10.43/4.64	YES
12.34/5.20	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.34/5.20	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.34/5.20	
12.34/5.20	
12.34/5.20	H-Termination with start terms of the given HASKELL could be proven:
12.34/5.20	
12.34/5.20	(0) HASKELL
12.34/5.20	(1) LR [EQUIVALENT, 0 ms]
12.34/5.20	(2) HASKELL
12.34/5.20	(3) BR [EQUIVALENT, 0 ms]
12.34/5.20	(4) HASKELL
12.34/5.20	(5) COR [EQUIVALENT, 0 ms]
12.34/5.20	(6) HASKELL
12.34/5.20	(7) Narrow [SOUND, 0 ms]
12.34/5.20	(8) AND
12.34/5.20	    (9) QDP
12.34/5.20	        (10) TransformationProof [EQUIVALENT, 0 ms]
12.34/5.20	        (11) QDP
12.34/5.20	        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.34/5.20	        (13) YES
12.34/5.20	    (14) QDP
12.34/5.20	        (15) TransformationProof [EQUIVALENT, 0 ms]
12.34/5.20	        (16) QDP
12.34/5.20	        (17) TransformationProof [EQUIVALENT, 0 ms]
12.34/5.20	        (18) QDP
12.34/5.20	        (19) TransformationProof [EQUIVALENT, 0 ms]
12.34/5.20	        (20) QDP
12.34/5.20	        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.34/5.20	        (22) YES
12.34/5.20	    (23) QDP
12.34/5.20	        (24) DependencyGraphProof [EQUIVALENT, 0 ms]
12.34/5.20	        (25) AND
12.34/5.20	            (26) QDP
12.34/5.20	                (27) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.34/5.20	                (28) YES
12.34/5.20	            (29) QDP
12.34/5.20	                (30) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.34/5.20	                (31) YES
12.34/5.20	            (32) QDP
12.34/5.20	                (33) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.34/5.20	                (34) YES
12.34/5.20	    (35) QDP
12.34/5.20	        (36) TransformationProof [EQUIVALENT, 0 ms]
12.34/5.20	        (37) QDP
12.34/5.20	        (38) TransformationProof [EQUIVALENT, 0 ms]
12.34/5.20	        (39) QDP
12.34/5.20	        (40) QDPSizeChangeProof [EQUIVALENT, 1 ms]
12.34/5.20	        (41) YES
12.34/5.20	
12.34/5.20	
12.34/5.20	----------------------------------------
12.34/5.20	
12.34/5.20	(0)
12.34/5.20	Obligation:
12.34/5.20	mainModule Main 
12.34/5.20	module FiniteMap where {
12.34/5.20	import qualified Main;
12.34/5.20	import qualified Maybe;
12.34/5.20	import qualified Prelude;
12.34/5.20	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.34/5.20	
12.34/5.20	foldFM_LE :: Ord a => (a  ->  c  ->  b  ->  b)  ->  b  ->  a  ->  FiniteMap a c  ->  b;
12.34/5.20	foldFM_LE k z fr EmptyFM = z;
12.34/5.20	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
12.34/5.20	 | otherwise = foldFM_LE k z fr fm_l;
12.34/5.20	
12.34/5.20	keysFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [a];
12.34/5.20	keysFM_LE fm fr = foldFM_LE (\key elt rest ->key : rest) [] fr fm;
12.34/5.20	
12.34/5.20	}
12.34/5.20	module Maybe where {
12.34/5.20	import qualified FiniteMap;
12.34/5.20	import qualified Main;
12.34/5.20	import qualified Prelude;
12.34/5.20	}
12.34/5.20	module Main where {
12.34/5.20	import qualified FiniteMap;
12.34/5.20	import qualified Maybe;
12.34/5.20	import qualified Prelude;
12.34/5.20	}
12.34/5.20	
12.34/5.20	----------------------------------------
12.34/5.20	
12.34/5.20	(1) LR (EQUIVALENT)
12.34/5.20	Lambda Reductions:
12.34/5.20	The following Lambda expression
12.34/5.20	"\keyeltrest->key : rest"
12.34/5.20	is transformed to
12.34/5.20	"keysFM_LE0 key elt rest = key : rest;
12.34/5.20	"
12.34/5.20	
12.34/5.20	----------------------------------------
12.34/5.20	
12.34/5.20	(2)
12.34/5.20	Obligation:
12.34/5.20	mainModule Main 
12.34/5.20	module FiniteMap where {
12.34/5.20	import qualified Main;
12.34/5.20	import qualified Maybe;
12.34/5.20	import qualified Prelude;
12.34/5.20	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.34/5.20	
12.34/5.20	foldFM_LE :: Ord b => (b  ->  a  ->  c  ->  c)  ->  c  ->  b  ->  FiniteMap b a  ->  c;
12.34/5.20	foldFM_LE k z fr EmptyFM = z;
12.34/5.20	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
12.34/5.20	 | otherwise = foldFM_LE k z fr fm_l;
12.34/5.20	
12.34/5.20	keysFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [b];
12.34/5.20	keysFM_LE fm fr = foldFM_LE keysFM_LE0 [] fr fm;
12.34/5.20	
12.34/5.20	keysFM_LE0 key elt rest = key : rest;
12.34/5.20	
12.34/5.20	}
12.34/5.20	module Maybe where {
12.34/5.20	import qualified FiniteMap;
12.34/5.20	import qualified Main;
12.34/5.20	import qualified Prelude;
12.34/5.20	}
12.34/5.20	module Main where {
12.34/5.20	import qualified FiniteMap;
12.34/5.20	import qualified Maybe;
12.34/5.20	import qualified Prelude;
12.34/5.20	}
12.34/5.20	
12.34/5.20	----------------------------------------
12.34/5.20	
12.34/5.20	(3) BR (EQUIVALENT)
12.34/5.20	Replaced joker patterns by fresh variables and removed binding patterns.
