17.12/7.70	YES
19.67/8.41	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
19.67/8.41	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
19.67/8.41	
19.67/8.41	
19.67/8.41	H-Termination with start terms of the given HASKELL could be proven:
19.67/8.41	
19.67/8.41	(0) HASKELL
19.67/8.41	(1) IFR [EQUIVALENT, 0 ms]
19.67/8.41	(2) HASKELL
19.67/8.41	(3) BR [EQUIVALENT, 0 ms]
19.67/8.41	(4) HASKELL
19.67/8.41	(5) COR [EQUIVALENT, 16 ms]
19.67/8.41	(6) HASKELL
19.67/8.41	(7) LetRed [EQUIVALENT, 0 ms]
19.67/8.41	(8) HASKELL
19.67/8.41	(9) Narrow [SOUND, 0 ms]
19.67/8.41	(10) AND
19.67/8.41	    (11) QDP
19.67/8.41	        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
19.67/8.41	        (13) YES
19.67/8.41	    (14) QDP
19.67/8.41	        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
19.67/8.41	        (16) YES
19.67/8.41	    (17) QDP
19.67/8.41	        (18) TransformationProof [EQUIVALENT, 32 ms]
19.67/8.41	        (19) QDP
19.67/8.41	        (20) UsableRulesProof [EQUIVALENT, 0 ms]
19.67/8.41	        (21) QDP
19.67/8.41	        (22) QReductionProof [EQUIVALENT, 0 ms]
19.67/8.41	        (23) QDP
19.67/8.41	        (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
19.67/8.41	        (25) YES
19.67/8.41	    (26) QDP
19.67/8.41	        (27) DependencyGraphProof [EQUIVALENT, 0 ms]
19.67/8.41	        (28) QDP
19.67/8.41	        (29) TransformationProof [EQUIVALENT, 0 ms]
19.67/8.41	        (30) QDP
19.67/8.41	        (31) QDPSizeChangeProof [EQUIVALENT, 0 ms]
19.67/8.41	        (32) YES
19.67/8.41	    (33) QDP
19.67/8.41	        (34) QDPSizeChangeProof [EQUIVALENT, 0 ms]
19.67/8.41	        (35) YES
19.67/8.41	    (36) QDP
19.67/8.41	        (37) QDPSizeChangeProof [EQUIVALENT, 0 ms]
19.67/8.41	        (38) YES
19.67/8.41	    (39) QDP
19.67/8.41	        (40) QDPSizeChangeProof [EQUIVALENT, 0 ms]
19.67/8.41	        (41) YES
19.67/8.41	
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(0)
19.67/8.41	Obligation:
19.67/8.41	mainModule Main 
19.67/8.41	module Maybe where {
19.67/8.41	import qualified List;
19.67/8.41	import qualified Main;
19.67/8.41	import qualified Prelude;
19.67/8.41	}
19.67/8.41	module List where {
19.67/8.41	import qualified Main;
19.67/8.41	import qualified Maybe;
19.67/8.41	import qualified Prelude;
19.67/8.41	deleteBy :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  [a];
19.67/8.41	deleteBy _ _ [] = [];
19.67/8.41	deleteBy eq x (y : ys) =  if x `eq` y then ys else y : deleteBy eq x ys;
19.67/8.41	
19.67/8.41	elem_by :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  Bool;
19.67/8.41	elem_by _ _ [] = False;
19.67/8.41	elem_by eq y (x : xs) = x `eq` y || elem_by eq y xs;
19.67/8.41	
19.67/8.41	nubBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a];
19.67/8.41	nubBy eq l = nubBy' l [] where { 
19.67/8.41	nubBy' [] _ = [];
19.67/8.41	nubBy' (y : ys) xs  | elem_by eq y xs = nubBy' ys xs
19.67/8.41	 | otherwise = y : nubBy' ys (y : xs);
19.67/8.41	 };
19.67/8.41	
19.67/8.41	union :: Eq a => [a]  ->  [a]  ->  [a];
19.67/8.41	union = unionBy (==);
19.67/8.41	
19.67/8.41	unionBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
19.67/8.41	unionBy eq xs ys = xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs;
19.67/8.41	
19.67/8.41	}
19.67/8.41	module Main where {
19.67/8.41	import qualified List;
19.67/8.41	import qualified Maybe;
19.67/8.41	import qualified Prelude;
19.67/8.41	}
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(1) IFR (EQUIVALENT)
19.67/8.41	If Reductions:
19.67/8.41	The following If expression
19.67/8.41	"if eq x y then ys else y : deleteBy eq x ys"
19.67/8.41	is transformed to
19.67/8.41	"deleteBy0 ys y eq x True = ys;
19.67/8.41	deleteBy0 ys y eq x False = y : deleteBy eq x ys;
19.67/8.41	"
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(2)
19.67/8.41	Obligation:
19.67/8.41	mainModule Main 
19.67/8.41	module Maybe where {
19.67/8.41	import qualified List;
19.67/8.41	import qualified Main;
19.67/8.41	import qualified Prelude;
19.67/8.41	}
19.67/8.41	module List where {
19.67/8.41	import qualified Main;
19.67/8.41	import qualified Maybe;
19.67/8.41	import qualified Prelude;
19.67/8.41	deleteBy :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  [a];
19.67/8.41	deleteBy _ _ [] = [];
19.67/8.41	deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y);
19.67/8.41	
19.67/8.41	deleteBy0 ys y eq x True = ys;
19.67/8.41	deleteBy0 ys y eq x False = y : deleteBy eq x ys;
19.67/8.41	
19.67/8.41	elem_by :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  Bool;
19.67/8.41	elem_by _ _ [] = False;
19.67/8.41	elem_by eq y (x : xs) = x `eq` y || elem_by eq y xs;
19.67/8.41	
19.67/8.41	nubBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a];
19.67/8.41	nubBy eq l = nubBy' l [] where { 
19.67/8.41	nubBy' [] _ = [];
19.67/8.41	nubBy' (y : ys) xs  | elem_by eq y xs = nubBy' ys xs
19.67/8.41	 | otherwise = y : nubBy' ys (y : xs);
19.67/8.41	 };
19.67/8.41	
19.67/8.41	union :: Eq a => [a]  ->  [a]  ->  [a];
19.67/8.41	union = unionBy (==);
19.67/8.41	
19.67/8.41	unionBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
19.67/8.41	unionBy eq xs ys = xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs;
19.67/8.41	
19.67/8.41	}
19.67/8.41	module Main where {
19.67/8.41	import qualified List;
19.67/8.41	import qualified Maybe;
19.67/8.41	import qualified Prelude;
19.67/8.41	}
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(3) BR (EQUIVALENT)
19.67/8.41	Replaced joker patterns by fresh variables and removed binding patterns.
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(4)
19.67/8.41	Obligation:
19.67/8.41	mainModule Main 
19.67/8.41	module Maybe where {
19.67/8.41	import qualified List;
19.67/8.41	import qualified Main;
19.67/8.41	import qualified Prelude;
19.67/8.41	}
19.67/8.41	module List where {
19.67/8.41	import qualified Main;
19.67/8.41	import qualified Maybe;
19.67/8.41	import qualified Prelude;
19.67/8.41	deleteBy :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  [a];
19.67/8.41	deleteBy wx wy [] = [];
19.67/8.41	deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y);
19.67/8.41	
19.67/8.41	deleteBy0 ys y eq x True = ys;
19.67/8.41	deleteBy0 ys y eq x False = y : deleteBy eq x ys;
19.67/8.41	
19.67/8.41	elem_by :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  Bool;
19.67/8.41	elem_by wu wv [] = False;
19.67/8.41	elem_by eq y (x : xs) = x `eq` y || elem_by eq y xs;
19.67/8.41	
19.67/8.41	nubBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a];
19.67/8.41	nubBy eq l = nubBy' l [] where { 
19.67/8.41	nubBy' [] ww = [];
19.67/8.41	nubBy' (y : ys) xs  | elem_by eq y xs = nubBy' ys xs
19.67/8.41	 | otherwise = y : nubBy' ys (y : xs);
19.67/8.41	 };
19.67/8.41	
19.67/8.41	union :: Eq a => [a]  ->  [a]  ->  [a];
19.67/8.41	union = unionBy (==);
19.67/8.41	
19.67/8.41	unionBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
19.67/8.41	unionBy eq xs ys = xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs;
19.67/8.41	
19.67/8.41	}
19.67/8.41	module Main where {
19.67/8.41	import qualified List;
19.67/8.41	import qualified Maybe;
19.67/8.41	import qualified Prelude;
19.67/8.41	}
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(5) COR (EQUIVALENT)
19.67/8.41	Cond Reductions:
19.67/8.41	The following Function with conditions
19.67/8.41	"undefined |Falseundefined;
19.67/8.41	"
19.67/8.41	is transformed to
19.67/8.41	"undefined  = undefined1;
19.67/8.41	"
19.67/8.41	"undefined0 True = undefined;
19.67/8.41	"
19.67/8.41	"undefined1  = undefined0 False;
19.67/8.41	"
19.67/8.41	The following Function with conditions
19.67/8.41	"nubBy' [] ww = [];
19.67/8.41	nubBy' (y : ys) xs|elem_by eq y xsnubBy' ys xs|otherwisey : nubBy' ys (y : xs);
19.67/8.41	"
19.67/8.41	is transformed to
19.67/8.41	"nubBy' [] ww = nubBy'3 [] ww;
19.67/8.41	nubBy' (y : ys) xs = nubBy'2 (y : ys) xs;
19.67/8.41	"
19.67/8.41	"nubBy'0 y ys xs True = y : nubBy' ys (y : xs);
19.67/8.41	"
19.67/8.41	"nubBy'1 y ys xs True = nubBy' ys xs;
19.67/8.41	nubBy'1 y ys xs False = nubBy'0 y ys xs otherwise;
19.67/8.41	"
19.67/8.41	"nubBy'2 (y : ys) xs = nubBy'1 y ys xs (elem_by eq y xs);
19.67/8.41	"
19.67/8.41	"nubBy'3 [] ww = [];
19.67/8.41	nubBy'3 xv xw = nubBy'2 xv xw;
19.67/8.41	"
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(6)
19.67/8.41	Obligation:
19.67/8.41	mainModule Main 
19.67/8.41	module Maybe where {
19.67/8.41	import qualified List;
19.67/8.41	import qualified Main;
19.67/8.41	import qualified Prelude;
19.67/8.41	}
19.67/8.41	module List where {
19.67/8.41	import qualified Main;
19.67/8.41	import qualified Maybe;
19.67/8.41	import qualified Prelude;
19.67/8.41	deleteBy :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  [a];
19.67/8.41	deleteBy wx wy [] = [];
19.67/8.41	deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y);
19.67/8.41	
19.67/8.41	deleteBy0 ys y eq x True = ys;
19.67/8.41	deleteBy0 ys y eq x False = y : deleteBy eq x ys;
19.67/8.41	
19.67/8.41	elem_by :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  Bool;
19.67/8.41	elem_by wu wv [] = False;
19.67/8.41	elem_by eq y (x : xs) = x `eq` y || elem_by eq y xs;
19.67/8.41	
19.67/8.41	nubBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a];
19.67/8.41	nubBy eq l = nubBy' l [] where { 
19.67/8.41	nubBy' [] ww = nubBy'3 [] ww;
19.67/8.41	nubBy' (y : ys) xs = nubBy'2 (y : ys) xs;
19.67/8.41	nubBy'0 y ys xs True = y : nubBy' ys (y : xs);
19.67/8.41	nubBy'1 y ys xs True = nubBy' ys xs;
19.67/8.41	nubBy'1 y ys xs False = nubBy'0 y ys xs otherwise;
19.67/8.41	nubBy'2 (y : ys) xs = nubBy'1 y ys xs (elem_by eq y xs);
19.67/8.41	nubBy'3 [] ww = [];
19.67/8.41	nubBy'3 xv xw = nubBy'2 xv xw;
19.67/8.41	 };
19.67/8.41	
19.67/8.41	union :: Eq a => [a]  ->  [a]  ->  [a];
19.67/8.41	union = unionBy (==);
19.67/8.41	
19.67/8.41	unionBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
19.67/8.41	unionBy eq xs ys = xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs;
19.67/8.41	
19.67/8.41	}
19.67/8.41	module Main where {
19.67/8.41	import qualified List;
19.67/8.41	import qualified Maybe;
19.67/8.41	import qualified Prelude;
19.67/8.41	}
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(7) LetRed (EQUIVALENT)
19.67/8.41	Let/Where Reductions:
19.67/8.41	The bindings of the following Let/Where expression
19.67/8.41	"nubBy' l [] where {
19.67/8.41	nubBy' [] ww = nubBy'3 [] ww;
19.67/8.41	nubBy' (y : ys) xs = nubBy'2 (y : ys) xs;
19.67/8.41	;
19.67/8.41	nubBy'0 y ys xs True = y : nubBy' ys (y : xs);
19.67/8.41	;
19.67/8.41	nubBy'1 y ys xs True = nubBy' ys xs;
19.67/8.41	nubBy'1 y ys xs False = nubBy'0 y ys xs otherwise;
19.67/8.41	;
19.67/8.41	nubBy'2 (y : ys) xs = nubBy'1 y ys xs (elem_by eq y xs);
19.67/8.41	;
19.67/8.41	nubBy'3 [] ww = [];
19.67/8.41	nubBy'3 xv xw = nubBy'2 xv xw;
19.67/8.41	} 
19.67/8.41	"
19.67/8.41	are unpacked to the following functions on top level
19.67/8.41	"nubByNubBy'1 xx y ys xs True = nubByNubBy' xx ys xs;
19.67/8.41	nubByNubBy'1 xx y ys xs False = nubByNubBy'0 xx y ys xs otherwise;
19.67/8.41	"
19.67/8.41	"nubByNubBy' xx [] ww = nubByNubBy'3 xx [] ww;
19.67/8.41	nubByNubBy' xx (y : ys) xs = nubByNubBy'2 xx (y : ys) xs;
19.67/8.41	"
19.67/8.41	"nubByNubBy'0 xx y ys xs True = y : nubByNubBy' xx ys (y : xs);
19.67/8.41	"
19.67/8.41	"nubByNubBy'3 xx [] ww = [];
19.67/8.41	nubByNubBy'3 xx xv xw = nubByNubBy'2 xx xv xw;
19.67/8.41	"
19.67/8.41	"nubByNubBy'2 xx (y : ys) xs = nubByNubBy'1 xx y ys xs (elem_by xx y xs);
19.67/8.41	"
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(8)
19.67/8.41	Obligation:
19.67/8.41	mainModule Main 
19.67/8.41	module Maybe where {
19.67/8.41	import qualified List;
19.67/8.41	import qualified Main;
19.67/8.41	import qualified Prelude;
19.67/8.41	}
19.67/8.41	module List where {
19.67/8.41	import qualified Main;
19.67/8.41	import qualified Maybe;
19.67/8.41	import qualified Prelude;
19.67/8.41	deleteBy :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  [a];
19.67/8.41	deleteBy wx wy [] = [];
19.67/8.41	deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y);
19.67/8.41	
19.67/8.41	deleteBy0 ys y eq x True = ys;
19.67/8.41	deleteBy0 ys y eq x False = y : deleteBy eq x ys;
19.67/8.41	
19.67/8.41	elem_by :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  Bool;
19.67/8.41	elem_by wu wv [] = False;
19.67/8.41	elem_by eq y (x : xs) = x `eq` y || elem_by eq y xs;
19.67/8.41	
19.67/8.41	nubBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a];
19.67/8.41	nubBy eq l = nubByNubBy' eq l [];
19.67/8.41	
19.67/8.41	nubByNubBy' xx [] ww = nubByNubBy'3 xx [] ww;
19.67/8.41	nubByNubBy' xx (y : ys) xs = nubByNubBy'2 xx (y : ys) xs;
19.67/8.41	
19.67/8.41	nubByNubBy'0 xx y ys xs True = y : nubByNubBy' xx ys (y : xs);
19.67/8.41	
19.67/8.41	nubByNubBy'1 xx y ys xs True = nubByNubBy' xx ys xs;
19.67/8.41	nubByNubBy'1 xx y ys xs False = nubByNubBy'0 xx y ys xs otherwise;
19.67/8.41	
19.67/8.41	nubByNubBy'2 xx (y : ys) xs = nubByNubBy'1 xx y ys xs (elem_by xx y xs);
19.67/8.41	
19.67/8.41	nubByNubBy'3 xx [] ww = [];
19.67/8.41	nubByNubBy'3 xx xv xw = nubByNubBy'2 xx xv xw;
19.67/8.41	
19.67/8.41	union :: Eq a => [a]  ->  [a]  ->  [a];
19.67/8.41	union = unionBy (==);
19.67/8.41	
19.67/8.41	unionBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
19.67/8.41	unionBy eq xs ys = xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs;
19.67/8.41	
19.67/8.41	}
19.67/8.41	module Main where {
19.67/8.41	import qualified List;
19.67/8.41	import qualified Maybe;
19.67/8.41	import qualified Prelude;
19.67/8.41	}
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(9) Narrow (SOUND)
19.67/8.41	Haskell To QDPs
19.67/8.41	
19.67/8.41	digraph dp_graph {
19.67/8.41	node [outthreshold=100, inthreshold=100];1[label="List.union",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
19.67/8.41	3[label="List.union xy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
19.67/8.41	4[label="List.union xy3 xy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
19.67/8.41	5[label="List.unionBy (==) xy3 xy4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
19.67/8.41	6[label="xy3 ++ foldl (flip (List.deleteBy (==))) (List.nubBy (==) xy4) xy3",fontsize=16,color="burlywood",shape="box"];5374[label="xy3/xy30 : xy31",fontsize=10,color="white",style="solid",shape="box"];6 -> 5374[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5374 -> 7[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5375[label="xy3/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 5375[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5375 -> 8[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	7[label="(xy30 : xy31) ++ foldl (flip (List.deleteBy (==))) (List.nubBy (==) xy4) (xy30 : xy31)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
19.67/8.41	8[label="[] ++ foldl (flip (List.deleteBy (==))) (List.nubBy (==) xy4) []",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
19.67/8.41	9[label="xy30 : xy31 ++ foldl (flip (List.deleteBy (==))) (List.nubBy (==) xy4) (xy30 : xy31)",fontsize=16,color="green",shape="box"];9 -> 11[label="",style="dashed", color="green", weight=3];
19.67/8.41	10[label="foldl (flip (List.deleteBy (==))) (List.nubBy (==) xy4) []",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
19.67/8.41	11 -> 99[label="",style="dashed", color="red", weight=0];
19.67/8.41	11[label="xy31 ++ foldl (flip (List.deleteBy (==))) (List.nubBy (==) xy4) (xy30 : xy31)",fontsize=16,color="magenta"];11 -> 100[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	11 -> 101[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	11 -> 102[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	11 -> 103[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	12[label="List.nubBy (==) xy4",fontsize=16,color="black",shape="triangle"];12 -> 15[label="",style="solid", color="black", weight=3];
