11.87/4.79	YES
14.00/5.37	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
14.00/5.37	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
14.00/5.37	
14.00/5.37	
14.00/5.37	H-Termination with start terms of the given HASKELL could be proven:
14.00/5.37	
14.00/5.37	(0) HASKELL
14.00/5.37	(1) BR [EQUIVALENT, 0 ms]
14.00/5.37	(2) HASKELL
14.00/5.37	(3) COR [EQUIVALENT, 29 ms]
14.00/5.37	(4) HASKELL
14.00/5.37	(5) LetRed [EQUIVALENT, 0 ms]
14.00/5.37	(6) HASKELL
14.00/5.37	(7) Narrow [SOUND, 0 ms]
14.00/5.37	(8) QDP
14.00/5.37	(9) DependencyGraphProof [EQUIVALENT, 0 ms]
14.00/5.37	(10) QDP
14.00/5.37	(11) TransformationProof [EQUIVALENT, 17 ms]
14.00/5.37	(12) QDP
14.00/5.37	(13) DependencyGraphProof [EQUIVALENT, 0 ms]
14.00/5.37	(14) QDP
14.00/5.37	(15) UsableRulesProof [EQUIVALENT, 0 ms]
14.00/5.37	(16) QDP
14.00/5.37	(17) QReductionProof [EQUIVALENT, 0 ms]
14.00/5.37	(18) QDP
14.00/5.37	(19) TransformationProof [EQUIVALENT, 0 ms]
14.00/5.37	(20) QDP
14.00/5.37	(21) TransformationProof [EQUIVALENT, 0 ms]
14.00/5.37	(22) QDP
14.00/5.37	(23) TransformationProof [EQUIVALENT, 0 ms]
14.00/5.37	(24) QDP
14.00/5.37	(25) TransformationProof [EQUIVALENT, 0 ms]
14.00/5.37	(26) QDP
14.00/5.37	(27) TransformationProof [EQUIVALENT, 0 ms]
14.00/5.37	(28) QDP
14.00/5.37	(29) QDPSizeChangeProof [EQUIVALENT, 0 ms]
14.00/5.37	(30) YES
14.00/5.37	
14.00/5.37	
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(0)
14.00/5.37	Obligation:
14.00/5.37	mainModule Main 
14.00/5.37	module Maybe where {
14.00/5.37	import qualified List;
14.00/5.37	import qualified Main;
14.00/5.37	import qualified Prelude;
14.00/5.37	}
14.00/5.37	module List where {
14.00/5.37	import qualified Main;
14.00/5.37	import qualified Maybe;
14.00/5.37	import qualified Prelude;
14.00/5.37	nub :: Eq a => [a]  ->  [a];
14.00/5.37	nub l = nub' l [] where { 
14.00/5.37	nub' [] _ = [];
14.00/5.37	nub' (x : xs) ls  | x `elem` ls = nub' xs ls
14.00/5.37	 | otherwise = x : nub' xs (x : ls);
14.00/5.37	 };
14.00/5.37	
14.00/5.37	}
14.00/5.37	module Main where {
14.00/5.37	import qualified List;
14.00/5.37	import qualified Maybe;
14.00/5.37	import qualified Prelude;
14.00/5.37	}
14.00/5.37	
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(1) BR (EQUIVALENT)
14.00/5.37	Replaced joker patterns by fresh variables and removed binding patterns.
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(2)
14.00/5.37	Obligation:
14.00/5.37	mainModule Main 
14.00/5.37	module Maybe where {
14.00/5.37	import qualified List;
14.00/5.37	import qualified Main;
14.00/5.37	import qualified Prelude;
14.00/5.37	}
14.00/5.37	module List where {
14.00/5.37	import qualified Main;
14.00/5.37	import qualified Maybe;
14.00/5.37	import qualified Prelude;
14.00/5.37	nub :: Eq a => [a]  ->  [a];
14.00/5.37	nub l = nub' l [] where { 
14.00/5.37	nub' [] vy = [];
14.00/5.37	nub' (x : xs) ls  | x `elem` ls = nub' xs ls
14.00/5.37	 | otherwise = x : nub' xs (x : ls);
14.00/5.37	 };
14.00/5.37	
14.00/5.37	}
14.00/5.37	module Main where {
14.00/5.37	import qualified List;
14.00/5.37	import qualified Maybe;
14.00/5.37	import qualified Prelude;
14.00/5.37	}
14.00/5.37	
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(3) COR (EQUIVALENT)
14.00/5.37	Cond Reductions:
14.00/5.37	The following Function with conditions
14.00/5.37	"undefined |Falseundefined;
14.00/5.37	"
14.00/5.37	is transformed to
14.00/5.37	"undefined  = undefined1;
14.00/5.37	"
14.00/5.37	"undefined0 True = undefined;
14.00/5.37	"
14.00/5.37	"undefined1  = undefined0 False;
14.00/5.37	"
14.00/5.37	The following Function with conditions
14.00/5.37	"nub' [] vy = [];
14.00/5.37	nub' (x : xs) ls|x `elem` lsnub' xs ls|otherwisex : nub' xs (x : ls);
14.00/5.37	"
14.00/5.37	is transformed to
14.00/5.37	"nub' [] vy = nub'3 [] vy;
14.00/5.37	nub' (x : xs) ls = nub'2 (x : xs) ls;
14.00/5.37	"
14.00/5.37	"nub'1 x xs ls True = nub' xs ls;
14.00/5.37	nub'1 x xs ls False = nub'0 x xs ls otherwise;
14.00/5.37	"
14.00/5.37	"nub'0 x xs ls True = x : nub' xs (x : ls);
14.00/5.37	"
14.00/5.37	"nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls);
14.00/5.37	"
14.00/5.37	"nub'3 [] vy = [];
14.00/5.37	nub'3 wv ww = nub'2 wv ww;
14.00/5.37	"
14.00/5.37	
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(4)
14.00/5.37	Obligation:
14.00/5.37	mainModule Main 
14.00/5.37	module Maybe where {
14.00/5.37	import qualified List;
14.00/5.37	import qualified Main;
14.00/5.37	import qualified Prelude;
14.00/5.37	}
14.00/5.37	module List where {
14.00/5.37	import qualified Main;
14.00/5.37	import qualified Maybe;
14.00/5.37	import qualified Prelude;
14.00/5.37	nub :: Eq a => [a]  ->  [a];
14.00/5.37	nub l = nub' l [] where { 
14.00/5.37	nub' [] vy = nub'3 [] vy;
14.00/5.37	nub' (x : xs) ls = nub'2 (x : xs) ls;
14.00/5.37	nub'0 x xs ls True = x : nub' xs (x : ls);
14.00/5.37	nub'1 x xs ls True = nub' xs ls;
14.00/5.37	nub'1 x xs ls False = nub'0 x xs ls otherwise;
14.00/5.37	nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls);
14.00/5.37	nub'3 [] vy = [];
14.00/5.37	nub'3 wv ww = nub'2 wv ww;
14.00/5.37	 };
14.00/5.37	
14.00/5.37	}
14.00/5.37	module Main where {
14.00/5.37	import qualified List;
14.00/5.37	import qualified Maybe;
14.00/5.37	import qualified Prelude;
14.00/5.37	}
14.00/5.37	
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(5) LetRed (EQUIVALENT)
14.00/5.37	Let/Where Reductions:
14.00/5.37	The bindings of the following Let/Where expression
14.00/5.37	"nub' l [] where {
14.00/5.37	nub' [] vy = nub'3 [] vy;
14.00/5.37	nub' (x : xs) ls = nub'2 (x : xs) ls;
14.00/5.37	;
14.00/5.37	nub'0 x xs ls True = x : nub' xs (x : ls);
14.00/5.37	;
14.00/5.37	nub'1 x xs ls True = nub' xs ls;
14.00/5.37	nub'1 x xs ls False = nub'0 x xs ls otherwise;
14.00/5.37	;
14.00/5.37	nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls);
14.00/5.37	;
14.00/5.37	nub'3 [] vy = [];
14.00/5.37	nub'3 wv ww = nub'2 wv ww;
14.00/5.37	} 
14.00/5.37	"
14.00/5.37	are unpacked to the following functions on top level
14.00/5.37	"nubNub' [] vy = nubNub'3 [] vy;
14.00/5.37	nubNub' (x : xs) ls = nubNub'2 (x : xs) ls;
14.00/5.37	"
14.00/5.37	"nubNub'2 (x : xs) ls = nubNub'1 x xs ls (x `elem` ls);
14.00/5.37	"
14.00/5.37	"nubNub'0 x xs ls True = x : nubNub' xs (x : ls);
14.00/5.37	"
14.00/5.37	"nubNub'3 [] vy = [];
14.00/5.37	nubNub'3 wv ww = nubNub'2 wv ww;
14.00/5.37	"
14.00/5.37	"nubNub'1 x xs ls True = nubNub' xs ls;
14.00/5.37	nubNub'1 x xs ls False = nubNub'0 x xs ls otherwise;
14.00/5.37	"
14.00/5.37	
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(6)
14.00/5.37	Obligation:
14.00/5.37	mainModule Main 
14.00/5.37	module Maybe where {
14.00/5.37	import qualified List;
14.00/5.37	import qualified Main;
14.00/5.37	import qualified Prelude;
14.00/5.37	}
14.00/5.37	module List where {
14.00/5.37	import qualified Main;
14.00/5.37	import qualified Maybe;
14.00/5.37	import qualified Prelude;
14.00/5.37	nub :: Eq a => [a]  ->  [a];
14.00/5.37	nub l = nubNub' l [];
14.00/5.37	
14.00/5.37	nubNub' [] vy = nubNub'3 [] vy;
14.00/5.37	nubNub' (x : xs) ls = nubNub'2 (x : xs) ls;
14.00/5.37	
14.00/5.37	nubNub'0 x xs ls True = x : nubNub' xs (x : ls);
14.00/5.37	
14.00/5.37	nubNub'1 x xs ls True = nubNub' xs ls;
14.00/5.37	nubNub'1 x xs ls False = nubNub'0 x xs ls otherwise;
14.00/5.37	
14.00/5.37	nubNub'2 (x : xs) ls = nubNub'1 x xs ls (x `elem` ls);
14.00/5.37	
14.00/5.37	nubNub'3 [] vy = [];
14.00/5.37	nubNub'3 wv ww = nubNub'2 wv ww;
14.00/5.37	
14.00/5.37	}
14.00/5.37	module Main where {
14.00/5.37	import qualified List;
14.00/5.37	import qualified Maybe;
14.00/5.37	import qualified Prelude;
14.00/5.37	}
14.00/5.37	
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(7) Narrow (SOUND)
14.00/5.37	Haskell To QDPs
14.00/5.37	
14.00/5.37	digraph dp_graph {
14.00/5.37	node [outthreshold=100, inthreshold=100];1[label="List.nub",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
14.00/5.37	3[label="List.nub wx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
14.00/5.37	4[label="List.nubNub' wx3 []",fontsize=16,color="burlywood",shape="box"];941[label="wx3/wx30 : wx31",fontsize=10,color="white",style="solid",shape="box"];4 -> 941[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	941 -> 5[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	942[label="wx3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 942[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	942 -> 6[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	5[label="List.nubNub' (wx30 : wx31) []",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
14.00/5.37	6[label="List.nubNub' [] []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
14.00/5.37	7[label="List.nubNub'2 (wx30 : wx31) []",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
14.00/5.37	8[label="List.nubNub'3 [] []",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
14.00/5.37	9[label="List.nubNub'1 wx30 wx31 [] (wx30 `elem` [])",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
14.00/5.37	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];
14.00/5.37	12[label="List.nubNub'1 wx30 wx31 [] (any ((==) wx30) [])",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
14.00/5.37	13 -> 404[label="",style="dashed", color="red", weight=0];
14.00/5.37	13[label="List.nubNub'1 wx30 wx31 [] (or . map ((==) wx30))",fontsize=16,color="magenta"];13 -> 405[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	13 -> 406[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	13 -> 407[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	405[label="wx30",fontsize=16,color="green",shape="box"];406[label="[]",fontsize=16,color="green",shape="box"];407[label="wx31",fontsize=16,color="green",shape="box"];404[label="List.nubNub'1 wx5 wx6 wx7 (or . map ((==) wx5))",fontsize=16,color="black",shape="triangle"];404 -> 447[label="",style="solid", color="black", weight=3];
