10.30/4.55	YES
12.48/5.16	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
12.48/5.16	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.48/5.16	
12.48/5.16	
12.48/5.16	H-Termination with start terms of the given HASKELL could be proven:
12.48/5.16	
12.48/5.16	(0) HASKELL
12.48/5.16	(1) LR [EQUIVALENT, 0 ms]
12.48/5.16	(2) HASKELL
12.48/5.16	(3) BR [EQUIVALENT, 0 ms]
12.48/5.16	(4) HASKELL
12.48/5.16	(5) COR [EQUIVALENT, 0 ms]
12.48/5.16	(6) HASKELL
12.48/5.16	(7) Narrow [SOUND, 0 ms]
12.48/5.16	(8) AND
12.48/5.16	    (9) QDP
12.48/5.16	        (10) TransformationProof [EQUIVALENT, 0 ms]
12.48/5.16	        (11) QDP
12.48/5.16	        (12) TransformationProof [EQUIVALENT, 0 ms]
12.48/5.16	        (13) QDP
12.48/5.16	        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.48/5.16	        (15) YES
12.48/5.16	    (16) QDP
12.48/5.16	        (17) DependencyGraphProof [EQUIVALENT, 0 ms]
12.48/5.16	        (18) AND
12.48/5.16	            (19) QDP
12.48/5.16	                (20) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.48/5.16	                (21) YES
12.48/5.16	            (22) QDP
12.48/5.16	                (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.48/5.16	                (24) YES
12.48/5.16	    (25) QDP
12.48/5.16	        (26) TransformationProof [EQUIVALENT, 0 ms]
12.48/5.16	        (27) QDP
12.48/5.16	        (28) QDPSizeChangeProof [EQUIVALENT, 0 ms]
12.48/5.16	        (29) YES
12.48/5.16	
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(0)
12.48/5.16	Obligation:
12.48/5.16	mainModule Main 
12.48/5.16	module FiniteMap where {
12.48/5.16	import qualified Main;
12.48/5.16	import qualified Maybe;
12.48/5.16	import qualified Prelude;
12.48/5.16	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.48/5.16	
12.48/5.16	foldFM_LE :: Ord b => (b  ->  a  ->  c  ->  c)  ->  c  ->  b  ->  FiniteMap b a  ->  c;
12.48/5.16	foldFM_LE k z fr EmptyFM = z;
12.48/5.16	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
12.48/5.16	 | otherwise = foldFM_LE k z fr fm_l;
12.48/5.16	
12.48/5.16	keysFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [b];
12.48/5.16	keysFM_LE fm fr = foldFM_LE (\key elt rest ->key : rest) [] fr fm;
12.48/5.16	
12.48/5.16	}
12.48/5.16	module Maybe where {
12.48/5.16	import qualified FiniteMap;
12.48/5.16	import qualified Main;
12.48/5.16	import qualified Prelude;
12.48/5.16	}
12.48/5.16	module Main where {
12.48/5.16	import qualified FiniteMap;
12.48/5.16	import qualified Maybe;
12.48/5.16	import qualified Prelude;
12.48/5.16	}
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(1) LR (EQUIVALENT)
12.48/5.16	Lambda Reductions:
12.48/5.16	The following Lambda expression
12.48/5.16	"\keyeltrest->key : rest"
12.48/5.16	is transformed to
12.48/5.16	"keysFM_LE0 key elt rest = key : rest;
12.48/5.16	"
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(2)
12.48/5.16	Obligation:
12.48/5.16	mainModule Main 
12.48/5.16	module FiniteMap where {
12.48/5.16	import qualified Main;
12.48/5.16	import qualified Maybe;
12.48/5.16	import qualified Prelude;
12.48/5.16	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.48/5.16	
12.48/5.16	foldFM_LE :: Ord a => (a  ->  b  ->  c  ->  c)  ->  c  ->  a  ->  FiniteMap a b  ->  c;
12.48/5.16	foldFM_LE k z fr EmptyFM = z;
12.48/5.16	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
12.48/5.16	 | otherwise = foldFM_LE k z fr fm_l;
12.48/5.16	
12.48/5.16	keysFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [a];
12.48/5.16	keysFM_LE fm fr = foldFM_LE keysFM_LE0 [] fr fm;
12.48/5.16	
12.48/5.16	keysFM_LE0 key elt rest = key : rest;
12.48/5.16	
12.48/5.16	}
12.48/5.16	module Maybe where {
12.48/5.16	import qualified FiniteMap;
12.48/5.16	import qualified Main;
12.48/5.16	import qualified Prelude;
12.48/5.16	}
12.48/5.16	module Main where {
12.48/5.16	import qualified FiniteMap;
12.48/5.16	import qualified Maybe;
12.48/5.16	import qualified Prelude;
12.48/5.16	}
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(3) BR (EQUIVALENT)
12.48/5.16	Replaced joker patterns by fresh variables and removed binding patterns.