19.67/8.41	100[label="xy31",fontsize=16,color="green",shape="box"];101 -> 12[label="",style="dashed", color="red", weight=0];
19.67/8.41	101[label="List.nubBy (==) xy4",fontsize=16,color="magenta"];102[label="xy30",fontsize=16,color="green",shape="box"];103[label="xy31",fontsize=16,color="green",shape="box"];99[label="xy8 ++ foldl (flip (List.deleteBy (==))) xy9 (xy10 : xy11)",fontsize=16,color="burlywood",shape="triangle"];5376[label="xy8/xy80 : xy81",fontsize=10,color="white",style="solid",shape="box"];99 -> 5376[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5376 -> 128[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5377[label="xy8/[]",fontsize=10,color="white",style="solid",shape="box"];99 -> 5377[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5377 -> 129[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	15[label="List.nubByNubBy' (==) xy4 []",fontsize=16,color="burlywood",shape="box"];5378[label="xy4/xy40 : xy41",fontsize=10,color="white",style="solid",shape="box"];15 -> 5378[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5378 -> 18[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5379[label="xy4/[]",fontsize=10,color="white",style="solid",shape="box"];15 -> 5379[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5379 -> 19[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	128[label="(xy80 : xy81) ++ foldl (flip (List.deleteBy (==))) xy9 (xy10 : xy11)",fontsize=16,color="black",shape="box"];128 -> 131[label="",style="solid", color="black", weight=3];
19.67/8.41	129[label="[] ++ foldl (flip (List.deleteBy (==))) xy9 (xy10 : xy11)",fontsize=16,color="black",shape="box"];129 -> 132[label="",style="solid", color="black", weight=3];
19.67/8.41	18[label="List.nubByNubBy' (==) (xy40 : xy41) []",fontsize=16,color="black",shape="box"];18 -> 23[label="",style="solid", color="black", weight=3];
19.67/8.41	19[label="List.nubByNubBy' (==) [] []",fontsize=16,color="black",shape="box"];19 -> 24[label="",style="solid", color="black", weight=3];
19.67/8.41	131[label="xy80 : xy81 ++ foldl (flip (List.deleteBy (==))) xy9 (xy10 : xy11)",fontsize=16,color="green",shape="box"];131 -> 134[label="",style="dashed", color="green", weight=3];
19.67/8.41	132[label="foldl (flip (List.deleteBy (==))) xy9 (xy10 : xy11)",fontsize=16,color="black",shape="box"];132 -> 135[label="",style="solid", color="black", weight=3];
19.67/8.41	23[label="List.nubByNubBy'2 (==) (xy40 : xy41) []",fontsize=16,color="black",shape="box"];23 -> 28[label="",style="solid", color="black", weight=3];
19.67/8.41	24[label="List.nubByNubBy'3 (==) [] []",fontsize=16,color="black",shape="box"];24 -> 29[label="",style="solid", color="black", weight=3];
19.67/8.41	134 -> 99[label="",style="dashed", color="red", weight=0];
19.67/8.41	134[label="xy81 ++ foldl (flip (List.deleteBy (==))) xy9 (xy10 : xy11)",fontsize=16,color="magenta"];134 -> 137[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	135[label="foldl (flip (List.deleteBy (==))) (flip (List.deleteBy (==)) xy9 xy10) xy11",fontsize=16,color="burlywood",shape="triangle"];5380[label="xy11/xy110 : xy111",fontsize=10,color="white",style="solid",shape="box"];135 -> 5380[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5380 -> 138[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5381[label="xy11/[]",fontsize=10,color="white",style="solid",shape="box"];135 -> 5381[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5381 -> 139[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	28[label="List.nubByNubBy'1 (==) xy40 xy41 [] (List.elem_by (==) xy40 [])",fontsize=16,color="black",shape="box"];28 -> 33[label="",style="solid", color="black", weight=3];
19.67/8.41	29[label="[]",fontsize=16,color="green",shape="box"];137[label="xy81",fontsize=16,color="green",shape="box"];138[label="foldl (flip (List.deleteBy (==))) (flip (List.deleteBy (==)) xy9 xy10) (xy110 : xy111)",fontsize=16,color="black",shape="box"];138 -> 142[label="",style="solid", color="black", weight=3];
19.67/8.41	139[label="foldl (flip (List.deleteBy (==))) (flip (List.deleteBy (==)) xy9 xy10) []",fontsize=16,color="black",shape="box"];139 -> 143[label="",style="solid", color="black", weight=3];
19.67/8.41	33[label="List.nubByNubBy'1 (==) xy40 xy41 [] False",fontsize=16,color="black",shape="box"];33 -> 37[label="",style="solid", color="black", weight=3];
19.67/8.41	142 -> 135[label="",style="dashed", color="red", weight=0];
19.67/8.41	142[label="foldl (flip (List.deleteBy (==))) (flip (List.deleteBy (==)) (flip (List.deleteBy (==)) xy9 xy10) xy110) xy111",fontsize=16,color="magenta"];142 -> 148[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	142 -> 149[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	142 -> 150[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	143[label="flip (List.deleteBy (==)) xy9 xy10",fontsize=16,color="black",shape="triangle"];143 -> 151[label="",style="solid", color="black", weight=3];
19.67/8.41	37[label="List.nubByNubBy'0 (==) xy40 xy41 [] otherwise",fontsize=16,color="black",shape="box"];37 -> 42[label="",style="solid", color="black", weight=3];
19.67/8.41	148[label="xy111",fontsize=16,color="green",shape="box"];149 -> 143[label="",style="dashed", color="red", weight=0];
19.67/8.41	149[label="flip (List.deleteBy (==)) xy9 xy10",fontsize=16,color="magenta"];150[label="xy110",fontsize=16,color="green",shape="box"];151[label="List.deleteBy (==) xy10 xy9",fontsize=16,color="burlywood",shape="triangle"];5382[label="xy9/xy90 : xy91",fontsize=10,color="white",style="solid",shape="box"];151 -> 5382[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5382 -> 156[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5383[label="xy9/[]",fontsize=10,color="white",style="solid",shape="box"];151 -> 5383[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5383 -> 157[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	42[label="List.nubByNubBy'0 (==) xy40 xy41 [] True",fontsize=16,color="black",shape="box"];42 -> 49[label="",style="solid", color="black", weight=3];
19.67/8.41	156[label="List.deleteBy (==) xy10 (xy90 : xy91)",fontsize=16,color="black",shape="box"];156 -> 166[label="",style="solid", color="black", weight=3];
19.67/8.41	157[label="List.deleteBy (==) xy10 []",fontsize=16,color="black",shape="box"];157 -> 167[label="",style="solid", color="black", weight=3];
19.67/8.41	49[label="xy40 : List.nubByNubBy' (==) xy41 (xy40 : [])",fontsize=16,color="green",shape="box"];49 -> 54[label="",style="dashed", color="green", weight=3];
19.67/8.41	166 -> 184[label="",style="dashed", color="red", weight=0];
19.67/8.41	166[label="List.deleteBy0 xy91 xy90 (==) xy10 ((==) xy10 xy90)",fontsize=16,color="magenta"];166 -> 185[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	166 -> 186[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	166 -> 187[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	166 -> 188[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	167[label="[]",fontsize=16,color="green",shape="box"];54[label="List.nubByNubBy' (==) xy41 (xy40 : [])",fontsize=16,color="burlywood",shape="box"];5384[label="xy41/xy410 : xy411",fontsize=10,color="white",style="solid",shape="box"];54 -> 5384[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5384 -> 58[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5385[label="xy41/[]",fontsize=10,color="white",style="solid",shape="box"];54 -> 5385[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5385 -> 59[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	185[label="xy91",fontsize=16,color="green",shape="box"];186[label="xy10",fontsize=16,color="green",shape="box"];187[label="xy90",fontsize=16,color="green",shape="box"];188[label="(==) xy10 xy90",fontsize=16,color="blue",shape="box"];5386[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];188 -> 5386[label="",style="solid", color="blue", weight=9];
19.67/8.41	5386 -> 189[label="",style="solid", color="blue", weight=3];
19.67/8.41	5387[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];188 -> 5387[label="",style="solid", color="blue", weight=9];
19.67/8.41	5387 -> 190[label="",style="solid", color="blue", weight=3];
19.67/8.41	5388[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];188 -> 5388[label="",style="solid", color="blue", weight=9];
19.67/8.41	5388 -> 191[label="",style="solid", color="blue", weight=3];
19.67/8.41	5389[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];188 -> 5389[label="",style="solid", color="blue", weight=9];
19.67/8.41	5389 -> 192[label="",style="solid", color="blue", weight=3];
19.67/8.41	5390[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];188 -> 5390[label="",style="solid", color="blue", weight=9];
19.67/8.41	5390 -> 193[label="",style="solid", color="blue", weight=3];
19.67/8.41	5391[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];188 -> 5391[label="",style="solid", color="blue", weight=9];
19.67/8.41	5391 -> 194[label="",style="solid", color="blue", weight=3];
19.67/8.41	5392[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];188 -> 5392[label="",style="solid", color="blue", weight=9];
19.67/8.41	5392 -> 195[label="",style="solid", color="blue", weight=3];
19.67/8.41	5393[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];188 -> 5393[label="",style="solid", color="blue", weight=9];
19.67/8.41	5393 -> 196[label="",style="solid", color="blue", weight=3];
19.67/8.41	5394[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];188 -> 5394[label="",style="solid", color="blue", weight=9];
19.67/8.41	5394 -> 197[label="",style="solid", color="blue", weight=3];
19.67/8.41	5395[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];188 -> 5395[label="",style="solid", color="blue", weight=9];
19.67/8.41	5395 -> 198[label="",style="solid", color="blue", weight=3];
19.67/8.41	5396[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];188 -> 5396[label="",style="solid", color="blue", weight=9];
19.67/8.41	5396 -> 199[label="",style="solid", color="blue", weight=3];
19.67/8.41	5397[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];188 -> 5397[label="",style="solid", color="blue", weight=9];
19.67/8.41	5397 -> 200[label="",style="solid", color="blue", weight=3];
19.67/8.41	5398[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];188 -> 5398[label="",style="solid", color="blue", weight=9];
19.67/8.41	5398 -> 201[label="",style="solid", color="blue", weight=3];
19.67/8.41	5399[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];188 -> 5399[label="",style="solid", color="blue", weight=9];
19.67/8.41	5399 -> 202[label="",style="solid", color="blue", weight=3];
19.67/8.41	184[label="List.deleteBy0 xy17 xy18 (==) xy19 xy20",fontsize=16,color="burlywood",shape="triangle"];5400[label="xy20/False",fontsize=10,color="white",style="solid",shape="box"];184 -> 5400[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5400 -> 203[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5401[label="xy20/True",fontsize=10,color="white",style="solid",shape="box"];184 -> 5401[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5401 -> 204[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	58[label="List.nubByNubBy' (==) (xy410 : xy411) (xy40 : [])",fontsize=16,color="black",shape="box"];58 -> 66[label="",style="solid", color="black", weight=3];
19.67/8.41	59[label="List.nubByNubBy' (==) [] (xy40 : [])",fontsize=16,color="black",shape="box"];59 -> 67[label="",style="solid", color="black", weight=3];
19.67/8.41	189[label="(==) xy10 xy90",fontsize=16,color="black",shape="triangle"];189 -> 221[label="",style="solid", color="black", weight=3];
19.67/8.41	190[label="(==) xy10 xy90",fontsize=16,color="black",shape="box"];190 -> 222[label="",style="solid", color="black", weight=3];
19.67/8.41	191[label="(==) xy10 xy90",fontsize=16,color="black",shape="box"];191 -> 223[label="",style="solid", color="black", weight=3];
19.67/8.41	192[label="(==) xy10 xy90",fontsize=16,color="black",shape="box"];192 -> 224[label="",style="solid", color="black", weight=3];
19.67/8.41	193[label="(==) xy10 xy90",fontsize=16,color="black",shape="box"];193 -> 225[label="",style="solid", color="black", weight=3];
19.67/8.41	194[label="(==) xy10 xy90",fontsize=16,color="black",shape="box"];194 -> 226[label="",style="solid", color="black", weight=3];
19.67/8.41	195[label="(==) xy10 xy90",fontsize=16,color="black",shape="box"];195 -> 227[label="",style="solid", color="black", weight=3];
19.67/8.41	196[label="(==) xy10 xy90",fontsize=16,color="black",shape="box"];196 -> 228[label="",style="solid", color="black", weight=3];
19.67/8.41	197[label="(==) xy10 xy90",fontsize=16,color="black",shape="box"];197 -> 229[label="",style="solid", color="black", weight=3];
19.67/8.41	198[label="(==) xy10 xy90",fontsize=16,color="black",shape="box"];198 -> 230[label="",style="solid", color="black", weight=3];
19.67/8.41	199[label="(==) xy10 xy90",fontsize=16,color="black",shape="box"];199 -> 231[label="",style="solid", color="black", weight=3];
19.67/8.41	200[label="(==) xy10 xy90",fontsize=16,color="black",shape="box"];200 -> 232[label="",style="solid", color="black", weight=3];
19.67/8.41	201[label="(==) xy10 xy90",fontsize=16,color="black",shape="box"];201 -> 233[label="",style="solid", color="black", weight=3];
19.67/8.41	202[label="(==) xy10 xy90",fontsize=16,color="black",shape="box"];202 -> 234[label="",style="solid", color="black", weight=3];
19.67/8.41	203[label="List.deleteBy0 xy17 xy18 (==) xy19 False",fontsize=16,color="black",shape="box"];203 -> 235[label="",style="solid", color="black", weight=3];
19.67/8.41	204[label="List.deleteBy0 xy17 xy18 (==) xy19 True",fontsize=16,color="black",shape="box"];204 -> 236[label="",style="solid", color="black", weight=3];
19.67/8.41	66[label="List.nubByNubBy'2 (==) (xy410 : xy411) (xy40 : [])",fontsize=16,color="black",shape="box"];66 -> 72[label="",style="solid", color="black", weight=3];
19.67/8.41	67[label="List.nubByNubBy'3 (==) [] (xy40 : [])",fontsize=16,color="black",shape="box"];67 -> 73[label="",style="solid", color="black", weight=3];
19.67/8.41	221[label="primEqInt xy10 xy90",fontsize=16,color="burlywood",shape="triangle"];5402[label="xy10/Pos xy100",fontsize=10,color="white",style="solid",shape="box"];221 -> 5402[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5402 -> 257[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5403[label="xy10/Neg xy100",fontsize=10,color="white",style="solid",shape="box"];221 -> 5403[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5403 -> 258[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	222[label="error []",fontsize=16,color="red",shape="box"];223[label="primEqFloat xy10 xy90",fontsize=16,color="burlywood",shape="triangle"];5404[label="xy10/Float xy100 xy101",fontsize=10,color="white",style="solid",shape="box"];223 -> 5404[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5404 -> 259[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	224[label="error []",fontsize=16,color="red",shape="box"];225[label="error []",fontsize=16,color="red",shape="box"];226[label="error []",fontsize=16,color="red",shape="box"];227[label="error []",fontsize=16,color="red",shape="box"];228[label="error []",fontsize=16,color="red",shape="box"];229[label="error []",fontsize=16,color="red",shape="box"];230[label="error []",fontsize=16,color="red",shape="box"];231[label="error []",fontsize=16,color="red",shape="box"];232[label="error []",fontsize=16,color="red",shape="box"];233[label="error []",fontsize=16,color="red",shape="box"];234[label="error []",fontsize=16,color="red",shape="box"];235[label="xy18 : List.deleteBy (==) xy19 xy17",fontsize=16,color="green",shape="box"];235 -> 260[label="",style="dashed", color="green", weight=3];
19.67/8.41	236[label="xy17",fontsize=16,color="green",shape="box"];72[label="List.nubByNubBy'1 (==) xy410 xy411 (xy40 : []) (List.elem_by (==) xy410 (xy40 : []))",fontsize=16,color="black",shape="box"];72 -> 77[label="",style="solid", color="black", weight=3];
