10.90/5.22	YES
13.19/5.81	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
13.19/5.81	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
13.19/5.81	
13.19/5.81	
13.19/5.81	H-Termination with start terms of the given HASKELL could be proven:
13.19/5.81	
13.19/5.81	(0) HASKELL
13.19/5.81	(1) BR [EQUIVALENT, 0 ms]
13.19/5.81	(2) HASKELL
13.19/5.81	(3) COR [EQUIVALENT, 21 ms]
13.19/5.81	(4) HASKELL
13.19/5.81	(5) LetRed [EQUIVALENT, 0 ms]
13.19/5.81	(6) HASKELL
13.19/5.81	(7) Narrow [SOUND, 0 ms]
13.19/5.81	(8) AND
13.19/5.81	    (9) QDP
13.19/5.81	        (10) DependencyGraphProof [EQUIVALENT, 0 ms]
13.19/5.81	        (11) AND
13.19/5.81	            (12) QDP
13.19/5.81	                (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.19/5.81	                (14) YES
13.19/5.81	            (15) QDP
13.19/5.81	                (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.19/5.81	                (17) YES
13.19/5.81	    (18) QDP
13.19/5.81	        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.19/5.81	        (20) YES
13.19/5.81	    (21) QDP
13.19/5.81	        (22) QDPSizeChangeProof [EQUIVALENT, 0 ms]
13.19/5.81	        (23) YES
13.19/5.81	
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(0)
13.19/5.81	Obligation:
13.19/5.81	mainModule Main 
13.19/5.81	module Maybe where {
13.19/5.81	import qualified List;
13.19/5.81	import qualified Main;
13.19/5.81	import qualified Prelude;
13.19/5.81	}
13.19/5.81	module List where {
13.19/5.81	import qualified Main;
13.19/5.81	import qualified Maybe;
13.19/5.81	import qualified Prelude;
13.19/5.81	nub :: Eq a => [a]  ->  [a];
13.19/5.81	nub l = nub' l [] where { 
13.19/5.81	nub' [] _ = [];
13.19/5.81	nub' (x : xs) ls  | x `elem` ls = nub' xs ls
13.19/5.81	 | otherwise = x : nub' xs (x : ls);
13.19/5.81	 };
13.19/5.81	
13.19/5.81	}
13.19/5.81	module Main where {
13.19/5.81	import qualified List;
13.19/5.81	import qualified Maybe;
13.19/5.81	import qualified Prelude;
13.19/5.81	}
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(1) BR (EQUIVALENT)
13.19/5.81	Replaced joker patterns by fresh variables and removed binding patterns.
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(2)
13.19/5.81	Obligation:
13.19/5.81	mainModule Main 
13.19/5.81	module Maybe where {
13.19/5.81	import qualified List;
13.19/5.81	import qualified Main;
13.19/5.81	import qualified Prelude;
13.19/5.81	}
13.19/5.81	module List where {
13.19/5.81	import qualified Main;
13.19/5.81	import qualified Maybe;
13.19/5.81	import qualified Prelude;
13.19/5.81	nub :: Eq a => [a]  ->  [a];
13.19/5.81	nub l = nub' l [] where { 
13.19/5.81	nub' [] vy = [];
13.19/5.81	nub' (x : xs) ls  | x `elem` ls = nub' xs ls
13.19/5.81	 | otherwise = x : nub' xs (x : ls);
13.19/5.81	 };
13.19/5.81	
13.19/5.81	}
13.19/5.81	module Main where {
13.19/5.81	import qualified List;
13.19/5.81	import qualified Maybe;
13.19/5.81	import qualified Prelude;
13.19/5.81	}
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(3) COR (EQUIVALENT)
13.19/5.81	Cond Reductions:
13.19/5.81	The following Function with conditions
13.19/5.81	"undefined |Falseundefined;
13.19/5.81	"
13.19/5.81	is transformed to
13.19/5.81	"undefined  = undefined1;
13.19/5.81	"
13.19/5.81	"undefined0 True = undefined;
13.19/5.81	"
13.19/5.81	"undefined1  = undefined0 False;
13.19/5.81	"
13.19/5.81	The following Function with conditions
13.19/5.81	"nub' [] vy = [];
13.19/5.81	nub' (x : xs) ls|x `elem` lsnub' xs ls|otherwisex : nub' xs (x : ls);
13.19/5.81	"
13.19/5.81	is transformed to
13.19/5.81	"nub' [] vy = nub'3 [] vy;
13.19/5.81	nub' (x : xs) ls = nub'2 (x : xs) ls;
13.19/5.81	"
13.19/5.81	"nub'0 x xs ls True = x : nub' xs (x : ls);
13.19/5.81	"
13.19/5.81	"nub'1 x xs ls True = nub' xs ls;
13.19/5.81	nub'1 x xs ls False = nub'0 x xs ls otherwise;
13.19/5.81	"
13.19/5.81	"nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls);
13.19/5.81	"
13.19/5.81	"nub'3 [] vy = [];
13.19/5.81	nub'3 wv ww = nub'2 wv ww;
13.19/5.81	"
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(4)
13.19/5.81	Obligation:
13.19/5.81	mainModule Main 
13.19/5.81	module Maybe where {
13.19/5.81	import qualified List;
13.19/5.81	import qualified Main;
13.19/5.81	import qualified Prelude;
13.19/5.81	}
13.19/5.81	module List where {
13.19/5.81	import qualified Main;
13.19/5.81	import qualified Maybe;
13.19/5.81	import qualified Prelude;
13.19/5.81	nub :: Eq a => [a]  ->  [a];
13.19/5.81	nub l = nub' l [] where { 
13.19/5.81	nub' [] vy = nub'3 [] vy;