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(4)
12.48/5.16	Obligation:
12.48/5.16	mainModule Main 
12.48/5.16	module FiniteMap where {
12.48/5.16	import qualified Main;
12.48/5.16	import qualified Maybe;
12.48/5.16	import qualified Prelude;
12.48/5.16	data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) ;
12.48/5.16	
12.48/5.16	foldFM_LE :: Ord c => (c  ->  a  ->  b  ->  b)  ->  b  ->  c  ->  FiniteMap c a  ->  b;
12.48/5.16	foldFM_LE k z fr EmptyFM = z;
12.48/5.16	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
12.48/5.16	 | otherwise = foldFM_LE k z fr fm_l;
12.48/5.16	
12.48/5.16	keysFM_LE :: Ord b => FiniteMap b a  ->  b  ->  [b];
12.48/5.16	keysFM_LE fm fr = foldFM_LE keysFM_LE0 [] fr fm;
12.48/5.16	
12.48/5.16	keysFM_LE0 key elt rest = key : rest;
12.48/5.16	
12.48/5.16	}
12.48/5.16	module Maybe where {
12.48/5.16	import qualified FiniteMap;
12.48/5.16	import qualified Main;
12.48/5.16	import qualified Prelude;
12.48/5.16	}
12.48/5.16	module Main where {
12.48/5.16	import qualified FiniteMap;
12.48/5.16	import qualified Maybe;
12.48/5.16	import qualified Prelude;
12.48/5.16	}
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(5) COR (EQUIVALENT)
12.48/5.16	Cond Reductions:
12.48/5.16	The following Function with conditions
12.48/5.16	"undefined |Falseundefined;
12.48/5.16	"
12.48/5.16	is transformed to
12.48/5.16	"undefined  = undefined1;
12.48/5.16	"
12.48/5.16	"undefined0 True = undefined;
12.48/5.16	"
12.48/5.16	"undefined1  = undefined0 False;
12.48/5.16	"
12.48/5.16	The following Function with conditions
12.48/5.16	"foldFM_LE k z fr EmptyFM = z;
12.48/5.16	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;
12.48/5.16	"
12.48/5.16	is transformed to
12.48/5.16	"foldFM_LE k z fr EmptyFM = foldFM_LE3 k z fr EmptyFM;
12.48/5.16	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);
12.48/5.16	"
12.48/5.16	"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;
12.48/5.16	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;
12.48/5.16	"
12.48/5.16	"foldFM_LE0 k z fr key elt vy fm_l fm_r True = foldFM_LE k z fr fm_l;
12.48/5.16	"
12.48/5.16	"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);
12.48/5.16	"
12.48/5.16	"foldFM_LE3 k z fr EmptyFM = z;
12.48/5.16	foldFM_LE3 wv ww wx wy = foldFM_LE2 wv ww wx wy;
12.48/5.16	"
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(6)
12.48/5.16	Obligation:
12.48/5.16	mainModule Main 
12.48/5.16	module FiniteMap where {
12.48/5.16	import qualified Main;
12.48/5.16	import qualified Maybe;
12.48/5.16	import qualified Prelude;
12.48/5.16	data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) ;
12.48/5.16	
12.48/5.16	foldFM_LE :: Ord a => (a  ->  b  ->  c  ->  c)  ->  c  ->  a  ->  FiniteMap a b  ->  c;
12.48/5.16	foldFM_LE k z fr EmptyFM = foldFM_LE3 k z fr EmptyFM;
12.48/5.16	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);
12.48/5.16	
12.48/5.16	foldFM_LE0 k z fr key elt vy fm_l fm_r True = foldFM_LE k z fr fm_l;
12.48/5.16	
12.48/5.16	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;
12.48/5.16	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;
12.48/5.16	
12.48/5.16	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);
12.48/5.16	
12.48/5.16	foldFM_LE3 k z fr EmptyFM = z;
12.48/5.16	foldFM_LE3 wv ww wx wy = foldFM_LE2 wv ww wx wy;
12.48/5.16	
12.48/5.16	keysFM_LE :: Ord a => FiniteMap a b  ->  a  ->  [a];
12.48/5.16	keysFM_LE fm fr = foldFM_LE keysFM_LE0 [] fr fm;
12.48/5.16	
12.48/5.16	keysFM_LE0 key elt rest = key : rest;
12.48/5.16	
12.48/5.16	}
12.48/5.16	module Maybe where {
12.48/5.16	import qualified FiniteMap;
12.48/5.16	import qualified Main;
12.48/5.16	import qualified Prelude;
12.48/5.16	}
12.48/5.16	module Main where {
12.48/5.16	import qualified FiniteMap;
12.48/5.16	import qualified Maybe;
12.48/5.16	import qualified Prelude;
12.48/5.16	}
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(7) Narrow (SOUND)
12.48/5.16	Haskell To QDPs
12.48/5.16	
12.48/5.16	digraph dp_graph {
12.48/5.16	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];
12.48/5.16	3[label="FiniteMap.keysFM_LE wz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
12.48/5.16	4[label="FiniteMap.keysFM_LE wz3 wz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
12.48/5.16	5[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 [] wz4 wz3",fontsize=16,color="burlywood",shape="triangle"];114[label="wz3/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];5 -> 114[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	114 -> 6[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	115[label="wz3/FiniteMap.Branch wz30 wz31 wz32 wz33 wz34",fontsize=10,color="white",style="solid",shape="box"];5 -> 115[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	115 -> 7[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	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];
12.48/5.16	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];
12.48/5.16	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];
12.48/5.16	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];
12.48/5.16	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"];116[label="wz30/False",fontsize=10,color="white",style="solid",shape="box"];11 -> 116[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	116 -> 12[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	117[label="wz30/True",fontsize=10,color="white",style="solid",shape="box"];11 -> 117[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	117 -> 13[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	12[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] wz4 False wz31 wz32 wz33 wz34 (False <= wz4)",fontsize=16,color="burlywood",shape="box"];118[label="wz4/False",fontsize=10,color="white",style="solid",shape="box"];12 -> 118[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	118 -> 14[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	119[label="wz4/True",fontsize=10,color="white",style="solid",shape="box"];12 -> 119[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	119 -> 15[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	13[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] wz4 True wz31 wz32 wz33 wz34 (True <= wz4)",fontsize=16,color="burlywood",shape="box"];120[label="wz4/False",fontsize=10,color="white",style="solid",shape="box"];13 -> 120[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	120 -> 16[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	121[label="wz4/True",fontsize=10,color="white",style="solid",shape="box"];13 -> 121[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	121 -> 17[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	14[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] False False wz31 wz32 wz33 wz34 (False <= False)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
12.48/5.16	15[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] True False wz31 wz32 wz33 wz34 (False <= True)",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
12.48/5.16	16[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] False True wz31 wz32 wz33 wz34 (True <= False)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
12.48/5.16	17[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] True True wz31 wz32 wz33 wz34 (True <= True)",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
12.48/5.16	18[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] False False wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