14.00/5.37	447[label="List.nubNub'1 wx5 wx6 wx7 (or (map ((==) wx5) wx7))",fontsize=16,color="black",shape="box"];447 -> 448[label="",style="solid", color="black", weight=3];
14.00/5.37	448[label="List.nubNub'1 wx5 wx6 wx7 (foldr (||) False (map ((==) wx5) wx7))",fontsize=16,color="burlywood",shape="box"];943[label="wx7/wx70 : wx71",fontsize=10,color="white",style="solid",shape="box"];448 -> 943[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	943 -> 449[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	944[label="wx7/[]",fontsize=10,color="white",style="solid",shape="box"];448 -> 944[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	944 -> 450[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	449[label="List.nubNub'1 wx5 wx6 (wx70 : wx71) (foldr (||) False (map ((==) wx5) (wx70 : wx71)))",fontsize=16,color="black",shape="box"];449 -> 451[label="",style="solid", color="black", weight=3];
14.00/5.37	450[label="List.nubNub'1 wx5 wx6 [] (foldr (||) False (map ((==) wx5) []))",fontsize=16,color="black",shape="box"];450 -> 452[label="",style="solid", color="black", weight=3];
14.00/5.37	451 -> 822[label="",style="dashed", color="red", weight=0];
14.00/5.37	451[label="List.nubNub'1 wx5 wx6 (wx70 : wx71) (foldr (||) False (((==) wx5 wx70) : map ((==) wx5) wx71))",fontsize=16,color="magenta"];451 -> 823[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	451 -> 824[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	451 -> 825[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	451 -> 826[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	451 -> 827[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	451 -> 828[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	452[label="List.nubNub'1 wx5 wx6 [] (foldr (||) False [])",fontsize=16,color="black",shape="box"];452 -> 454[label="",style="solid", color="black", weight=3];
14.00/5.37	823[label="wx71",fontsize=16,color="green",shape="box"];824[label="wx5",fontsize=16,color="green",shape="box"];825[label="wx70",fontsize=16,color="green",shape="box"];826[label="wx70",fontsize=16,color="green",shape="box"];827[label="wx6",fontsize=16,color="green",shape="box"];828[label="wx71",fontsize=16,color="green",shape="box"];822[label="List.nubNub'1 wx84 wx85 (wx86 : wx87) (foldr (||) False (((==) wx84 wx88) : map ((==) wx84) wx89))",fontsize=16,color="black",shape="triangle"];822 -> 859[label="",style="solid", color="black", weight=3];
14.00/5.37	454[label="List.nubNub'1 wx5 wx6 [] False",fontsize=16,color="black",shape="box"];454 -> 461[label="",style="solid", color="black", weight=3];
14.00/5.37	859 -> 860[label="",style="dashed", color="red", weight=0];
14.00/5.37	859[label="List.nubNub'1 wx84 wx85 (wx86 : wx87) ((||) (==) wx84 wx88 foldr (||) False (map ((==) wx84) wx89))",fontsize=16,color="magenta"];859 -> 861[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	859 -> 862[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	859 -> 863[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	859 -> 864[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	859 -> 865[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	859 -> 866[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	461[label="List.nubNub'0 wx5 wx6 [] otherwise",fontsize=16,color="black",shape="box"];461 -> 478[label="",style="solid", color="black", weight=3];
14.00/5.37	861[label="wx86",fontsize=16,color="green",shape="box"];862[label="(==) wx84 wx88",fontsize=16,color="blue",shape="box"];945[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];862 -> 945[label="",style="solid", color="blue", weight=9];
14.00/5.37	945 -> 867[label="",style="solid", color="blue", weight=3];
14.00/5.37	946[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];862 -> 946[label="",style="solid", color="blue", weight=9];
14.00/5.37	946 -> 868[label="",style="solid", color="blue", weight=3];
14.00/5.37	947[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];862 -> 947[label="",style="solid", color="blue", weight=9];
14.00/5.37	947 -> 869[label="",style="solid", color="blue", weight=3];
14.00/5.37	948[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];862 -> 948[label="",style="solid", color="blue", weight=9];
14.00/5.37	948 -> 870[label="",style="solid", color="blue", weight=3];
14.00/5.37	949[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];862 -> 949[label="",style="solid", color="blue", weight=9];
14.00/5.37	949 -> 871[label="",style="solid", color="blue", weight=3];
14.00/5.37	950[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];862 -> 950[label="",style="solid", color="blue", weight=9];
14.00/5.37	950 -> 872[label="",style="solid", color="blue", weight=3];
14.00/5.37	951[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];862 -> 951[label="",style="solid", color="blue", weight=9];
14.00/5.37	951 -> 873[label="",style="solid", color="blue", weight=3];
14.00/5.37	952[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];862 -> 952[label="",style="solid", color="blue", weight=9];
14.00/5.37	952 -> 874[label="",style="solid", color="blue", weight=3];
14.00/5.37	953[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];862 -> 953[label="",style="solid", color="blue", weight=9];
14.00/5.37	953 -> 875[label="",style="solid", color="blue", weight=3];
14.00/5.37	954[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];862 -> 954[label="",style="solid", color="blue", weight=9];
14.00/5.37	954 -> 876[label="",style="solid", color="blue", weight=3];
14.00/5.37	955[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];862 -> 955[label="",style="solid", color="blue", weight=9];
14.00/5.37	955 -> 877[label="",style="solid", color="blue", weight=3];
14.00/5.37	956[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];862 -> 956[label="",style="solid", color="blue", weight=9];
14.00/5.37	956 -> 878[label="",style="solid", color="blue", weight=3];
14.00/5.37	957[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];862 -> 957[label="",style="solid", color="blue", weight=9];
14.00/5.37	957 -> 879[label="",style="solid", color="blue", weight=3];
14.00/5.37	958[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];862 -> 958[label="",style="solid", color="blue", weight=9];
14.00/5.37	958 -> 880[label="",style="solid", color="blue", weight=3];
14.00/5.37	863[label="wx84",fontsize=16,color="green",shape="box"];864[label="wx85",fontsize=16,color="green",shape="box"];865[label="wx87",fontsize=16,color="green",shape="box"];866[label="wx89",fontsize=16,color="green",shape="box"];860[label="List.nubNub'1 wx97 wx98 (wx99 : wx100) ((||) wx101 foldr (||) False (map ((==) wx97) wx102))",fontsize=16,color="burlywood",shape="triangle"];959[label="wx101/False",fontsize=10,color="white",style="solid",shape="box"];860 -> 959[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	959 -> 881[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	960[label="wx101/True",fontsize=10,color="white",style="solid",shape="box"];860 -> 960[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	960 -> 882[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	478[label="List.nubNub'0 wx5 wx6 [] True",fontsize=16,color="black",shape="box"];478 -> 497[label="",style="solid", color="black", weight=3];
14.00/5.37	867[label="(==) wx84 wx88",fontsize=16,color="black",shape="box"];867 -> 883[label="",style="solid", color="black", weight=3];
14.00/5.37	868[label="(==) wx84 wx88",fontsize=16,color="black",shape="box"];868 -> 884[label="",style="solid", color="black", weight=3];
14.00/5.37	869[label="(==) wx84 wx88",fontsize=16,color="black",shape="box"];869 -> 885[label="",style="solid", color="black", weight=3];
14.00/5.37	870[label="(==) wx84 wx88",fontsize=16,color="black",shape="box"];870 -> 886[label="",style="solid", color="black", weight=3];
14.00/5.37	871[label="(==) wx84 wx88",fontsize=16,color="burlywood",shape="box"];961[label="wx84/LT",fontsize=10,color="white",style="solid",shape="box"];871 -> 961[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	961 -> 887[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	962[label="wx84/EQ",fontsize=10,color="white",style="solid",shape="box"];871 -> 962[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	962 -> 888[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	963[label="wx84/GT",fontsize=10,color="white",style="solid",shape="box"];871 -> 963[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	963 -> 889[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	872[label="(==) wx84 wx88",fontsize=16,color="black",shape="box"];872 -> 890[label="",style="solid", color="black", weight=3];
14.00/5.37	873[label="(==) wx84 wx88",fontsize=16,color="black",shape="box"];873 -> 891[label="",style="solid", color="black", weight=3];
14.00/5.37	874[label="(==) wx84 wx88",fontsize=16,color="black",shape="box"];874 -> 892[label="",style="solid", color="black", weight=3];
14.00/5.37	875[label="(==) wx84 wx88",fontsize=16,color="black",shape="box"];875 -> 893[label="",style="solid", color="black", weight=3];
14.00/5.37	876[label="(==) wx84 wx88",fontsize=16,color="black",shape="box"];876 -> 894[label="",style="solid", color="black", weight=3];
14.00/5.37	877[label="(==) wx84 wx88",fontsize=16,color="black",shape="box"];877 -> 895[label="",style="solid", color="black", weight=3];
14.00/5.37	878[label="(==) wx84 wx88",fontsize=16,color="black",shape="box"];878 -> 896[label="",style="solid", color="black", weight=3];
14.00/5.37	879[label="(==) wx84 wx88",fontsize=16,color="black",shape="box"];879 -> 897[label="",style="solid", color="black", weight=3];