13.19/5.81	nub' (x : xs) ls = nub'2 (x : xs) ls;
13.19/5.81	nub'0 x xs ls True = x : nub' xs (x : ls);
13.19/5.81	nub'1 x xs ls True = nub' xs ls;
13.19/5.81	nub'1 x xs ls False = nub'0 x xs ls otherwise;
13.19/5.81	nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls);
13.19/5.81	nub'3 [] vy = [];
13.19/5.81	nub'3 wv ww = nub'2 wv ww;
13.19/5.81	 };
13.19/5.81	
13.19/5.81	}
13.19/5.81	module Main where {
13.19/5.81	import qualified List;
13.19/5.81	import qualified Maybe;
13.19/5.81	import qualified Prelude;
13.19/5.81	}
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(5) LetRed (EQUIVALENT)
13.19/5.81	Let/Where Reductions:
13.19/5.81	The bindings of the following Let/Where expression
13.19/5.81	"nub' l [] where {
13.19/5.81	nub' [] vy = nub'3 [] vy;
13.19/5.81	nub' (x : xs) ls = nub'2 (x : xs) ls;
13.19/5.81	;
13.19/5.81	nub'0 x xs ls True = x : nub' xs (x : ls);
13.19/5.81	;
13.19/5.81	nub'1 x xs ls True = nub' xs ls;
13.19/5.81	nub'1 x xs ls False = nub'0 x xs ls otherwise;
13.19/5.81	;
13.19/5.81	nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls);
13.19/5.81	;
13.19/5.81	nub'3 [] vy = [];
13.19/5.81	nub'3 wv ww = nub'2 wv ww;
13.19/5.81	} 
13.19/5.81	"
13.19/5.81	are unpacked to the following functions on top level
13.19/5.81	"nubNub'0 x xs ls True = x : nubNub' xs (x : ls);
13.19/5.81	"
13.19/5.81	"nubNub'1 x xs ls True = nubNub' xs ls;
13.19/5.81	nubNub'1 x xs ls False = nubNub'0 x xs ls otherwise;
13.19/5.81	"
13.19/5.81	"nubNub'3 [] vy = [];
13.19/5.81	nubNub'3 wv ww = nubNub'2 wv ww;
13.19/5.81	"
13.19/5.81	"nubNub' [] vy = nubNub'3 [] vy;
13.19/5.81	nubNub' (x : xs) ls = nubNub'2 (x : xs) ls;
13.19/5.81	"
13.19/5.81	"nubNub'2 (x : xs) ls = nubNub'1 x xs ls (x `elem` ls);
13.19/5.81	"
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(6)
13.19/5.81	Obligation:
13.19/5.81	mainModule Main 
13.19/5.81	module Maybe where {
13.19/5.81	import qualified List;
13.19/5.81	import qualified Main;
13.19/5.81	import qualified Prelude;
13.19/5.81	}
13.19/5.81	module List where {
13.19/5.81	import qualified Main;
13.19/5.81	import qualified Maybe;
13.19/5.81	import qualified Prelude;
13.19/5.81	nub :: Eq a => [a]  ->  [a];
13.19/5.81	nub l = nubNub' l [];
13.19/5.81	
13.19/5.81	nubNub' [] vy = nubNub'3 [] vy;
13.19/5.81	nubNub' (x : xs) ls = nubNub'2 (x : xs) ls;
13.19/5.81	
13.19/5.81	nubNub'0 x xs ls True = x : nubNub' xs (x : ls);
13.19/5.81	
13.19/5.81	nubNub'1 x xs ls True = nubNub' xs ls;
13.19/5.81	nubNub'1 x xs ls False = nubNub'0 x xs ls otherwise;
13.19/5.81	
13.19/5.81	nubNub'2 (x : xs) ls = nubNub'1 x xs ls (x `elem` ls);
13.19/5.81	
13.19/5.81	nubNub'3 [] vy = [];
13.19/5.81	nubNub'3 wv ww = nubNub'2 wv ww;
13.19/5.81	
13.19/5.81	}
13.19/5.81	module Main where {
13.19/5.81	import qualified List;
13.19/5.81	import qualified Maybe;
13.19/5.81	import qualified Prelude;
13.19/5.81	}
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(7) Narrow (SOUND)
13.19/5.81	Haskell To QDPs
13.19/5.81	
13.19/5.81	digraph dp_graph {
13.19/5.81	node [outthreshold=100, inthreshold=100];1[label="List.nub",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
13.19/5.81	3[label="List.nub wx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
13.19/5.81	4[label="List.nubNub' wx3 []",fontsize=16,color="burlywood",shape="box"];121[label="wx3/wx30 : wx31",fontsize=10,color="white",style="solid",shape="box"];4 -> 121[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	121 -> 5[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	122[label="wx3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 122[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	122 -> 6[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	5[label="List.nubNub' (wx30 : wx31) []",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
13.19/5.81	6[label="List.nubNub' [] []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
13.19/5.81	7[label="List.nubNub'2 (wx30 : wx31) []",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
13.19/5.81	8[label="List.nubNub'3 [] []",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
13.19/5.81	9[label="List.nubNub'1 wx30 wx31 [] (wx30 `elem` [])",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
13.19/5.81	10[label="[]",fontsize=16,color="green",shape="box"];11[label="List.nubNub'1 wx30 wx31 [] (any . (==))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
13.19/5.81	12[label="List.nubNub'1 wx30 wx31 [] (any ((==) wx30) [])",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