12.48/5.16	19[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] True False wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
12.48/5.16	20[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] False True wz31 wz32 wz33 wz34 False",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
12.48/5.16	21[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 [] True True wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
12.48/5.16	22 -> 26[label="",style="dashed", color="red", weight=0];
12.48/5.16	22[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz31 (FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 [] False wz33)) False wz34",fontsize=16,color="magenta"];22 -> 27[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	23 -> 28[label="",style="dashed", color="red", weight=0];
12.48/5.16	23[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz31 (FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 [] True wz33)) True wz34",fontsize=16,color="magenta"];23 -> 29[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	24[label="FiniteMap.foldFM_LE0 FiniteMap.keysFM_LE0 [] False True wz31 wz32 wz33 wz34 otherwise",fontsize=16,color="black",shape="box"];24 -> 30[label="",style="solid", color="black", weight=3];
12.48/5.16	25 -> 31[label="",style="dashed", color="red", weight=0];
12.48/5.16	25[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 True wz31 (FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 [] True wz33)) True wz34",fontsize=16,color="magenta"];25 -> 32[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	27 -> 5[label="",style="dashed", color="red", weight=0];
12.48/5.16	27[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 [] False wz33",fontsize=16,color="magenta"];27 -> 33[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	27 -> 34[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	26[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz31 wz5) False wz34",fontsize=16,color="burlywood",shape="triangle"];122[label="wz34/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];26 -> 122[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	122 -> 35[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	123[label="wz34/FiniteMap.Branch wz340 wz341 wz342 wz343 wz344",fontsize=10,color="white",style="solid",shape="box"];26 -> 123[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	123 -> 36[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	29 -> 5[label="",style="dashed", color="red", weight=0];
12.48/5.16	29[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 [] True wz33",fontsize=16,color="magenta"];29 -> 37[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	29 -> 38[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	28[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz31 wz6) True wz34",fontsize=16,color="burlywood",shape="triangle"];124[label="wz34/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];28 -> 124[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	124 -> 39[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	125[label="wz34/FiniteMap.Branch wz340 wz341 wz342 wz343 wz344",fontsize=10,color="white",style="solid",shape="box"];28 -> 125[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	125 -> 40[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	30[label="FiniteMap.foldFM_LE0 FiniteMap.keysFM_LE0 [] False True wz31 wz32 wz33 wz34 True",fontsize=16,color="black",shape="box"];30 -> 41[label="",style="solid", color="black", weight=3];
12.48/5.16	32 -> 5[label="",style="dashed", color="red", weight=0];
12.48/5.16	32[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 [] True wz33",fontsize=16,color="magenta"];32 -> 42[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	32 -> 43[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	31[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 True wz31 wz7) True wz34",fontsize=16,color="burlywood",shape="triangle"];126[label="wz34/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];31 -> 126[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	126 -> 44[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	127[label="wz34/FiniteMap.Branch wz340 wz341 wz342 wz343 wz344",fontsize=10,color="white",style="solid",shape="box"];31 -> 127[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	127 -> 45[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	33[label="False",fontsize=16,color="green",shape="box"];34[label="wz33",fontsize=16,color="green",shape="box"];35[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz31 wz5) False FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];35 -> 46[label="",style="solid", color="black", weight=3];
12.48/5.16	36[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz31 wz5) False (FiniteMap.Branch wz340 wz341 wz342 wz343 wz344)",fontsize=16,color="black",shape="box"];36 -> 47[label="",style="solid", color="black", weight=3];
12.48/5.16	37[label="True",fontsize=16,color="green",shape="box"];38[label="wz33",fontsize=16,color="green",shape="box"];39[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz31 wz6) True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];39 -> 48[label="",style="solid", color="black", weight=3];
12.48/5.16	40[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz31 wz6) True (FiniteMap.Branch wz340 wz341 wz342 wz343 wz344)",fontsize=16,color="black",shape="box"];40 -> 49[label="",style="solid", color="black", weight=3];
12.48/5.16	41 -> 5[label="",style="dashed", color="red", weight=0];
12.48/5.16	41[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 [] False wz33",fontsize=16,color="magenta"];41 -> 50[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	41 -> 51[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	42[label="True",fontsize=16,color="green",shape="box"];43[label="wz33",fontsize=16,color="green",shape="box"];44[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 True wz31 wz7) True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];44 -> 52[label="",style="solid", color="black", weight=3];
12.48/5.16	45[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 True wz31 wz7) True (FiniteMap.Branch wz340 wz341 wz342 wz343 wz344)",fontsize=16,color="black",shape="box"];45 -> 53[label="",style="solid", color="black", weight=3];
12.48/5.16	46[label="FiniteMap.foldFM_LE3 FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz31 wz5) False FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];46 -> 54[label="",style="solid", color="black", weight=3];
12.48/5.16	47[label="FiniteMap.foldFM_LE2 FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz31 wz5) False (FiniteMap.Branch wz340 wz341 wz342 wz343 wz344)",fontsize=16,color="black",shape="box"];47 -> 55[label="",style="solid", color="black", weight=3];
12.48/5.16	48[label="FiniteMap.foldFM_LE3 FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz31 wz6) True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];48 -> 56[label="",style="solid", color="black", weight=3];
12.48/5.16	49[label="FiniteMap.foldFM_LE2 FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz31 wz6) True (FiniteMap.Branch wz340 wz341 wz342 wz343 wz344)",fontsize=16,color="black",shape="box"];49 -> 57[label="",style="solid", color="black", weight=3];
12.48/5.16	50[label="False",fontsize=16,color="green",shape="box"];51[label="wz33",fontsize=16,color="green",shape="box"];52[label="FiniteMap.foldFM_LE3 FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 True wz31 wz7) True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];52 -> 58[label="",style="solid", color="black", weight=3];