14.00/5.37	880[label="(==) wx84 wx88",fontsize=16,color="black",shape="box"];880 -> 898[label="",style="solid", color="black", weight=3];
14.00/5.37	881[label="List.nubNub'1 wx97 wx98 (wx99 : wx100) ((||) False foldr (||) False (map ((==) wx97) wx102))",fontsize=16,color="black",shape="box"];881 -> 899[label="",style="solid", color="black", weight=3];
14.00/5.37	882[label="List.nubNub'1 wx97 wx98 (wx99 : wx100) ((||) True foldr (||) False (map ((==) wx97) wx102))",fontsize=16,color="black",shape="box"];882 -> 900[label="",style="solid", color="black", weight=3];
14.00/5.37	497[label="wx5 : List.nubNub' wx6 (wx5 : [])",fontsize=16,color="green",shape="box"];497 -> 510[label="",style="dashed", color="green", weight=3];
14.00/5.37	883[label="error []",fontsize=16,color="red",shape="box"];884[label="error []",fontsize=16,color="red",shape="box"];885[label="error []",fontsize=16,color="red",shape="box"];886[label="error []",fontsize=16,color="red",shape="box"];887[label="(==) LT wx88",fontsize=16,color="burlywood",shape="box"];964[label="wx88/LT",fontsize=10,color="white",style="solid",shape="box"];887 -> 964[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	964 -> 901[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	965[label="wx88/EQ",fontsize=10,color="white",style="solid",shape="box"];887 -> 965[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	965 -> 902[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	966[label="wx88/GT",fontsize=10,color="white",style="solid",shape="box"];887 -> 966[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	966 -> 903[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	888[label="(==) EQ wx88",fontsize=16,color="burlywood",shape="box"];967[label="wx88/LT",fontsize=10,color="white",style="solid",shape="box"];888 -> 967[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	967 -> 904[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	968[label="wx88/EQ",fontsize=10,color="white",style="solid",shape="box"];888 -> 968[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	968 -> 905[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	969[label="wx88/GT",fontsize=10,color="white",style="solid",shape="box"];888 -> 969[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	969 -> 906[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	889[label="(==) GT wx88",fontsize=16,color="burlywood",shape="box"];970[label="wx88/LT",fontsize=10,color="white",style="solid",shape="box"];889 -> 970[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	970 -> 907[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	971[label="wx88/EQ",fontsize=10,color="white",style="solid",shape="box"];889 -> 971[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	971 -> 908[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	972[label="wx88/GT",fontsize=10,color="white",style="solid",shape="box"];889 -> 972[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	972 -> 909[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	890[label="error []",fontsize=16,color="red",shape="box"];891[label="error []",fontsize=16,color="red",shape="box"];892[label="error []",fontsize=16,color="red",shape="box"];893[label="error []",fontsize=16,color="red",shape="box"];894[label="error []",fontsize=16,color="red",shape="box"];895[label="error []",fontsize=16,color="red",shape="box"];896[label="error []",fontsize=16,color="red",shape="box"];897[label="error []",fontsize=16,color="red",shape="box"];898[label="error []",fontsize=16,color="red",shape="box"];899[label="List.nubNub'1 wx97 wx98 (wx99 : wx100) (foldr (||) False (map ((==) wx97) wx102))",fontsize=16,color="burlywood",shape="box"];973[label="wx102/wx1020 : wx1021",fontsize=10,color="white",style="solid",shape="box"];899 -> 973[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	973 -> 910[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	974[label="wx102/[]",fontsize=10,color="white",style="solid",shape="box"];899 -> 974[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	974 -> 911[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	900[label="List.nubNub'1 wx97 wx98 (wx99 : wx100) True",fontsize=16,color="black",shape="box"];900 -> 912[label="",style="solid", color="black", weight=3];
14.00/5.37	510 -> 509[label="",style="dashed", color="red", weight=0];
14.00/5.37	510[label="List.nubNub' wx6 (wx5 : [])",fontsize=16,color="magenta"];510 -> 524[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	510 -> 525[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	510 -> 526[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	901[label="(==) LT LT",fontsize=16,color="black",shape="box"];901 -> 913[label="",style="solid", color="black", weight=3];
14.00/5.37	902[label="(==) LT EQ",fontsize=16,color="black",shape="box"];902 -> 914[label="",style="solid", color="black", weight=3];
14.00/5.37	903[label="(==) LT GT",fontsize=16,color="black",shape="box"];903 -> 915[label="",style="solid", color="black", weight=3];
14.00/5.37	904[label="(==) EQ LT",fontsize=16,color="black",shape="box"];904 -> 916[label="",style="solid", color="black", weight=3];
14.00/5.37	905[label="(==) EQ EQ",fontsize=16,color="black",shape="box"];905 -> 917[label="",style="solid", color="black", weight=3];
14.00/5.37	906[label="(==) EQ GT",fontsize=16,color="black",shape="box"];906 -> 918[label="",style="solid", color="black", weight=3];
14.00/5.37	907[label="(==) GT LT",fontsize=16,color="black",shape="box"];907 -> 919[label="",style="solid", color="black", weight=3];
14.00/5.37	908[label="(==) GT EQ",fontsize=16,color="black",shape="box"];908 -> 920[label="",style="solid", color="black", weight=3];
14.00/5.37	909[label="(==) GT GT",fontsize=16,color="black",shape="box"];909 -> 921[label="",style="solid", color="black", weight=3];
14.00/5.37	910[label="List.nubNub'1 wx97 wx98 (wx99 : wx100) (foldr (||) False (map ((==) wx97) (wx1020 : wx1021)))",fontsize=16,color="black",shape="box"];910 -> 922[label="",style="solid", color="black", weight=3];
14.00/5.37	911[label="List.nubNub'1 wx97 wx98 (wx99 : wx100) (foldr (||) False (map ((==) wx97) []))",fontsize=16,color="black",shape="box"];911 -> 923[label="",style="solid", color="black", weight=3];
14.00/5.37	912 -> 509[label="",style="dashed", color="red", weight=0];
14.00/5.37	912[label="List.nubNub' wx98 (wx99 : wx100)",fontsize=16,color="magenta"];912 -> 924[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	912 -> 925[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	912 -> 926[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	524[label="wx5",fontsize=16,color="green",shape="box"];525[label="wx6",fontsize=16,color="green",shape="box"];526[label="[]",fontsize=16,color="green",shape="box"];509[label="List.nubNub' wx15 (wx16 : wx17)",fontsize=16,color="burlywood",shape="triangle"];975[label="wx15/wx150 : wx151",fontsize=10,color="white",style="solid",shape="box"];509 -> 975[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	975 -> 522[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	976[label="wx15/[]",fontsize=10,color="white",style="solid",shape="box"];509 -> 976[label="",style="solid", color="burlywood", weight=9];
14.00/5.37	976 -> 523[label="",style="solid", color="burlywood", weight=3];
14.00/5.37	913[label="True",fontsize=16,color="green",shape="box"];914[label="False",fontsize=16,color="green",shape="box"];915[label="False",fontsize=16,color="green",shape="box"];916[label="False",fontsize=16,color="green",shape="box"];917[label="True",fontsize=16,color="green",shape="box"];918[label="False",fontsize=16,color="green",shape="box"];919[label="False",fontsize=16,color="green",shape="box"];920[label="False",fontsize=16,color="green",shape="box"];921[label="True",fontsize=16,color="green",shape="box"];922 -> 822[label="",style="dashed", color="red", weight=0];
14.00/5.37	922[label="List.nubNub'1 wx97 wx98 (wx99 : wx100) (foldr (||) False (((==) wx97 wx1020) : map ((==) wx97) wx1021))",fontsize=16,color="magenta"];922 -> 927[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	922 -> 928[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	922 -> 929[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	922 -> 930[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	922 -> 931[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	922 -> 932[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	923[label="List.nubNub'1 wx97 wx98 (wx99 : wx100) (foldr (||) False [])",fontsize=16,color="black",shape="box"];923 -> 933[label="",style="solid", color="black", weight=3];
14.00/5.37	924[label="wx99",fontsize=16,color="green",shape="box"];925[label="wx98",fontsize=16,color="green",shape="box"];926[label="wx100",fontsize=16,color="green",shape="box"];522[label="List.nubNub' (wx150 : wx151) (wx16 : wx17)",fontsize=16,color="black",shape="box"];522 -> 529[label="",style="solid", color="black", weight=3];
14.00/5.37	523[label="List.nubNub' [] (wx16 : wx17)",fontsize=16,color="black",shape="box"];523 -> 530[label="",style="solid", color="black", weight=3];
14.00/5.37	927[label="wx1021",fontsize=16,color="green",shape="box"];928[label="wx97",fontsize=16,color="green",shape="box"];929[label="wx99",fontsize=16,color="green",shape="box"];930[label="wx1020",fontsize=16,color="green",shape="box"];931[label="wx98",fontsize=16,color="green",shape="box"];932[label="wx100",fontsize=16,color="green",shape="box"];933[label="List.nubNub'1 wx97 wx98 (wx99 : wx100) False",fontsize=16,color="black",shape="box"];933 -> 934[label="",style="solid", color="black", weight=3];