13.19/5.81	13[label="List.nubNub'1 wx30 wx31 [] (or . map ((==) wx30))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
13.19/5.81	14[label="List.nubNub'1 wx30 wx31 [] (or (map ((==) wx30) []))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
13.19/5.81	15[label="List.nubNub'1 wx30 wx31 [] (foldr (||) False (map ((==) wx30) []))",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3];
13.19/5.81	16[label="List.nubNub'1 wx30 wx31 [] (foldr (||) False [])",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3];
13.19/5.81	17[label="List.nubNub'1 wx30 wx31 [] False",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3];
13.19/5.81	18[label="List.nubNub'0 wx30 wx31 [] otherwise",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3];
13.19/5.81	19[label="List.nubNub'0 wx30 wx31 [] True",fontsize=16,color="black",shape="box"];19 -> 20[label="",style="solid", color="black", weight=3];
13.19/5.81	20[label="wx30 : List.nubNub' wx31 (wx30 : [])",fontsize=16,color="green",shape="box"];20 -> 21[label="",style="dashed", color="green", weight=3];
13.19/5.81	21[label="List.nubNub' wx31 (wx30 : [])",fontsize=16,color="burlywood",shape="triangle"];123[label="wx31/wx310 : wx311",fontsize=10,color="white",style="solid",shape="box"];21 -> 123[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	123 -> 22[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	124[label="wx31/[]",fontsize=10,color="white",style="solid",shape="box"];21 -> 124[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	124 -> 23[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	22[label="List.nubNub' (wx310 : wx311) (wx30 : [])",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3];
13.19/5.81	23[label="List.nubNub' [] (wx30 : [])",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3];
13.19/5.81	24[label="List.nubNub'2 (wx310 : wx311) (wx30 : [])",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
13.19/5.81	25[label="List.nubNub'3 [] (wx30 : [])",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3];
13.19/5.81	26[label="List.nubNub'1 wx310 wx311 (wx30 : []) (wx310 `elem` wx30 : [])",fontsize=16,color="black",shape="box"];26 -> 28[label="",style="solid", color="black", weight=3];
13.19/5.81	27[label="[]",fontsize=16,color="green",shape="box"];28[label="List.nubNub'1 wx310 wx311 (wx30 : []) (any . (==))",fontsize=16,color="black",shape="box"];28 -> 29[label="",style="solid", color="black", weight=3];
13.19/5.81	29[label="List.nubNub'1 wx310 wx311 (wx30 : []) (any ((==) wx310) (wx30 : []))",fontsize=16,color="black",shape="box"];29 -> 30[label="",style="solid", color="black", weight=3];
13.19/5.81	30[label="List.nubNub'1 wx310 wx311 (wx30 : []) (or . map ((==) wx310))",fontsize=16,color="black",shape="box"];30 -> 31[label="",style="solid", color="black", weight=3];
13.19/5.81	31[label="List.nubNub'1 wx310 wx311 (wx30 : []) (or (map ((==) wx310) (wx30 : [])))",fontsize=16,color="black",shape="box"];31 -> 32[label="",style="solid", color="black", weight=3];
13.19/5.81	32[label="List.nubNub'1 wx310 wx311 (wx30 : []) (foldr (||) False (map ((==) wx310) (wx30 : [])))",fontsize=16,color="black",shape="box"];32 -> 33[label="",style="solid", color="black", weight=3];
13.19/5.81	33[label="List.nubNub'1 wx310 wx311 (wx30 : []) (foldr (||) False (((==) wx310 wx30) : map ((==) wx310) []))",fontsize=16,color="black",shape="box"];33 -> 34[label="",style="solid", color="black", weight=3];
13.19/5.81	34[label="List.nubNub'1 wx310 wx311 (wx30 : []) ((||) (==) wx310 wx30 foldr (||) False (map ((==) wx310) []))",fontsize=16,color="burlywood",shape="box"];125[label="wx310/False",fontsize=10,color="white",style="solid",shape="box"];34 -> 125[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	125 -> 35[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	126[label="wx310/True",fontsize=10,color="white",style="solid",shape="box"];34 -> 126[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	126 -> 36[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	35[label="List.nubNub'1 False wx311 (wx30 : []) ((||) (==) False wx30 foldr (||) False (map ((==) False) []))",fontsize=16,color="burlywood",shape="box"];127[label="wx30/False",fontsize=10,color="white",style="solid",shape="box"];35 -> 127[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	127 -> 37[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	128[label="wx30/True",fontsize=10,color="white",style="solid",shape="box"];35 -> 128[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	128 -> 38[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	