12.48/5.16	53[label="FiniteMap.foldFM_LE2 FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 True wz31 wz7) True (FiniteMap.Branch wz340 wz341 wz342 wz343 wz344)",fontsize=16,color="black",shape="box"];53 -> 59[label="",style="solid", color="black", weight=3];
12.48/5.16	54[label="FiniteMap.keysFM_LE0 False wz31 wz5",fontsize=16,color="black",shape="triangle"];54 -> 60[label="",style="solid", color="black", weight=3];
12.48/5.16	55 -> 61[label="",style="dashed", color="red", weight=0];
12.48/5.16	55[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz31 wz5) False wz340 wz341 wz342 wz343 wz344 (wz340 <= False)",fontsize=16,color="magenta"];55 -> 62[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	56 -> 54[label="",style="dashed", color="red", weight=0];
12.48/5.16	56[label="FiniteMap.keysFM_LE0 False wz31 wz6",fontsize=16,color="magenta"];56 -> 63[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	57 -> 64[label="",style="dashed", color="red", weight=0];
12.48/5.16	57[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz31 wz6) True wz340 wz341 wz342 wz343 wz344 (wz340 <= True)",fontsize=16,color="magenta"];57 -> 65[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	58[label="FiniteMap.keysFM_LE0 True wz31 wz7",fontsize=16,color="black",shape="triangle"];58 -> 67[label="",style="solid", color="black", weight=3];
12.48/5.16	59 -> 64[label="",style="dashed", color="red", weight=0];
12.48/5.16	59[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 True wz31 wz7) True wz340 wz341 wz342 wz343 wz344 (wz340 <= True)",fontsize=16,color="magenta"];59 -> 66[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	60[label="False : wz5",fontsize=16,color="green",shape="box"];62 -> 54[label="",style="dashed", color="red", weight=0];
12.48/5.16	62[label="FiniteMap.keysFM_LE0 False wz31 wz5",fontsize=16,color="magenta"];61[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 wz8 False wz340 wz341 wz342 wz343 wz344 (wz340 <= False)",fontsize=16,color="burlywood",shape="triangle"];128[label="wz340/False",fontsize=10,color="white",style="solid",shape="box"];61 -> 128[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	128 -> 68[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	129[label="wz340/True",fontsize=10,color="white",style="solid",shape="box"];61 -> 129[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	129 -> 69[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	63[label="wz6",fontsize=16,color="green",shape="box"];65 -> 54[label="",style="dashed", color="red", weight=0];
12.48/5.16	65[label="FiniteMap.keysFM_LE0 False wz31 wz6",fontsize=16,color="magenta"];65 -> 70[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	64[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 wz9 True wz340 wz341 wz342 wz343 wz344 (wz340 <= True)",fontsize=16,color="burlywood",shape="triangle"];130[label="wz340/False",fontsize=10,color="white",style="solid",shape="box"];64 -> 130[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	130 -> 71[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	131[label="wz340/True",fontsize=10,color="white",style="solid",shape="box"];64 -> 131[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	131 -> 72[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	67[label="True : wz7",fontsize=16,color="green",shape="box"];66 -> 58[label="",style="dashed", color="red", weight=0];
12.48/5.16	66[label="FiniteMap.keysFM_LE0 True wz31 wz7",fontsize=16,color="magenta"];68[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 wz8 False False wz341 wz342 wz343 wz344 (False <= False)",fontsize=16,color="black",shape="box"];68 -> 73[label="",style="solid", color="black", weight=3];
12.48/5.16	69[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 wz8 False True wz341 wz342 wz343 wz344 (True <= False)",fontsize=16,color="black",shape="box"];69 -> 74[label="",style="solid", color="black", weight=3];
12.48/5.16	70[label="wz6",fontsize=16,color="green",shape="box"];71[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 wz9 True False wz341 wz342 wz343 wz344 (False <= True)",fontsize=16,color="black",shape="box"];71 -> 75[label="",style="solid", color="black", weight=3];
12.48/5.16	72[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 wz9 True True wz341 wz342 wz343 wz344 (True <= True)",fontsize=16,color="black",shape="box"];72 -> 76[label="",style="solid", color="black", weight=3];
12.48/5.16	73[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 wz8 False False wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];73 -> 77[label="",style="solid", color="black", weight=3];
12.48/5.16	74[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 wz8 False True wz341 wz342 wz343 wz344 False",fontsize=16,color="black",shape="box"];74 -> 78[label="",style="solid", color="black", weight=3];
12.48/5.16	75[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 wz9 True False wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];75 -> 79[label="",style="solid", color="black", weight=3];
12.48/5.16	76[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 wz9 True True wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];76 -> 80[label="",style="solid", color="black", weight=3];
12.48/5.16	77 -> 26[label="",style="dashed", color="red", weight=0];
12.48/5.16	77[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz341 (FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 wz8 False wz343)) False wz344",fontsize=16,color="magenta"];77 -> 81[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	77 -> 82[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	77 -> 83[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	78[label="FiniteMap.foldFM_LE0 FiniteMap.keysFM_LE0 wz8 False True wz341 wz342 wz343 wz344 otherwise",fontsize=16,color="black",shape="box"];78 -> 84[label="",style="solid", color="black", weight=3];
12.48/5.16	79 -> 28[label="",style="dashed", color="red", weight=0];
12.48/5.16	79[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 False wz341 (FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 wz9 True wz343)) True wz344",fontsize=16,color="magenta"];79 -> 85[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	79 -> 86[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	79 -> 87[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	80 -> 31[label="",style="dashed", color="red", weight=0];
12.48/5.16	80[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 (FiniteMap.keysFM_LE0 True wz341 (FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 wz9 True wz343)) True wz344",fontsize=16,color="magenta"];80 -> 88[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	80 -> 89[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	80 -> 90[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	81[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 wz8 False wz343",fontsize=16,color="burlywood",shape="triangle"];132[label="wz343/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];81 -> 132[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	132 -> 91[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	133[label="wz343/FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434",fontsize=10,color="white",style="solid",shape="box"];81 -> 133[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	133 -> 92[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	82[label="wz344",fontsize=16,color="green",shape="box"];83[label="wz341",fontsize=16,color="green",shape="box"];84[label="FiniteMap.foldFM_LE0 FiniteMap.keysFM_LE0 wz8 False True wz341 wz342 wz343 wz344 True",fontsize=16,color="black",shape="box"];84 -> 93[label="",style="solid", color="black", weight=3];