12.34/5.20	----------------------------------------
12.34/5.20	
12.34/5.20	(4)
12.34/5.20	Obligation:
12.34/5.20	mainModule Main 
12.34/5.20	module FiniteMap where {
12.34/5.20	import qualified Main;
12.34/5.20	import qualified Maybe;
12.34/5.20	import qualified Prelude;
12.34/5.20	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.34/5.20	
12.34/5.20	foldFM_LE :: Ord c => (c  ->  a  ->  b  ->  b)  ->  b  ->  c  ->  FiniteMap c a  ->  b;
12.34/5.20	foldFM_LE k z fr EmptyFM = z;
12.34/5.20	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
12.34/5.20	 | otherwise = foldFM_LE k z fr fm_l;
12.34/5.20	
12.34/5.20	keysFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [b];
12.34/5.20	keysFM_LE fm fr = foldFM_LE keysFM_LE0 [] fr fm;
12.34/5.20	
12.34/5.20	keysFM_LE0 key elt rest = key : rest;
12.34/5.20	
12.34/5.20	}
12.34/5.20	module Maybe where {
12.34/5.20	import qualified FiniteMap;
12.34/5.20	import qualified Main;
12.34/5.20	import qualified Prelude;
12.34/5.20	}
12.34/5.20	module Main where {
12.34/5.20	import qualified FiniteMap;
12.34/5.20	import qualified Maybe;
12.34/5.20	import qualified Prelude;
12.34/5.20	}
12.34/5.20	
12.34/5.20	----------------------------------------
12.34/5.20	
12.34/5.20	(5) COR (EQUIVALENT)
12.34/5.20	Cond Reductions:
12.34/5.20	The following Function with conditions
12.34/5.20	"undefined |Falseundefined;
12.34/5.20	"
12.34/5.20	is transformed to
12.34/5.20	"undefined  = undefined1;
12.34/5.20	"
12.34/5.20	"undefined0 True = undefined;
12.34/5.20	"
12.34/5.20	"undefined1  = undefined0 False;
12.34/5.20	"
12.34/5.20	The following Function with conditions
12.34/5.20	"foldFM_LE k z fr EmptyFM = z;
12.34/5.20	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;
12.34/5.20	"
12.34/5.20	is transformed to
12.34/5.20	"foldFM_LE k z fr EmptyFM = foldFM_LE3 k z fr EmptyFM;
12.34/5.20	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);
12.34/5.20	"
12.34/5.20	"foldFM_LE0 k z fr key elt vy fm_l fm_r True = foldFM_LE k z fr fm_l;
12.34/5.20	"
12.34/5.20	"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;
12.34/5.20	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;
12.34/5.20	"
12.34/5.20	"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);
12.34/5.20	"
12.34/5.20	"foldFM_LE3 k z fr EmptyFM = z;
12.34/5.20	foldFM_LE3 wv ww wx wy = foldFM_LE2 wv ww wx wy;
12.34/5.20	"
12.34/5.20	
12.34/5.20	----------------------------------------
12.34/5.20	
12.34/5.20	(6)
12.34/5.20	Obligation:
12.34/5.20	mainModule Main 
12.34/5.20	module FiniteMap where {
12.34/5.20	import qualified Main;
12.34/5.20	import qualified Maybe;
12.34/5.20	import qualified Prelude;
12.34/5.20	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.34/5.20	
12.34/5.20	foldFM_LE :: Ord c => (c  ->  b  ->  a  ->  a)  ->  a  ->  c  ->  FiniteMap c b  ->  a;
12.34/5.20	foldFM_LE k z fr EmptyFM = foldFM_LE3 k z fr EmptyFM;
12.34/5.20	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);
12.34/5.20	
12.34/5.20	foldFM_LE0 k z fr key elt vy fm_l fm_r True = foldFM_LE k z fr fm_l;
12.34/5.20	
12.34/5.20	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;
12.34/5.20	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;
12.34/5.20	
12.34/5.20	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);
12.34/5.20	
12.34/5.20	foldFM_LE3 k z fr EmptyFM = z;
12.34/5.20	foldFM_LE3 wv ww wx wy = foldFM_LE2 wv ww wx wy;
12.34/5.20	
12.34/5.20	keysFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [b];
12.34/5.20	keysFM_LE fm fr = foldFM_LE keysFM_LE0 [] fr fm;
12.34/5.20	
12.34/5.20	keysFM_LE0 key elt rest = key : rest;
12.34/5.20	
12.34/5.20	}
12.34/5.20	module Maybe where {
12.34/5.20	import qualified FiniteMap;
12.34/5.20	import qualified Main;
12.34/5.20	import qualified Prelude;
12.34/5.20	}
12.34/5.20	module Main where {
12.34/5.20	import qualified FiniteMap;
12.34/5.20	import qualified Maybe;
12.34/5.20	import qualified Prelude;
12.34/5.20	}
12.34/5.20	
12.34/5.20	----------------------------------------
12.34/5.20	
12.34/5.20	(7) Narrow (SOUND)
12.34/5.20	Haskell To QDPs
12.34/5.20	
12.34/5.20	digraph dp_graph {
12.34/5.20	node [outthreshold=100, inthreshold=100];1[label="FiniteMap.keysFM_LE",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
12.34/5.20	3[label="FiniteMap.keysFM_LE wz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
12.34/5.20	4[label="FiniteMap.keysFM_LE wz3 wz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
12.34/5.20	5[label="FiniteMap.foldFM_LE FiniteMap.keysFM_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];
12.34/5.20	216 -> 6[label="",style="solid", color="burlywood", weight=3];
12.34/5.20	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];
12.34/5.20	217 -> 7[label="",style="solid", color="burlywood", weight=3];
12.34/5.20	6[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 [] wz4 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
12.34/5.20	7[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 [] wz4 (FiniteMap.Branch wz30 wz31 wz32 wz33 wz34)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
12.34/5.20	8[label="FiniteMap.foldFM_LE3 FiniteMap.keysFM_LE0 [] wz4 FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
12.34/5.20	9[label="FiniteMap.foldFM_LE2 FiniteMap.keysFM_LE0 [] wz4 (FiniteMap.Branch wz30 wz31 wz32 wz33 wz34)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
12.34/5.20	10[label="[]",fontsize=16,color="green",shape="box"];11[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_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];
12.34/5.20	218 -> 12[label="",style="solid", color="burlywood", weight=3];
12.34/5.20	219[label="wz30/EQ",fontsize=10,color="white",style="solid",shape="box"];11 -> 219[label="",style="solid", color="burlywood", weight=9];
12.34/5.20	219 -> 13[label="",style="solid", color="burlywood", weight=3];
12.34/5.20	220[label="wz30/GT",fontsize=10,color="white",style="solid",shape="box"];11 -> 220[label="",style="solid", color="burlywood", weight=9];
12.34/5.20	220 -> 14[label="",style="solid", color="burlywood", weight=3];
12.34/5.20	12[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_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];
12.34/5.20	221 -> 15[label="",style="solid", color="burlywood", weight=3];
12.34/5.20	222[label="wz4/EQ",fontsize=10,color="white",style="solid",shape="box"];12 -> 222[label="",style="solid", color="burlywood", weight=9];
12.34/5.20	222 -> 16[label="",style="solid", color="burlywood", weight=3];
12.34/5.20	223[label="wz4/GT",fontsize=10,color="white",style="solid",shape="box"];12 -> 223[label="",style="solid", color="burlywood", weight=9];
12.34/5.20	223 -> 17[label="",style="solid", color="burlywood", weight=3];
12.34/5.20	13[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_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];