14.00/5.37	529[label="List.nubNub'2 (wx150 : wx151) (wx16 : wx17)",fontsize=16,color="black",shape="box"];529 -> 539[label="",style="solid", color="black", weight=3];
14.00/5.37	530[label="List.nubNub'3 [] (wx16 : wx17)",fontsize=16,color="black",shape="box"];530 -> 540[label="",style="solid", color="black", weight=3];
14.00/5.37	934[label="List.nubNub'0 wx97 wx98 (wx99 : wx100) otherwise",fontsize=16,color="black",shape="box"];934 -> 935[label="",style="solid", color="black", weight=3];
14.00/5.37	539[label="List.nubNub'1 wx150 wx151 (wx16 : wx17) (wx150 `elem` wx16 : wx17)",fontsize=16,color="black",shape="box"];539 -> 558[label="",style="solid", color="black", weight=3];
14.00/5.37	540[label="[]",fontsize=16,color="green",shape="box"];935[label="List.nubNub'0 wx97 wx98 (wx99 : wx100) True",fontsize=16,color="black",shape="box"];935 -> 936[label="",style="solid", color="black", weight=3];
14.00/5.37	558[label="List.nubNub'1 wx150 wx151 (wx16 : wx17) (any . (==))",fontsize=16,color="black",shape="box"];558 -> 590[label="",style="solid", color="black", weight=3];
14.00/5.37	936[label="wx97 : List.nubNub' wx98 (wx97 : wx99 : wx100)",fontsize=16,color="green",shape="box"];936 -> 937[label="",style="dashed", color="green", weight=3];
14.00/5.37	590[label="List.nubNub'1 wx150 wx151 (wx16 : wx17) (any ((==) wx150) (wx16 : wx17))",fontsize=16,color="black",shape="box"];590 -> 598[label="",style="solid", color="black", weight=3];
14.00/5.37	937 -> 509[label="",style="dashed", color="red", weight=0];
14.00/5.37	937[label="List.nubNub' wx98 (wx97 : wx99 : wx100)",fontsize=16,color="magenta"];937 -> 938[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	937 -> 939[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	937 -> 940[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	598 -> 404[label="",style="dashed", color="red", weight=0];
14.00/5.37	598[label="List.nubNub'1 wx150 wx151 (wx16 : wx17) (or . map ((==) wx150))",fontsize=16,color="magenta"];598 -> 603[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	598 -> 604[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	598 -> 605[label="",style="dashed", color="magenta", weight=3];
14.00/5.37	938[label="wx97",fontsize=16,color="green",shape="box"];939[label="wx98",fontsize=16,color="green",shape="box"];940[label="wx99 : wx100",fontsize=16,color="green",shape="box"];603[label="wx150",fontsize=16,color="green",shape="box"];604[label="wx16 : wx17",fontsize=16,color="green",shape="box"];605[label="wx151",fontsize=16,color="green",shape="box"];}
14.00/5.37	
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(8)
14.00/5.37	Obligation:
14.00/5.37	Q DP problem:
14.00/5.37	The TRS P consists of the following rules:
14.00/5.37	
14.00/5.37	   new_nubNub'1(wx84, wx85, wx86, wx87, wx88, wx89, ba) -> new_nubNub'10(wx84, wx85, wx86, wx87, new_esEs(wx84, wx88, ba), wx89, ba)
14.00/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, False, [], bb) -> new_nubNub'(wx98, wx97, :(wx99, wx100), bb)
14.00/5.37	   new_nubNub'11(wx5, wx6, :(wx70, wx71), bd) -> new_nubNub'1(wx5, wx6, wx70, wx71, wx70, wx71, bd)
14.00/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, False, :(wx1020, wx1021), bb) -> new_nubNub'1(wx97, wx98, wx99, wx100, wx1020, wx1021, bb)
14.00/5.37	   new_nubNub'11(wx5, wx6, [], bd) -> new_nubNub'(wx6, wx5, [], bd)
14.00/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, True, wx102, bb) -> new_nubNub'(wx98, wx99, wx100, bb)
14.00/5.37	   new_nubNub'(:(wx150, wx151), wx16, wx17, bc) -> new_nubNub'11(wx150, wx151, :(wx16, wx17), bc)
14.00/5.37	
14.00/5.37	The TRS R consists of the following rules:
14.00/5.37	
14.00/5.37	   new_esEs(LT, GT, ty_Ordering) -> False
14.00/5.37	   new_esEs(GT, LT, ty_Ordering) -> False
14.00/5.37	   new_esEs(GT, GT, ty_Ordering) -> True
14.00/5.37	   new_esEs(wx84, wx88, app(ty_Ratio, cf)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, app(app(app(ty_@3, cc), cd), ce)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Integer) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, app(ty_[], cb)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, app(app(ty_@2, bh), ca)) -> error([])
14.00/5.37	   new_esEs(EQ, GT, ty_Ordering) -> False
14.00/5.37	   new_esEs(GT, EQ, ty_Ordering) -> False
14.00/5.37	   new_esEs(wx84, wx88, ty_Bool) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Float) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_@0) -> error([])
14.00/5.37	   new_esEs(EQ, EQ, ty_Ordering) -> True
14.00/5.37	   new_esEs(wx84, wx88, app(app(ty_Either, be), bf)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Int) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Char) -> error([])
14.00/5.37	   new_esEs(LT, LT, ty_Ordering) -> True
14.00/5.37	   new_esEs(wx84, wx88, app(ty_Maybe, bg)) -> error([])
14.00/5.37	   new_esEs(LT, EQ, ty_Ordering) -> False
14.00/5.37	   new_esEs(EQ, LT, ty_Ordering) -> False
14.00/5.37	   new_esEs(wx84, wx88, ty_Double) -> error([])
14.00/5.37	
14.00/5.37	The set Q consists of the following terms:
14.00/5.37	
14.00/5.37	   new_esEs(x0, x1, ty_Int)
14.00/5.37	   new_esEs(x0, x1, ty_Float)
14.00/5.37	   new_esEs(EQ, GT, ty_Ordering)
14.00/5.37	   new_esEs(GT, EQ, ty_Ordering)
14.00/5.37	   new_esEs(EQ, EQ, ty_Ordering)
14.00/5.37	   new_esEs(LT, EQ, ty_Ordering)
14.00/5.37	   new_esEs(EQ, LT, ty_Ordering)
14.00/5.37	   new_esEs(x0, x1, ty_Bool)
14.00/5.37	   new_esEs(x0, x1, app(ty_[], x2))
14.00/5.37	   new_esEs(x0, x1, ty_@0)
14.00/5.37	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
14.00/5.37	   new_esEs(x0, x1, ty_Double)
14.00/5.37	   new_esEs(x0, x1, ty_Integer)
14.00/5.37	   new_esEs(x0, x1, app(ty_Ratio, x2))
14.00/5.37	   new_esEs(GT, GT, ty_Ordering)
14.00/5.37	   new_esEs(LT, GT, ty_Ordering)
14.00/5.37	   new_esEs(GT, LT, ty_Ordering)
14.00/5.37	   new_esEs(LT, LT, ty_Ordering)
14.00/5.37	   new_esEs(x0, x1, ty_Char)
14.00/5.37	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
14.00/5.37	   new_esEs(x0, x1, app(ty_Maybe, x2))
14.00/5.37	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.00/5.37	
14.00/5.37	We have to consider all minimal (P,Q,R)-chains.
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(9) DependencyGraphProof (EQUIVALENT)
14.00/5.37	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(10)
14.00/5.37	Obligation:
14.00/5.37	Q DP problem:
14.00/5.37	The TRS P consists of the following rules:
14.00/5.37	
14.00/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, False, [], bb) -> new_nubNub'(wx98, wx97, :(wx99, wx100), bb)
14.00/5.37	   new_nubNub'(:(wx150, wx151), wx16, wx17, bc) -> new_nubNub'11(wx150, wx151, :(wx16, wx17), bc)
14.00/5.37	   new_nubNub'11(wx5, wx6, :(wx70, wx71), bd) -> new_nubNub'1(wx5, wx6, wx70, wx71, wx70, wx71, bd)
14.00/5.37	   new_nubNub'1(wx84, wx85, wx86, wx87, wx88, wx89, ba) -> new_nubNub'10(wx84, wx85, wx86, wx87, new_esEs(wx84, wx88, ba), wx89, ba)
14.00/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, False, :(wx1020, wx1021), bb) -> new_nubNub'1(wx97, wx98, wx99, wx100, wx1020, wx1021, bb)
14.00/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, True, wx102, bb) -> new_nubNub'(wx98, wx99, wx100, bb)
14.00/5.37	
14.00/5.37	The TRS R consists of the following rules:
14.00/5.37	
14.00/5.37	   new_esEs(LT, GT, ty_Ordering) -> False
14.00/5.37	   new_esEs(GT, LT, ty_Ordering) -> False
14.00/5.37	   new_esEs(GT, GT, ty_Ordering) -> True
14.00/5.37	   new_esEs(wx84, wx88, app(ty_Ratio, cf)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, app(app(app(ty_@3, cc), cd), ce)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Integer) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, app(ty_[], cb)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, app(app(ty_@2, bh), ca)) -> error([])
14.00/5.37	   new_esEs(EQ, GT, ty_Ordering) -> False
14.00/5.37	   new_esEs(GT, EQ, ty_Ordering) -> False
14.00/5.37	   new_esEs(wx84, wx88, ty_Bool) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Float) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_@0) -> error([])
14.00/5.37	   new_esEs(EQ, EQ, ty_Ordering) -> True
14.00/5.37	   new_esEs(wx84, wx88, app(app(ty_Either, be), bf)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Int) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Char) -> error([])
14.00/5.37	   new_esEs(LT, LT, ty_Ordering) -> True
14.00/5.37	   new_esEs(wx84, wx88, app(ty_Maybe, bg)) -> error([])
14.00/5.37	   new_esEs(LT, EQ, ty_Ordering) -> False
14.00/5.37	   new_esEs(EQ, LT, ty_Ordering) -> False
14.00/5.37	   new_esEs(wx84, wx88, ty_Double) -> error([])
14.00/5.37	
14.00/5.37	The set Q consists of the following terms:
14.00/5.37	
14.00/5.37	   new_esEs(x0, x1, ty_Int)
14.00/5.37	   new_esEs(x0, x1, ty_Float)
14.00/5.37	   new_esEs(EQ, GT, ty_Ordering)
14.00/5.37	   new_esEs(GT, EQ, ty_Ordering)
14.00/5.37	   new_esEs(EQ, EQ, ty_Ordering)
14.00/5.37	   new_esEs(LT, EQ, ty_Ordering)
14.00/5.37	   new_esEs(EQ, LT, ty_Ordering)
14.00/5.37	   new_esEs(x0, x1, ty_Bool)
14.00/5.37	   new_esEs(x0, x1, app(ty_[], x2))
14.00/5.37	   new_esEs(x0, x1, ty_@0)
14.00/5.37	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
14.00/5.37	   new_esEs(x0, x1, ty_Double)
14.00/5.37	   new_esEs(x0, x1, ty_Integer)
14.00/5.37	   new_esEs(x0, x1, app(ty_Ratio, x2))
14.00/5.37	   new_esEs(GT, GT, ty_Ordering)
14.00/5.37	   new_esEs(LT, GT, ty_Ordering)
14.00/5.37	   new_esEs(GT, LT, ty_Ordering)
14.00/5.37	   new_esEs(LT, LT, ty_Ordering)
14.00/5.37	   new_esEs(x0, x1, ty_Char)
14.00/5.37	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
14.00/5.37	   new_esEs(x0, x1, app(ty_Maybe, x2))
14.00/5.37	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.00/5.37	
14.00/5.37	We have to consider all minimal (P,Q,R)-chains.