12.48/5.16	85[label="wz344",fontsize=16,color="green",shape="box"];86[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 wz9 True wz343",fontsize=16,color="burlywood",shape="triangle"];134[label="wz343/FiniteMap.EmptyFM",fontsize=10,color="white",style="solid",shape="box"];86 -> 134[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	134 -> 94[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	135[label="wz343/FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434",fontsize=10,color="white",style="solid",shape="box"];86 -> 135[label="",style="solid", color="burlywood", weight=9];
12.48/5.16	135 -> 95[label="",style="solid", color="burlywood", weight=3];
12.48/5.16	87[label="wz341",fontsize=16,color="green",shape="box"];88 -> 86[label="",style="dashed", color="red", weight=0];
12.48/5.16	88[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 wz9 True wz343",fontsize=16,color="magenta"];89[label="wz344",fontsize=16,color="green",shape="box"];90[label="wz341",fontsize=16,color="green",shape="box"];91[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 wz8 False FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];91 -> 96[label="",style="solid", color="black", weight=3];
12.48/5.16	92[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 wz8 False (FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434)",fontsize=16,color="black",shape="box"];92 -> 97[label="",style="solid", color="black", weight=3];
12.48/5.16	93 -> 81[label="",style="dashed", color="red", weight=0];
12.48/5.16	93[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 wz8 False wz343",fontsize=16,color="magenta"];94[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 wz9 True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];94 -> 98[label="",style="solid", color="black", weight=3];
12.48/5.16	95[label="FiniteMap.foldFM_LE FiniteMap.keysFM_LE0 wz9 True (FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434)",fontsize=16,color="black",shape="box"];95 -> 99[label="",style="solid", color="black", weight=3];
12.48/5.16	96[label="FiniteMap.foldFM_LE3 FiniteMap.keysFM_LE0 wz8 False FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];96 -> 100[label="",style="solid", color="black", weight=3];
12.48/5.16	97[label="FiniteMap.foldFM_LE2 FiniteMap.keysFM_LE0 wz8 False (FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434)",fontsize=16,color="black",shape="box"];97 -> 101[label="",style="solid", color="black", weight=3];
12.48/5.16	98[label="FiniteMap.foldFM_LE3 FiniteMap.keysFM_LE0 wz9 True FiniteMap.EmptyFM",fontsize=16,color="black",shape="box"];98 -> 102[label="",style="solid", color="black", weight=3];
12.48/5.16	99[label="FiniteMap.foldFM_LE2 FiniteMap.keysFM_LE0 wz9 True (FiniteMap.Branch wz3430 wz3431 wz3432 wz3433 wz3434)",fontsize=16,color="black",shape="box"];99 -> 103[label="",style="solid", color="black", weight=3];
12.48/5.16	100[label="wz8",fontsize=16,color="green",shape="box"];101 -> 61[label="",style="dashed", color="red", weight=0];
12.48/5.16	101[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 wz8 False wz3430 wz3431 wz3432 wz3433 wz3434 (wz3430 <= False)",fontsize=16,color="magenta"];101 -> 104[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	101 -> 105[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	101 -> 106[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	101 -> 107[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	101 -> 108[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	102[label="wz9",fontsize=16,color="green",shape="box"];103 -> 64[label="",style="dashed", color="red", weight=0];
12.48/5.16	103[label="FiniteMap.foldFM_LE1 FiniteMap.keysFM_LE0 wz9 True wz3430 wz3431 wz3432 wz3433 wz3434 (wz3430 <= True)",fontsize=16,color="magenta"];103 -> 109[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	103 -> 110[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	103 -> 111[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	103 -> 112[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	103 -> 113[label="",style="dashed", color="magenta", weight=3];
12.48/5.16	104[label="wz3430",fontsize=16,color="green",shape="box"];105[label="wz3432",fontsize=16,color="green",shape="box"];106[label="wz3434",fontsize=16,color="green",shape="box"];107[label="wz3433",fontsize=16,color="green",shape="box"];108[label="wz3431",fontsize=16,color="green",shape="box"];109[label="wz3430",fontsize=16,color="green",shape="box"];110[label="wz3432",fontsize=16,color="green",shape="box"];111[label="wz3434",fontsize=16,color="green",shape="box"];112[label="wz3433",fontsize=16,color="green",shape="box"];113[label="wz3431",fontsize=16,color="green",shape="box"];}
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(8)
12.48/5.16	Complex Obligation (AND)
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(9)
12.48/5.16	Obligation:
12.48/5.16	Q DP problem:
12.48/5.16	The TRS P consists of the following rules:
12.48/5.16	
12.48/5.16	   new_foldFM_LE(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_keysFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	   new_foldFM_LE3(wz9, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	   new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz9, wz343, h)
12.48/5.16	   new_foldFM_LE1(wz9, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h)
12.48/5.16	   new_foldFM_LE2(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_keysFM_LE00(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	   new_foldFM_LE1(wz9, False, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	   new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h)
12.48/5.16	
12.48/5.16	The TRS R consists of the following rules:
12.48/5.16	
12.48/5.16	   new_foldFM_LE0(wz9, EmptyFM, h) -> wz9
12.48/5.16	   new_keysFM_LE00(wz31, wz7, h) -> :(True, wz7)
12.48/5.16	   new_foldFM_LE4(wz31, wz7, EmptyFM, h) -> new_keysFM_LE00(wz31, wz7, h)
12.48/5.16	   new_foldFM_LE4(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE00(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	   new_keysFM_LE0(wz31, wz5, h) -> :(False, wz5)
12.48/5.16	   new_foldFM_LE10(wz9, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE5(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h)
12.48/5.16	   new_foldFM_LE5(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	   new_foldFM_LE0(wz9, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE10(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	   new_foldFM_LE5(wz31, wz6, EmptyFM, h) -> new_keysFM_LE0(wz31, wz6, h)
12.48/5.16	   new_foldFM_LE10(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h)
12.48/5.16	
12.48/5.16	The set Q consists of the following terms:
12.48/5.16	
12.48/5.16	   new_foldFM_LE10(x0, True, x1, x2, x3, x4, x5)
12.48/5.16	   new_foldFM_LE0(x0, Branch(x1, x2, x3, x4, x5), x6)
12.48/5.16	   new_keysFM_LE00(x0, x1, x2)
12.48/5.16	   new_keysFM_LE0(x0, x1, x2)
12.48/5.16	   new_foldFM_LE0(x0, EmptyFM, x1)
12.48/5.16	   new_foldFM_LE10(x0, False, x1, x2, x3, x4, x5)
12.48/5.16	   new_foldFM_LE4(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.48/5.16	   new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.48/5.16	   new_foldFM_LE4(x0, x1, EmptyFM, x2)
12.48/5.16	   new_foldFM_LE5(x0, x1, EmptyFM, x2)
12.48/5.16	
12.48/5.16	We have to consider all minimal (P,Q,R)-chains.