36[label="List.nubNub'1 True wx311 (wx30 : []) ((||) (==) True wx30 foldr (||) False (map ((==) True) []))",fontsize=16,color="burlywood",shape="box"];129[label="wx30/False",fontsize=10,color="white",style="solid",shape="box"];36 -> 129[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	129 -> 39[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	130[label="wx30/True",fontsize=10,color="white",style="solid",shape="box"];36 -> 130[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	130 -> 40[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	37[label="List.nubNub'1 False wx311 (False : []) ((||) (==) False False foldr (||) False (map ((==) False) []))",fontsize=16,color="black",shape="box"];37 -> 41[label="",style="solid", color="black", weight=3];
13.19/5.81	38[label="List.nubNub'1 False wx311 (True : []) ((||) (==) False True foldr (||) False (map ((==) False) []))",fontsize=16,color="black",shape="box"];38 -> 42[label="",style="solid", color="black", weight=3];
13.19/5.81	39[label="List.nubNub'1 True wx311 (False : []) ((||) (==) True False foldr (||) False (map ((==) True) []))",fontsize=16,color="black",shape="box"];39 -> 43[label="",style="solid", color="black", weight=3];
13.19/5.81	40[label="List.nubNub'1 True wx311 (True : []) ((||) (==) True True foldr (||) False (map ((==) True) []))",fontsize=16,color="black",shape="box"];40 -> 44[label="",style="solid", color="black", weight=3];
13.19/5.81	41[label="List.nubNub'1 False wx311 (False : []) ((||) True foldr (||) False (map ((==) False) []))",fontsize=16,color="black",shape="box"];41 -> 45[label="",style="solid", color="black", weight=3];
13.19/5.81	42[label="List.nubNub'1 False wx311 (True : []) ((||) False foldr (||) False (map ((==) False) []))",fontsize=16,color="black",shape="box"];42 -> 46[label="",style="solid", color="black", weight=3];
13.19/5.81	43[label="List.nubNub'1 True wx311 (False : []) ((||) False foldr (||) False (map ((==) True) []))",fontsize=16,color="black",shape="box"];43 -> 47[label="",style="solid", color="black", weight=3];
13.19/5.81	44[label="List.nubNub'1 True wx311 (True : []) ((||) True foldr (||) False (map ((==) True) []))",fontsize=16,color="black",shape="box"];44 -> 48[label="",style="solid", color="black", weight=3];
13.19/5.81	45[label="List.nubNub'1 False wx311 (False : []) True",fontsize=16,color="black",shape="box"];45 -> 49[label="",style="solid", color="black", weight=3];
13.19/5.81	46[label="List.nubNub'1 False wx311 (True : []) (foldr (||) False (map ((==) False) []))",fontsize=16,color="black",shape="box"];46 -> 50[label="",style="solid", color="black", weight=3];
13.19/5.81	47[label="List.nubNub'1 True wx311 (False : []) (foldr (||) False (map ((==) True) []))",fontsize=16,color="black",shape="box"];47 -> 51[label="",style="solid", color="black", weight=3];
13.19/5.81	48[label="List.nubNub'1 True wx311 (True : []) True",fontsize=16,color="black",shape="box"];48 -> 52[label="",style="solid", color="black", weight=3];
13.19/5.81	49 -> 21[label="",style="dashed", color="red", weight=0];
13.19/5.81	49[label="List.nubNub' wx311 (False : [])",fontsize=16,color="magenta"];49 -> 53[label="",style="dashed", color="magenta", weight=3];
13.19/5.81	49 -> 54[label="",style="dashed", color="magenta", weight=3];
13.19/5.81	50[label="List.nubNub'1 False wx311 (True : []) (foldr (||) False [])",fontsize=16,color="black",shape="box"];50 -> 55[label="",style="solid", color="black", weight=3];
13.19/5.81	51[label="List.nubNub'1 True wx311 (False : []) (foldr (||) False [])",fontsize=16,color="black",shape="box"];51 -> 56[label="",style="solid", color="black", weight=3];
13.19/5.81	52 -> 21[label="",style="dashed", color="red", weight=0];
13.19/5.81	52[label="List.nubNub' wx311 (True : [])",fontsize=16,color="magenta"];52 -> 57[label="",style="dashed", color="magenta", weight=3];
13.19/5.81	52 -> 58[label="",style="dashed", color="magenta", weight=3];
13.19/5.81	53[label="False",fontsize=16,color="green",shape="box"];54[label="wx311",fontsize=16,color="green",shape="box"];55[label="List.nubNub'1 False wx311 (True : []) False",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3];
13.19/5.81	56[label="List.nubNub'1 True wx311 (False : []) False",fontsize=16,color="black",shape="box"];56 -> 60[label="",style="solid", color="black", weight=3];
13.19/5.81	57[label="True",fontsize=16,color="green",shape="box"];58[label="wx311",fontsize=16,color="green",shape="box"];59[label="List.nubNub'0 False wx311 (True : []) otherwise",fontsize=16,color="black",shape="box"];59 -> 61[label="",style="solid", color="black", weight=3];