19.67/8.41	73[label="[]",fontsize=16,color="green",shape="box"];257[label="primEqInt (Pos xy100) xy90",fontsize=16,color="burlywood",shape="box"];5405[label="xy100/Succ xy1000",fontsize=10,color="white",style="solid",shape="box"];257 -> 5405[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5405 -> 266[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5406[label="xy100/Zero",fontsize=10,color="white",style="solid",shape="box"];257 -> 5406[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5406 -> 267[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	258[label="primEqInt (Neg xy100) xy90",fontsize=16,color="burlywood",shape="box"];5407[label="xy100/Succ xy1000",fontsize=10,color="white",style="solid",shape="box"];258 -> 5407[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5407 -> 268[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5408[label="xy100/Zero",fontsize=10,color="white",style="solid",shape="box"];258 -> 5408[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5408 -> 269[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	259[label="primEqFloat (Float xy100 xy101) xy90",fontsize=16,color="burlywood",shape="box"];5409[label="xy90/Float xy900 xy901",fontsize=10,color="white",style="solid",shape="box"];259 -> 5409[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5409 -> 270[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	260 -> 151[label="",style="dashed", color="red", weight=0];
19.67/8.41	260[label="List.deleteBy (==) xy19 xy17",fontsize=16,color="magenta"];260 -> 271[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	260 -> 272[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	77[label="List.nubByNubBy'1 (==) xy410 xy411 (xy40 : []) ((==) xy40 xy410 || List.elem_by (==) xy410 [])",fontsize=16,color="black",shape="box"];77 -> 85[label="",style="solid", color="black", weight=3];
19.67/8.41	266[label="primEqInt (Pos (Succ xy1000)) xy90",fontsize=16,color="burlywood",shape="box"];5410[label="xy90/Pos xy900",fontsize=10,color="white",style="solid",shape="box"];266 -> 5410[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5410 -> 280[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5411[label="xy90/Neg xy900",fontsize=10,color="white",style="solid",shape="box"];266 -> 5411[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5411 -> 281[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	267[label="primEqInt (Pos Zero) xy90",fontsize=16,color="burlywood",shape="box"];5412[label="xy90/Pos xy900",fontsize=10,color="white",style="solid",shape="box"];267 -> 5412[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5412 -> 282[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5413[label="xy90/Neg xy900",fontsize=10,color="white",style="solid",shape="box"];267 -> 5413[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5413 -> 283[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	268[label="primEqInt (Neg (Succ xy1000)) xy90",fontsize=16,color="burlywood",shape="box"];5414[label="xy90/Pos xy900",fontsize=10,color="white",style="solid",shape="box"];268 -> 5414[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5414 -> 284[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5415[label="xy90/Neg xy900",fontsize=10,color="white",style="solid",shape="box"];268 -> 5415[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5415 -> 285[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	269[label="primEqInt (Neg Zero) xy90",fontsize=16,color="burlywood",shape="box"];5416[label="xy90/Pos xy900",fontsize=10,color="white",style="solid",shape="box"];269 -> 5416[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5416 -> 286[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5417[label="xy90/Neg xy900",fontsize=10,color="white",style="solid",shape="box"];269 -> 5417[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5417 -> 287[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	270[label="primEqFloat (Float xy100 xy101) (Float xy900 xy901)",fontsize=16,color="black",shape="box"];270 -> 288[label="",style="solid", color="black", weight=3];
19.67/8.41	271[label="xy17",fontsize=16,color="green",shape="box"];272[label="xy19",fontsize=16,color="green",shape="box"];85 -> 5336[label="",style="dashed", color="red", weight=0];
19.67/8.41	85[label="List.nubByNubBy'1 primEqFloat xy410 xy411 (xy40 : []) (primEqFloat xy40 xy410 || List.elem_by primEqFloat xy410 [])",fontsize=16,color="magenta"];85 -> 5337[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	85 -> 5338[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	85 -> 5339[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	85 -> 5340[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	85 -> 5341[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	85 -> 5342[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	280[label="primEqInt (Pos (Succ xy1000)) (Pos xy900)",fontsize=16,color="burlywood",shape="box"];5418[label="xy900/Succ xy9000",fontsize=10,color="white",style="solid",shape="box"];280 -> 5418[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5418 -> 296[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5419[label="xy900/Zero",fontsize=10,color="white",style="solid",shape="box"];280 -> 5419[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5419 -> 297[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	281[label="primEqInt (Pos (Succ xy1000)) (Neg xy900)",fontsize=16,color="black",shape="box"];281 -> 298[label="",style="solid", color="black", weight=3];
19.67/8.41	282[label="primEqInt (Pos Zero) (Pos xy900)",fontsize=16,color="burlywood",shape="box"];5420[label="xy900/Succ xy9000",fontsize=10,color="white",style="solid",shape="box"];282 -> 5420[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5420 -> 299[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5421[label="xy900/Zero",fontsize=10,color="white",style="solid",shape="box"];282 -> 5421[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5421 -> 300[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	283[label="primEqInt (Pos Zero) (Neg xy900)",fontsize=16,color="burlywood",shape="box"];5422[label="xy900/Succ xy9000",fontsize=10,color="white",style="solid",shape="box"];283 -> 5422[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5422 -> 301[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5423[label="xy900/Zero",fontsize=10,color="white",style="solid",shape="box"];283 -> 5423[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5423 -> 302[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	284[label="primEqInt (Neg (Succ xy1000)) (Pos xy900)",fontsize=16,color="black",shape="box"];284 -> 303[label="",style="solid", color="black", weight=3];
19.67/8.41	285[label="primEqInt (Neg (Succ xy1000)) (Neg xy900)",fontsize=16,color="burlywood",shape="box"];5424[label="xy900/Succ xy9000",fontsize=10,color="white",style="solid",shape="box"];285 -> 5424[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5424 -> 304[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5425[label="xy900/Zero",fontsize=10,color="white",style="solid",shape="box"];285 -> 5425[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5425 -> 305[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	286[label="primEqInt (Neg Zero) (Pos xy900)",fontsize=16,color="burlywood",shape="box"];5426[label="xy900/Succ xy9000",fontsize=10,color="white",style="solid",shape="box"];286 -> 5426[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5426 -> 306[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5427[label="xy900/Zero",fontsize=10,color="white",style="solid",shape="box"];286 -> 5427[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5427 -> 307[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	287[label="primEqInt (Neg Zero) (Neg xy900)",fontsize=16,color="burlywood",shape="box"];5428[label="xy900/Succ xy9000",fontsize=10,color="white",style="solid",shape="box"];287 -> 5428[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5428 -> 308[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5429[label="xy900/Zero",fontsize=10,color="white",style="solid",shape="box"];287 -> 5429[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5429 -> 309[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	288 -> 189[label="",style="dashed", color="red", weight=0];
19.67/8.41	288[label="xy100 * xy901 == xy101 * xy900",fontsize=16,color="magenta"];288 -> 310[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	288 -> 311[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	5337[label="xy40",fontsize=16,color="green",shape="box"];5338[label="[]",fontsize=16,color="green",shape="box"];5339[label="xy411",fontsize=16,color="green",shape="box"];5340[label="[]",fontsize=16,color="green",shape="box"];5341[label="xy410",fontsize=16,color="green",shape="box"];5342 -> 223[label="",style="dashed", color="red", weight=0];
19.67/8.41	5342[label="primEqFloat xy40 xy410",fontsize=16,color="magenta"];5342 -> 5344[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	5342 -> 5345[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	5336[label="List.nubByNubBy'1 primEqFloat xy363 xy364 (xy365 : xy366) (xy369 || List.elem_by primEqFloat xy363 xy368)",fontsize=16,color="burlywood",shape="triangle"];5430[label="xy369/False",fontsize=10,color="white",style="solid",shape="box"];5336 -> 5430[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5430 -> 5346[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5431[label="xy369/True",fontsize=10,color="white",style="solid",shape="box"];5336 -> 5431[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5431 -> 5347[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	296[label="primEqInt (Pos (Succ xy1000)) (Pos (Succ xy9000))",fontsize=16,color="black",shape="box"];296 -> 321[label="",style="solid", color="black", weight=3];
19.67/8.41	297[label="primEqInt (Pos (Succ xy1000)) (Pos Zero)",fontsize=16,color="black",shape="box"];297 -> 322[label="",style="solid", color="black", weight=3];
19.67/8.41	298[label="False",fontsize=16,color="green",shape="box"];299[label="primEqInt (Pos Zero) (Pos (Succ xy9000))",fontsize=16,color="black",shape="box"];299 -> 323[label="",style="solid", color="black", weight=3];
19.67/8.41	300[label="primEqInt (Pos Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];300 -> 324[label="",style="solid", color="black", weight=3];
19.67/8.41	301[label="primEqInt (Pos Zero) (Neg (Succ xy9000))",fontsize=16,color="black",shape="box"];301 -> 325[label="",style="solid", color="black", weight=3];
19.67/8.41	302[label="primEqInt (Pos Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];302 -> 326[label="",style="solid", color="black", weight=3];
19.67/8.41	303[label="False",fontsize=16,color="green",shape="box"];304[label="primEqInt (Neg (Succ xy1000)) (Neg (Succ xy9000))",fontsize=16,color="black",shape="box"];304 -> 327[label="",style="solid", color="black", weight=3];
19.67/8.41	305[label="primEqInt (Neg (Succ xy1000)) (Neg Zero)",fontsize=16,color="black",shape="box"];305 -> 328[label="",style="solid", color="black", weight=3];
19.67/8.41	306[label="primEqInt (Neg Zero) (Pos (Succ xy9000))",fontsize=16,color="black",shape="box"];306 -> 329[label="",style="solid", color="black", weight=3];
19.67/8.41	307[label="primEqInt (Neg Zero) (Pos Zero)",fontsize=16,color="black",shape="box"];307 -> 330[label="",style="solid", color="black", weight=3];
19.67/8.41	308[label="primEqInt (Neg Zero) (Neg (Succ xy9000))",fontsize=16,color="black",shape="box"];308 -> 331[label="",style="solid", color="black", weight=3];
19.67/8.41	309[label="primEqInt (Neg Zero) (Neg Zero)",fontsize=16,color="black",shape="box"];309 -> 332[label="",style="solid", color="black", weight=3];
19.67/8.41	310[label="xy101 * xy900",fontsize=16,color="black",shape="triangle"];310 -> 333[label="",style="solid", color="black", weight=3];
19.67/8.41	311 -> 310[label="",style="dashed", color="red", weight=0];
19.67/8.41	311[label="xy100 * xy901",fontsize=16,color="magenta"];311 -> 334[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	311 -> 335[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	5344[label="xy410",fontsize=16,color="green",shape="box"];5345[label="xy40",fontsize=16,color="green",shape="box"];5346[label="List.nubByNubBy'1 primEqFloat xy363 xy364 (xy365 : xy366) (False || List.elem_by primEqFloat xy363 xy368)",fontsize=16,color="black",shape="box"];5346 -> 5348[label="",style="solid", color="black", weight=3];
19.67/8.41	5347[label="List.nubByNubBy'1 primEqFloat xy363 xy364 (xy365 : xy366) (True || List.elem_by primEqFloat xy363 xy368)",fontsize=16,color="black",shape="box"];5347 -> 5349[label="",style="solid", color="black", weight=3];
19.67/8.41	321[label="primEqNat xy1000 xy9000",fontsize=16,color="burlywood",shape="triangle"];5432[label="xy1000/Succ xy10000",fontsize=10,color="white",style="solid",shape="box"];321 -> 5432[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5432 -> 343[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5433[label="xy1000/Zero",fontsize=10,color="white",style="solid",shape="box"];321 -> 5433[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5433 -> 344[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	322[label="False",fontsize=16,color="green",shape="box"];323[label="False",fontsize=16,color="green",shape="box"];324[label="True",fontsize=16,color="green",shape="box"];325[label="False",fontsize=16,color="green",shape="box"];326[label="True",fontsize=16,color="green",shape="box"];327 -> 321[label="",style="dashed", color="red", weight=0];
19.67/8.41	327[label="primEqNat xy1000 xy9000",fontsize=16,color="magenta"];327 -> 345[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	327 -> 346[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	328[label="False",fontsize=16,color="green",shape="box"];329[label="False",fontsize=16,color="green",shape="box"];330[label="True",fontsize=16,color="green",shape="box"];331[label="False",fontsize=16,color="green",shape="box"];332[label="True",fontsize=16,color="green",shape="box"];333[label="primMulInt xy101 xy900",fontsize=16,color="burlywood",shape="box"];5434[label="xy101/Pos xy1010",fontsize=10,color="white",style="solid",shape="box"];333 -> 5434[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5434 -> 347[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5435[label="xy101/Neg xy1010",fontsize=10,color="white",style="solid",shape="box"];333 -> 5435[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5435 -> 348[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	334[label="xy901",fontsize=16,color="green",shape="box"];335[label="xy100",fontsize=16,color="green",shape="box"];5348[label="List.nubByNubBy'1 primEqFloat xy363 xy364 (xy365 : xy366) (List.elem_by primEqFloat xy363 xy368)",fontsize=16,color="burlywood",shape="triangle"];5436[label="xy368/xy3680 : xy3681",fontsize=10,color="white",style="solid",shape="box"];5348 -> 5436[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5436 -> 5350[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5437[label="xy368/[]",fontsize=10,color="white",style="solid",shape="box"];5348 -> 5437[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5437 -> 5351[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5349[label="List.nubByNubBy'1 primEqFloat xy363 xy364 (xy365 : xy366) True",fontsize=16,color="black",shape="box"];5349 -> 5352[label="",style="solid", color="black", weight=3];