12.34/5.20	224 -> 18[label="",style="solid", color="burlywood", weight=3];
12.34/5.20	225[label="wz4/EQ",fontsize=10,color="white",style="solid",shape="box"];13 -> 225[label="",style="solid", color="burlywood", weight=9];
12.34/5.20	225 -> 19[label="",style="solid", color="burlywood", weight=3];
12.34/5.20	226[label="wz4/GT",fontsize=10,color="white",style="solid",shape="box"];13 -> 226[label="",style="solid", color="burlywood", weight=9];
12.34/5.20	226 -> 20[label="",style="solid", color="burlywood", weight=3];
12.34/5.20	14[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_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];
12.34/5.20	227 -> 21[label="",style="solid", color="burlywood", weight=3];
12.34/5.20	228[label="wz4/EQ",fontsize=10,color="white",style="solid",shape="box"];14 -> 228[label="",style="solid", color="burlywood", weight=9];
12.34/5.20	228 -> 22[label="",style="solid", color="burlywood", weight=3];
12.34/5.20	229[label="wz4/GT",fontsize=10,color="white",style="solid",shape="box"];14 -> 229[label="",style="solid", color="burlywood", weight=9];
12.34/5.20	229 -> 23[label="",style="solid", color="burlywood", weight=3];
12.34/5.20	15[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] LT LT wz31 wz32 wz33 wz34 (LT <= LT)",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
12.34/5.20	16[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] EQ LT wz31 wz32 wz33 wz34 (LT <= EQ)",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
12.34/5.20	17[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] GT LT wz31 wz32 wz33 wz34 (LT <= GT)",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
12.34/5.20	18[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] LT EQ wz31 wz32 wz33 wz34 (EQ <= LT)",fontsize=16,color="black",shape="box"];18 -> 27[label="",style="solid", color="black", weight=3];
12.34/5.20	19[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] EQ EQ wz31 wz32 wz33 wz34 (EQ <= EQ)",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
12.34/5.20	20[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] GT EQ wz31 wz32 wz33 wz34 (EQ <= GT)",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
12.34/5.20	21[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] LT GT wz31 wz32 wz33 wz34 (GT <= LT)",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
12.34/5.20	22[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] EQ GT wz31 wz32 wz33 wz34 (GT <= EQ)",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
12.34/5.20	23[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] GT GT wz31 wz32 wz33 wz34 (GT <= GT)",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
12.34/5.20	24[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] LT LT wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
12.34/5.20	25[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] EQ LT wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
12.34/5.20	26[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] GT LT wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
12.34/5.20	27[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] LT EQ wz31 wz32 wz33 wz34 False",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
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12.34/5.20	198 -> 207[label="",style="dashed", color="magenta", weight=3];
12.34/5.20	198 -> 208[label="",style="dashed", color="magenta", weight=3];
12.34/5.20	198 -> 209[label="",style="dashed", color="magenta", weight=3];
12.34/5.20	198 -> 210[label="",style="dashed", color="magenta", weight=3];
12.34/5.20	199[label="wz13",fontsize=16,color="green",shape="box"];200 -> 122[label="",style="dashed", color="red", weight=0];
12.34/5.20	200[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 wz13 GT wz3430 wz3431 wz3432 wz3433 wz3434 (wz3430 <= GT)",fontsize=16,color="magenta"];200 -> 211[label="",style="dashed", color="magenta", weight=3];
12.34/5.20	200 -> 212[label="",style="dashed", color="magenta", weight=3];
12.34/5.20	200 -> 213[label="",style="dashed", color="magenta", weight=3];
12.34/5.20	200 -> 214[label="",style="dashed", color="magenta", weight=3];
12.34/5.20	200 -> 215[label="",style="dashed", color="magenta", weight=3];
12.34/5.20	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"];}
12.34/5.20	
12.34/5.20	----------------------------------------
12.34/5.20	
12.34/5.20	(8)
12.34/5.20	Complex Obligation (AND)
12.34/5.20	
12.34/5.20	----------------------------------------
12.34/5.20	
12.34/5.20	(9)
12.34/5.20	Obligation:
12.34/5.20	Q DP problem:
12.34/5.20	The TRS P consists of the following rules:
12.34/5.20	
12.34/5.20	   new_foldFM_LE18(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE17(new_keysFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.20	   new_foldFM_LE17(wz11, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE20(wz11, wz343, h)
12.34/5.20	   new_foldFM_LE17(wz11, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE18(wz341, new_foldFM_LE19(wz11, wz343, h), wz344, h)
12.34/5.20	   new_foldFM_LE20(wz11, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE17(wz11, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.20	   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)
12.34/5.20	   new_foldFM_LE17(wz11, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE20(wz11, wz343, h)
12.34/5.20	
12.34/5.20	The TRS R consists of the following rules:
12.34/5.20	
12.34/5.20	   new_keysFM_LE0(wz31, wz5, h) -> :(LT, wz5)
12.34/5.20	   new_foldFM_LE110(wz11, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE21(wz341, new_foldFM_LE19(wz11, wz343, h), wz344, h)
12.34/5.20	   new_foldFM_LE19(wz11, EmptyFM, h) -> wz11
12.34/5.20	   new_foldFM_LE110(wz11, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE19(wz11, wz343, h)
12.34/5.20	   new_foldFM_LE19(wz11, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE110(wz11, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.20	   new_foldFM_LE21(wz31, wz5, EmptyFM, h) -> new_keysFM_LE0(wz31, wz5, h)
12.34/5.20	   new_foldFM_LE21(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE110(new_keysFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.20	   new_foldFM_LE110(wz11, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE19(wz11, wz343, h)
12.34/5.20	
12.34/5.20	The set Q consists of the following terms:
12.34/5.20	
12.34/5.20	   new_foldFM_LE19(x0, EmptyFM, x1)
12.34/5.20	   new_foldFM_LE110(x0, LT, x1, x2, x3, x4, x5)
12.34/5.20	   new_foldFM_LE110(x0, EQ, x1, x2, x3, x4, x5)
12.34/5.20	   new_foldFM_LE110(x0, GT, x1, x2, x3, x4, x5)
12.34/5.20	   new_foldFM_LE21(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.20	   new_keysFM_LE0(x0, x1, x2)
12.34/5.20	   new_foldFM_LE19(x0, Branch(x1, x2, x3, x4, x5), x6)
12.34/5.20	   new_foldFM_LE21(x0, x1, EmptyFM, x2)
12.34/5.20	
12.34/5.20	We have to consider all minimal (P,Q,R)-chains.