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(10) TransformationProof (EQUIVALENT)
12.48/5.16	By rewriting [LPAR04] the rule new_foldFM_LE(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_keysFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]:
12.48/5.16	
12.48/5.16	   (new_foldFM_LE(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(False, wz6), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(False, wz6), wz340, wz341, wz342, wz343, wz344, h))
12.48/5.16	
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(11)
12.48/5.16	Obligation:
12.48/5.16	Q DP problem:
12.48/5.16	The TRS P consists of the following rules:
12.48/5.16	
12.48/5.16	   new_foldFM_LE3(wz9, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	   new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz9, wz343, h)
12.48/5.16	   new_foldFM_LE1(wz9, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h)
12.48/5.16	   new_foldFM_LE2(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_keysFM_LE00(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	   new_foldFM_LE1(wz9, False, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	   new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h)
12.48/5.16	   new_foldFM_LE(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(False, wz6), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	
12.48/5.16	The TRS R consists of the following rules:
12.48/5.16	
12.48/5.16	   new_foldFM_LE0(wz9, EmptyFM, h) -> wz9
12.48/5.16	   new_keysFM_LE00(wz31, wz7, h) -> :(True, wz7)
12.48/5.16	   new_foldFM_LE4(wz31, wz7, EmptyFM, h) -> new_keysFM_LE00(wz31, wz7, h)
12.48/5.16	   new_foldFM_LE4(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE00(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	   new_keysFM_LE0(wz31, wz5, h) -> :(False, wz5)
12.48/5.16	   new_foldFM_LE10(wz9, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE5(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h)
12.48/5.16	   new_foldFM_LE5(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	   new_foldFM_LE0(wz9, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE10(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	   new_foldFM_LE5(wz31, wz6, EmptyFM, h) -> new_keysFM_LE0(wz31, wz6, h)
12.48/5.16	   new_foldFM_LE10(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h)
12.48/5.16	
12.48/5.16	The set Q consists of the following terms:
12.48/5.16	
12.48/5.16	   new_foldFM_LE10(x0, True, x1, x2, x3, x4, x5)
12.48/5.16	   new_foldFM_LE0(x0, Branch(x1, x2, x3, x4, x5), x6)
12.48/5.16	   new_keysFM_LE00(x0, x1, x2)
12.48/5.16	   new_keysFM_LE0(x0, x1, x2)
12.48/5.16	   new_foldFM_LE0(x0, EmptyFM, x1)
12.48/5.16	   new_foldFM_LE10(x0, False, x1, x2, x3, x4, x5)
12.48/5.16	   new_foldFM_LE4(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.48/5.16	   new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.48/5.16	   new_foldFM_LE4(x0, x1, EmptyFM, x2)
12.48/5.16	   new_foldFM_LE5(x0, x1, EmptyFM, x2)
12.48/5.16	
12.48/5.16	We have to consider all minimal (P,Q,R)-chains.
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(12) TransformationProof (EQUIVALENT)
12.48/5.16	By rewriting [LPAR04] the rule new_foldFM_LE2(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(new_keysFM_LE00(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]:
12.48/5.16	
12.48/5.16	   (new_foldFM_LE2(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(True, wz7), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE2(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(True, wz7), wz340, wz341, wz342, wz343, wz344, h))
12.48/5.16	
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(13)
12.48/5.16	Obligation:
12.48/5.16	Q DP problem:
12.48/5.16	The TRS P consists of the following rules:
12.48/5.16	
12.48/5.16	   new_foldFM_LE3(wz9, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	   new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz9, wz343, h)
12.48/5.16	   new_foldFM_LE1(wz9, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h)
12.48/5.16	   new_foldFM_LE1(wz9, False, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	   new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h)
12.48/5.16	   new_foldFM_LE(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(False, wz6), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	   new_foldFM_LE2(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(True, wz7), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	
12.48/5.16	The TRS R consists of the following rules:
12.48/5.16	
12.48/5.16	   new_foldFM_LE0(wz9, EmptyFM, h) -> wz9
12.48/5.16	   new_keysFM_LE00(wz31, wz7, h) -> :(True, wz7)
12.48/5.16	   new_foldFM_LE4(wz31, wz7, EmptyFM, h) -> new_keysFM_LE00(wz31, wz7, h)
12.48/5.16	   new_foldFM_LE4(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE00(wz31, wz7, h), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	   new_keysFM_LE0(wz31, wz5, h) -> :(False, wz5)
12.48/5.16	   new_foldFM_LE10(wz9, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE5(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h)
12.48/5.16	   new_foldFM_LE5(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE10(new_keysFM_LE0(wz31, wz6, h), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	   new_foldFM_LE0(wz9, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE10(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	   new_foldFM_LE5(wz31, wz6, EmptyFM, h) -> new_keysFM_LE0(wz31, wz6, h)
12.48/5.16	   new_foldFM_LE10(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE4(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h)
12.48/5.16	
12.48/5.16	The set Q consists of the following terms:
12.48/5.16	
12.48/5.16	   new_foldFM_LE10(x0, True, x1, x2, x3, x4, x5)
12.48/5.16	   new_foldFM_LE0(x0, Branch(x1, x2, x3, x4, x5), x6)
12.48/5.16	   new_keysFM_LE00(x0, x1, x2)
12.48/5.16	   new_keysFM_LE0(x0, x1, x2)
12.48/5.16	   new_foldFM_LE0(x0, EmptyFM, x1)
12.48/5.16	   new_foldFM_LE10(x0, False, x1, x2, x3, x4, x5)
12.48/5.16	   new_foldFM_LE4(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.48/5.16	   new_foldFM_LE5(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.48/5.16	   new_foldFM_LE4(x0, x1, EmptyFM, x2)
12.48/5.16	   new_foldFM_LE5(x0, x1, EmptyFM, x2)
12.48/5.16	
12.48/5.16	We have to consider all minimal (P,Q,R)-chains.