19.67/8.41	343[label="primEqNat (Succ xy10000) xy9000",fontsize=16,color="burlywood",shape="box"];5438[label="xy9000/Succ xy90000",fontsize=10,color="white",style="solid",shape="box"];343 -> 5438[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5438 -> 356[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5439[label="xy9000/Zero",fontsize=10,color="white",style="solid",shape="box"];343 -> 5439[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5439 -> 357[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	344[label="primEqNat Zero xy9000",fontsize=16,color="burlywood",shape="box"];5440[label="xy9000/Succ xy90000",fontsize=10,color="white",style="solid",shape="box"];344 -> 5440[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5440 -> 358[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5441[label="xy9000/Zero",fontsize=10,color="white",style="solid",shape="box"];344 -> 5441[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5441 -> 359[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	345[label="xy9000",fontsize=16,color="green",shape="box"];346[label="xy1000",fontsize=16,color="green",shape="box"];347[label="primMulInt (Pos xy1010) xy900",fontsize=16,color="burlywood",shape="box"];5442[label="xy900/Pos xy9000",fontsize=10,color="white",style="solid",shape="box"];347 -> 5442[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5442 -> 360[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5443[label="xy900/Neg xy9000",fontsize=10,color="white",style="solid",shape="box"];347 -> 5443[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5443 -> 361[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	348[label="primMulInt (Neg xy1010) xy900",fontsize=16,color="burlywood",shape="box"];5444[label="xy900/Pos xy9000",fontsize=10,color="white",style="solid",shape="box"];348 -> 5444[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5444 -> 362[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5445[label="xy900/Neg xy9000",fontsize=10,color="white",style="solid",shape="box"];348 -> 5445[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5445 -> 363[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5350[label="List.nubByNubBy'1 primEqFloat xy363 xy364 (xy365 : xy366) (List.elem_by primEqFloat xy363 (xy3680 : xy3681))",fontsize=16,color="black",shape="box"];5350 -> 5353[label="",style="solid", color="black", weight=3];
19.67/8.41	5351[label="List.nubByNubBy'1 primEqFloat xy363 xy364 (xy365 : xy366) (List.elem_by primEqFloat xy363 [])",fontsize=16,color="black",shape="box"];5351 -> 5354[label="",style="solid", color="black", weight=3];
19.67/8.41	5352[label="List.nubByNubBy' primEqFloat xy364 (xy365 : xy366)",fontsize=16,color="burlywood",shape="triangle"];5446[label="xy364/xy3640 : xy3641",fontsize=10,color="white",style="solid",shape="box"];5352 -> 5446[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5446 -> 5355[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5447[label="xy364/[]",fontsize=10,color="white",style="solid",shape="box"];5352 -> 5447[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5447 -> 5356[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	356[label="primEqNat (Succ xy10000) (Succ xy90000)",fontsize=16,color="black",shape="box"];356 -> 373[label="",style="solid", color="black", weight=3];
19.67/8.41	357[label="primEqNat (Succ xy10000) Zero",fontsize=16,color="black",shape="box"];357 -> 374[label="",style="solid", color="black", weight=3];
19.67/8.41	358[label="primEqNat Zero (Succ xy90000)",fontsize=16,color="black",shape="box"];358 -> 375[label="",style="solid", color="black", weight=3];
19.67/8.41	359[label="primEqNat Zero Zero",fontsize=16,color="black",shape="box"];359 -> 376[label="",style="solid", color="black", weight=3];
19.67/8.41	360[label="primMulInt (Pos xy1010) (Pos xy9000)",fontsize=16,color="black",shape="box"];360 -> 377[label="",style="solid", color="black", weight=3];
19.67/8.41	361[label="primMulInt (Pos xy1010) (Neg xy9000)",fontsize=16,color="black",shape="box"];361 -> 378[label="",style="solid", color="black", weight=3];
19.67/8.41	362[label="primMulInt (Neg xy1010) (Pos xy9000)",fontsize=16,color="black",shape="box"];362 -> 379[label="",style="solid", color="black", weight=3];
19.67/8.41	363[label="primMulInt (Neg xy1010) (Neg xy9000)",fontsize=16,color="black",shape="box"];363 -> 380[label="",style="solid", color="black", weight=3];
19.67/8.41	5353 -> 5336[label="",style="dashed", color="red", weight=0];
19.67/8.41	5353[label="List.nubByNubBy'1 primEqFloat xy363 xy364 (xy365 : xy366) (primEqFloat xy3680 xy363 || List.elem_by primEqFloat xy363 xy3681)",fontsize=16,color="magenta"];5353 -> 5357[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	5353 -> 5358[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	5354[label="List.nubByNubBy'1 primEqFloat xy363 xy364 (xy365 : xy366) False",fontsize=16,color="black",shape="box"];5354 -> 5359[label="",style="solid", color="black", weight=3];
19.67/8.41	5355[label="List.nubByNubBy' primEqFloat (xy3640 : xy3641) (xy365 : xy366)",fontsize=16,color="black",shape="box"];5355 -> 5360[label="",style="solid", color="black", weight=3];
19.67/8.41	5356[label="List.nubByNubBy' primEqFloat [] (xy365 : xy366)",fontsize=16,color="black",shape="box"];5356 -> 5361[label="",style="solid", color="black", weight=3];
19.67/8.41	373 -> 321[label="",style="dashed", color="red", weight=0];
19.67/8.41	373[label="primEqNat xy10000 xy90000",fontsize=16,color="magenta"];373 -> 388[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	373 -> 389[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	374[label="False",fontsize=16,color="green",shape="box"];375[label="False",fontsize=16,color="green",shape="box"];376[label="True",fontsize=16,color="green",shape="box"];377[label="Pos (primMulNat xy1010 xy9000)",fontsize=16,color="green",shape="box"];377 -> 390[label="",style="dashed", color="green", weight=3];
19.67/8.41	378[label="Neg (primMulNat xy1010 xy9000)",fontsize=16,color="green",shape="box"];378 -> 391[label="",style="dashed", color="green", weight=3];
19.67/8.41	379[label="Neg (primMulNat xy1010 xy9000)",fontsize=16,color="green",shape="box"];379 -> 392[label="",style="dashed", color="green", weight=3];
19.67/8.41	380[label="Pos (primMulNat xy1010 xy9000)",fontsize=16,color="green",shape="box"];380 -> 393[label="",style="dashed", color="green", weight=3];
19.67/8.41	5357[label="xy3681",fontsize=16,color="green",shape="box"];5358 -> 223[label="",style="dashed", color="red", weight=0];
19.67/8.41	5358[label="primEqFloat xy3680 xy363",fontsize=16,color="magenta"];5358 -> 5362[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	5358 -> 5363[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	5359[label="List.nubByNubBy'0 primEqFloat xy363 xy364 (xy365 : xy366) otherwise",fontsize=16,color="black",shape="box"];5359 -> 5364[label="",style="solid", color="black", weight=3];
19.67/8.41	5360[label="List.nubByNubBy'2 primEqFloat (xy3640 : xy3641) (xy365 : xy366)",fontsize=16,color="black",shape="box"];5360 -> 5365[label="",style="solid", color="black", weight=3];
19.67/8.41	5361[label="List.nubByNubBy'3 primEqFloat [] (xy365 : xy366)",fontsize=16,color="black",shape="box"];5361 -> 5366[label="",style="solid", color="black", weight=3];
19.67/8.41	388[label="xy90000",fontsize=16,color="green",shape="box"];389[label="xy10000",fontsize=16,color="green",shape="box"];390[label="primMulNat xy1010 xy9000",fontsize=16,color="burlywood",shape="triangle"];5448[label="xy1010/Succ xy10100",fontsize=10,color="white",style="solid",shape="box"];390 -> 5448[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5448 -> 401[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5449[label="xy1010/Zero",fontsize=10,color="white",style="solid",shape="box"];390 -> 5449[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5449 -> 402[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	391 -> 390[label="",style="dashed", color="red", weight=0];
19.67/8.41	391[label="primMulNat xy1010 xy9000",fontsize=16,color="magenta"];391 -> 403[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	392 -> 390[label="",style="dashed", color="red", weight=0];
19.67/8.41	392[label="primMulNat xy1010 xy9000",fontsize=16,color="magenta"];392 -> 404[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	393 -> 390[label="",style="dashed", color="red", weight=0];
19.67/8.41	393[label="primMulNat xy1010 xy9000",fontsize=16,color="magenta"];393 -> 405[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	393 -> 406[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	5362[label="xy363",fontsize=16,color="green",shape="box"];5363[label="xy3680",fontsize=16,color="green",shape="box"];5364[label="List.nubByNubBy'0 primEqFloat xy363 xy364 (xy365 : xy366) True",fontsize=16,color="black",shape="box"];5364 -> 5367[label="",style="solid", color="black", weight=3];
19.67/8.41	5365 -> 5348[label="",style="dashed", color="red", weight=0];
19.67/8.41	5365[label="List.nubByNubBy'1 primEqFloat xy3640 xy3641 (xy365 : xy366) (List.elem_by primEqFloat xy3640 (xy365 : xy366))",fontsize=16,color="magenta"];5365 -> 5368[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	5365 -> 5369[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	5365 -> 5370[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	5366[label="[]",fontsize=16,color="green",shape="box"];401[label="primMulNat (Succ xy10100) xy9000",fontsize=16,color="burlywood",shape="box"];5450[label="xy9000/Succ xy90000",fontsize=10,color="white",style="solid",shape="box"];401 -> 5450[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5450 -> 416[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5451[label="xy9000/Zero",fontsize=10,color="white",style="solid",shape="box"];401 -> 5451[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5451 -> 417[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	402[label="primMulNat Zero xy9000",fontsize=16,color="burlywood",shape="box"];5452[label="xy9000/Succ xy90000",fontsize=10,color="white",style="solid",shape="box"];402 -> 5452[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5452 -> 418[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5453[label="xy9000/Zero",fontsize=10,color="white",style="solid",shape="box"];402 -> 5453[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5453 -> 419[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	403[label="xy9000",fontsize=16,color="green",shape="box"];404[label="xy1010",fontsize=16,color="green",shape="box"];405[label="xy1010",fontsize=16,color="green",shape="box"];406[label="xy9000",fontsize=16,color="green",shape="box"];5367[label="xy363 : List.nubByNubBy' primEqFloat xy364 (xy363 : xy365 : xy366)",fontsize=16,color="green",shape="box"];5367 -> 5371[label="",style="dashed", color="green", weight=3];
19.67/8.41	5368[label="xy365 : xy366",fontsize=16,color="green",shape="box"];5369[label="xy3641",fontsize=16,color="green",shape="box"];5370[label="xy3640",fontsize=16,color="green",shape="box"];416[label="primMulNat (Succ xy10100) (Succ xy90000)",fontsize=16,color="black",shape="box"];416 -> 427[label="",style="solid", color="black", weight=3];
19.67/8.41	417[label="primMulNat (Succ xy10100) Zero",fontsize=16,color="black",shape="box"];417 -> 428[label="",style="solid", color="black", weight=3];
19.67/8.41	418[label="primMulNat Zero (Succ xy90000)",fontsize=16,color="black",shape="box"];418 -> 429[label="",style="solid", color="black", weight=3];
19.67/8.41	419[label="primMulNat Zero Zero",fontsize=16,color="black",shape="box"];419 -> 430[label="",style="solid", color="black", weight=3];
19.67/8.41	5371 -> 5352[label="",style="dashed", color="red", weight=0];
19.67/8.41	5371[label="List.nubByNubBy' primEqFloat xy364 (xy363 : xy365 : xy366)",fontsize=16,color="magenta"];5371 -> 5372[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	5371 -> 5373[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	427 -> 438[label="",style="dashed", color="red", weight=0];
19.67/8.41	427[label="primPlusNat (primMulNat xy10100 (Succ xy90000)) (Succ xy90000)",fontsize=16,color="magenta"];427 -> 439[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	428[label="Zero",fontsize=16,color="green",shape="box"];429[label="Zero",fontsize=16,color="green",shape="box"];430[label="Zero",fontsize=16,color="green",shape="box"];5372[label="xy363",fontsize=16,color="green",shape="box"];5373[label="xy365 : xy366",fontsize=16,color="green",shape="box"];439 -> 390[label="",style="dashed", color="red", weight=0];
19.67/8.41	439[label="primMulNat xy10100 (Succ xy90000)",fontsize=16,color="magenta"];439 -> 440[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	439 -> 441[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	438[label="primPlusNat xy40 (Succ xy90000)",fontsize=16,color="burlywood",shape="triangle"];5454[label="xy40/Succ xy400",fontsize=10,color="white",style="solid",shape="box"];438 -> 5454[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5454 -> 442[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5455[label="xy40/Zero",fontsize=10,color="white",style="solid",shape="box"];438 -> 5455[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5455 -> 443[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	440[label="xy10100",fontsize=16,color="green",shape="box"];441[label="Succ xy90000",fontsize=16,color="green",shape="box"];442[label="primPlusNat (Succ xy400) (Succ xy90000)",fontsize=16,color="black",shape="box"];442 -> 450[label="",style="solid", color="black", weight=3];
19.67/8.41	443[label="primPlusNat Zero (Succ xy90000)",fontsize=16,color="black",shape="box"];443 -> 451[label="",style="solid", color="black", weight=3];
19.67/8.41	450[label="Succ (Succ (primPlusNat xy400 xy90000))",fontsize=16,color="green",shape="box"];450 -> 454[label="",style="dashed", color="green", weight=3];
19.67/8.41	451[label="Succ xy90000",fontsize=16,color="green",shape="box"];454[label="primPlusNat xy400 xy90000",fontsize=16,color="burlywood",shape="triangle"];5456[label="xy400/Succ xy4000",fontsize=10,color="white",style="solid",shape="box"];454 -> 5456[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5456 -> 515[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5457[label="xy400/Zero",fontsize=10,color="white",style="solid",shape="box"];454 -> 5457[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5457 -> 516[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	515[label="primPlusNat (Succ xy4000) xy90000",fontsize=16,color="burlywood",shape="box"];5458[label="xy90000/Succ xy900000",fontsize=10,color="white",style="solid",shape="box"];515 -> 5458[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5458 -> 573[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5459[label="xy90000/Zero",fontsize=10,color="white",style="solid",shape="box"];515 -> 5459[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5459 -> 574[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	516[label="primPlusNat Zero xy90000",fontsize=16,color="burlywood",shape="box"];5460[label="xy90000/Succ xy900000",fontsize=10,color="white",style="solid",shape="box"];516 -> 5460[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5460 -> 575[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	5461[label="xy90000/Zero",fontsize=10,color="white",style="solid",shape="box"];516 -> 5461[label="",style="solid", color="burlywood", weight=9];
19.67/8.41	5461 -> 576[label="",style="solid", color="burlywood", weight=3];
19.67/8.41	573[label="primPlusNat (Succ xy4000) (Succ xy900000)",fontsize=16,color="black",shape="box"];573 -> 637[label="",style="solid", color="black", weight=3];
19.67/8.41	574[label="primPlusNat (Succ xy4000) Zero",fontsize=16,color="black",shape="box"];574 -> 638[label="",style="solid", color="black", weight=3];
19.67/8.41	575[label="primPlusNat Zero (Succ xy900000)",fontsize=16,color="black",shape="box"];575 -> 639[label="",style="solid", color="black", weight=3];
19.67/8.41	576[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];576 -> 640[label="",style="solid", color="black", weight=3];