12.34/5.20	----------------------------------------
12.34/5.20	
12.34/5.20	(10) TransformationProof (EQUIVALENT)
12.34/5.20	By rewriting [LPAR04] the rule new_foldFM_LE18(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE17(new_keysFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]:
12.34/5.20	
12.34/5.20	   (new_foldFM_LE18(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE17(:(LT, wz5), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE18(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE17(:(LT, wz5), wz340, wz341, wz342, wz343, wz344, h))
12.34/5.20	
12.34/5.20	
12.34/5.20	----------------------------------------
12.34/5.20	
12.34/5.20	(11)
12.34/5.20	Obligation:
12.34/5.20	Q DP problem:
12.34/5.20	The TRS P consists of the following rules:
12.34/5.20	
12.34/5.20	   new_foldFM_LE17(wz11, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE20(wz11, wz343, h)
12.34/5.20	   new_foldFM_LE17(wz11, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE18(wz341, new_foldFM_LE19(wz11, wz343, h), wz344, h)
12.34/5.20	   new_foldFM_LE20(wz11, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE17(wz11, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.20	   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)
12.34/5.20	   new_foldFM_LE17(wz11, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE20(wz11, wz343, h)
12.34/5.20	   new_foldFM_LE18(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE17(:(LT, wz5), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.20	
12.34/5.20	The TRS R consists of the following rules:
12.34/5.20	
12.34/5.20	   new_keysFM_LE0(wz31, wz5, h) -> :(LT, wz5)
12.34/5.20	   new_foldFM_LE110(wz11, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE21(wz341, new_foldFM_LE19(wz11, wz343, h), wz344, h)
12.34/5.20	   new_foldFM_LE19(wz11, EmptyFM, h) -> wz11
12.34/5.20	   new_foldFM_LE110(wz11, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE19(wz11, wz343, h)
12.34/5.20	   new_foldFM_LE19(wz11, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE110(wz11, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.20	   new_foldFM_LE21(wz31, wz5, EmptyFM, h) -> new_keysFM_LE0(wz31, wz5, h)
12.34/5.20	   new_foldFM_LE21(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE110(new_keysFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.20	   new_foldFM_LE110(wz11, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE19(wz11, wz343, h)
12.34/5.20	
12.34/5.20	The set Q consists of the following terms:
12.34/5.20	
12.34/5.20	   new_foldFM_LE19(x0, EmptyFM, x1)
12.34/5.20	   new_foldFM_LE110(x0, LT, x1, x2, x3, x4, x5)
12.34/5.20	   new_foldFM_LE110(x0, EQ, x1, x2, x3, x4, x5)
12.34/5.20	   new_foldFM_LE110(x0, GT, x1, x2, x3, x4, x5)
12.34/5.20	   new_foldFM_LE21(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.20	   new_keysFM_LE0(x0, x1, x2)
12.34/5.20	   new_foldFM_LE19(x0, Branch(x1, x2, x3, x4, x5), x6)
12.34/5.20	   new_foldFM_LE21(x0, x1, EmptyFM, x2)
12.34/5.20	
12.34/5.20	We have to consider all minimal (P,Q,R)-chains.
12.34/5.20	----------------------------------------
12.34/5.20	
12.34/5.20	(12) QDPSizeChangeProof (EQUIVALENT)
12.34/5.20	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. 