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(11) TransformationProof (EQUIVALENT)
14.00/5.37	By narrowing [LPAR04] the rule new_nubNub'1(wx84, wx85, wx86, wx87, wx88, wx89, ba) -> new_nubNub'10(wx84, wx85, wx86, wx87, new_esEs(wx84, wx88, ba), wx89, ba) at position [4] we obtained the following new rules [LPAR04]:
14.00/5.37	
14.00/5.37	   (new_nubNub'1(LT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering),new_nubNub'1(LT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering))
14.00/5.37	   (new_nubNub'1(GT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering),new_nubNub'1(GT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering))
14.00/5.37	   (new_nubNub'1(GT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, True, y5, ty_Ordering),new_nubNub'1(GT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, True, y5, ty_Ordering))
14.00/5.37	   (new_nubNub'1(x0, y1, y2, y3, x1, y5, app(ty_Ratio, x2)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(ty_Ratio, x2)),new_nubNub'1(x0, y1, y2, y3, x1, y5, app(ty_Ratio, x2)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(ty_Ratio, x2)))
14.00/5.37	   (new_nubNub'1(x0, y1, y2, y3, x1, y5, app(app(app(ty_@3, x2), x3), x4)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(app(app(ty_@3, x2), x3), x4)),new_nubNub'1(x0, y1, y2, y3, x1, y5, app(app(app(ty_@3, x2), x3), x4)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(app(app(ty_@3, x2), x3), x4)))
14.00/5.37	   (new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Integer) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Integer),new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Integer) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Integer))
14.00/5.37	   (new_nubNub'1(x0, y1, y2, y3, x1, y5, app(ty_[], x2)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(ty_[], x2)),new_nubNub'1(x0, y1, y2, y3, x1, y5, app(ty_[], x2)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(ty_[], x2)))
14.00/5.37	   (new_nubNub'1(x0, y1, y2, y3, x1, y5, app(app(ty_@2, x2), x3)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(app(ty_@2, x2), x3)),new_nubNub'1(x0, y1, y2, y3, x1, y5, app(app(ty_@2, x2), x3)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(app(ty_@2, x2), x3)))
14.00/5.37	   (new_nubNub'1(EQ, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering),new_nubNub'1(EQ, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering))
14.00/5.37	   (new_nubNub'1(GT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering),new_nubNub'1(GT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering))
14.00/5.37	   (new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Bool) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Bool),new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Bool) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Bool))
14.00/5.37	   (new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Float) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Float),new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Float) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Float))
14.00/5.37	   (new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_@0) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_@0),new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_@0) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_@0))
14.00/5.37	   (new_nubNub'1(EQ, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, True, y5, ty_Ordering),new_nubNub'1(EQ, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, True, y5, ty_Ordering))
14.00/5.37	   (new_nubNub'1(x0, y1, y2, y3, x1, y5, app(app(ty_Either, x2), x3)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(app(ty_Either, x2), x3)),new_nubNub'1(x0, y1, y2, y3, x1, y5, app(app(ty_Either, x2), x3)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(app(ty_Either, x2), x3)))
14.00/5.37	   (new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Int) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Int),new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Int) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Int))
14.00/5.37	   (new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Char) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Char),new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Char) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Char))
14.00/5.37	   (new_nubNub'1(LT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, True, y5, ty_Ordering),new_nubNub'1(LT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, True, y5, ty_Ordering))
14.00/5.37	   (new_nubNub'1(x0, y1, y2, y3, x1, y5, app(ty_Maybe, x2)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(ty_Maybe, x2)),new_nubNub'1(x0, y1, y2, y3, x1, y5, app(ty_Maybe, x2)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(ty_Maybe, x2)))
14.00/5.37	   (new_nubNub'1(LT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering),new_nubNub'1(LT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering))
14.00/5.37	   (new_nubNub'1(EQ, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering),new_nubNub'1(EQ, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering))
14.00/5.37	   (new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Double) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Double),new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Double) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Double))
14.00/5.37	
14.00/5.37	
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(12)
14.00/5.37	Obligation:
14.00/5.37	Q DP problem:
14.00/5.37	The TRS P consists of the following rules:
14.00/5.37	
14.00/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, False, [], bb) -> new_nubNub'(wx98, wx97, :(wx99, wx100), bb)
14.00/5.37	   new_nubNub'(:(wx150, wx151), wx16, wx17, bc) -> new_nubNub'11(wx150, wx151, :(wx16, wx17), bc)
14.00/5.37	   new_nubNub'11(wx5, wx6, :(wx70, wx71), bd) -> new_nubNub'1(wx5, wx6, wx70, wx71, wx70, wx71, bd)
14.00/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, False, :(wx1020, wx1021), bb) -> new_nubNub'1(wx97, wx98, wx99, wx100, wx1020, wx1021, bb)
14.00/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, True, wx102, bb) -> new_nubNub'(wx98, wx99, wx100, bb)
14.00/5.37	   new_nubNub'1(LT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(GT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(GT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, True, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(x0, y1, y2, y3, x1, y5, app(ty_Ratio, x2)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(ty_Ratio, x2))
14.00/5.37	   new_nubNub'1(x0, y1, y2, y3, x1, y5, app(app(app(ty_@3, x2), x3), x4)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(app(app(ty_@3, x2), x3), x4))
14.00/5.37	   new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Integer) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Integer)
14.00/5.37	   new_nubNub'1(x0, y1, y2, y3, x1, y5, app(ty_[], x2)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(ty_[], x2))
14.00/5.37	   new_nubNub'1(x0, y1, y2, y3, x1, y5, app(app(ty_@2, x2), x3)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(app(ty_@2, x2), x3))
14.00/5.37	   new_nubNub'1(EQ, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(GT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Bool) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Bool)
14.00/5.37	   new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Float) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Float)
14.00/5.37	   new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_@0) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_@0)
14.00/5.37	   new_nubNub'1(EQ, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, True, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(x0, y1, y2, y3, x1, y5, app(app(ty_Either, x2), x3)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(app(ty_Either, x2), x3))
14.00/5.37	   new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Int) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Int)
14.00/5.37	   new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Char) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Char)
14.00/5.37	   new_nubNub'1(LT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, True, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(x0, y1, y2, y3, x1, y5, app(ty_Maybe, x2)) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, app(ty_Maybe, x2))
14.00/5.37	   new_nubNub'1(LT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(EQ, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(x0, y1, y2, y3, x1, y5, ty_Double) -> new_nubNub'10(x0, y1, y2, y3, error([]), y5, ty_Double)
14.00/5.37	
14.00/5.37	The TRS R consists of the following rules:
14.00/5.37	
14.00/5.37	   new_esEs(LT, GT, ty_Ordering) -> False
14.00/5.37	   new_esEs(GT, LT, ty_Ordering) -> False
14.00/5.37	   new_esEs(GT, GT, ty_Ordering) -> True
14.00/5.37	   new_esEs(wx84, wx88, app(ty_Ratio, cf)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, app(app(app(ty_@3, cc), cd), ce)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Integer) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, app(ty_[], cb)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, app(app(ty_@2, bh), ca)) -> error([])
14.00/5.37	   new_esEs(EQ, GT, ty_Ordering) -> False
14.00/5.37	   new_esEs(GT, EQ, ty_Ordering) -> False
14.00/5.37	   new_esEs(wx84, wx88, ty_Bool) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Float) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_@0) -> error([])
14.00/5.37	   new_esEs(EQ, EQ, ty_Ordering) -> True
14.00/5.37	   new_esEs(wx84, wx88, app(app(ty_Either, be), bf)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Int) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Char) -> error([])
14.00/5.37	   new_esEs(LT, LT, ty_Ordering) -> True
14.00/5.37	   new_esEs(wx84, wx88, app(ty_Maybe, bg)) -> error([])
14.00/5.37	   new_esEs(LT, EQ, ty_Ordering) -> False
14.00/5.37	   new_esEs(EQ, LT, ty_Ordering) -> False
14.00/5.37	   new_esEs(wx84, wx88, ty_Double) -> error([])
14.00/5.37	
14.00/5.37	The set Q consists of the following terms:
14.00/5.37	
14.00/5.37	   new_esEs(x0, x1, ty_Int)
14.00/5.37	   new_esEs(x0, x1, ty_Float)
14.00/5.37	   new_esEs(EQ, GT, ty_Ordering)
14.00/5.37	   new_esEs(GT, EQ, ty_Ordering)
14.00/5.37	   new_esEs(EQ, EQ, ty_Ordering)
14.00/5.37	   new_esEs(LT, EQ, ty_Ordering)
14.00/5.37	   new_esEs(EQ, LT, ty_Ordering)
14.00/5.37	   new_esEs(x0, x1, ty_Bool)
14.00/5.37	   new_esEs(x0, x1, app(ty_[], x2))
14.00/5.37	   new_esEs(x0, x1, ty_@0)
14.00/5.37	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
14.00/5.37	   new_esEs(x0, x1, ty_Double)
14.00/5.37	   new_esEs(x0, x1, ty_Integer)
14.00/5.37	   new_esEs(x0, x1, app(ty_Ratio, x2))
14.00/5.37	   new_esEs(GT, GT, ty_Ordering)
14.00/5.37	   new_esEs(LT, GT, ty_Ordering)
14.00/5.37	   new_esEs(GT, LT, ty_Ordering)
14.00/5.37	   new_esEs(LT, LT, ty_Ordering)
14.00/5.37	   new_esEs(x0, x1, ty_Char)
14.00/5.37	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
14.00/5.37	   new_esEs(x0, x1, app(ty_Maybe, x2))
14.00/5.37	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.00/5.37	
14.00/5.37	We have to consider all minimal (P,Q,R)-chains.
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(13) DependencyGraphProof (EQUIVALENT)
14.00/5.37	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 13 less nodes.