13.19/5.81	60[label="List.nubNub'0 True wx311 (False : []) otherwise",fontsize=16,color="black",shape="box"];60 -> 62[label="",style="solid", color="black", weight=3];
13.19/5.81	61[label="List.nubNub'0 False wx311 (True : []) True",fontsize=16,color="black",shape="box"];61 -> 63[label="",style="solid", color="black", weight=3];
13.19/5.81	62[label="List.nubNub'0 True wx311 (False : []) True",fontsize=16,color="black",shape="box"];62 -> 64[label="",style="solid", color="black", weight=3];
13.19/5.81	63[label="False : List.nubNub' wx311 (False : True : [])",fontsize=16,color="green",shape="box"];63 -> 65[label="",style="dashed", color="green", weight=3];
13.19/5.81	64[label="True : List.nubNub' wx311 (True : False : [])",fontsize=16,color="green",shape="box"];64 -> 66[label="",style="dashed", color="green", weight=3];
13.19/5.81	65[label="List.nubNub' wx311 (False : True : [])",fontsize=16,color="burlywood",shape="triangle"];131[label="wx311/wx3110 : wx3111",fontsize=10,color="white",style="solid",shape="box"];65 -> 131[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	131 -> 67[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	132[label="wx311/[]",fontsize=10,color="white",style="solid",shape="box"];65 -> 132[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	132 -> 68[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	66[label="List.nubNub' wx311 (True : False : [])",fontsize=16,color="burlywood",shape="triangle"];133[label="wx311/wx3110 : wx3111",fontsize=10,color="white",style="solid",shape="box"];66 -> 133[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	133 -> 69[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	134[label="wx311/[]",fontsize=10,color="white",style="solid",shape="box"];66 -> 134[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	134 -> 70[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	67[label="List.nubNub' (wx3110 : wx3111) (False : True : [])",fontsize=16,color="black",shape="box"];67 -> 71[label="",style="solid", color="black", weight=3];
13.19/5.81	68[label="List.nubNub' [] (False : True : [])",fontsize=16,color="black",shape="box"];68 -> 72[label="",style="solid", color="black", weight=3];
13.19/5.81	69[label="List.nubNub' (wx3110 : wx3111) (True : False : [])",fontsize=16,color="black",shape="box"];69 -> 73[label="",style="solid", color="black", weight=3];
13.19/5.81	70[label="List.nubNub' [] (True : False : [])",fontsize=16,color="black",shape="box"];70 -> 74[label="",style="solid", color="black", weight=3];
13.19/5.81	71[label="List.nubNub'2 (wx3110 : wx3111) (False : True : [])",fontsize=16,color="black",shape="box"];71 -> 75[label="",style="solid", color="black", weight=3];
13.19/5.81	72[label="List.nubNub'3 [] (False : True : [])",fontsize=16,color="black",shape="box"];72 -> 76[label="",style="solid", color="black", weight=3];
13.19/5.81	73[label="List.nubNub'2 (wx3110 : wx3111) (True : False : [])",fontsize=16,color="black",shape="box"];73 -> 77[label="",style="solid", color="black", weight=3];
13.19/5.81	74[label="List.nubNub'3 [] (True : False : [])",fontsize=16,color="black",shape="box"];74 -> 78[label="",style="solid", color="black", weight=3];
13.19/5.81	75[label="List.nubNub'1 wx3110 wx3111 (False : True : []) (wx3110 `elem` False : True : [])",fontsize=16,color="black",shape="box"];75 -> 79[label="",style="solid", color="black", weight=3];
13.19/5.81	76[label="[]",fontsize=16,color="green",shape="box"];77[label="List.nubNub'1 wx3110 wx3111 (True : False : []) (wx3110 `elem` True : False : [])",fontsize=16,color="black",shape="box"];77 -> 80[label="",style="solid", color="black", weight=3];
13.19/5.81	78[label="[]",fontsize=16,color="green",shape="box"];79[label="List.nubNub'1 wx3110 wx3111 (False : True : []) (any . (==))",fontsize=16,color="black",shape="box"];79 -> 81[label="",style="solid", color="black", weight=3];
13.19/5.81	80[label="List.nubNub'1 wx3110 wx3111 (True : False : []) (any . (==))",fontsize=16,color="black",shape="box"];80 -> 82[label="",style="solid", color="black", weight=3];
13.19/5.81	81[label="List.nubNub'1 wx3110 wx3111 (False : True : []) (any ((==) wx3110) (False : True : []))",fontsize=16,color="black",shape="box"];81 -> 83[label="",style="solid", color="black", weight=3];
13.19/5.81	82[label="List.nubNub'1 wx3110 wx3111 (True : False : []) (any ((==) wx3110) (True : False : []))",fontsize=16,color="black",shape="box"];82 -> 84[label="",style="solid", color="black", weight=3];