12.34/5.20	
12.34/5.20	From the DPs we obtained the following set of size-change graphs:
12.34/5.20	*new_foldFM_LE20(wz11, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE17(wz11, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.20	The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 7
12.34/5.20	
12.34/5.20	
12.34/5.20	*new_foldFM_LE18(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE17(:(LT, wz5), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.20	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.34/5.21	
12.34/5.21	
12.34/5.21	*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)
12.34/5.21	The graph contains the following edges 1 >= 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 5 > 6, 7 >= 7
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE17(wz11, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE18(wz341, new_foldFM_LE19(wz11, wz343, h), wz344, h)
12.34/5.21	The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE17(wz11, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE20(wz11, wz343, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE17(wz11, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE20(wz11, wz343, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3
12.34/5.21	
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(13)
12.34/5.21	YES
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(14)
12.34/5.21	Obligation:
12.34/5.21	Q DP problem:
12.34/5.21	The TRS P consists of the following rules:
12.34/5.21	
12.34/5.21	   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)
12.34/5.21	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.34/5.21	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.34/5.21	   new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_keysFM_LE0(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_keysFM_LE01(wz31, wz10, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE3(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE1(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_keysFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	
12.34/5.21	The TRS R consists of the following rules:
12.34/5.21	
12.34/5.21	   new_keysFM_LE00(wz31, wz8, h) -> :(EQ, wz8)
12.34/5.21	   new_keysFM_LE0(wz31, wz5, h) -> :(LT, wz5)
12.34/5.21	   new_foldFM_LE6(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE01(wz31, wz10, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE10(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE6(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE5(wz31, wz9, EmptyFM, h) -> new_keysFM_LE00(wz31, wz9, h)
12.34/5.21	   new_foldFM_LE7(wz31, wz7, EmptyFM, h) -> new_keysFM_LE0(wz31, wz7, h)
12.34/5.21	   new_keysFM_LE01(wz31, wz10, h) -> :(GT, wz10)
12.34/5.21	   new_foldFM_LE10(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE5(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE7(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE0(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE5(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE0(wz13, EmptyFM, h) -> wz13
12.34/5.21	   new_foldFM_LE10(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE7(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE0(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE10(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	   new_foldFM_LE6(wz31, wz10, EmptyFM, h) -> new_keysFM_LE01(wz31, wz10, h)
12.34/5.21	
12.34/5.21	The set Q consists of the following terms:
12.34/5.21	
12.34/5.21	   new_foldFM_LE7(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	   new_foldFM_LE7(x0, x1, EmptyFM, x2)
12.34/5.21	   new_keysFM_LE0(x0, x1, x2)
12.34/5.21	   new_foldFM_LE10(x0, LT, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE0(x0, Branch(x1, x2, x3, x4, x5), x6)
12.34/5.21	   new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	   new_foldFM_LE6(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	   new_foldFM_LE10(x0, EQ, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE5(x0, x1, EmptyFM, x2)
12.34/5.21	   new_keysFM_LE01(x0, x1, x2)
12.34/5.21	   new_keysFM_LE00(x0, x1, x2)
12.34/5.21	   new_foldFM_LE6(x0, x1, EmptyFM, x2)
12.34/5.21	   new_foldFM_LE0(x0, EmptyFM, x1)
12.34/5.21	   new_foldFM_LE10(x0, GT, x1, x2, x3, x4, x5)
12.34/5.21	
12.34/5.21	We have to consider all minimal (P,Q,R)-chains.
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(15) TransformationProof (EQUIVALENT)
12.34/5.21	By rewriting [LPAR04] the rule new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_keysFM_LE0(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]:
12.34/5.21	
12.34/5.21	   (new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(LT, wz7), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(LT, wz7), wz340, wz341, wz342, wz343, wz344, h))
12.34/5.21	
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(16)
12.34/5.21	Obligation:
12.34/5.21	Q DP problem:
12.34/5.21	The TRS P consists of the following rules:
12.34/5.21	
12.34/5.21	   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)
12.34/5.21	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.34/5.21	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.34/5.21	   new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_keysFM_LE01(wz31, wz10, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE3(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE1(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_keysFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(LT, wz7), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	
12.34/5.21	The TRS R consists of the following rules:
12.34/5.21	
12.34/5.21	   new_keysFM_LE00(wz31, wz8, h) -> :(EQ, wz8)
12.34/5.21	   new_keysFM_LE0(wz31, wz5, h) -> :(LT, wz5)
12.34/5.21	   new_foldFM_LE6(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE01(wz31, wz10, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE10(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE6(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE5(wz31, wz9, EmptyFM, h) -> new_keysFM_LE00(wz31, wz9, h)
12.34/5.21	   new_foldFM_LE7(wz31, wz7, EmptyFM, h) -> new_keysFM_LE0(wz31, wz7, h)
12.34/5.21	   new_keysFM_LE01(wz31, wz10, h) -> :(GT, wz10)
12.34/5.21	   new_foldFM_LE10(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE5(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE7(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE0(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE5(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE0(wz13, EmptyFM, h) -> wz13
12.34/5.21	   new_foldFM_LE10(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE7(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE0(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE10(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	   new_foldFM_LE6(wz31, wz10, EmptyFM, h) -> new_keysFM_LE01(wz31, wz10, h)
12.34/5.21	
12.34/5.21	The set Q consists of the following terms:
12.34/5.21	
12.34/5.21	   new_foldFM_LE7(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	   new_foldFM_LE7(x0, x1, EmptyFM, x2)
12.34/5.21	   new_keysFM_LE0(x0, x1, x2)
12.34/5.21	   new_foldFM_LE10(x0, LT, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE0(x0, Branch(x1, x2, x3, x4, x5), x6)
12.34/5.21	   new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	   new_foldFM_LE6(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	   new_foldFM_LE10(x0, EQ, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE5(x0, x1, EmptyFM, x2)
12.34/5.21	   new_keysFM_LE01(x0, x1, x2)
12.34/5.21	   new_keysFM_LE00(x0, x1, x2)
12.34/5.21	   new_foldFM_LE6(x0, x1, EmptyFM, x2)
12.34/5.21	   new_foldFM_LE0(x0, EmptyFM, x1)
12.34/5.21	   new_foldFM_LE10(x0, GT, x1, x2, x3, x4, x5)
12.34/5.21	
12.34/5.21	We have to consider all minimal (P,Q,R)-chains.