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(14) QDPSizeChangeProof (EQUIVALENT)
12.48/5.16	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
12.48/5.16	
12.48/5.16	From the DPs we obtained the following set of size-change graphs:
12.48/5.16	*new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE3(wz9, wz343, h)
12.48/5.16	The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3
12.48/5.16	
12.48/5.16	
12.48/5.16	*new_foldFM_LE1(wz9, False, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	The graph contains the following edges 1 >= 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 5 > 6, 7 >= 7
12.48/5.16	
12.48/5.16	
12.48/5.16	*new_foldFM_LE3(wz9, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE1(wz9, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 7
12.48/5.16	
12.48/5.16	
12.48/5.16	*new_foldFM_LE(wz31, wz6, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(False, wz6), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.48/5.16	
12.48/5.16	
12.48/5.16	*new_foldFM_LE2(wz31, wz7, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE1(:(True, wz7), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.48/5.16	
12.48/5.16	
12.48/5.16	*new_foldFM_LE1(wz9, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h)
12.48/5.16	The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4
12.48/5.16	
12.48/5.16	
12.48/5.16	*new_foldFM_LE1(wz9, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE2(wz341, new_foldFM_LE0(wz9, wz343, h), wz344, h)
12.48/5.16	The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4
12.48/5.16	
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(15)
12.48/5.16	YES
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(16)
12.48/5.16	Obligation:
12.48/5.16	Q DP problem:
12.48/5.16	The TRS P consists of the following rules:
12.48/5.16	
12.48/5.16	   new_foldFM_LE13(True, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(True, wz33, h)
12.48/5.16	   new_foldFM_LE13(False, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(False, wz33, h)
12.48/5.16	   new_foldFM_LE13(False, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(False, wz33, h)
12.48/5.16	   new_foldFM_LE13(True, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(True, wz33, h)
12.48/5.16	
12.48/5.16	R is empty.
12.48/5.16	Q is empty.
12.48/5.16	We have to consider all minimal (P,Q,R)-chains.
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(17) DependencyGraphProof (EQUIVALENT)
12.48/5.16	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs.
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(18)
12.48/5.16	Complex Obligation (AND)
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(19)
12.48/5.16	Obligation:
12.48/5.16	Q DP problem:
12.48/5.16	The TRS P consists of the following rules:
12.48/5.16	
12.48/5.16	   new_foldFM_LE13(False, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(False, wz33, h)
12.48/5.16	   new_foldFM_LE13(False, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(False, wz33, h)
12.48/5.16	
12.48/5.16	R is empty.
12.48/5.16	Q is empty.
12.48/5.16	We have to consider all minimal (P,Q,R)-chains.
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(20) QDPSizeChangeProof (EQUIVALENT)
12.48/5.16	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
12.48/5.16	
12.48/5.16	From the DPs we obtained the following set of size-change graphs:
12.48/5.16	*new_foldFM_LE13(False, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(False, wz33, h)
12.48/5.16	The graph contains the following edges 1 >= 1, 2 > 1, 2 > 2, 3 >= 3
12.48/5.16	
12.48/5.16	
12.48/5.16	*new_foldFM_LE13(False, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(False, wz33, h)
12.48/5.16	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.48/5.16	
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(21)
12.48/5.16	YES
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(22)
12.48/5.16	Obligation:
12.48/5.16	Q DP problem:
12.48/5.16	The TRS P consists of the following rules:
12.48/5.16	
12.48/5.16	   new_foldFM_LE13(True, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(True, wz33, h)
12.48/5.16	   new_foldFM_LE13(True, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(True, wz33, h)
12.48/5.16	
12.48/5.16	R is empty.
12.48/5.16	Q is empty.
12.48/5.16	We have to consider all minimal (P,Q,R)-chains.
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(23) QDPSizeChangeProof (EQUIVALENT)
12.48/5.16	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
12.48/5.16	
12.48/5.16	From the DPs we obtained the following set of size-change graphs:
12.48/5.16	*new_foldFM_LE13(True, Branch(True, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(True, wz33, h)
12.48/5.16	The graph contains the following edges 1 >= 1, 2 > 1, 2 > 2, 3 >= 3
12.48/5.16	
12.48/5.16	
12.48/5.16	*new_foldFM_LE13(True, Branch(False, wz31, wz32, wz33, wz34), h) -> new_foldFM_LE13(True, wz33, h)
12.48/5.16	The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3
12.48/5.16	
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(24)
12.48/5.16	YES
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(25)
12.48/5.16	Obligation:
12.48/5.16	Q DP problem:
12.48/5.16	The TRS P consists of the following rules:
12.48/5.16	
12.48/5.16	   new_foldFM_LE11(wz8, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE8(wz8, wz343, h)
12.48/5.16	   new_foldFM_LE8(wz8, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE11(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	   new_foldFM_LE6(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(new_keysFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	   new_foldFM_LE11(wz8, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE6(wz341, new_foldFM_LE7(wz8, wz343, h), wz344, h)
12.48/5.16	   new_foldFM_LE11(wz8, False, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE11(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	
12.48/5.16	The TRS R consists of the following rules:
12.48/5.16	
12.48/5.16	   new_foldFM_LE9(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE12(new_keysFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	   new_foldFM_LE7(wz8, EmptyFM, h) -> wz8
12.48/5.16	   new_foldFM_LE7(wz8, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE12(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	   new_foldFM_LE9(wz31, wz5, EmptyFM, h) -> new_keysFM_LE0(wz31, wz5, h)
12.48/5.16	   new_foldFM_LE12(wz8, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE7(wz8, wz343, h)
12.48/5.16	   new_keysFM_LE0(wz31, wz5, h) -> :(False, wz5)
12.48/5.16	   new_foldFM_LE12(wz8, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE9(wz341, new_foldFM_LE7(wz8, wz343, h), wz344, h)
12.48/5.16	
12.48/5.16	The set Q consists of the following terms:
12.48/5.16	
12.48/5.16	   new_foldFM_LE9(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.48/5.16	   new_foldFM_LE12(x0, False, x1, x2, x3, x4, x5)
12.48/5.16	   new_foldFM_LE9(x0, x1, EmptyFM, x2)
12.48/5.16	   new_keysFM_LE0(x0, x1, x2)
12.48/5.16	   new_foldFM_LE12(x0, True, x1, x2, x3, x4, x5)
12.48/5.16	   new_foldFM_LE7(x0, EmptyFM, x1)
12.48/5.16	   new_foldFM_LE7(x0, Branch(x1, x2, x3, x4, x5), x6)
12.48/5.16	
12.48/5.16	We have to consider all minimal (P,Q,R)-chains.