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(14)
14.00/5.37	Obligation:
14.00/5.37	Q DP problem:
14.00/5.37	The TRS P consists of the following rules:
14.00/5.37	
14.00/5.37	   new_nubNub'(:(wx150, wx151), wx16, wx17, bc) -> new_nubNub'11(wx150, wx151, :(wx16, wx17), bc)
14.00/5.37	   new_nubNub'11(wx5, wx6, :(wx70, wx71), bd) -> new_nubNub'1(wx5, wx6, wx70, wx71, wx70, wx71, bd)
14.00/5.37	   new_nubNub'1(LT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.00/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, False, [], bb) -> new_nubNub'(wx98, wx97, :(wx99, wx100), bb)
14.00/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, False, :(wx1020, wx1021), bb) -> new_nubNub'1(wx97, wx98, wx99, wx100, wx1020, wx1021, bb)
14.00/5.37	   new_nubNub'1(GT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(GT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, True, y5, ty_Ordering)
14.00/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, True, wx102, bb) -> new_nubNub'(wx98, wx99, wx100, bb)
14.00/5.37	   new_nubNub'1(EQ, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(GT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(EQ, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, True, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(LT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, True, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(LT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(EQ, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.00/5.37	
14.00/5.37	The TRS R consists of the following rules:
14.00/5.37	
14.00/5.37	   new_esEs(LT, GT, ty_Ordering) -> False
14.00/5.37	   new_esEs(GT, LT, ty_Ordering) -> False
14.00/5.37	   new_esEs(GT, GT, ty_Ordering) -> True
14.00/5.37	   new_esEs(wx84, wx88, app(ty_Ratio, cf)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, app(app(app(ty_@3, cc), cd), ce)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Integer) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, app(ty_[], cb)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, app(app(ty_@2, bh), ca)) -> error([])
14.00/5.37	   new_esEs(EQ, GT, ty_Ordering) -> False
14.00/5.37	   new_esEs(GT, EQ, ty_Ordering) -> False
14.00/5.37	   new_esEs(wx84, wx88, ty_Bool) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Float) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_@0) -> error([])
14.00/5.37	   new_esEs(EQ, EQ, ty_Ordering) -> True
14.00/5.37	   new_esEs(wx84, wx88, app(app(ty_Either, be), bf)) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Int) -> error([])
14.00/5.37	   new_esEs(wx84, wx88, ty_Char) -> error([])
14.00/5.37	   new_esEs(LT, LT, ty_Ordering) -> True
14.00/5.37	   new_esEs(wx84, wx88, app(ty_Maybe, bg)) -> error([])
14.00/5.37	   new_esEs(LT, EQ, ty_Ordering) -> False
14.00/5.37	   new_esEs(EQ, LT, ty_Ordering) -> False
14.00/5.37	   new_esEs(wx84, wx88, ty_Double) -> error([])
14.00/5.37	
14.00/5.37	The set Q consists of the following terms:
14.00/5.37	
14.00/5.37	   new_esEs(x0, x1, ty_Int)
14.00/5.37	   new_esEs(x0, x1, ty_Float)
14.00/5.37	   new_esEs(EQ, GT, ty_Ordering)
14.00/5.37	   new_esEs(GT, EQ, ty_Ordering)
14.00/5.37	   new_esEs(EQ, EQ, ty_Ordering)
14.00/5.37	   new_esEs(LT, EQ, ty_Ordering)
14.00/5.37	   new_esEs(EQ, LT, ty_Ordering)
14.00/5.37	   new_esEs(x0, x1, ty_Bool)
14.00/5.37	   new_esEs(x0, x1, app(ty_[], x2))
14.00/5.37	   new_esEs(x0, x1, ty_@0)
14.00/5.37	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
14.00/5.37	   new_esEs(x0, x1, ty_Double)
14.00/5.37	   new_esEs(x0, x1, ty_Integer)
14.00/5.37	   new_esEs(x0, x1, app(ty_Ratio, x2))
14.00/5.37	   new_esEs(GT, GT, ty_Ordering)
14.00/5.37	   new_esEs(LT, GT, ty_Ordering)
14.00/5.37	   new_esEs(GT, LT, ty_Ordering)
14.00/5.37	   new_esEs(LT, LT, ty_Ordering)
14.00/5.37	   new_esEs(x0, x1, ty_Char)
14.00/5.37	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
14.00/5.37	   new_esEs(x0, x1, app(ty_Maybe, x2))
14.00/5.37	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.00/5.37	
14.00/5.37	We have to consider all minimal (P,Q,R)-chains.
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(15) UsableRulesProof (EQUIVALENT)
14.00/5.37	As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.
14.00/5.37	----------------------------------------
14.00/5.37	
14.00/5.37	(16)
14.00/5.37	Obligation:
14.00/5.37	Q DP problem:
14.00/5.37	The TRS P consists of the following rules:
14.00/5.37	
14.00/5.37	   new_nubNub'(:(wx150, wx151), wx16, wx17, bc) -> new_nubNub'11(wx150, wx151, :(wx16, wx17), bc)
14.00/5.37	   new_nubNub'11(wx5, wx6, :(wx70, wx71), bd) -> new_nubNub'1(wx5, wx6, wx70, wx71, wx70, wx71, bd)
14.00/5.37	   new_nubNub'1(LT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.00/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, False, [], bb) -> new_nubNub'(wx98, wx97, :(wx99, wx100), bb)
14.00/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, False, :(wx1020, wx1021), bb) -> new_nubNub'1(wx97, wx98, wx99, wx100, wx1020, wx1021, bb)
14.00/5.37	   new_nubNub'1(GT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.00/5.37	   new_nubNub'1(GT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, True, y5, ty_Ordering)
14.00/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, True, wx102, bb) -> new_nubNub'(wx98, wx99, wx100, bb)
14.04/5.37	   new_nubNub'1(EQ, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(GT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(EQ, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(LT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(LT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(EQ, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	
14.04/5.37	R is empty.
14.04/5.37	The set Q consists of the following terms:
14.04/5.37	
14.04/5.37	   new_esEs(x0, x1, ty_Int)
14.04/5.37	   new_esEs(x0, x1, ty_Float)
14.04/5.37	   new_esEs(EQ, GT, ty_Ordering)
14.04/5.37	   new_esEs(GT, EQ, ty_Ordering)
14.04/5.37	   new_esEs(EQ, EQ, ty_Ordering)
14.04/5.37	   new_esEs(LT, EQ, ty_Ordering)
14.04/5.37	   new_esEs(EQ, LT, ty_Ordering)
14.04/5.37	   new_esEs(x0, x1, ty_Bool)
14.04/5.37	   new_esEs(x0, x1, app(ty_[], x2))
14.04/5.37	   new_esEs(x0, x1, ty_@0)
14.04/5.37	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
14.04/5.37	   new_esEs(x0, x1, ty_Double)
14.04/5.37	   new_esEs(x0, x1, ty_Integer)
14.04/5.37	   new_esEs(x0, x1, app(ty_Ratio, x2))
14.04/5.37	   new_esEs(GT, GT, ty_Ordering)
14.04/5.37	   new_esEs(LT, GT, ty_Ordering)
14.04/5.37	   new_esEs(GT, LT, ty_Ordering)
14.04/5.37	   new_esEs(LT, LT, ty_Ordering)
14.04/5.37	   new_esEs(x0, x1, ty_Char)
14.04/5.37	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
14.04/5.37	   new_esEs(x0, x1, app(ty_Maybe, x2))
14.04/5.37	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.04/5.37	
14.04/5.37	We have to consider all minimal (P,Q,R)-chains.
14.04/5.37	----------------------------------------
14.04/5.37	
14.04/5.37	(17) QReductionProof (EQUIVALENT)
14.04/5.37	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
14.04/5.37	
14.04/5.37	   new_esEs(x0, x1, ty_Int)
14.04/5.37	   new_esEs(x0, x1, ty_Float)
14.04/5.37	   new_esEs(EQ, GT, ty_Ordering)
14.04/5.37	   new_esEs(GT, EQ, ty_Ordering)
14.04/5.37	   new_esEs(EQ, EQ, ty_Ordering)
14.04/5.37	   new_esEs(LT, EQ, ty_Ordering)
14.04/5.37	   new_esEs(EQ, LT, ty_Ordering)
14.04/5.37	   new_esEs(x0, x1, ty_Bool)
14.04/5.37	   new_esEs(x0, x1, app(ty_[], x2))
14.04/5.37	   new_esEs(x0, x1, ty_@0)
14.04/5.37	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
14.04/5.37	   new_esEs(x0, x1, ty_Double)
14.04/5.37	   new_esEs(x0, x1, ty_Integer)
14.04/5.37	   new_esEs(x0, x1, app(ty_Ratio, x2))
14.04/5.37	   new_esEs(GT, GT, ty_Ordering)
14.04/5.37	   new_esEs(LT, GT, ty_Ordering)
14.04/5.37	   new_esEs(GT, LT, ty_Ordering)
14.04/5.37	   new_esEs(LT, LT, ty_Ordering)
14.04/5.37	   new_esEs(x0, x1, ty_Char)
14.04/5.37	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
14.04/5.37	   new_esEs(x0, x1, app(ty_Maybe, x2))
14.04/5.37	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.04/5.37	
14.04/5.37	
14.04/5.37	----------------------------------------
14.04/5.37	
14.04/5.37	(18)
14.04/5.37	Obligation:
14.04/5.37	Q DP problem:
14.04/5.37	The TRS P consists of the following rules:
14.04/5.37	
14.04/5.37	   new_nubNub'(:(wx150, wx151), wx16, wx17, bc) -> new_nubNub'11(wx150, wx151, :(wx16, wx17), bc)
14.04/5.37	   new_nubNub'11(wx5, wx6, :(wx70, wx71), bd) -> new_nubNub'1(wx5, wx6, wx70, wx71, wx70, wx71, bd)
14.04/5.37	   new_nubNub'1(LT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, False, [], bb) -> new_nubNub'(wx98, wx97, :(wx99, wx100), bb)
14.04/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, False, :(wx1020, wx1021), bb) -> new_nubNub'1(wx97, wx98, wx99, wx100, wx1020, wx1021, bb)
14.04/5.37	   new_nubNub'1(GT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(GT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, True, wx102, bb) -> new_nubNub'(wx98, wx99, wx100, bb)
14.04/5.37	   new_nubNub'1(EQ, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(GT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(EQ, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(LT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(LT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(EQ, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	
14.04/5.37	R is empty.
14.04/5.37	Q is empty.
14.04/5.37	We have to consider all minimal (P,Q,R)-chains.