13.19/5.81	83[label="List.nubNub'1 wx3110 wx3111 (False : True : []) (or . map ((==) wx3110))",fontsize=16,color="black",shape="box"];83 -> 85[label="",style="solid", color="black", weight=3];
13.19/5.81	84[label="List.nubNub'1 wx3110 wx3111 (True : False : []) (or . map ((==) wx3110))",fontsize=16,color="black",shape="box"];84 -> 86[label="",style="solid", color="black", weight=3];
13.19/5.81	85[label="List.nubNub'1 wx3110 wx3111 (False : True : []) (or (map ((==) wx3110) (False : True : [])))",fontsize=16,color="black",shape="box"];85 -> 87[label="",style="solid", color="black", weight=3];
13.19/5.81	86[label="List.nubNub'1 wx3110 wx3111 (True : False : []) (or (map ((==) wx3110) (True : False : [])))",fontsize=16,color="black",shape="box"];86 -> 88[label="",style="solid", color="black", weight=3];
13.19/5.81	87[label="List.nubNub'1 wx3110 wx3111 (False : True : []) (foldr (||) False (map ((==) wx3110) (False : True : [])))",fontsize=16,color="black",shape="box"];87 -> 89[label="",style="solid", color="black", weight=3];
13.19/5.81	88[label="List.nubNub'1 wx3110 wx3111 (True : False : []) (foldr (||) False (map ((==) wx3110) (True : False : [])))",fontsize=16,color="black",shape="box"];88 -> 90[label="",style="solid", color="black", weight=3];
13.19/5.81	89[label="List.nubNub'1 wx3110 wx3111 (False : True : []) (foldr (||) False (((==) wx3110 False) : map ((==) wx3110) (True : [])))",fontsize=16,color="black",shape="box"];89 -> 91[label="",style="solid", color="black", weight=3];
13.19/5.81	90[label="List.nubNub'1 wx3110 wx3111 (True : False : []) (foldr (||) False (((==) wx3110 True) : map ((==) wx3110) (False : [])))",fontsize=16,color="black",shape="box"];90 -> 92[label="",style="solid", color="black", weight=3];
13.19/5.81	91[label="List.nubNub'1 wx3110 wx3111 (False : True : []) ((||) (==) wx3110 False foldr (||) False (map ((==) wx3110) (True : [])))",fontsize=16,color="burlywood",shape="box"];135[label="wx3110/False",fontsize=10,color="white",style="solid",shape="box"];91 -> 135[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	135 -> 93[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	136[label="wx3110/True",fontsize=10,color="white",style="solid",shape="box"];91 -> 136[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	136 -> 94[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	92[label="List.nubNub'1 wx3110 wx3111 (True : False : []) ((||) (==) wx3110 True foldr (||) False (map ((==) wx3110) (False : [])))",fontsize=16,color="burlywood",shape="box"];137[label="wx3110/False",fontsize=10,color="white",style="solid",shape="box"];92 -> 137[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	137 -> 95[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	138[label="wx3110/True",fontsize=10,color="white",style="solid",shape="box"];92 -> 138[label="",style="solid", color="burlywood", weight=9];
13.19/5.81	138 -> 96[label="",style="solid", color="burlywood", weight=3];
13.19/5.81	93[label="List.nubNub'1 False wx3111 (False : True : []) ((||) (==) False False foldr (||) False (map ((==) False) (True : [])))",fontsize=16,color="black",shape="box"];93 -> 97[label="",style="solid", color="black", weight=3];
13.19/5.81	94[label="List.nubNub'1 True wx3111 (False : True : []) ((||) (==) True False foldr (||) False (map ((==) True) (True : [])))",fontsize=16,color="black",shape="box"];94 -> 98[label="",style="solid", color="black", weight=3];
13.19/5.81	95[label="List.nubNub'1 False wx3111 (True : False : []) ((||) (==) False True foldr (||) False (map ((==) False) (False : [])))",fontsize=16,color="black",shape="box"];95 -> 99[label="",style="solid", color="black", weight=3];
13.19/5.81	96[label="List.nubNub'1 True wx3111 (True : False : []) ((||) (==) True True foldr (||) False (map ((==) True) (False : [])))",fontsize=16,color="black",shape="box"];96 -> 100[label="",style="solid", color="black", weight=3];
13.19/5.81	97[label="List.nubNub'1 False wx3111 (False : True : []) ((||) True foldr (||) False (map ((==) False) (True : [])))",fontsize=16,color="black",shape="box"];97 -> 101[label="",style="solid", color="black", weight=3];
13.19/5.81	98[label="List.nubNub'1 True wx3111 (False : True : []) ((||) False foldr (||) False (map ((==) True) (True : [])))",fontsize=16,color="black",shape="box"];98 -> 102[label="",style="solid", color="black", weight=3];