19.67/8.41	637[label="Succ (Succ (primPlusNat xy4000 xy900000))",fontsize=16,color="green",shape="box"];637 -> 693[label="",style="dashed", color="green", weight=3];
19.67/8.41	638[label="Succ xy4000",fontsize=16,color="green",shape="box"];639[label="Succ xy900000",fontsize=16,color="green",shape="box"];640[label="Zero",fontsize=16,color="green",shape="box"];693 -> 454[label="",style="dashed", color="red", weight=0];
19.67/8.41	693[label="primPlusNat xy4000 xy900000",fontsize=16,color="magenta"];693 -> 738[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	693 -> 739[label="",style="dashed", color="magenta", weight=3];
19.67/8.41	738[label="xy900000",fontsize=16,color="green",shape="box"];739[label="xy4000",fontsize=16,color="green",shape="box"];}
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(10)
19.67/8.41	Complex Obligation (AND)
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(11)
19.67/8.41	Obligation:
19.67/8.41	Q DP problem:
19.67/8.41	The TRS P consists of the following rules:
19.67/8.41	
19.67/8.41	   new_deleteBy(xy10, :(xy90, xy91), bb) -> new_deleteBy0(xy91, xy90, xy10, new_esEs0(xy10, xy90, bb), bb)
19.67/8.41	   new_deleteBy0(xy17, xy18, xy19, False, ba) -> new_deleteBy(xy19, xy17, ba)
19.67/8.41	
19.67/8.41	The TRS R consists of the following rules:
19.67/8.41	
19.67/8.41	   new_primEqFloat(Float(xy100, xy101), Float(xy900, xy901)) -> new_esEs(new_sr(xy100, xy901), new_sr(xy101, xy900))
19.67/8.41	   new_primEqInt(Pos(Zero), Pos(Zero)) -> True
19.67/8.41	   new_primMulNat0(Zero, Zero) -> Zero
19.67/8.41	   new_primEqInt(Neg(Zero), Neg(Zero)) -> True
19.67/8.41	   new_primMulNat0(Succ(xy10100), Succ(xy90000)) -> new_primPlusNat0(new_primMulNat0(xy10100, Succ(xy90000)), xy90000)
19.67/8.41	   new_esEs0(xy10, xy90, app(ty_[], cc)) -> error([])
19.67/8.41	   new_sr(Neg(xy1010), Neg(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.67/8.41	   new_esEs0(xy10, xy90, app(app(ty_Either, bh), ca)) -> error([])
19.67/8.41	   new_esEs0(xy10, xy90, app(ty_Ratio, cb)) -> error([])
19.67/8.41	   new_esEs0(xy10, xy90, ty_Integer) -> error([])
19.67/8.41	   new_primPlusNat1(Succ(xy4000), Zero) -> Succ(xy4000)
19.67/8.41	   new_primPlusNat1(Zero, Succ(xy900000)) -> Succ(xy900000)
19.67/8.41	   new_esEs0(xy10, xy90, ty_Ordering) -> error([])
19.67/8.41	   new_primEqNat0(Succ(xy10000), Zero) -> False
19.67/8.41	   new_primEqNat0(Zero, Succ(xy90000)) -> False
19.67/8.41	   new_esEs0(xy10, xy90, ty_Double) -> error([])
19.67/8.41	   new_esEs0(xy10, xy90, ty_Int) -> new_esEs(xy10, xy90)
19.67/8.41	   new_esEs0(xy10, xy90, app(ty_Maybe, cd)) -> error([])
19.67/8.41	   new_primEqInt(Pos(Zero), Neg(Succ(xy9000))) -> False
19.67/8.41	   new_primEqInt(Neg(Zero), Pos(Succ(xy9000))) -> False
19.67/8.41	   new_primEqInt(Pos(Zero), Neg(Zero)) -> True
19.67/8.41	   new_primEqInt(Neg(Zero), Pos(Zero)) -> True
19.67/8.41	   new_esEs0(xy10, xy90, app(app(app(ty_@3, be), bf), bg)) -> error([])
19.67/8.41	   new_esEs0(xy10, xy90, ty_@0) -> error([])
19.67/8.41	   new_primEqNat0(Zero, Zero) -> True
19.67/8.41	   new_esEs0(xy10, xy90, ty_Char) -> error([])
19.67/8.41	   new_primEqInt(Neg(Succ(xy1000)), Neg(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.67/8.41	   new_primEqInt(Neg(Succ(xy1000)), Neg(Zero)) -> False
19.67/8.41	   new_primEqInt(Neg(Zero), Neg(Succ(xy9000))) -> False
19.67/8.41	   new_primPlusNat0(Succ(xy400), xy90000) -> Succ(Succ(new_primPlusNat1(xy400, xy90000)))
19.67/8.41	   new_primEqInt(Pos(Succ(xy1000)), Pos(Zero)) -> False
19.67/8.41	   new_primEqInt(Pos(Zero), Pos(Succ(xy9000))) -> False
19.67/8.41	   new_primEqInt(Pos(Succ(xy1000)), Pos(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.67/8.41	   new_esEs(xy10, xy90) -> new_primEqInt(xy10, xy90)
19.67/8.41	   new_esEs0(xy10, xy90, ty_Float) -> new_primEqFloat(xy10, xy90)
19.67/8.41	   new_esEs0(xy10, xy90, ty_Bool) -> error([])
19.67/8.41	   new_sr(Pos(xy1010), Neg(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.67/8.41	   new_sr(Neg(xy1010), Pos(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.67/8.41	   new_primPlusNat1(Succ(xy4000), Succ(xy900000)) -> Succ(Succ(new_primPlusNat1(xy4000, xy900000)))
19.67/8.41	   new_primPlusNat1(Zero, Zero) -> Zero
19.67/8.41	   new_primEqNat0(Succ(xy10000), Succ(xy90000)) -> new_primEqNat0(xy10000, xy90000)
19.67/8.41	   new_primMulNat0(Succ(xy10100), Zero) -> Zero
19.67/8.41	   new_primMulNat0(Zero, Succ(xy90000)) -> Zero
19.67/8.41	   new_primEqInt(Pos(Succ(xy1000)), Neg(xy900)) -> False
19.67/8.41	   new_primEqInt(Neg(Succ(xy1000)), Pos(xy900)) -> False
19.67/8.41	   new_sr(Pos(xy1010), Pos(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.67/8.41	   new_primPlusNat0(Zero, xy90000) -> Succ(xy90000)
19.67/8.41	   new_esEs0(xy10, xy90, app(app(ty_@2, bc), bd)) -> error([])
19.67/8.41	
19.67/8.41	The set Q consists of the following terms:
19.67/8.41	
19.67/8.41	   new_esEs0(x0, x1, ty_Float)
19.67/8.41	   new_primEqNat0(Zero, Zero)
19.67/8.41	   new_primEqInt(Neg(Zero), Neg(Succ(x0)))
19.67/8.41	   new_primEqInt(Pos(Zero), Neg(Zero))
19.67/8.41	   new_primEqInt(Neg(Zero), Pos(Zero))
19.67/8.41	   new_esEs0(x0, x1, ty_Int)
19.67/8.41	   new_primEqInt(Pos(Succ(x0)), Neg(x1))
19.67/8.41	   new_primEqInt(Neg(Succ(x0)), Pos(x1))
19.67/8.41	   new_esEs0(x0, x1, ty_Bool)
19.67/8.41	   new_primEqInt(Pos(Zero), Pos(Zero))
19.67/8.41	   new_primPlusNat1(Succ(x0), Succ(x1))
19.67/8.41	   new_sr(Neg(x0), Neg(x1))
19.67/8.41	   new_primMulNat0(Zero, Succ(x0))
19.67/8.41	   new_primMulNat0(Succ(x0), Succ(x1))
19.67/8.41	   new_primPlusNat1(Succ(x0), Zero)
19.67/8.41	   new_primPlusNat0(Zero, x0)
19.67/8.41	   new_primEqNat0(Succ(x0), Zero)
19.67/8.41	   new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
19.67/8.41	   new_primEqInt(Pos(Zero), Neg(Succ(x0)))
19.67/8.41	   new_primEqInt(Neg(Zero), Pos(Succ(x0)))
19.67/8.41	   new_esEs0(x0, x1, app(ty_[], x2))
19.67/8.41	   new_sr(Pos(x0), Neg(x1))
19.67/8.41	   new_sr(Neg(x0), Pos(x1))
19.67/8.41	   new_esEs0(x0, x1, app(ty_Ratio, x2))
19.67/8.41	   new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
19.67/8.41	   new_esEs0(x0, x1, ty_Integer)
19.67/8.41	   new_esEs(x0, x1)
19.67/8.41	   new_primEqInt(Pos(Succ(x0)), Pos(Zero))
19.67/8.41	   new_esEs0(x0, x1, app(app(ty_Either, x2), x3))
19.67/8.41	   new_sr(Pos(x0), Pos(x1))
19.67/8.41	   new_esEs0(x0, x1, app(ty_Maybe, x2))
19.67/8.41	   new_primMulNat0(Zero, Zero)
19.67/8.41	   new_primEqInt(Neg(Succ(x0)), Neg(Zero))
19.67/8.41	   new_primMulNat0(Succ(x0), Zero)
19.67/8.41	   new_primEqNat0(Succ(x0), Succ(x1))
19.67/8.41	   new_primPlusNat0(Succ(x0), x1)
19.67/8.41	   new_primPlusNat1(Zero, Zero)
19.67/8.41	   new_esEs0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
19.67/8.41	   new_primPlusNat1(Zero, Succ(x0))
19.67/8.41	   new_primEqFloat(Float(x0, x1), Float(x2, x3))
19.67/8.41	   new_primEqNat0(Zero, Succ(x0))
19.67/8.41	   new_primEqInt(Pos(Zero), Pos(Succ(x0)))
19.67/8.41	   new_esEs0(x0, x1, ty_Char)
19.67/8.41	   new_primEqInt(Neg(Zero), Neg(Zero))
19.67/8.41	   new_esEs0(x0, x1, app(app(ty_@2, x2), x3))
19.67/8.41	   new_esEs0(x0, x1, ty_Ordering)
19.67/8.41	   new_esEs0(x0, x1, ty_@0)
19.67/8.41	   new_esEs0(x0, x1, ty_Double)
19.67/8.41	
19.67/8.41	We have to consider all minimal (P,Q,R)-chains.
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(12) QDPSizeChangeProof (EQUIVALENT)
19.67/8.41	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. 
19.67/8.41	
19.67/8.41	From the DPs we obtained the following set of size-change graphs:
19.67/8.41	*new_deleteBy0(xy17, xy18, xy19, False, ba) -> new_deleteBy(xy19, xy17, ba)
19.67/8.41	The graph contains the following edges 3 >= 1, 1 >= 2, 5 >= 3
19.67/8.41	
19.67/8.41	
19.67/8.41	*new_deleteBy(xy10, :(xy90, xy91), bb) -> new_deleteBy0(xy91, xy90, xy10, new_esEs0(xy10, xy90, bb), bb)
19.67/8.41	The graph contains the following edges 2 > 1, 2 > 2, 1 >= 3, 3 >= 5
19.67/8.41	
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(13)
19.67/8.41	YES
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(14)
19.67/8.41	Obligation:
19.67/8.41	Q DP problem:
19.67/8.41	The TRS P consists of the following rules:
19.67/8.41	
19.67/8.41	   new_psPs(:(xy80, xy81), xy9, xy10, xy11, ba) -> new_psPs(xy81, xy9, xy10, xy11, ba)
19.67/8.41	
19.67/8.41	R is empty.
19.67/8.41	Q is empty.
19.67/8.41	We have to consider all minimal (P,Q,R)-chains.
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(15) QDPSizeChangeProof (EQUIVALENT)
19.67/8.41	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. 
19.67/8.41	
19.67/8.41	From the DPs we obtained the following set of size-change graphs:
19.67/8.41	*new_psPs(:(xy80, xy81), xy9, xy10, xy11, ba) -> new_psPs(xy81, xy9, xy10, xy11, ba)
19.67/8.41	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
19.67/8.41	
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(16)
19.67/8.41	YES
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(17)
19.67/8.41	Obligation:
19.67/8.41	Q DP problem:
19.67/8.41	The TRS P consists of the following rules:
19.67/8.41	
19.67/8.41	   new_foldl(xy9, xy10, :(xy110, xy111), ba) -> new_foldl(new_flip(xy9, xy10, ba), xy110, xy111, ba)
19.67/8.41	
19.67/8.41	The TRS R consists of the following rules:
19.67/8.41	
19.67/8.41	   new_primEqFloat(Float(xy100, xy101), Float(xy900, xy901)) -> new_esEs(new_sr(xy100, xy901), new_sr(xy101, xy900))
19.67/8.41	   new_primEqInt(Pos(Zero), Pos(Zero)) -> True
19.67/8.41	   new_primMulNat0(Zero, Zero) -> Zero
19.67/8.41	   new_primEqInt(Neg(Zero), Neg(Zero)) -> True
19.67/8.41	   new_primMulNat0(Succ(xy10100), Succ(xy90000)) -> new_primPlusNat0(new_primMulNat0(xy10100, Succ(xy90000)), xy90000)
19.67/8.41	   new_esEs0(xy10, xy90, app(ty_[], cb)) -> error([])
19.67/8.41	   new_sr(Neg(xy1010), Neg(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.67/8.41	   new_esEs0(xy10, xy90, app(app(ty_Either, bg), bh)) -> error([])
19.67/8.41	   new_esEs0(xy10, xy90, app(ty_Ratio, ca)) -> error([])
19.67/8.41	   new_esEs0(xy10, xy90, ty_Integer) -> error([])
19.67/8.41	   new_deleteBy00(xy17, xy18, xy19, True, cd) -> xy17
19.67/8.41	   new_primPlusNat1(Succ(xy4000), Zero) -> Succ(xy4000)
19.67/8.41	   new_primPlusNat1(Zero, Succ(xy900000)) -> Succ(xy900000)
19.67/8.41	   new_esEs0(xy10, xy90, ty_Ordering) -> error([])
19.67/8.41	   new_esEs0(xy10, xy90, ty_Double) -> error([])
19.67/8.41	   new_primEqNat0(Succ(xy10000), Zero) -> False
19.67/8.41	   new_primEqNat0(Zero, Succ(xy90000)) -> False
19.67/8.41	   new_esEs0(xy10, xy90, ty_Int) -> new_esEs(xy10, xy90)
19.67/8.41	   new_esEs0(xy10, xy90, app(ty_Maybe, cc)) -> error([])
19.67/8.41	   new_primEqInt(Pos(Zero), Neg(Succ(xy9000))) -> False
19.67/8.41	   new_primEqInt(Neg(Zero), Pos(Succ(xy9000))) -> False
19.67/8.41	   new_primEqInt(Pos(Zero), Neg(Zero)) -> True
19.67/8.41	   new_primEqInt(Neg(Zero), Pos(Zero)) -> True
19.67/8.41	   new_deleteBy00(xy17, xy18, xy19, False, cd) -> :(xy18, new_deleteBy1(xy19, xy17, cd))
19.67/8.41	   new_esEs0(xy10, xy90, app(app(app(ty_@3, bd), be), bf)) -> error([])
19.67/8.41	   new_esEs0(xy10, xy90, ty_@0) -> error([])
19.67/8.41	   new_esEs0(xy10, xy90, ty_Char) -> error([])
19.67/8.41	   new_primEqNat0(Zero, Zero) -> True
19.67/8.41	   new_primEqInt(Neg(Succ(xy1000)), Neg(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.67/8.41	   new_primEqInt(Neg(Succ(xy1000)), Neg(Zero)) -> False
19.67/8.41	   new_primEqInt(Neg(Zero), Neg(Succ(xy9000))) -> False
19.67/8.41	   new_primPlusNat0(Succ(xy400), xy90000) -> Succ(Succ(new_primPlusNat1(xy400, xy90000)))
19.67/8.41	   new_primEqInt(Pos(Succ(xy1000)), Pos(Zero)) -> False
19.67/8.41	   new_primEqInt(Pos(Zero), Pos(Succ(xy9000))) -> False
19.67/8.41	   new_primEqInt(Pos(Succ(xy1000)), Pos(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.67/8.41	   new_esEs(xy10, xy90) -> new_primEqInt(xy10, xy90)
19.67/8.41	   new_esEs0(xy10, xy90, ty_Float) -> new_primEqFloat(xy10, xy90)
19.67/8.41	   new_esEs0(xy10, xy90, ty_Bool) -> error([])
19.67/8.41	   new_deleteBy1(xy10, :(xy90, xy91), ba) -> new_deleteBy00(xy91, xy90, xy10, new_esEs0(xy10, xy90, ba), ba)
19.67/8.41	   new_sr(Pos(xy1010), Neg(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.67/8.41	   new_sr(Neg(xy1010), Pos(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.67/8.41	   new_primPlusNat1(Succ(xy4000), Succ(xy900000)) -> Succ(Succ(new_primPlusNat1(xy4000, xy900000)))
19.67/8.41	   new_primPlusNat1(Zero, Zero) -> Zero
19.67/8.41	   new_flip(xy9, xy10, ba) -> new_deleteBy1(xy10, xy9, ba)
19.67/8.41	   new_primEqNat0(Succ(xy10000), Succ(xy90000)) -> new_primEqNat0(xy10000, xy90000)
19.67/8.41	   new_primMulNat0(Succ(xy10100), Zero) -> Zero
19.67/8.41	   new_primMulNat0(Zero, Succ(xy90000)) -> Zero
19.67/8.41	   new_primEqInt(Pos(Succ(xy1000)), Neg(xy900)) -> False
19.67/8.41	   new_primEqInt(Neg(Succ(xy1000)), Pos(xy900)) -> False
19.67/8.41	   new_sr(Pos(xy1010), Pos(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.67/8.41	   new_primPlusNat0(Zero, xy90000) -> Succ(xy90000)
19.67/8.41	   new_deleteBy1(xy10, [], ba) -> []
19.67/8.41	   new_esEs0(xy10, xy90, app(app(ty_@2, bb), bc)) -> error([])
19.67/8.41	
19.67/8.41	The set Q consists of the following terms:
19.67/8.41	
19.67/8.41	   new_esEs0(x0, x1, ty_Float)
19.67/8.41	   new_primEqNat0(Zero, Zero)
19.67/8.41	   new_esEs0(x0, x1, ty_Bool)
19.67/8.41	   new_primPlusNat1(Succ(x0), Succ(x1))
19.67/8.41	   new_sr(Neg(x0), Neg(x1))
19.67/8.41	   new_primMulNat0(Zero, Succ(x0))
19.67/8.41	   new_primPlusNat0(Zero, x0)
19.67/8.41	   new_primEqNat0(Succ(x0), Zero)
19.67/8.41	   new_flip(x0, x1, x2)
19.67/8.41	   new_sr(Pos(x0), Neg(x1))
19.67/8.41	   new_sr(Neg(x0), Pos(x1))
19.67/8.41	   new_esEs(x0, x1)
19.67/8.41	   new_deleteBy1(x0, [], x1)
19.67/8.41	   new_primMulNat0(Zero, Zero)
19.67/8.41	   new_primEqNat0(Succ(x0), Succ(x1))
19.67/8.41	   new_primPlusNat1(Zero, Zero)
19.67/8.41	   new_primPlusNat1(Zero, Succ(x0))
19.67/8.41	   new_primEqFloat(Float(x0, x1), Float(x2, x3))
19.67/8.41	   new_esEs0(x0, x1, ty_Char)
19.67/8.41	   new_esEs0(x0, x1, app(ty_Maybe, x2))
19.67/8.41	   new_esEs0(x0, x1, ty_Double)
19.67/8.41	   new_esEs0(x0, x1, app(ty_Ratio, x2))
19.67/8.41	   new_deleteBy00(x0, x1, x2, False, x3)
19.67/8.41	   new_deleteBy00(x0, x1, x2, True, x3)
19.67/8.41	   new_primEqInt(Pos(Zero), Neg(Zero))
19.67/8.41	   new_primEqInt(Neg(Zero), Pos(Zero))
19.67/8.41	   new_primEqInt(Neg(Zero), Neg(Succ(x0)))
19.67/8.41	   new_esEs0(x0, x1, ty_Int)
19.67/8.41	   new_primEqInt(Pos(Succ(x0)), Neg(x1))
19.67/8.41	   new_primEqInt(Neg(Succ(x0)), Pos(x1))
19.67/8.41	   new_primEqInt(Pos(Zero), Pos(Zero))
19.67/8.41	   new_primMulNat0(Succ(x0), Succ(x1))
19.67/8.41	   new_primPlusNat1(Succ(x0), Zero)
19.67/8.41	   new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
19.67/8.41	   new_primEqInt(Pos(Zero), Neg(Succ(x0)))
19.67/8.41	   new_primEqInt(Neg(Zero), Pos(Succ(x0)))
19.67/8.41	   new_esEs0(x0, x1, app(app(ty_@2, x2), x3))
19.67/8.41	   new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
19.67/8.41	   new_esEs0(x0, x1, ty_Integer)
19.67/8.41	   new_primEqInt(Pos(Succ(x0)), Pos(Zero))
19.67/8.41	   new_sr(Pos(x0), Pos(x1))
19.67/8.41	   new_esEs0(x0, x1, app(ty_[], x2))
19.67/8.41	   new_esEs0(x0, x1, app(app(ty_Either, x2), x3))
19.67/8.41	   new_primEqInt(Neg(Succ(x0)), Neg(Zero))
19.67/8.41	   new_primMulNat0(Succ(x0), Zero)
19.67/8.41	   new_primPlusNat0(Succ(x0), x1)
19.67/8.41	   new_primEqNat0(Zero, Succ(x0))
19.67/8.41	   new_primEqInt(Pos(Zero), Pos(Succ(x0)))
19.67/8.41	   new_esEs0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
19.67/8.41	   new_primEqInt(Neg(Zero), Neg(Zero))
19.67/8.41	   new_deleteBy1(x0, :(x1, x2), x3)
19.67/8.41	   new_esEs0(x0, x1, ty_Ordering)
19.67/8.41	   new_esEs0(x0, x1, ty_@0)
19.67/8.41	
19.67/8.41	We have to consider all minimal (P,Q,R)-chains.
