.57/5.23	
12.57/5.23	   new_eltsFM_LE0(wz31, wz5, h) -> :(wz31, wz5)
12.57/5.23	   new_foldFM_LE110(wz11, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE21(wz341, new_foldFM_LE19(wz11, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE19(wz11, EmptyFM, h) -> wz11
12.57/5.23	   new_foldFM_LE110(wz11, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE19(wz11, wz343, h)
12.57/5.23	   new_foldFM_LE19(wz11, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE110(wz11, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE21(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE110(new_eltsFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE21(wz31, wz5, EmptyFM, h) -> new_eltsFM_LE0(wz31, wz5, h)
12.57/5.23	   new_foldFM_LE110(wz11, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE19(wz11, wz343, h)
12.57/5.23	
12.57/5.23	The set Q consists of the following terms:
12.57/5.23	
12.57/5.23	   new_foldFM_LE19(x0, EmptyFM, x1)
12.57/5.23	   new_foldFM_LE110(x0, LT, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE110(x0, EQ, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE110(x0, GT, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE21(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE19(x0, Branch(x1, x2, x3, x4, x5), x6)
12.57/5.23	   new_eltsFM_LE0(x0, x1, x2)
12.57/5.23	   new_foldFM_LE21(x0, x1, EmptyFM, x2)
12.57/5.23	
12.57/5.23	We have to consider all minimal (P,Q,R)-chains.
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(38) TransformationProof (EQUIVALENT)
12.57/5.23	By rewriting [LPAR04] the rule new_foldFM_LE18(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE17(new_eltsFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]:
12.57/5.23	
12.57/5.23	   (new_foldFM_LE18(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE17(:(wz31, wz5), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE18(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE17(:(wz31, wz5), wz340, wz341, wz342, wz343, wz344, h))
12.57/5.23	
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(39)
12.57/5.23	Obligation:
12.57/5.23	Q DP problem:
12.57/5.23	The TRS P consists of the following rules:
12.57/5.23	
12.57/5.23	   new_foldFM_LE17(wz11, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE20(wz11, wz343, h)
12.57/5.23	   new_foldFM_LE17(wz11, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE18(wz341, new_foldFM_LE19(wz11, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE20(wz11, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE17(wz11, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE17(wz11, LT, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE17(wz11, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE17(wz11, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE20(wz11, wz343, h)
12.57/5.23	   new_foldFM_LE18(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE17(:(wz31, wz5), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	
12.57/5.23	The TRS R consists of the following rules:
12.57/5.23	
12.57/5.23	   new_eltsFM_LE0(wz31, wz5, h) -> :(wz31, wz5)
12.57/5.23	   new_foldFM_LE110(wz11, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE21(wz341, new_foldFM_LE19(wz11, wz343, h), wz344, h)
12.57/5.23	   new_foldFM_LE19(wz11, EmptyFM, h) -> wz11
12.57/5.23	   new_foldFM_LE110(wz11, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE19(wz11, wz343, h)
12.57/5.23	   new_foldFM_LE19(wz11, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE110(wz11, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	   new_foldFM_LE21(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE110(new_eltsFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	   new_foldFM_LE21(wz31, wz5, EmptyFM, h) -> new_eltsFM_LE0(wz31, wz5, h)
12.57/5.23	   new_foldFM_LE110(wz11, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE19(wz11, wz343, h)
12.57/5.23	
12.57/5.23	The set Q consists of the following terms:
12.57/5.23	
12.57/5.23	   new_foldFM_LE19(x0, EmptyFM, x1)
12.57/5.23	   new_foldFM_LE110(x0, LT, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE110(x0, EQ, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE110(x0, GT, x1, x2, x3, x4, x5)
12.57/5.23	   new_foldFM_LE21(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.57/5.23	   new_foldFM_LE19(x0, Branch(x1, x2, x3, x4, x5), x6)
12.57/5.23	   new_eltsFM_LE0(x0, x1, x2)
12.57/5.23	   new_foldFM_LE21(x0, x1, EmptyFM, x2)
12.57/5.23	
12.57/5.23	We have to consider all minimal (P,Q,R)-chains.
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(40) QDPSizeChangeProof (EQUIVALENT)
12.57/5.23	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. 
12.57/5.23	
12.57/5.23	From the DPs we obtained the following set of size-change graphs:
12.57/5.23	*new_foldFM_LE20(wz11, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE17(wz11, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 7
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE18(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE17(:(wz31, wz5), wz340, wz341, wz342, wz343, wz344, h)
12.57/5.23	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE17(wz11, LT, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE17(wz11, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 5 > 6, 7 >= 7
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE17(wz11, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE18(wz341, new_foldFM_LE19(wz11, wz343, h), wz344, h)
12.57/5.23	The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE17(wz11, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE20(wz11, wz343, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3
12.57/5.23	
12.57/5.23	
12.57/5.23	*new_foldFM_LE17(wz11, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE20(wz11, wz343, h)
12.57/5.23	The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3
12.57/5.23	
12.57/5.23	
12.57/5.23	----------------------------------------
12.57/5.23	
12.57/5.23	(41)
12.57/5.23	YES
12.57/5.26	EOF