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(17) TransformationProof (EQUIVALENT)
12.34/5.21	By rewriting [LPAR04] the rule new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_keysFM_LE01(wz31, wz10, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]:
12.34/5.21	
12.34/5.21	   (new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(GT, wz10), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(GT, wz10), wz340, wz341, wz342, wz343, wz344, h))
12.34/5.21	
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(18)
12.34/5.21	Obligation:
12.34/5.21	Q DP problem:
12.34/5.21	The TRS P consists of the following rules:
12.34/5.21	
12.34/5.21	   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)
12.34/5.21	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.34/5.21	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.34/5.21	   new_foldFM_LE3(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE1(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_keysFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(LT, wz7), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(GT, wz10), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	
12.34/5.21	The TRS R consists of the following rules:
12.34/5.21	
12.34/5.21	   new_keysFM_LE00(wz31, wz8, h) -> :(EQ, wz8)
12.34/5.21	   new_keysFM_LE0(wz31, wz5, h) -> :(LT, wz5)
12.34/5.21	   new_foldFM_LE6(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE01(wz31, wz10, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE10(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE6(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE5(wz31, wz9, EmptyFM, h) -> new_keysFM_LE00(wz31, wz9, h)
12.34/5.21	   new_foldFM_LE7(wz31, wz7, EmptyFM, h) -> new_keysFM_LE0(wz31, wz7, h)
12.34/5.21	   new_keysFM_LE01(wz31, wz10, h) -> :(GT, wz10)
12.34/5.21	   new_foldFM_LE10(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE5(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE7(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE0(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE5(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE0(wz13, EmptyFM, h) -> wz13
12.34/5.21	   new_foldFM_LE10(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE7(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE0(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE10(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	   new_foldFM_LE6(wz31, wz10, EmptyFM, h) -> new_keysFM_LE01(wz31, wz10, h)
12.34/5.21	
12.34/5.21	The set Q consists of the following terms:
12.34/5.21	
12.34/5.21	   new_foldFM_LE7(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	   new_foldFM_LE7(x0, x1, EmptyFM, x2)
12.34/5.21	   new_keysFM_LE0(x0, x1, x2)
12.34/5.21	   new_foldFM_LE10(x0, LT, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE0(x0, Branch(x1, x2, x3, x4, x5), x6)
12.34/5.21	   new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	   new_foldFM_LE6(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	   new_foldFM_LE10(x0, EQ, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE5(x0, x1, EmptyFM, x2)
12.34/5.21	   new_keysFM_LE01(x0, x1, x2)
12.34/5.21	   new_keysFM_LE00(x0, x1, x2)
12.34/5.21	   new_foldFM_LE6(x0, x1, EmptyFM, x2)
12.34/5.21	   new_foldFM_LE0(x0, EmptyFM, x1)
12.34/5.21	   new_foldFM_LE10(x0, GT, x1, x2, x3, x4, x5)
12.34/5.21	
12.34/5.21	We have to consider all minimal (P,Q,R)-chains.
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(19) TransformationProof (EQUIVALENT)
12.34/5.21	By rewriting [LPAR04] the rule new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_keysFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]:
12.34/5.21	
12.34/5.21	   (new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(EQ, wz9), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(EQ, wz9), wz340, wz341, wz342, wz343, wz344, h))
12.34/5.21	
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(20)
12.34/5.21	Obligation:
12.34/5.21	Q DP problem:
12.34/5.21	The TRS P consists of the following rules:
12.34/5.21	
12.34/5.21	   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)
12.34/5.21	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.34/5.21	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.34/5.21	   new_foldFM_LE3(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	   new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE1(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(LT, wz7), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(GT, wz10), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(EQ, wz9), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	
12.34/5.21	The TRS R consists of the following rules:
12.34/5.21	
12.34/5.21	   new_keysFM_LE00(wz31, wz8, h) -> :(EQ, wz8)
12.34/5.21	   new_keysFM_LE0(wz31, wz5, h) -> :(LT, wz5)
12.34/5.21	   new_foldFM_LE6(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE01(wz31, wz10, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE10(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE6(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE5(wz31, wz9, EmptyFM, h) -> new_keysFM_LE00(wz31, wz9, h)
12.34/5.21	   new_foldFM_LE7(wz31, wz7, EmptyFM, h) -> new_keysFM_LE0(wz31, wz7, h)
12.34/5.21	   new_keysFM_LE01(wz31, wz10, h) -> :(GT, wz10)
12.34/5.21	   new_foldFM_LE10(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE5(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE7(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE0(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE5(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE00(wz31, wz9, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE0(wz13, EmptyFM, h) -> wz13
12.34/5.21	   new_foldFM_LE10(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE7(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE0(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE10(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	   new_foldFM_LE6(wz31, wz10, EmptyFM, h) -> new_keysFM_LE01(wz31, wz10, h)
12.34/5.21	
12.34/5.21	The set Q consists of the following terms:
12.34/5.21	
12.34/5.21	   new_foldFM_LE7(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	   new_foldFM_LE7(x0, x1, EmptyFM, x2)
12.34/5.21	   new_keysFM_LE0(x0, x1, x2)
12.34/5.21	   new_foldFM_LE10(x0, LT, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE0(x0, Branch(x1, x2, x3, x4, x5), x6)
12.34/5.21	   new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	   new_foldFM_LE6(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	   new_foldFM_LE10(x0, EQ, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE5(x0, x1, EmptyFM, x2)
12.34/5.21	   new_keysFM_LE01(x0, x1, x2)
12.34/5.21	   new_keysFM_LE00(x0, x1, x2)
12.34/5.21	   new_foldFM_LE6(x0, x1, EmptyFM, x2)
12.34/5.21	   new_foldFM_LE0(x0, EmptyFM, x1)
12.34/5.21	   new_foldFM_LE10(x0, GT, x1, x2, x3, x4, x5)
12.34/5.21	
12.34/5.21	We have to consider all minimal (P,Q,R)-chains.
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(21) QDPSizeChangeProof (EQUIVALENT)
12.34/5.21	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. 
12.34/5.21	
12.34/5.21	From the DPs we obtained the following set of size-change graphs:
12.34/5.21	*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)
12.34/5.21	The graph contains the following edges 1 >= 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 5 > 6, 7 >= 7
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE3(wz13, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz13, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 7
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE2(wz31, wz9, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(EQ, wz9), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE4(wz31, wz10, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(GT, wz10), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(LT, wz7), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE1(wz13, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz13, wz343, h), wz344, h)
12.34/5.21	The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE1(wz13, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE1(wz13, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz13, wz343, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3
12.34/5.21	
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(22)
12.34/5.21	YES
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(23)
12.34/5.21	Obligation:
12.34/5.21	Q DP problem:
12.34/5.21	The TRS P consists of the following rules:
12.34/5.21	
12.34/5.21	   new_foldFM_LE22(EQ, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.34/5.21	   new_foldFM_LE22(EQ, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.34/5.21	   new_foldFM_LE22(LT, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.34/5.21	   new_foldFM_LE22(LT, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.34/5.21	   new_foldFM_LE22(GT, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.34/5.21	   new_foldFM_LE22(GT, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.34/5.21	   new_foldFM_LE22(EQ, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.34/5.21	   new_foldFM_LE22(LT, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.34/5.21	   new_foldFM_LE22(GT, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.34/5.21	
12.34/5.21	R is empty.
12.34/5.21	Q is empty.