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(18) TransformationProof (EQUIVALENT)
19.67/8.41	By rewriting [LPAR04] the rule new_foldl(xy9, xy10, :(xy110, xy111), ba) -> new_foldl(new_flip(xy9, xy10, ba), xy110, xy111, ba) at position [0] we obtained the following new rules [LPAR04]:
19.67/8.41	
19.67/8.41	   (new_foldl(xy9, xy10, :(xy110, xy111), ba) -> new_foldl(new_deleteBy1(xy10, xy9, ba), xy110, xy111, ba),new_foldl(xy9, xy10, :(xy110, xy111), ba) -> new_foldl(new_deleteBy1(xy10, xy9, ba), xy110, xy111, ba))
19.67/8.41	
19.67/8.41	
19.67/8.41	----------------------------------------
19.67/8.41	
19.67/8.41	(19)
19.67/8.41	Obligation:
19.67/8.41	Q DP problem:
19.67/8.41	The TRS P consists of the following rules:
19.67/8.41	
19.67/8.41	   new_foldl(xy9, xy10, :(xy110, xy111), ba) -> new_foldl(new_deleteBy1(xy10, xy9, ba), xy110, xy111, ba)
19.67/8.41	
19.67/8.41	The TRS R consists of the following rules:
19.67/8.41	
19.67/8.41	   new_primEqFloat(Float(xy100, xy101), Float(xy900, xy901)) -> new_esEs(new_sr(xy100, xy901), new_sr(xy101, xy900))
19.67/8.41	   new_primEqInt(Pos(Zero), Pos(Zero)) -> True
19.67/8.41	   new_primMulNat0(Zero, Zero) -> Zero
19.67/8.41	   new_primEqInt(Neg(Zero), Neg(Zero)) -> True
19.67/8.41	   new_primMulNat0(Succ(xy10100), Succ(xy90000)) -> new_primPlusNat0(new_primMulNat0(xy10100, Succ(xy90000)), xy90000)
19.67/8.41	   new_esEs0(xy10, xy90, app(ty_[], cb)) -> error([])
19.67/8.41	   new_sr(Neg(xy1010), Neg(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.67/8.41	   new_esEs0(xy10, xy90, app(app(ty_Either, bg), bh)) -> error([])
19.67/8.41	   new_esEs0(xy10, xy90, app(ty_Ratio, ca)) -> error([])
19.67/8.41	   new_esEs0(xy10, xy90, ty_Integer) -> error([])
19.67/8.41	   new_deleteBy00(xy17, xy18, xy19, True, cd) -> xy17
19.67/8.41	   new_primPlusNat1(Succ(xy4000), Zero) -> Succ(xy4000)
19.67/8.41	   new_primPlusNat1(Zero, Succ(xy900000)) -> Succ(xy900000)
19.67/8.41	   new_esEs0(xy10, xy90, ty_Ordering) -> error([])
19.67/8.41	   new_esEs0(xy10, xy90, ty_Double) -> error([])
19.67/8.41	   new_primEqNat0(Succ(xy10000), Zero) -> False
19.67/8.41	   new_primEqNat0(Zero, Succ(xy90000)) -> False
19.67/8.41	   new_esEs0(xy10, xy90, ty_Int) -> new_esEs(xy10, xy90)
19.67/8.41	   new_esEs0(xy10, xy90, app(ty_Maybe, cc)) -> error([])
19.67/8.41	   new_primEqInt(Pos(Zero), Neg(Succ(xy9000))) -> False
19.67/8.41	   new_primEqInt(Neg(Zero), Pos(Succ(xy9000))) -> False
19.67/8.41	   new_primEqInt(Pos(Zero), Neg(Zero)) -> True
19.67/8.41	   new_primEqInt(Neg(Zero), Pos(Zero)) -> True
19.67/8.41	   new_deleteBy00(xy17, xy18, xy19, False, cd) -> :(xy18, new_deleteBy1(xy19, xy17, cd))
19.67/8.41	   new_esEs0(xy10, xy90, app(app(app(ty_@3, bd), be), bf)) -> error([])
19.67/8.41	   new_esEs0(xy10, xy90, ty_@0) -> error([])
19.67/8.41	   new_esEs0(xy10, xy90, ty_Char) -> error([])
19.67/8.41	   new_primEqNat0(Zero, Zero) -> True
19.67/8.41	   new_primEqInt(Neg(Succ(xy1000)), Neg(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.67/8.41	   new_primEqInt(Neg(Succ(xy1000)), Neg(Zero)) -> False
19.67/8.41	   new_primEqInt(Neg(Zero), Neg(Succ(xy9000))) -> False
19.67/8.41	   new_primPlusNat0(Succ(xy400), xy90000) -> Succ(Succ(new_primPlusNat1(xy400, xy90000)))
19.67/8.41	   new_primEqInt(Pos(Succ(xy1000)), Pos(Zero)) -> False
19.67/8.41	   new_primEqInt(Pos(Zero), Pos(Succ(xy9000))) -> False
19.67/8.41	   new_primEqInt(Pos(Succ(xy1000)), Pos(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.67/8.41	   new_esEs(xy10, xy90) -> new_primEqInt(xy10, xy90)
19.67/8.41	   new_esEs0(xy10, xy90, ty_Float) -> new_primEqFloat(xy10, xy90)
19.67/8.41	   new_esEs0(xy10, xy90, ty_Bool) -> error([])
19.67/8.41	   new_deleteBy1(xy10, :(xy90, xy91), ba) -> new_deleteBy00(xy91, xy90, xy10, new_esEs0(xy10, xy90, ba), ba)
19.67/8.41	   new_sr(Pos(xy1010), Neg(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.67/8.41	   new_sr(Neg(xy1010), Pos(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.67/8.41	   new_primPlusNat1(Succ(xy4000), Succ(xy900000)) -> Succ(Succ(new_primPlusNat1(xy4000, xy900000)))
19.84/8.41	   new_primPlusNat1(Zero, Zero) -> Zero
19.84/8.41	   new_flip(xy9, xy10, ba) -> new_deleteBy1(xy10, xy9, ba)
19.84/8.41	   new_primEqNat0(Succ(xy10000), Succ(xy90000)) -> new_primEqNat0(xy10000, xy90000)
19.84/8.41	   new_primMulNat0(Succ(xy10100), Zero) -> Zero
19.84/8.41	   new_primMulNat0(Zero, Succ(xy90000)) -> Zero
19.84/8.41	   new_primEqInt(Pos(Succ(xy1000)), Neg(xy900)) -> False
19.84/8.41	   new_primEqInt(Neg(Succ(xy1000)), Pos(xy900)) -> False
19.84/8.41	   new_sr(Pos(xy1010), Pos(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.84/8.41	   new_primPlusNat0(Zero, xy90000) -> Succ(xy90000)
19.84/8.41	   new_deleteBy1(xy10, [], ba) -> []
19.84/8.41	   new_esEs0(xy10, xy90, app(app(ty_@2, bb), bc)) -> error([])
19.84/8.41	
19.84/8.41	The set Q consists of the following terms:
19.84/8.41	
19.84/8.41	   new_esEs0(x0, x1, ty_Float)
19.84/8.41	   new_primEqNat0(Zero, Zero)
19.84/8.41	   new_esEs0(x0, x1, ty_Bool)
19.84/8.41	   new_primPlusNat1(Succ(x0), Succ(x1))
19.84/8.41	   new_sr(Neg(x0), Neg(x1))
19.84/8.41	   new_primMulNat0(Zero, Succ(x0))
19.84/8.41	   new_primPlusNat0(Zero, x0)
19.84/8.41	   new_primEqNat0(Succ(x0), Zero)
19.84/8.41	   new_flip(x0, x1, x2)
19.84/8.41	   new_sr(Pos(x0), Neg(x1))
19.84/8.41	   new_sr(Neg(x0), Pos(x1))
19.84/8.41	   new_esEs(x0, x1)
19.84/8.41	   new_deleteBy1(x0, [], x1)
19.84/8.41	   new_primMulNat0(Zero, Zero)
19.84/8.41	   new_primEqNat0(Succ(x0), Succ(x1))
19.84/8.41	   new_primPlusNat1(Zero, Zero)
19.84/8.41	   new_primPlusNat1(Zero, Succ(x0))
19.84/8.41	   new_primEqFloat(Float(x0, x1), Float(x2, x3))
19.84/8.41	   new_esEs0(x0, x1, ty_Char)
19.84/8.41	   new_esEs0(x0, x1, app(ty_Maybe, x2))
19.84/8.41	   new_esEs0(x0, x1, ty_Double)
19.84/8.41	   new_esEs0(x0, x1, app(ty_Ratio, x2))
19.84/8.41	   new_deleteBy00(x0, x1, x2, False, x3)
19.84/8.41	   new_deleteBy00(x0, x1, x2, True, x3)
19.84/8.41	   new_primEqInt(Pos(Zero), Neg(Zero))
19.84/8.41	   new_primEqInt(Neg(Zero), Pos(Zero))
19.84/8.41	   new_primEqInt(Neg(Zero), Neg(Succ(x0)))
19.84/8.41	   new_esEs0(x0, x1, ty_Int)
19.84/8.41	   new_primEqInt(Pos(Succ(x0)), Neg(x1))
19.84/8.41	   new_primEqInt(Neg(Succ(x0)), Pos(x1))
19.84/8.41	   new_primEqInt(Pos(Zero), Pos(Zero))
19.84/8.41	   new_primMulNat0(Succ(x0), Succ(x1))
19.84/8.41	   new_primPlusNat1(Succ(x0), Zero)
19.84/8.41	   new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
19.84/8.41	   new_primEqInt(Pos(Zero), Neg(Succ(x0)))
19.84/8.41	   new_primEqInt(Neg(Zero), Pos(Succ(x0)))
19.84/8.41	   new_esEs0(x0, x1, app(app(ty_@2, x2), x3))
19.84/8.41	   new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
19.84/8.41	   new_esEs0(x0, x1, ty_Integer)
19.84/8.41	   new_primEqInt(Pos(Succ(x0)), Pos(Zero))
19.84/8.41	   new_sr(Pos(x0), Pos(x1))
19.84/8.41	   new_esEs0(x0, x1, app(ty_[], x2))
19.84/8.41	   new_esEs0(x0, x1, app(app(ty_Either, x2), x3))
19.84/8.41	   new_primEqInt(Neg(Succ(x0)), Neg(Zero))
19.84/8.41	   new_primMulNat0(Succ(x0), Zero)
19.84/8.41	   new_primPlusNat0(Succ(x0), x1)
19.84/8.41	   new_primEqNat0(Zero, Succ(x0))
19.84/8.41	   new_primEqInt(Pos(Zero), Pos(Succ(x0)))
19.84/8.41	   new_esEs0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
19.84/8.41	   new_primEqInt(Neg(Zero), Neg(Zero))
19.84/8.41	   new_deleteBy1(x0, :(x1, x2), x3)
19.84/8.41	   new_esEs0(x0, x1, ty_Ordering)
19.84/8.41	   new_esEs0(x0, x1, ty_@0)
19.84/8.41	
19.84/8.41	We have to consider all minimal (P,Q,R)-chains.
19.84/8.41	----------------------------------------
19.84/8.41	
19.84/8.41	(20) UsableRulesProof (EQUIVALENT)
19.84/8.41	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.