14.04/5.37	----------------------------------------
14.04/5.37	
14.04/5.37	(19) TransformationProof (EQUIVALENT)
14.04/5.37	By instantiating [LPAR04] the rule new_nubNub'10(wx97, wx98, wx99, wx100, False, [], bb) -> new_nubNub'(wx98, wx97, :(wx99, wx100), bb) we obtained the following new rules [LPAR04]:
14.04/5.37	
14.04/5.37	   (new_nubNub'10(LT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, LT, :(z1, z2), ty_Ordering),new_nubNub'10(LT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, LT, :(z1, z2), ty_Ordering))
14.04/5.37	   (new_nubNub'10(GT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, GT, :(z1, z2), ty_Ordering),new_nubNub'10(GT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, GT, :(z1, z2), ty_Ordering))
14.04/5.37	   (new_nubNub'10(EQ, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, EQ, :(z1, z2), ty_Ordering),new_nubNub'10(EQ, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, EQ, :(z1, z2), ty_Ordering))
14.04/5.37	
14.04/5.37	
14.04/5.37	----------------------------------------
14.04/5.37	
14.04/5.37	(20)
14.04/5.37	Obligation:
14.04/5.37	Q DP problem:
14.04/5.37	The TRS P consists of the following rules:
14.04/5.37	
14.04/5.37	   new_nubNub'(:(wx150, wx151), wx16, wx17, bc) -> new_nubNub'11(wx150, wx151, :(wx16, wx17), bc)
14.04/5.37	   new_nubNub'11(wx5, wx6, :(wx70, wx71), bd) -> new_nubNub'1(wx5, wx6, wx70, wx71, wx70, wx71, bd)
14.04/5.37	   new_nubNub'1(LT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, False, :(wx1020, wx1021), bb) -> new_nubNub'1(wx97, wx98, wx99, wx100, wx1020, wx1021, bb)
14.04/5.37	   new_nubNub'1(GT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(GT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, True, wx102, bb) -> new_nubNub'(wx98, wx99, wx100, bb)
14.04/5.37	   new_nubNub'1(EQ, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(GT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(EQ, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(LT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(LT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(EQ, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'10(LT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, LT, :(z1, z2), ty_Ordering)
14.04/5.37	   new_nubNub'10(GT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, GT, :(z1, z2), ty_Ordering)
14.04/5.37	   new_nubNub'10(EQ, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, EQ, :(z1, z2), ty_Ordering)
14.04/5.37	
14.04/5.37	R is empty.
14.04/5.37	Q is empty.
14.04/5.37	We have to consider all minimal (P,Q,R)-chains.
14.04/5.37	----------------------------------------
14.04/5.37	
14.04/5.37	(21) TransformationProof (EQUIVALENT)
14.04/5.37	By instantiating [LPAR04] the rule new_nubNub'10(wx97, wx98, wx99, wx100, False, :(wx1020, wx1021), bb) -> new_nubNub'1(wx97, wx98, wx99, wx100, wx1020, wx1021, bb) we obtained the following new rules [LPAR04]:
14.04/5.37	
14.04/5.37	   (new_nubNub'10(LT, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(LT, z0, z1, z2, x4, x5, ty_Ordering),new_nubNub'10(LT, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(LT, z0, z1, z2, x4, x5, ty_Ordering))
14.04/5.37	   (new_nubNub'10(GT, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(GT, z0, z1, z2, x4, x5, ty_Ordering),new_nubNub'10(GT, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(GT, z0, z1, z2, x4, x5, ty_Ordering))
14.04/5.37	   (new_nubNub'10(EQ, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(EQ, z0, z1, z2, x4, x5, ty_Ordering),new_nubNub'10(EQ, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(EQ, z0, z1, z2, x4, x5, ty_Ordering))
14.04/5.37	
14.04/5.37	
14.04/5.37	----------------------------------------
14.04/5.37	
14.04/5.37	(22)
14.04/5.37	Obligation:
14.04/5.37	Q DP problem:
14.04/5.37	The TRS P consists of the following rules:
14.04/5.37	
14.04/5.37	   new_nubNub'(:(wx150, wx151), wx16, wx17, bc) -> new_nubNub'11(wx150, wx151, :(wx16, wx17), bc)
14.04/5.37	   new_nubNub'11(wx5, wx6, :(wx70, wx71), bd) -> new_nubNub'1(wx5, wx6, wx70, wx71, wx70, wx71, bd)
14.04/5.37	   new_nubNub'1(LT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(GT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(GT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.37	   new_nubNub'10(wx97, wx98, wx99, wx100, True, wx102, bb) -> new_nubNub'(wx98, wx99, wx100, bb)
14.04/5.37	   new_nubNub'1(EQ, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(GT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(EQ, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(LT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(LT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(EQ, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'10(LT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, LT, :(z1, z2), ty_Ordering)
14.04/5.37	   new_nubNub'10(GT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, GT, :(z1, z2), ty_Ordering)
14.04/5.37	   new_nubNub'10(EQ, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, EQ, :(z1, z2), ty_Ordering)
14.04/5.37	   new_nubNub'10(LT, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(LT, z0, z1, z2, x4, x5, ty_Ordering)
14.04/5.37	   new_nubNub'10(GT, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(GT, z0, z1, z2, x4, x5, ty_Ordering)
14.04/5.37	   new_nubNub'10(EQ, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(EQ, z0, z1, z2, x4, x5, ty_Ordering)
14.04/5.37	
14.04/5.37	R is empty.
14.04/5.37	Q is empty.
14.04/5.37	We have to consider all minimal (P,Q,R)-chains.
14.04/5.37	----------------------------------------
14.04/5.37	
14.04/5.37	(23) TransformationProof (EQUIVALENT)
14.04/5.37	By instantiating [LPAR04] the rule new_nubNub'10(wx97, wx98, wx99, wx100, True, wx102, bb) -> new_nubNub'(wx98, wx99, wx100, bb) we obtained the following new rules [LPAR04]:
14.04/5.37	
14.04/5.37	   (new_nubNub'10(GT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering),new_nubNub'10(GT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering))
14.04/5.37	   (new_nubNub'10(EQ, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering),new_nubNub'10(EQ, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering))
14.04/5.37	   (new_nubNub'10(LT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering),new_nubNub'10(LT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering))
14.04/5.37	
14.04/5.37	
14.04/5.37	----------------------------------------
14.04/5.37	
14.04/5.37	(24)
14.04/5.37	Obligation:
14.04/5.37	Q DP problem:
14.04/5.37	The TRS P consists of the following rules:
14.04/5.37	
14.04/5.37	   new_nubNub'(:(wx150, wx151), wx16, wx17, bc) -> new_nubNub'11(wx150, wx151, :(wx16, wx17), bc)
14.04/5.37	   new_nubNub'11(wx5, wx6, :(wx70, wx71), bd) -> new_nubNub'1(wx5, wx6, wx70, wx71, wx70, wx71, bd)
14.04/5.37	   new_nubNub'1(LT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(GT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(GT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(EQ, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(GT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(EQ, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(LT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(LT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'1(EQ, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.37	   new_nubNub'10(LT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, LT, :(z1, z2), ty_Ordering)
14.04/5.37	   new_nubNub'10(GT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, GT, :(z1, z2), ty_Ordering)
14.04/5.37	   new_nubNub'10(EQ, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, EQ, :(z1, z2), ty_Ordering)
14.04/5.37	   new_nubNub'10(LT, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(LT, z0, z1, z2, x4, x5, ty_Ordering)
14.04/5.37	   new_nubNub'10(GT, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(GT, z0, z1, z2, x4, x5, ty_Ordering)
14.04/5.37	   new_nubNub'10(EQ, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(EQ, z0, z1, z2, x4, x5, ty_Ordering)
14.04/5.37	   new_nubNub'10(GT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering)
14.04/5.37	   new_nubNub'10(EQ, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering)
14.04/5.37	   new_nubNub'10(LT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering)
14.04/5.37	
14.04/5.37	R is empty.
14.04/5.37	Q is empty.
14.04/5.37	We have to consider all minimal (P,Q,R)-chains.
14.04/5.37	----------------------------------------
14.04/5.38	
14.04/5.38	(25) TransformationProof (EQUIVALENT)
14.04/5.38	By instantiating [LPAR04] the rule new_nubNub'(:(wx150, wx151), wx16, wx17, bc) -> new_nubNub'11(wx150, wx151, :(wx16, wx17), bc) we obtained the following new rules [LPAR04]:
14.04/5.38	
14.04/5.38	   (new_nubNub'(:(x0, x1), LT, :(z1, z2), ty_Ordering) -> new_nubNub'11(x0, x1, :(LT, :(z1, z2)), ty_Ordering),new_nubNub'(:(x0, x1), LT, :(z1, z2), ty_Ordering) -> new_nubNub'11(x0, x1, :(LT, :(z1, z2)), ty_Ordering))
14.04/5.38	   (new_nubNub'(:(x0, x1), GT, :(z1, z2), ty_Ordering) -> new_nubNub'11(x0, x1, :(GT, :(z1, z2)), ty_Ordering),new_nubNub'(:(x0, x1), GT, :(z1, z2), ty_Ordering) -> new_nubNub'11(x0, x1, :(GT, :(z1, z2)), ty_Ordering))
14.04/5.38	   (new_nubNub'(:(x0, x1), EQ, :(z1, z2), ty_Ordering) -> new_nubNub'11(x0, x1, :(EQ, :(z1, z2)), ty_Ordering),new_nubNub'(:(x0, x1), EQ, :(z1, z2), ty_Ordering) -> new_nubNub'11(x0, x1, :(EQ, :(z1, z2)), ty_Ordering))
14.04/5.38	   (new_nubNub'(:(x0, x1), z1, z2, ty_Ordering) -> new_nubNub'11(x0, x1, :(z1, z2), ty_Ordering),new_nubNub'(:(x0, x1), z1, z2, ty_Ordering) -> new_nubNub'11(x0, x1, :(z1, z2), ty_Ordering))
14.04/5.38	
14.04/5.38	
14.04/5.38	----------------------------------------
14.04/5.38	
14.04/5.38	(26)
14.04/5.38	Obligation:
14.04/5.38	Q DP problem:
14.04/5.38	The TRS P consists of the following rules:
14.04/5.38	
14.04/5.38	   new_nubNub'11(wx5, wx6, :(wx70, wx71), bd) -> new_nubNub'1(wx5, wx6, wx70, wx71, wx70, wx71, bd)
14.04/5.38	   new_nubNub'1(LT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(GT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(GT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(EQ, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(GT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(EQ, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(LT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(LT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(EQ, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	   new_nubNub'10(LT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, LT, :(z1, z2), ty_Ordering)
14.04/5.38	   new_nubNub'10(GT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, GT, :(z1, z2), ty_Ordering)
14.04/5.38	   new_nubNub'10(EQ, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, EQ, :(z1, z2), ty_Ordering)
14.04/5.38	   new_nubNub'10(LT, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(LT, z0, z1, z2, x4, x5, ty_Ordering)
14.04/5.38	   new_nubNub'10(GT, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(GT, z0, z1, z2, x4, x5, ty_Ordering)
14.04/5.38	   new_nubNub'10(EQ, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(EQ, z0, z1, z2, x4, x5, ty_Ordering)
14.04/5.38	   new_nubNub'10(GT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering)
14.04/5.38	   new_nubNub'10(EQ, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering)
14.04/5.38	   new_nubNub'10(LT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering)
14.04/5.38	   new_nubNub'(:(x0, x1), LT, :(z1, z2), ty_Ordering) -> new_nubNub'11(x0, x1, :(LT, :(z1, z2)), ty_Ordering)
14.04/5.38	   new_nubNub'(:(x0, x1), GT, :(z1, z2), ty_Ordering) -> new_nubNub'11(x0, x1, :(GT, :(z1, z2)), ty_Ordering)
14.04/5.38	   new_nubNub'(:(x0, x1), EQ, :(z1, z2), ty_Ordering) -> new_nubNub'11(x0, x1, :(EQ, :(z1, z2)), ty_Ordering)
14.04/5.38	   new_nubNub'(:(x0, x1), z1, z2, ty_Ordering) -> new_nubNub'11(x0, x1, :(z1, z2), ty_Ordering)
14.04/5.38	
14.04/5.38	R is empty.