12.34/5.21	We have to consider all minimal (P,Q,R)-chains.
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(24) DependencyGraphProof (EQUIVALENT)
12.34/5.21	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs.
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(25)
12.34/5.21	Complex Obligation (AND)
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(26)
12.34/5.21	Obligation:
12.34/5.21	Q DP problem:
12.34/5.21	The TRS P consists of the following rules:
12.34/5.21	
12.34/5.21	   new_foldFM_LE22(GT, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.34/5.21	   new_foldFM_LE22(GT, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.34/5.21	   new_foldFM_LE22(GT, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.34/5.21	
12.34/5.21	R is empty.
12.34/5.21	Q is empty.
12.34/5.21	We have to consider all minimal (P,Q,R)-chains.
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(27) QDPSizeChangeProof (EQUIVALENT)
12.34/5.21	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. 
12.34/5.21	
12.34/5.21	From the DPs we obtained the following set of size-change graphs:
12.34/5.21	*new_foldFM_LE22(GT, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE22(GT, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 2 > 1, 2 > 2, 3 >= 3
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE22(GT, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(GT, wz33, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.34/5.21	
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(28)
12.34/5.21	YES
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(29)
12.34/5.21	Obligation:
12.34/5.21	Q DP problem:
12.34/5.21	The TRS P consists of the following rules:
12.34/5.21	
12.34/5.21	   new_foldFM_LE22(LT, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.34/5.21	   new_foldFM_LE22(LT, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.34/5.21	   new_foldFM_LE22(LT, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.34/5.21	
12.34/5.21	R is empty.
12.34/5.21	Q is empty.
12.34/5.21	We have to consider all minimal (P,Q,R)-chains.
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(30) QDPSizeChangeProof (EQUIVALENT)
12.34/5.21	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. 
12.34/5.21	
12.34/5.21	From the DPs we obtained the following set of size-change graphs:
12.34/5.21	*new_foldFM_LE22(LT, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE22(LT, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 2 > 1, 2 > 2, 3 >= 3
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE22(LT, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(LT, wz33, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.34/5.21	
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(31)
12.34/5.21	YES
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(32)
12.34/5.21	Obligation:
12.34/5.21	Q DP problem:
12.34/5.21	The TRS P consists of the following rules:
12.34/5.21	
12.34/5.21	   new_foldFM_LE22(EQ, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.34/5.21	   new_foldFM_LE22(EQ, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.34/5.21	   new_foldFM_LE22(EQ, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.34/5.21	
12.34/5.21	R is empty.
12.34/5.21	Q is empty.
12.34/5.21	We have to consider all minimal (P,Q,R)-chains.
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(33) QDPSizeChangeProof (EQUIVALENT)
12.34/5.21	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. 
12.34/5.21	
12.34/5.21	From the DPs we obtained the following set of size-change graphs:
12.34/5.21	*new_foldFM_LE22(EQ, Branch(LT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE22(EQ, Branch(GT, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE22(EQ, Branch(EQ, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE22(EQ, wz33, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 2 > 1, 2 > 2, 3 >= 3
12.34/5.21	
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(34)
12.34/5.21	YES
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(35)
12.34/5.21	Obligation:
12.34/5.21	Q DP problem:
12.34/5.21	The TRS P consists of the following rules:
12.34/5.21	
12.34/5.21	   new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.34/5.21	   new_foldFM_LE8(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(new_keysFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE12(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE11(wz12, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.34/5.21	   new_foldFM_LE13(wz12, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE11(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	   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)
12.34/5.21	   new_foldFM_LE11(wz12, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE8(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE12(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(new_keysFM_LE00(wz31, wz8, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	
12.34/5.21	The TRS R consists of the following rules:
12.34/5.21	
12.34/5.21	   new_foldFM_LE16(wz31, wz8, EmptyFM, h) -> new_keysFM_LE00(wz31, wz8, h)
12.34/5.21	   new_foldFM_LE15(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE14(new_keysFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_keysFM_LE00(wz31, wz8, h) -> :(EQ, wz8)
12.34/5.21	   new_foldFM_LE14(wz12, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE9(wz12, wz343, h)
12.34/5.21	   new_keysFM_LE0(wz31, wz5, h) -> :(LT, wz5)
12.34/5.21	   new_foldFM_LE9(wz12, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE14(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	   new_foldFM_LE15(wz31, wz6, EmptyFM, h) -> new_keysFM_LE0(wz31, wz6, h)
12.34/5.21	   new_foldFM_LE14(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE16(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE16(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE14(new_keysFM_LE00(wz31, wz8, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE14(wz12, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE15(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE9(wz12, EmptyFM, h) -> wz12
12.34/5.21	
12.34/5.21	The set Q consists of the following terms:
12.34/5.21	
12.34/5.21	   new_foldFM_LE9(x0, Branch(x1, x2, x3, x4, x5), x6)
12.34/5.21	   new_foldFM_LE16(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	   new_foldFM_LE14(x0, GT, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE14(x0, EQ, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE16(x0, x1, EmptyFM, x2)
12.34/5.21	   new_keysFM_LE00(x0, x1, x2)
12.34/5.21	   new_keysFM_LE0(x0, x1, x2)
12.34/5.21	   new_foldFM_LE14(x0, LT, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE15(x0, x1, EmptyFM, x2)
12.34/5.21	   new_foldFM_LE9(x0, EmptyFM, x1)
12.34/5.21	   new_foldFM_LE15(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	
12.34/5.21	We have to consider all minimal (P,Q,R)-chains.