19.84/8.41	----------------------------------------
19.84/8.41	
19.84/8.41	(21)
19.84/8.41	Obligation:
19.84/8.41	Q DP problem:
19.84/8.41	The TRS P consists of the following rules:
19.84/8.41	
19.84/8.41	   new_foldl(xy9, xy10, :(xy110, xy111), ba) -> new_foldl(new_deleteBy1(xy10, xy9, ba), xy110, xy111, ba)
19.84/8.41	
19.84/8.41	The TRS R consists of the following rules:
19.84/8.41	
19.84/8.41	   new_deleteBy1(xy10, :(xy90, xy91), ba) -> new_deleteBy00(xy91, xy90, xy10, new_esEs0(xy10, xy90, ba), ba)
19.84/8.41	   new_deleteBy1(xy10, [], ba) -> []
19.84/8.41	   new_esEs0(xy10, xy90, app(ty_[], cb)) -> error([])
19.84/8.41	   new_esEs0(xy10, xy90, app(app(ty_Either, bg), bh)) -> error([])
19.84/8.41	   new_esEs0(xy10, xy90, app(ty_Ratio, ca)) -> error([])
19.84/8.41	   new_esEs0(xy10, xy90, ty_Integer) -> error([])
19.84/8.41	   new_esEs0(xy10, xy90, ty_Ordering) -> error([])
19.84/8.41	   new_esEs0(xy10, xy90, ty_Double) -> error([])
19.84/8.41	   new_esEs0(xy10, xy90, ty_Int) -> new_esEs(xy10, xy90)
19.84/8.41	   new_esEs0(xy10, xy90, app(ty_Maybe, cc)) -> error([])
19.84/8.41	   new_esEs0(xy10, xy90, app(app(app(ty_@3, bd), be), bf)) -> error([])
19.84/8.41	   new_esEs0(xy10, xy90, ty_@0) -> error([])
19.84/8.41	   new_esEs0(xy10, xy90, ty_Char) -> error([])
19.84/8.41	   new_esEs0(xy10, xy90, ty_Float) -> new_primEqFloat(xy10, xy90)
19.84/8.41	   new_esEs0(xy10, xy90, ty_Bool) -> error([])
19.84/8.41	   new_esEs0(xy10, xy90, app(app(ty_@2, bb), bc)) -> error([])
19.84/8.41	   new_deleteBy00(xy17, xy18, xy19, True, cd) -> xy17
19.84/8.41	   new_deleteBy00(xy17, xy18, xy19, False, cd) -> :(xy18, new_deleteBy1(xy19, xy17, cd))
19.84/8.41	   new_primEqFloat(Float(xy100, xy101), Float(xy900, xy901)) -> new_esEs(new_sr(xy100, xy901), new_sr(xy101, xy900))
19.84/8.41	   new_sr(Neg(xy1010), Neg(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.84/8.41	   new_sr(Pos(xy1010), Neg(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.84/8.41	   new_sr(Neg(xy1010), Pos(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.84/8.41	   new_sr(Pos(xy1010), Pos(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.84/8.41	   new_esEs(xy10, xy90) -> new_primEqInt(xy10, xy90)
19.84/8.41	   new_primEqInt(Pos(Zero), Pos(Zero)) -> True
19.84/8.41	   new_primEqInt(Neg(Zero), Neg(Zero)) -> True
19.84/8.41	   new_primEqInt(Pos(Zero), Neg(Succ(xy9000))) -> False
19.84/8.41	   new_primEqInt(Neg(Zero), Pos(Succ(xy9000))) -> False
19.84/8.41	   new_primEqInt(Pos(Zero), Neg(Zero)) -> True
19.84/8.41	   new_primEqInt(Neg(Zero), Pos(Zero)) -> True
19.84/8.41	   new_primEqInt(Neg(Succ(xy1000)), Neg(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.84/8.41	   new_primEqInt(Neg(Succ(xy1000)), Neg(Zero)) -> False
19.84/8.41	   new_primEqInt(Neg(Zero), Neg(Succ(xy9000))) -> False
19.84/8.41	   new_primEqInt(Pos(Succ(xy1000)), Pos(Zero)) -> False
19.84/8.41	   new_primEqInt(Pos(Zero), Pos(Succ(xy9000))) -> False
19.84/8.41	   new_primEqInt(Pos(Succ(xy1000)), Pos(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.84/8.41	   new_primEqInt(Pos(Succ(xy1000)), Neg(xy900)) -> False
19.84/8.41	   new_primEqInt(Neg(Succ(xy1000)), Pos(xy900)) -> False
19.84/8.41	   new_primEqNat0(Succ(xy10000), Zero) -> False
19.84/8.41	   new_primEqNat0(Zero, Succ(xy90000)) -> False
19.84/8.41	   new_primEqNat0(Zero, Zero) -> True
19.84/8.41	   new_primEqNat0(Succ(xy10000), Succ(xy90000)) -> new_primEqNat0(xy10000, xy90000)
19.84/8.41	   new_primMulNat0(Zero, Zero) -> Zero
19.84/8.41	   new_primMulNat0(Succ(xy10100), Succ(xy90000)) -> new_primPlusNat0(new_primMulNat0(xy10100, Succ(xy90000)), xy90000)
19.84/8.41	   new_primMulNat0(Succ(xy10100), Zero) -> Zero
19.84/8.41	   new_primMulNat0(Zero, Succ(xy90000)) -> Zero
19.84/8.41	   new_primPlusNat0(Succ(xy400), xy90000) -> Succ(Succ(new_primPlusNat1(xy400, xy90000)))
19.84/8.41	   new_primPlusNat0(Zero, xy90000) -> Succ(xy90000)
19.84/8.41	   new_primPlusNat1(Succ(xy4000), Zero) -> Succ(xy4000)
19.84/8.41	   new_primPlusNat1(Zero, Succ(xy900000)) -> Succ(xy900000)
19.84/8.41	   new_primPlusNat1(Succ(xy4000), Succ(xy900000)) -> Succ(Succ(new_primPlusNat1(xy4000, xy900000)))
19.84/8.41	   new_primPlusNat1(Zero, Zero) -> Zero
19.84/8.41	
19.84/8.41	The set Q consists of the following terms:
19.84/8.41	
19.84/8.41	   new_esEs0(x0, x1, ty_Float)
19.84/8.41	   new_primEqNat0(Zero, Zero)
19.84/8.41	   new_esEs0(x0, x1, ty_Bool)
19.84/8.41	   new_primPlusNat1(Succ(x0), Succ(x1))
19.84/8.41	   new_sr(Neg(x0), Neg(x1))
19.84/8.41	   new_primMulNat0(Zero, Succ(x0))
19.84/8.41	   new_primPlusNat0(Zero, x0)
19.84/8.41	   new_primEqNat0(Succ(x0), Zero)
19.84/8.41	   new_flip(x0, x1, x2)
19.84/8.41	   new_sr(Pos(x0), Neg(x1))
19.84/8.41	   new_sr(Neg(x0), Pos(x1))
19.84/8.41	   new_esEs(x0, x1)
19.84/8.41	   new_deleteBy1(x0, [], x1)
19.84/8.41	   new_primMulNat0(Zero, Zero)
19.84/8.41	   new_primEqNat0(Succ(x0), Succ(x1))
19.84/8.41	   new_primPlusNat1(Zero, Zero)
19.84/8.41	   new_primPlusNat1(Zero, Succ(x0))
19.84/8.41	   new_primEqFloat(Float(x0, x1), Float(x2, x3))
19.84/8.41	   new_esEs0(x0, x1, ty_Char)
19.84/8.41	   new_esEs0(x0, x1, app(ty_Maybe, x2))
19.84/8.41	   new_esEs0(x0, x1, ty_Double)
19.84/8.41	   new_esEs0(x0, x1, app(ty_Ratio, x2))
19.84/8.41	   new_deleteBy00(x0, x1, x2, False, x3)
19.84/8.41	   new_deleteBy00(x0, x1, x2, True, x3)
19.84/8.41	   new_primEqInt(Pos(Zero), Neg(Zero))
19.84/8.41	   new_primEqInt(Neg(Zero), Pos(Zero))
19.84/8.41	   new_primEqInt(Neg(Zero), Neg(Succ(x0)))
19.84/8.41	   new_esEs0(x0, x1, ty_Int)
19.84/8.41	   new_primEqInt(Pos(Succ(x0)), Neg(x1))
19.84/8.41	   new_primEqInt(Neg(Succ(x0)), Pos(x1))
19.84/8.41	   new_primEqInt(Pos(Zero), Pos(Zero))
19.84/8.41	   new_primMulNat0(Succ(x0), Succ(x1))
19.84/8.41	   new_primPlusNat1(Succ(x0), Zero)
19.84/8.41	   new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
19.84/8.41	   new_primEqInt(Pos(Zero), Neg(Succ(x0)))
19.84/8.41	   new_primEqInt(Neg(Zero), Pos(Succ(x0)))
19.84/8.41	   new_esEs0(x0, x1, app(app(ty_@2, x2), x3))
19.84/8.41	   new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
19.84/8.41	   new_esEs0(x0, x1, ty_Integer)
19.84/8.41	   new_primEqInt(Pos(Succ(x0)), Pos(Zero))
19.84/8.41	   new_sr(Pos(x0), Pos(x1))
19.84/8.41	   new_esEs0(x0, x1, app(ty_[], x2))
19.84/8.41	   new_esEs0(x0, x1, app(app(ty_Either, x2), x3))
19.84/8.41	   new_primEqInt(Neg(Succ(x0)), Neg(Zero))
19.84/8.41	   new_primMulNat0(Succ(x0), Zero)
19.84/8.41	   new_primPlusNat0(Succ(x0), x1)
19.84/8.41	   new_primEqNat0(Zero, Succ(x0))
19.84/8.41	   new_primEqInt(Pos(Zero), Pos(Succ(x0)))
19.84/8.41	   new_esEs0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
19.84/8.41	   new_primEqInt(Neg(Zero), Neg(Zero))
19.84/8.41	   new_deleteBy1(x0, :(x1, x2), x3)
19.84/8.41	   new_esEs0(x0, x1, ty_Ordering)
19.84/8.41	   new_esEs0(x0, x1, ty_@0)
19.84/8.41	
19.84/8.41	We have to consider all minimal (P,Q,R)-chains.
19.84/8.41	----------------------------------------
19.84/8.41	
19.84/8.41	(22) QReductionProof (EQUIVALENT)
19.84/8.41	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
19.84/8.41	
19.84/8.41	   new_flip(x0, x1, x2)
19.84/8.41	
19.84/8.41	
19.84/8.41	----------------------------------------
19.84/8.41	
19.84/8.41	(23)
19.84/8.41	Obligation:
19.84/8.41	Q DP problem:
19.84/8.41	The TRS P consists of the following rules:
19.84/8.41	
19.84/8.41	   new_foldl(xy9, xy10, :(xy110, xy111), ba) -> new_foldl(new_deleteBy1(xy10, xy9, ba), xy110, xy111, ba)
19.84/8.41	
19.84/8.41	The TRS R consists of the following rules:
19.84/8.41	
19.84/8.41	   new_deleteBy1(xy10, :(xy90, xy91), ba) -> new_deleteBy00(xy91, xy90, xy10, new_esEs0(xy10, xy90, ba), ba)
19.84/8.41	   new_deleteBy1(xy10, [], ba) -> []
19.84/8.41	   new_esEs0(xy10, xy90, app(ty_[], cb)) -> error([])
19.84/8.41	   new_esEs0(xy10, xy90, app(app(ty_Either, bg), bh)) -> error([])
19.84/8.42	   new_esEs0(xy10, xy90, app(ty_Ratio, ca)) -> error([])
19.84/8.42	   new_esEs0(xy10, xy90, ty_Integer) -> error([])
19.84/8.42	   new_esEs0(xy10, xy90, ty_Ordering) -> error([])
19.84/8.42	   new_esEs0(xy10, xy90, ty_Double) -> error([])
19.84/8.42	   new_esEs0(xy10, xy90, ty_Int) -> new_esEs(xy10, xy90)
19.84/8.42	   new_esEs0(xy10, xy90, app(ty_Maybe, cc)) -> error([])
19.84/8.42	   new_esEs0(xy10, xy90, app(app(app(ty_@3, bd), be), bf)) -> error([])
19.84/8.42	   new_esEs0(xy10, xy90, ty_@0) -> error([])
19.84/8.42	   new_esEs0(xy10, xy90, ty_Char) -> error([])
19.84/8.42	   new_esEs0(xy10, xy90, ty_Float) -> new_primEqFloat(xy10, xy90)
19.84/8.42	   new_esEs0(xy10, xy90, ty_Bool) -> error([])
19.84/8.42	   new_esEs0(xy10, xy90, app(app(ty_@2, bb), bc)) -> error([])
19.84/8.42	   new_deleteBy00(xy17, xy18, xy19, True, cd) -> xy17
19.84/8.42	   new_deleteBy00(xy17, xy18, xy19, False, cd) -> :(xy18, new_deleteBy1(xy19, xy17, cd))
19.84/8.42	   new_primEqFloat(Float(xy100, xy101), Float(xy900, xy901)) -> new_esEs(new_sr(xy100, xy901), new_sr(xy101, xy900))
19.84/8.42	   new_sr(Neg(xy1010), Neg(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_sr(Pos(xy1010), Neg(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_sr(Neg(xy1010), Pos(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_sr(Pos(xy1010), Pos(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_esEs(xy10, xy90) -> new_primEqInt(xy10, xy90)
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Zero)) -> True
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Zero)) -> True
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Succ(xy9000))) -> False
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Succ(xy9000))) -> False
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Zero)) -> True
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Zero)) -> True
19.84/8.42	   new_primEqInt(Neg(Succ(xy1000)), Neg(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.84/8.42	   new_primEqInt(Neg(Succ(xy1000)), Neg(Zero)) -> False
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Succ(xy9000))) -> False
19.84/8.42	   new_primEqInt(Pos(Succ(xy1000)), Pos(Zero)) -> False
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Succ(xy9000))) -> False
19.84/8.42	   new_primEqInt(Pos(Succ(xy1000)), Pos(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.84/8.42	   new_primEqInt(Pos(Succ(xy1000)), Neg(xy900)) -> False
19.84/8.42	   new_primEqInt(Neg(Succ(xy1000)), Pos(xy900)) -> False
19.84/8.42	   new_primEqNat0(Succ(xy10000), Zero) -> False
19.84/8.42	   new_primEqNat0(Zero, Succ(xy90000)) -> False
19.84/8.42	   new_primEqNat0(Zero, Zero) -> True
19.84/8.42	   new_primEqNat0(Succ(xy10000), Succ(xy90000)) -> new_primEqNat0(xy10000, xy90000)
19.84/8.42	   new_primMulNat0(Zero, Zero) -> Zero
19.84/8.42	   new_primMulNat0(Succ(xy10100), Succ(xy90000)) -> new_primPlusNat0(new_primMulNat0(xy10100, Succ(xy90000)), xy90000)
19.84/8.42	   new_primMulNat0(Succ(xy10100), Zero) -> Zero
19.84/8.42	   new_primMulNat0(Zero, Succ(xy90000)) -> Zero
19.84/8.42	   new_primPlusNat0(Succ(xy400), xy90000) -> Succ(Succ(new_primPlusNat1(xy400, xy90000)))
19.84/8.42	   new_primPlusNat0(Zero, xy90000) -> Succ(xy90000)
19.84/8.42	   new_primPlusNat1(Succ(xy4000), Zero) -> Succ(xy4000)
19.84/8.42	   new_primPlusNat1(Zero, Succ(xy900000)) -> Succ(xy900000)
19.84/8.42	   new_primPlusNat1(Succ(xy4000), Succ(xy900000)) -> Succ(Succ(new_primPlusNat1(xy4000, xy900000)))
19.84/8.42	   new_primPlusNat1(Zero, Zero) -> Zero
19.84/8.42	
19.84/8.42	The set Q consists of the following terms:
19.84/8.42	
19.84/8.42	   new_esEs0(x0, x1, ty_Float)
19.84/8.42	   new_primEqNat0(Zero, Zero)
19.84/8.42	   new_esEs0(x0, x1, ty_Bool)
19.84/8.42	   new_primPlusNat1(Succ(x0), Succ(x1))
19.84/8.42	   new_sr(Neg(x0), Neg(x1))
19.84/8.42	   new_primMulNat0(Zero, Succ(x0))
19.84/8.42	   new_primPlusNat0(Zero, x0)
19.84/8.42	   new_primEqNat0(Succ(x0), Zero)
19.84/8.42	   new_sr(Pos(x0), Neg(x1))
19.84/8.42	   new_sr(Neg(x0), Pos(x1))
19.84/8.42	   new_esEs(x0, x1)
19.84/8.42	   new_deleteBy1(x0, [], x1)
19.84/8.42	   new_primMulNat0(Zero, Zero)
19.84/8.42	   new_primEqNat0(Succ(x0), Succ(x1))
19.84/8.42	   new_primPlusNat1(Zero, Zero)
19.84/8.42	   new_primPlusNat1(Zero, Succ(x0))
19.84/8.42	   new_primEqFloat(Float(x0, x1), Float(x2, x3))
19.84/8.42	   new_esEs0(x0, x1, ty_Char)
19.84/8.42	   new_esEs0(x0, x1, app(ty_Maybe, x2))
19.84/8.42	   new_esEs0(x0, x1, ty_Double)
19.84/8.42	   new_esEs0(x0, x1, app(ty_Ratio, x2))
19.84/8.42	   new_deleteBy00(x0, x1, x2, False, x3)
19.84/8.42	   new_deleteBy00(x0, x1, x2, True, x3)
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Zero))
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Zero))
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Succ(x0)))
19.84/8.42	   new_esEs0(x0, x1, ty_Int)
19.84/8.42	   new_primEqInt(Pos(Succ(x0)), Neg(x1))
19.84/8.42	   new_primEqInt(Neg(Succ(x0)), Pos(x1))
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Zero))
19.84/8.42	   new_primMulNat0(Succ(x0), Succ(x1))
19.84/8.42	   new_primPlusNat1(Succ(x0), Zero)
19.84/8.42	   new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Succ(x0)))
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Succ(x0)))
19.84/8.42	   new_esEs0(x0, x1, app(app(ty_@2, x2), x3))
19.84/8.42	   new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
19.84/8.42	   new_esEs0(x0, x1, ty_Integer)
19.84/8.42	   new_primEqInt(Pos(Succ(x0)), Pos(Zero))
19.84/8.42	   new_sr(Pos(x0), Pos(x1))
19.84/8.42	   new_esEs0(x0, x1, app(ty_[], x2))
19.84/8.42	   new_esEs0(x0, x1, app(app(ty_Either, x2), x3))
19.84/8.42	   new_primEqInt(Neg(Succ(x0)), Neg(Zero))
19.84/8.42	   new_primMulNat0(Succ(x0), Zero)
19.84/8.42	   new_primPlusNat0(Succ(x0), x1)
19.84/8.42	   new_primEqNat0(Zero, Succ(x0))
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Succ(x0)))
19.84/8.42	   new_esEs0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Zero))
19.84/8.42	   new_deleteBy1(x0, :(x1, x2), x3)
19.84/8.42	   new_esEs0(x0, x1, ty_Ordering)
19.84/8.42	   new_esEs0(x0, x1, ty_@0)
19.84/8.42	
19.84/8.42	We have to consider all minimal (P,Q,R)-chains.