13.19/5.81	99[label="List.nubNub'1 False wx3111 (True : False : []) ((||) False foldr (||) False (map ((==) False) (False : [])))",fontsize=16,color="black",shape="box"];99 -> 103[label="",style="solid", color="black", weight=3];
13.19/5.81	100[label="List.nubNub'1 True wx3111 (True : False : []) ((||) True foldr (||) False (map ((==) True) (False : [])))",fontsize=16,color="black",shape="box"];100 -> 104[label="",style="solid", color="black", weight=3];
13.19/5.81	101[label="List.nubNub'1 False wx3111 (False : True : []) True",fontsize=16,color="black",shape="box"];101 -> 105[label="",style="solid", color="black", weight=3];
13.19/5.81	102[label="List.nubNub'1 True wx3111 (False : True : []) (foldr (||) False (map ((==) True) (True : [])))",fontsize=16,color="black",shape="box"];102 -> 106[label="",style="solid", color="black", weight=3];
13.19/5.81	103[label="List.nubNub'1 False wx3111 (True : False : []) (foldr (||) False (map ((==) False) (False : [])))",fontsize=16,color="black",shape="box"];103 -> 107[label="",style="solid", color="black", weight=3];
13.19/5.81	104[label="List.nubNub'1 True wx3111 (True : False : []) True",fontsize=16,color="black",shape="box"];104 -> 108[label="",style="solid", color="black", weight=3];
13.19/5.81	105 -> 65[label="",style="dashed", color="red", weight=0];
13.19/5.81	105[label="List.nubNub' wx3111 (False : True : [])",fontsize=16,color="magenta"];105 -> 109[label="",style="dashed", color="magenta", weight=3];
13.19/5.81	106[label="List.nubNub'1 True wx3111 (False : True : []) (foldr (||) False (((==) True True) : map ((==) True) []))",fontsize=16,color="black",shape="box"];106 -> 110[label="",style="solid", color="black", weight=3];
13.19/5.81	107[label="List.nubNub'1 False wx3111 (True : False : []) (foldr (||) False (((==) False False) : map ((==) False) []))",fontsize=16,color="black",shape="box"];107 -> 111[label="",style="solid", color="black", weight=3];
13.19/5.81	108 -> 66[label="",style="dashed", color="red", weight=0];
13.19/5.81	108[label="List.nubNub' wx3111 (True : False : [])",fontsize=16,color="magenta"];108 -> 112[label="",style="dashed", color="magenta", weight=3];
13.19/5.81	109[label="wx3111",fontsize=16,color="green",shape="box"];110[label="List.nubNub'1 True wx3111 (False : True : []) ((||) (==) True True foldr (||) False (map ((==) True) []))",fontsize=16,color="black",shape="box"];110 -> 113[label="",style="solid", color="black", weight=3];
13.19/5.81	111[label="List.nubNub'1 False wx3111 (True : False : []) ((||) (==) False False foldr (||) False (map ((==) False) []))",fontsize=16,color="black",shape="box"];111 -> 114[label="",style="solid", color="black", weight=3];
13.19/5.81	112[label="wx3111",fontsize=16,color="green",shape="box"];113[label="List.nubNub'1 True wx3111 (False : True : []) ((||) True foldr (||) False (map ((==) True) []))",fontsize=16,color="black",shape="box"];113 -> 115[label="",style="solid", color="black", weight=3];
13.19/5.81	114[label="List.nubNub'1 False wx3111 (True : False : []) ((||) True foldr (||) False (map ((==) False) []))",fontsize=16,color="black",shape="box"];114 -> 116[label="",style="solid", color="black", weight=3];
13.19/5.81	115[label="List.nubNub'1 True wx3111 (False : True : []) True",fontsize=16,color="black",shape="box"];115 -> 117[label="",style="solid", color="black", weight=3];
13.19/5.81	116[label="List.nubNub'1 False wx3111 (True : False : []) True",fontsize=16,color="black",shape="box"];116 -> 118[label="",style="solid", color="black", weight=3];
13.19/5.81	117 -> 65[label="",style="dashed", color="red", weight=0];
13.19/5.81	117[label="List.nubNub' wx3111 (False : True : [])",fontsize=16,color="magenta"];117 -> 119[label="",style="dashed", color="magenta", weight=3];
13.19/5.81	118 -> 66[label="",style="dashed", color="red", weight=0];
13.19/5.81	118[label="List.nubNub' wx3111 (True : False : [])",fontsize=16,color="magenta"];118 -> 120[label="",style="dashed", color="magenta", weight=3];
13.19/5.81	119[label="wx3111",fontsize=16,color="green",shape="box"];120[label="wx3111",fontsize=16,color="green",shape="box"];}
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(8)
13.19/5.81	Complex Obligation (AND)
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(9)
13.19/5.81	Obligation:
13.19/5.81	Q DP problem:
13.19/5.81	The TRS P consists of the following rules:
13.19/5.81	
13.19/5.81	   new_nubNub'1(:(False, wx311), False) -> new_nubNub'1(wx311, False)
13.19/5.81	   new_nubNub'1(:(True, wx311), True) -> new_nubNub'1(wx311, True)
13.19/5.81	
13.19/5.81	R is empty.