14.04/5.38	Q is empty.
14.04/5.38	We have to consider all minimal (P,Q,R)-chains.
14.04/5.38	----------------------------------------
14.04/5.38	
14.04/5.38	(27) TransformationProof (EQUIVALENT)
14.04/5.38	By instantiating [LPAR04] the rule new_nubNub'11(wx5, wx6, :(wx70, wx71), bd) -> new_nubNub'1(wx5, wx6, wx70, wx71, wx70, wx71, bd) we obtained the following new rules [LPAR04]:
14.04/5.38	
14.04/5.38	   (new_nubNub'11(z0, z1, :(LT, :(z2, z3)), ty_Ordering) -> new_nubNub'1(z0, z1, LT, :(z2, z3), LT, :(z2, z3), ty_Ordering),new_nubNub'11(z0, z1, :(LT, :(z2, z3)), ty_Ordering) -> new_nubNub'1(z0, z1, LT, :(z2, z3), LT, :(z2, z3), ty_Ordering))
14.04/5.38	   (new_nubNub'11(z0, z1, :(GT, :(z2, z3)), ty_Ordering) -> new_nubNub'1(z0, z1, GT, :(z2, z3), GT, :(z2, z3), ty_Ordering),new_nubNub'11(z0, z1, :(GT, :(z2, z3)), ty_Ordering) -> new_nubNub'1(z0, z1, GT, :(z2, z3), GT, :(z2, z3), ty_Ordering))
14.04/5.38	   (new_nubNub'11(z0, z1, :(EQ, :(z2, z3)), ty_Ordering) -> new_nubNub'1(z0, z1, EQ, :(z2, z3), EQ, :(z2, z3), ty_Ordering),new_nubNub'11(z0, z1, :(EQ, :(z2, z3)), ty_Ordering) -> new_nubNub'1(z0, z1, EQ, :(z2, z3), EQ, :(z2, z3), ty_Ordering))
14.04/5.38	   (new_nubNub'11(z0, z1, :(z2, z3), ty_Ordering) -> new_nubNub'1(z0, z1, z2, z3, z2, z3, ty_Ordering),new_nubNub'11(z0, z1, :(z2, z3), ty_Ordering) -> new_nubNub'1(z0, z1, z2, z3, z2, z3, ty_Ordering))
14.04/5.38	
14.04/5.38	
14.04/5.38	----------------------------------------
14.04/5.38	
14.04/5.38	(28)
14.04/5.38	Obligation:
14.04/5.38	Q DP problem:
14.04/5.38	The TRS P consists of the following rules:
14.04/5.38	
14.04/5.38	   new_nubNub'1(LT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(GT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(GT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(EQ, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(GT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(EQ, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(LT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(LT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	   new_nubNub'1(EQ, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	   new_nubNub'10(LT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, LT, :(z1, z2), ty_Ordering)
14.04/5.38	   new_nubNub'10(GT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, GT, :(z1, z2), ty_Ordering)
14.04/5.38	   new_nubNub'10(EQ, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, EQ, :(z1, z2), ty_Ordering)
14.04/5.38	   new_nubNub'10(LT, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(LT, z0, z1, z2, x4, x5, ty_Ordering)
14.04/5.38	   new_nubNub'10(GT, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(GT, z0, z1, z2, x4, x5, ty_Ordering)
14.04/5.38	   new_nubNub'10(EQ, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(EQ, z0, z1, z2, x4, x5, ty_Ordering)
14.04/5.38	   new_nubNub'10(GT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering)
14.04/5.38	   new_nubNub'10(EQ, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering)
14.04/5.38	   new_nubNub'10(LT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering)
14.04/5.38	   new_nubNub'(:(x0, x1), LT, :(z1, z2), ty_Ordering) -> new_nubNub'11(x0, x1, :(LT, :(z1, z2)), ty_Ordering)
14.04/5.38	   new_nubNub'(:(x0, x1), GT, :(z1, z2), ty_Ordering) -> new_nubNub'11(x0, x1, :(GT, :(z1, z2)), ty_Ordering)
14.04/5.38	   new_nubNub'(:(x0, x1), EQ, :(z1, z2), ty_Ordering) -> new_nubNub'11(x0, x1, :(EQ, :(z1, z2)), ty_Ordering)
14.04/5.38	   new_nubNub'(:(x0, x1), z1, z2, ty_Ordering) -> new_nubNub'11(x0, x1, :(z1, z2), ty_Ordering)
14.04/5.38	   new_nubNub'11(z0, z1, :(LT, :(z2, z3)), ty_Ordering) -> new_nubNub'1(z0, z1, LT, :(z2, z3), LT, :(z2, z3), ty_Ordering)
14.04/5.38	   new_nubNub'11(z0, z1, :(GT, :(z2, z3)), ty_Ordering) -> new_nubNub'1(z0, z1, GT, :(z2, z3), GT, :(z2, z3), ty_Ordering)
14.04/5.38	   new_nubNub'11(z0, z1, :(EQ, :(z2, z3)), ty_Ordering) -> new_nubNub'1(z0, z1, EQ, :(z2, z3), EQ, :(z2, z3), ty_Ordering)
14.04/5.38	   new_nubNub'11(z0, z1, :(z2, z3), ty_Ordering) -> new_nubNub'1(z0, z1, z2, z3, z2, z3, ty_Ordering)
14.04/5.38	
14.04/5.38	R is empty.
14.04/5.38	Q is empty.
14.04/5.38	We have to consider all minimal (P,Q,R)-chains.
14.04/5.38	----------------------------------------
14.04/5.38	
14.04/5.38	(29) QDPSizeChangeProof (EQUIVALENT)
14.04/5.38	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. 
14.04/5.38	
14.04/5.38	From the DPs we obtained the following set of size-change graphs:
14.04/5.38	*new_nubNub'10(LT, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(LT, z0, z1, z2, x4, x5, ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 > 5, 6 > 6, 7 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'10(LT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, LT, :(z1, z2), ty_Ordering)
14.04/5.38	The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'11(z0, z1, :(z2, z3), ty_Ordering) -> new_nubNub'1(z0, z1, z2, z3, z2, z3, ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'11(z0, z1, :(GT, :(z2, z3)), ty_Ordering) -> new_nubNub'1(z0, z1, GT, :(z2, z3), GT, :(z2, z3), ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'10(GT, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(GT, z0, z1, z2, x4, x5, ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 > 5, 6 > 6, 7 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'10(GT, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, GT, :(z1, z2), ty_Ordering)
14.04/5.38	The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'11(z0, z1, :(LT, :(z2, z3)), ty_Ordering) -> new_nubNub'1(z0, z1, LT, :(z2, z3), LT, :(z2, z3), ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'10(GT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering)
14.04/5.38	The graph contains the following edges 2 >= 1, 3 >= 2, 4 >= 3, 7 >= 4
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'10(EQ, z0, z1, z2, False, :(x4, x5), ty_Ordering) -> new_nubNub'1(EQ, z0, z1, z2, x4, x5, ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 > 5, 6 > 6, 7 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'10(EQ, z0, z1, z2, False, [], ty_Ordering) -> new_nubNub'(z0, EQ, :(z1, z2), ty_Ordering)
14.04/5.38	The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'11(z0, z1, :(EQ, :(z2, z3)), ty_Ordering) -> new_nubNub'1(z0, z1, EQ, :(z2, z3), EQ, :(z2, z3), ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 3 > 4, 3 > 5, 3 > 6, 4 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'10(EQ, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering)
14.04/5.38	The graph contains the following edges 2 >= 1, 3 >= 2, 4 >= 3, 7 >= 4
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'10(LT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubNub'(z0, z1, z2, ty_Ordering)
14.04/5.38	The graph contains the following edges 2 >= 1, 3 >= 2, 4 >= 3, 7 >= 4
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'(:(x0, x1), z1, z2, ty_Ordering) -> new_nubNub'11(x0, x1, :(z1, z2), ty_Ordering)
14.04/5.38	The graph contains the following edges 1 > 1, 1 > 2, 4 >= 4
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'(:(x0, x1), LT, :(z1, z2), ty_Ordering) -> new_nubNub'11(x0, x1, :(LT, :(z1, z2)), ty_Ordering)
14.04/5.38	The graph contains the following edges 1 > 1, 1 > 2, 4 >= 4
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'(:(x0, x1), GT, :(z1, z2), ty_Ordering) -> new_nubNub'11(x0, x1, :(GT, :(z1, z2)), ty_Ordering)
14.04/5.38	The graph contains the following edges 1 > 1, 1 > 2, 4 >= 4
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'(:(x0, x1), EQ, :(z1, z2), ty_Ordering) -> new_nubNub'11(x0, x1, :(EQ, :(z1, z2)), ty_Ordering)
14.04/5.38	The graph contains the following edges 1 > 1, 1 > 2, 4 >= 4
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'1(LT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 5 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 >= 6, 7 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'1(GT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 5 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 >= 6, 7 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'1(EQ, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, True, y5, ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 5 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 >= 6, 7 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'1(GT, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 >= 6, 7 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'1(GT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(GT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 >= 6, 7 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'1(EQ, y1, y2, y3, LT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 >= 6, 7 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'1(EQ, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(EQ, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 >= 6, 7 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'1(LT, y1, y2, y3, GT, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 >= 6, 7 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	*new_nubNub'1(LT, y1, y2, y3, EQ, y5, ty_Ordering) -> new_nubNub'10(LT, y1, y2, y3, False, y5, ty_Ordering)
14.04/5.38	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 >= 6, 7 >= 7
14.04/5.38	
14.04/5.38	
14.04/5.38	----------------------------------------
14.04/5.38	
14.04/5.38	(30)
14.04/5.38	YES
14.04/5.41	EOF