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(26) TransformationProof (EQUIVALENT)
12.48/5.16	By rewriting [LPAR04] the rule new_foldFM_LE6(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(new_keysFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h) at position [0] we obtained the following new rules [LPAR04]:
12.48/5.16	
12.48/5.16	   (new_foldFM_LE6(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(False, wz5), wz340, wz341, wz342, wz343, wz344, h),new_foldFM_LE6(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(False, wz5), wz340, wz341, wz342, wz343, wz344, h))
12.48/5.16	
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(27)
12.48/5.16	Obligation:
12.48/5.16	Q DP problem:
12.48/5.16	The TRS P consists of the following rules:
12.48/5.16	
12.48/5.16	   new_foldFM_LE11(wz8, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE8(wz8, wz343, h)
12.48/5.16	   new_foldFM_LE8(wz8, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE11(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	   new_foldFM_LE11(wz8, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE6(wz341, new_foldFM_LE7(wz8, wz343, h), wz344, h)
12.48/5.16	   new_foldFM_LE11(wz8, False, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE11(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	   new_foldFM_LE6(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(False, wz5), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	
12.48/5.16	The TRS R consists of the following rules:
12.48/5.16	
12.48/5.16	   new_foldFM_LE9(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE12(new_keysFM_LE0(wz31, wz5, h), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	   new_foldFM_LE7(wz8, EmptyFM, h) -> wz8
12.48/5.16	   new_foldFM_LE7(wz8, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE12(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	   new_foldFM_LE9(wz31, wz5, EmptyFM, h) -> new_keysFM_LE0(wz31, wz5, h)
12.48/5.16	   new_foldFM_LE12(wz8, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE7(wz8, wz343, h)
12.48/5.16	   new_keysFM_LE0(wz31, wz5, h) -> :(False, wz5)
12.48/5.16	   new_foldFM_LE12(wz8, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE9(wz341, new_foldFM_LE7(wz8, wz343, h), wz344, h)
12.48/5.16	
12.48/5.16	The set Q consists of the following terms:
12.48/5.16	
12.48/5.16	   new_foldFM_LE9(x0, x1, Branch(x2, x3, x4, x5, x6), x7)
12.48/5.16	   new_foldFM_LE12(x0, False, x1, x2, x3, x4, x5)
12.48/5.16	   new_foldFM_LE9(x0, x1, EmptyFM, x2)
12.48/5.16	   new_keysFM_LE0(x0, x1, x2)
12.48/5.16	   new_foldFM_LE12(x0, True, x1, x2, x3, x4, x5)
12.48/5.16	   new_foldFM_LE7(x0, EmptyFM, x1)
12.48/5.16	   new_foldFM_LE7(x0, Branch(x1, x2, x3, x4, x5), x6)
12.48/5.16	
12.48/5.16	We have to consider all minimal (P,Q,R)-chains.
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(28) QDPSizeChangeProof (EQUIVALENT)
12.48/5.16	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
12.48/5.16	
12.48/5.16	From the DPs we obtained the following set of size-change graphs:
12.48/5.16	*new_foldFM_LE8(wz8, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), h) -> new_foldFM_LE11(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	The graph contains the following edges 1 >= 1, 2 > 2, 2 > 3, 2 > 4, 2 > 5, 2 > 6, 3 >= 7
12.48/5.16	
12.48/5.16	
12.48/5.16	*new_foldFM_LE11(wz8, False, wz341, wz342, Branch(wz3430, wz3431, wz3432, wz3433, wz3434), wz344, h) -> new_foldFM_LE11(wz8, wz3430, wz3431, wz3432, wz3433, wz3434, h)
12.48/5.16	The graph contains the following edges 1 >= 1, 5 > 2, 5 > 3, 5 > 4, 5 > 5, 5 > 6, 7 >= 7
12.48/5.16	
12.48/5.16	
12.48/5.16	*new_foldFM_LE6(wz31, wz5, Branch(wz340, wz341, wz342, wz343, wz344), h) -> new_foldFM_LE11(:(False, wz5), wz340, wz341, wz342, wz343, wz344, h)
12.48/5.16	The graph contains the following edges 3 > 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
12.48/5.16	
12.48/5.16	
12.48/5.16	*new_foldFM_LE11(wz8, True, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE8(wz8, wz343, h)
12.48/5.16	The graph contains the following edges 1 >= 1, 5 >= 2, 7 >= 3
12.48/5.16	
12.48/5.16	
12.48/5.16	*new_foldFM_LE11(wz8, False, wz341, wz342, wz343, wz344, h) -> new_foldFM_LE6(wz341, new_foldFM_LE7(wz8, wz343, h), wz344, h)
12.48/5.16	The graph contains the following edges 3 >= 1, 6 >= 3, 7 >= 4
12.48/5.16	
12.48/5.16	
12.48/5.16	----------------------------------------
12.48/5.16	
12.48/5.16	(29)
12.48/5.16	YES
12.70/5.25	EOF