13.19/5.81	Q is empty.
13.19/5.81	We have to consider all minimal (P,Q,R)-chains.
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(10) DependencyGraphProof (EQUIVALENT)
13.19/5.81	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs.
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(11)
13.19/5.81	Complex Obligation (AND)
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(12)
13.19/5.81	Obligation:
13.19/5.81	Q DP problem:
13.19/5.81	The TRS P consists of the following rules:
13.19/5.81	
13.19/5.81	   new_nubNub'1(:(True, wx311), True) -> new_nubNub'1(wx311, True)
13.19/5.81	
13.19/5.81	R is empty.
13.19/5.81	Q is empty.
13.19/5.81	We have to consider all minimal (P,Q,R)-chains.
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(13) QDPSizeChangeProof (EQUIVALENT)
13.19/5.81	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. 
13.19/5.81	
13.19/5.81	From the DPs we obtained the following set of size-change graphs:
13.19/5.81	*new_nubNub'1(:(True, wx311), True) -> new_nubNub'1(wx311, True)
13.19/5.81	The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
13.19/5.81	
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(14)
13.19/5.81	YES
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(15)
13.19/5.81	Obligation:
13.19/5.81	Q DP problem:
13.19/5.81	The TRS P consists of the following rules:
13.19/5.81	
13.19/5.81	   new_nubNub'1(:(False, wx311), False) -> new_nubNub'1(wx311, False)
13.19/5.81	
13.19/5.81	R is empty.
13.19/5.81	Q is empty.
13.19/5.81	We have to consider all minimal (P,Q,R)-chains.
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(16) QDPSizeChangeProof (EQUIVALENT)
13.19/5.81	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. 
13.19/5.81	
13.19/5.81	From the DPs we obtained the following set of size-change graphs:
13.19/5.81	*new_nubNub'1(:(False, wx311), False) -> new_nubNub'1(wx311, False)
13.19/5.81	The graph contains the following edges 1 > 1, 1 > 2, 2 >= 2
13.19/5.81	
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(17)
13.19/5.81	YES
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(18)
13.19/5.81	Obligation:
13.19/5.81	Q DP problem:
13.19/5.81	The TRS P consists of the following rules:
13.19/5.81	
13.19/5.81	   new_nubNub'0(:(False, wx3111)) -> new_nubNub'0(wx3111)
13.19/5.81	   new_nubNub'0(:(True, wx3111)) -> new_nubNub'0(wx3111)
13.19/5.81	
13.19/5.81	R is empty.
13.19/5.81	Q is empty.
13.19/5.81	We have to consider all minimal (P,Q,R)-chains.
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(19) QDPSizeChangeProof (EQUIVALENT)
13.19/5.81	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. 
13.19/5.81	
13.19/5.81	From the DPs we obtained the following set of size-change graphs:
13.19/5.81	*new_nubNub'0(:(False, wx3111)) -> new_nubNub'0(wx3111)
13.19/5.81	The graph contains the following edges 1 > 1
13.19/5.81	
13.19/5.81	
13.19/5.81	*new_nubNub'0(:(True, wx3111)) -> new_nubNub'0(wx3111)
13.19/5.81	The graph contains the following edges 1 > 1
13.19/5.81	
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(20)
13.19/5.81	YES
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(21)
13.19/5.81	Obligation:
13.19/5.81	Q DP problem:
13.19/5.81	The TRS P consists of the following rules:
13.19/5.81	
13.19/5.81	   new_nubNub'(:(False, wx3111)) -> new_nubNub'(wx3111)
13.19/5.81	   new_nubNub'(:(True, wx3111)) -> new_nubNub'(wx3111)
13.19/5.81	
13.19/5.81	R is empty.
13.19/5.81	Q is empty.
13.19/5.81	We have to consider all minimal (P,Q,R)-chains.
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(22) QDPSizeChangeProof (EQUIVALENT)
13.19/5.81	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. 
13.19/5.81	
13.19/5.81	From the DPs we obtained the following set of size-change graphs:
13.19/5.81	*new_nubNub'(:(False, wx3111)) -> new_nubNub'(wx3111)
13.19/5.81	The graph contains the following edges 1 > 1
13.19/5.81	
13.19/5.81	
13.19/5.81	*new_nubNub'(:(True, wx3111)) -> new_nubNub'(wx3111)
13.19/5.81	The graph contains the following edges 1 > 1
13.19/5.81	
13.19/5.81	
13.19/5.81	----------------------------------------
13.19/5.81	
13.19/5.81	(23)
13.19/5.81	YES
13.24/5.91	EOF