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(36) TransformationProof (EQUIVALENT)
12.34/5.21	By rewriting [LPAR04] the rule new_foldFM_LE8(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(new_keysFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]:
12.34/5.21	
12.34/5.21	   (new_foldFM_LE8(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(LT, wz6), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE8(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(LT, wz6), wz340, wz341, wz342, wz343, wz344, h))
12.34/5.21	
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(37)
12.34/5.21	Obligation:
12.34/5.21	Q DP problem:
12.34/5.21	The TRS P consists of the following rules:
12.34/5.21	
12.34/5.21	   new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.34/5.21	   new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE12(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE11(wz12, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.34/5.21	   new_foldFM_LE13(wz12, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE11(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	   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)
12.34/5.21	   new_foldFM_LE11(wz12, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE8(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE12(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(new_keysFM_LE00(wz31, wz8, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE8(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(LT, wz6), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	
12.34/5.21	The TRS R consists of the following rules:
12.34/5.21	
12.34/5.21	   new_foldFM_LE16(wz31, wz8, EmptyFM, h) -> new_keysFM_LE00(wz31, wz8, h)
12.34/5.21	   new_foldFM_LE15(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE14(new_keysFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_keysFM_LE00(wz31, wz8, h) -> :(EQ, wz8)
12.34/5.21	   new_foldFM_LE14(wz12, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE9(wz12, wz343, h)
12.34/5.21	   new_keysFM_LE0(wz31, wz5, h) -> :(LT, wz5)
12.34/5.21	   new_foldFM_LE9(wz12, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE14(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	   new_foldFM_LE15(wz31, wz6, EmptyFM, h) -> new_keysFM_LE0(wz31, wz6, h)
12.34/5.21	   new_foldFM_LE14(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE16(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE16(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE14(new_keysFM_LE00(wz31, wz8, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE14(wz12, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE15(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE9(wz12, EmptyFM, h) -> wz12
12.34/5.21	
12.34/5.21	The set Q consists of the following terms:
12.34/5.21	
12.34/5.21	   new_foldFM_LE9(x0, Branch(x1, x2, x3, x4, x5), x6)
12.34/5.21	   new_foldFM_LE16(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	   new_foldFM_LE14(x0, GT, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE14(x0, EQ, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE16(x0, x1, EmptyFM, x2)
12.34/5.21	   new_keysFM_LE00(x0, x1, x2)
12.34/5.21	   new_keysFM_LE0(x0, x1, x2)
12.34/5.21	   new_foldFM_LE14(x0, LT, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE15(x0, x1, EmptyFM, x2)
12.34/5.21	   new_foldFM_LE9(x0, EmptyFM, x1)
12.34/5.21	   new_foldFM_LE15(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	
12.34/5.21	We have to consider all minimal (P,Q,R)-chains.
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(38) TransformationProof (EQUIVALENT)
12.34/5.21	By rewriting [LPAR04] the rule new_foldFM_LE12(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(new_keysFM_LE00(wz31, wz8, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]:
12.34/5.21	
12.34/5.21	   (new_foldFM_LE12(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(EQ, wz8), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE12(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(EQ, wz8), wz340, wz341, wz342, wz343, wz344, h))
12.34/5.21	
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(39)
12.34/5.21	Obligation:
12.34/5.21	Q DP problem:
12.34/5.21	The TRS P consists of the following rules:
12.34/5.21	
12.34/5.21	   new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.34/5.21	   new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE12(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE11(wz12, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.34/5.21	   new_foldFM_LE13(wz12, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE11(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	   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)
12.34/5.21	   new_foldFM_LE11(wz12, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE8(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE8(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(LT, wz6), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE12(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(EQ, wz8), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	
12.34/5.21	The TRS R consists of the following rules:
12.34/5.21	
12.34/5.21	   new_foldFM_LE16(wz31, wz8, EmptyFM, h) -> new_keysFM_LE00(wz31, wz8, h)
12.34/5.21	   new_foldFM_LE15(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE14(new_keysFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_keysFM_LE00(wz31, wz8, h) -> :(EQ, wz8)
12.34/5.21	   new_foldFM_LE14(wz12, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE9(wz12, wz343, h)
12.34/5.21	   new_keysFM_LE0(wz31, wz5, h) -> :(LT, wz5)
12.34/5.21	   new_foldFM_LE9(wz12, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE14(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	   new_foldFM_LE15(wz31, wz6, EmptyFM, h) -> new_keysFM_LE0(wz31, wz6, h)
12.34/5.21	   new_foldFM_LE14(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE16(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE16(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE14(new_keysFM_LE00(wz31, wz8, h), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	   new_foldFM_LE14(wz12, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE15(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.34/5.21	   new_foldFM_LE9(wz12, EmptyFM, h) -> wz12
12.34/5.21	
12.34/5.21	The set Q consists of the following terms:
12.34/5.21	
12.34/5.21	   new_foldFM_LE9(x0, Branch(x1, x2, x3, x4, x5), x6)
12.34/5.21	   new_foldFM_LE16(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	   new_foldFM_LE14(x0, GT, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE14(x0, EQ, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE16(x0, x1, EmptyFM, x2)
12.34/5.21	   new_keysFM_LE00(x0, x1, x2)
12.34/5.21	   new_keysFM_LE0(x0, x1, x2)
12.34/5.21	   new_foldFM_LE14(x0, LT, x1, x2, x3, x4, x5)
12.34/5.21	   new_foldFM_LE15(x0, x1, EmptyFM, x2)
12.34/5.21	   new_foldFM_LE9(x0, EmptyFM, x1)
12.34/5.21	   new_foldFM_LE15(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.34/5.21	
12.34/5.21	We have to consider all minimal (P,Q,R)-chains.
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(40) QDPSizeChangeProof (EQUIVALENT)
12.34/5.21	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. 
12.34/5.21	
12.34/5.21	From the DPs we obtained the following set of size-change graphs:
12.34/5.21	*new_foldFM_LE13(wz12, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE11(wz12, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 7
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE12(wz31, wz8, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(EQ, wz8), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.34/5.21	
12.34/5.21	
12.34/5.21	*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)
12.34/5.21	The graph contains the following edges 1 >= 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 5 > 6, 7 >= 7
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE8(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(LT, wz6), wz340, wz341, wz342, wz343, wz344, h)
12.34/5.21	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE11(wz12, LT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE8(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.34/5.21	The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE12(wz341, new_foldFM_LE9(wz12, wz343, h), wz344, h)
12.34/5.21	The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE11(wz12, EQ, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3
12.34/5.21	
12.34/5.21	
12.34/5.21	*new_foldFM_LE11(wz12, GT, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE13(wz12, wz343, h)
12.34/5.21	The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3
12.34/5.21	
12.34/5.21	
12.34/5.21	----------------------------------------
12.34/5.21	
12.34/5.21	(41)
12.34/5.21	YES
12.69/5.29	EOF