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(24) QDPSizeChangeProof (EQUIVALENT)
19.84/8.42	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. 
19.84/8.42	
19.84/8.42	From the DPs we obtained the following set of size-change graphs:
19.84/8.42	*new_foldl(xy9, xy10, :(xy110, xy111), ba) -> new_foldl(new_deleteBy1(xy10, xy9, ba), xy110, xy111, ba)
19.84/8.42	The graph contains the following edges 3 > 2, 3 > 3, 4 >= 4
19.84/8.42	
19.84/8.42	
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(25)
19.84/8.42	YES
19.84/8.42	
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(26)
19.84/8.42	Obligation:
19.84/8.42	Q DP problem:
19.84/8.42	The TRS P consists of the following rules:
19.84/8.42	
19.84/8.42	   new_nubByNubBy'1(xy363, xy364, xy365, xy366, False, []) -> new_nubByNubBy'(xy364, xy363, :(xy365, xy366))
19.84/8.42	   new_nubByNubBy'1(xy363, xy364, xy365, xy366, False, :(xy3680, xy3681)) -> new_nubByNubBy'1(xy363, xy364, xy365, xy366, new_primEqFloat(xy3680, xy363), xy3681)
19.84/8.42	   new_nubByNubBy'(:(xy3640, xy3641), xy365, xy366) -> new_nubByNubBy'10(xy3640, xy3641, xy365, xy366, :(xy365, xy366))
19.84/8.42	   new_nubByNubBy'10(xy363, xy364, xy365, xy366, []) -> new_nubByNubBy'(xy364, xy363, :(xy365, xy366))
19.84/8.42	   new_nubByNubBy'10(xy363, xy364, xy365, xy366, :(xy3680, xy3681)) -> new_nubByNubBy'1(xy363, xy364, xy365, xy366, new_primEqFloat(xy3680, xy363), xy3681)
19.84/8.42	   new_nubByNubBy'1(xy363, :(xy3640, xy3641), xy365, xy366, True, xy368) -> new_nubByNubBy'10(xy3640, xy3641, xy365, xy366, :(xy365, xy366))
19.84/8.42	
19.84/8.42	The TRS R consists of the following rules:
19.84/8.42	
19.84/8.42	   new_primEqFloat(Float(xy100, xy101), Float(xy900, xy901)) -> new_esEs(new_sr(xy100, xy901), new_sr(xy101, xy900))
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Zero)) -> True
19.84/8.42	   new_primEqNat0(Zero, Zero) -> True
19.84/8.42	   new_primMulNat0(Zero, Zero) -> Zero
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Zero)) -> True
19.84/8.42	   new_primEqInt(Neg(Succ(xy1000)), Neg(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.84/8.42	   new_primMulNat0(Succ(xy10100), Succ(xy90000)) -> new_primPlusNat0(new_primMulNat0(xy10100, Succ(xy90000)), xy90000)
19.84/8.42	   new_primEqInt(Neg(Succ(xy1000)), Neg(Zero)) -> False
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Succ(xy9000))) -> False
19.84/8.42	   new_primPlusNat0(Succ(xy400), xy90000) -> Succ(Succ(new_primPlusNat1(xy400, xy90000)))
19.84/8.42	   new_primEqInt(Pos(Succ(xy1000)), Pos(Zero)) -> False
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Succ(xy9000))) -> False
19.84/8.42	   new_primEqInt(Pos(Succ(xy1000)), Pos(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.84/8.42	   new_sr(Neg(xy1010), Neg(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_esEs(xy10, xy90) -> new_primEqInt(xy10, xy90)
19.84/8.42	   new_primPlusNat1(Succ(xy4000), Zero) -> Succ(xy4000)
19.84/8.42	   new_primPlusNat1(Zero, Succ(xy900000)) -> Succ(xy900000)
19.84/8.42	   new_sr(Pos(xy1010), Neg(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_sr(Neg(xy1010), Pos(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_primEqNat0(Succ(xy10000), Zero) -> False
19.84/8.42	   new_primEqNat0(Zero, Succ(xy90000)) -> False
19.84/8.42	   new_primPlusNat1(Succ(xy4000), Succ(xy900000)) -> Succ(Succ(new_primPlusNat1(xy4000, xy900000)))
19.84/8.42	   new_primPlusNat1(Zero, Zero) -> Zero
19.84/8.42	   new_primEqNat0(Succ(xy10000), Succ(xy90000)) -> new_primEqNat0(xy10000, xy90000)
19.84/8.42	   new_primMulNat0(Succ(xy10100), Zero) -> Zero
19.84/8.42	   new_primMulNat0(Zero, Succ(xy90000)) -> Zero
19.84/8.42	   new_primEqInt(Pos(Succ(xy1000)), Neg(xy900)) -> False
19.84/8.42	   new_primEqInt(Neg(Succ(xy1000)), Pos(xy900)) -> False
19.84/8.42	   new_sr(Pos(xy1010), Pos(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_primPlusNat0(Zero, xy90000) -> Succ(xy90000)
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Succ(xy9000))) -> False
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Succ(xy9000))) -> False
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Zero)) -> True
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Zero)) -> True
19.84/8.42	
19.84/8.42	The set Q consists of the following terms:
19.84/8.42	
19.84/8.42	   new_primEqNat0(Zero, Zero)
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Succ(x0)))
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Zero))
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Zero))
19.84/8.42	   new_primEqInt(Pos(Succ(x0)), Neg(x1))
19.84/8.42	   new_primEqInt(Neg(Succ(x0)), Pos(x1))
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Zero))
19.84/8.42	   new_primPlusNat1(Succ(x0), Succ(x1))
19.84/8.42	   new_sr(Neg(x0), Neg(x1))
19.84/8.42	   new_primMulNat0(Zero, Succ(x0))
19.84/8.42	   new_primMulNat0(Succ(x0), Succ(x1))
19.84/8.42	   new_primPlusNat1(Succ(x0), Zero)
19.84/8.42	   new_primPlusNat0(Zero, x0)
19.84/8.42	   new_primEqNat0(Succ(x0), Zero)
19.84/8.42	   new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Succ(x0)))
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Succ(x0)))
19.84/8.42	   new_sr(Pos(x0), Neg(x1))
19.84/8.42	   new_sr(Neg(x0), Pos(x1))
19.84/8.42	   new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
19.84/8.42	   new_esEs(x0, x1)
19.84/8.42	   new_primEqInt(Pos(Succ(x0)), Pos(Zero))
19.84/8.42	   new_sr(Pos(x0), Pos(x1))
19.84/8.42	   new_primMulNat0(Zero, Zero)
19.84/8.42	   new_primEqInt(Neg(Succ(x0)), Neg(Zero))
19.84/8.42	   new_primMulNat0(Succ(x0), Zero)
19.84/8.42	   new_primEqNat0(Succ(x0), Succ(x1))
19.84/8.42	   new_primPlusNat0(Succ(x0), x1)
19.84/8.42	   new_primPlusNat1(Zero, Zero)
19.84/8.42	   new_primPlusNat1(Zero, Succ(x0))
19.84/8.42	   new_primEqFloat(Float(x0, x1), Float(x2, x3))
19.84/8.42	   new_primEqNat0(Zero, Succ(x0))
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Succ(x0)))
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Zero))
19.84/8.42	
19.84/8.42	We have to consider all minimal (P,Q,R)-chains.
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(27) DependencyGraphProof (EQUIVALENT)
19.84/8.42	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(28)
19.84/8.42	Obligation:
19.84/8.42	Q DP problem:
19.84/8.42	The TRS P consists of the following rules:
19.84/8.42	
19.84/8.42	   new_nubByNubBy'(:(xy3640, xy3641), xy365, xy366) -> new_nubByNubBy'10(xy3640, xy3641, xy365, xy366, :(xy365, xy366))
19.84/8.42	   new_nubByNubBy'10(xy363, xy364, xy365, xy366, :(xy3680, xy3681)) -> new_nubByNubBy'1(xy363, xy364, xy365, xy366, new_primEqFloat(xy3680, xy363), xy3681)
19.84/8.42	   new_nubByNubBy'1(xy363, xy364, xy365, xy366, False, []) -> new_nubByNubBy'(xy364, xy363, :(xy365, xy366))
19.84/8.42	   new_nubByNubBy'1(xy363, xy364, xy365, xy366, False, :(xy3680, xy3681)) -> new_nubByNubBy'1(xy363, xy364, xy365, xy366, new_primEqFloat(xy3680, xy363), xy3681)
19.84/8.42	   new_nubByNubBy'1(xy363, :(xy3640, xy3641), xy365, xy366, True, xy368) -> new_nubByNubBy'10(xy3640, xy3641, xy365, xy366, :(xy365, xy366))
19.84/8.42	
19.84/8.42	The TRS R consists of the following rules:
19.84/8.42	
19.84/8.42	   new_primEqFloat(Float(xy100, xy101), Float(xy900, xy901)) -> new_esEs(new_sr(xy100, xy901), new_sr(xy101, xy900))
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Zero)) -> True
19.84/8.42	   new_primEqNat0(Zero, Zero) -> True
19.84/8.42	   new_primMulNat0(Zero, Zero) -> Zero
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Zero)) -> True
19.84/8.42	   new_primEqInt(Neg(Succ(xy1000)), Neg(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.84/8.42	   new_primMulNat0(Succ(xy10100), Succ(xy90000)) -> new_primPlusNat0(new_primMulNat0(xy10100, Succ(xy90000)), xy90000)
19.84/8.42	   new_primEqInt(Neg(Succ(xy1000)), Neg(Zero)) -> False
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Succ(xy9000))) -> False
19.84/8.42	   new_primPlusNat0(Succ(xy400), xy90000) -> Succ(Succ(new_primPlusNat1(xy400, xy90000)))
19.84/8.42	   new_primEqInt(Pos(Succ(xy1000)), Pos(Zero)) -> False
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Succ(xy9000))) -> False
19.84/8.42	   new_primEqInt(Pos(Succ(xy1000)), Pos(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.84/8.42	   new_sr(Neg(xy1010), Neg(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_esEs(xy10, xy90) -> new_primEqInt(xy10, xy90)
19.84/8.42	   new_primPlusNat1(Succ(xy4000), Zero) -> Succ(xy4000)
19.84/8.42	   new_primPlusNat1(Zero, Succ(xy900000)) -> Succ(xy900000)
19.84/8.42	   new_sr(Pos(xy1010), Neg(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_sr(Neg(xy1010), Pos(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_primEqNat0(Succ(xy10000), Zero) -> False
19.84/8.42	   new_primEqNat0(Zero, Succ(xy90000)) -> False
19.84/8.42	   new_primPlusNat1(Succ(xy4000), Succ(xy900000)) -> Succ(Succ(new_primPlusNat1(xy4000, xy900000)))
19.84/8.42	   new_primPlusNat1(Zero, Zero) -> Zero
19.84/8.42	   new_primEqNat0(Succ(xy10000), Succ(xy90000)) -> new_primEqNat0(xy10000, xy90000)
19.84/8.42	   new_primMulNat0(Succ(xy10100), Zero) -> Zero
19.84/8.42	   new_primMulNat0(Zero, Succ(xy90000)) -> Zero
19.84/8.42	   new_primEqInt(Pos(Succ(xy1000)), Neg(xy900)) -> False
19.84/8.42	   new_primEqInt(Neg(Succ(xy1000)), Pos(xy900)) -> False
19.84/8.42	   new_sr(Pos(xy1010), Pos(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_primPlusNat0(Zero, xy90000) -> Succ(xy90000)
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Succ(xy9000))) -> False
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Succ(xy9000))) -> False
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Zero)) -> True
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Zero)) -> True
19.84/8.42	
19.84/8.42	The set Q consists of the following terms:
19.84/8.42	
19.84/8.42	   new_primEqNat0(Zero, Zero)
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Succ(x0)))
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Zero))
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Zero))
19.84/8.42	   new_primEqInt(Pos(Succ(x0)), Neg(x1))
19.84/8.42	   new_primEqInt(Neg(Succ(x0)), Pos(x1))
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Zero))
19.84/8.42	   new_primPlusNat1(Succ(x0), Succ(x1))
19.84/8.42	   new_sr(Neg(x0), Neg(x1))
19.84/8.42	   new_primMulNat0(Zero, Succ(x0))
19.84/8.42	   new_primMulNat0(Succ(x0), Succ(x1))
19.84/8.42	   new_primPlusNat1(Succ(x0), Zero)
19.84/8.42	   new_primPlusNat0(Zero, x0)
19.84/8.42	   new_primEqNat0(Succ(x0), Zero)
19.84/8.42	   new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Succ(x0)))
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Succ(x0)))
19.84/8.42	   new_sr(Pos(x0), Neg(x1))
19.84/8.42	   new_sr(Neg(x0), Pos(x1))
19.84/8.42	   new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
19.84/8.42	   new_esEs(x0, x1)
19.84/8.42	   new_primEqInt(Pos(Succ(x0)), Pos(Zero))
19.84/8.42	   new_sr(Pos(x0), Pos(x1))
19.84/8.42	   new_primMulNat0(Zero, Zero)
19.84/8.42	   new_primEqInt(Neg(Succ(x0)), Neg(Zero))
19.84/8.42	   new_primMulNat0(Succ(x0), Zero)
19.84/8.42	   new_primEqNat0(Succ(x0), Succ(x1))
19.84/8.42	   new_primPlusNat0(Succ(x0), x1)
19.84/8.42	   new_primPlusNat1(Zero, Zero)
19.84/8.42	   new_primPlusNat1(Zero, Succ(x0))
19.84/8.42	   new_primEqFloat(Float(x0, x1), Float(x2, x3))
19.84/8.42	   new_primEqNat0(Zero, Succ(x0))
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Succ(x0)))
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Zero))
19.84/8.42	
19.84/8.42	We have to consider all minimal (P,Q,R)-chains.
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(29) TransformationProof (EQUIVALENT)
19.84/8.42	By instantiating [LPAR04] the rule new_nubByNubBy'10(xy363, xy364, xy365, xy366, :(xy3680, xy3681)) -> new_nubByNubBy'1(xy363, xy364, xy365, xy366, new_primEqFloat(xy3680, xy363), xy3681) we obtained the following new rules [LPAR04]:
19.84/8.42	
19.84/8.42	   (new_nubByNubBy'10(z0, z1, z2, z3, :(z2, z3)) -> new_nubByNubBy'1(z0, z1, z2, z3, new_primEqFloat(z2, z0), z3),new_nubByNubBy'10(z0, z1, z2, z3, :(z2, z3)) -> new_nubByNubBy'1(z0, z1, z2, z3, new_primEqFloat(z2, z0), z3))
19.84/8.42	
19.84/8.42	
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(30)
19.84/8.42	Obligation:
19.84/8.42	Q DP problem:
19.84/8.42	The TRS P consists of the following rules:
19.84/8.42	
19.84/8.42	   new_nubByNubBy'(:(xy3640, xy3641), xy365, xy366) -> new_nubByNubBy'10(xy3640, xy3641, xy365, xy366, :(xy365, xy366))
19.84/8.42	   new_nubByNubBy'1(xy363, xy364, xy365, xy366, False, []) -> new_nubByNubBy'(xy364, xy363, :(xy365, xy366))
19.84/8.42	   new_nubByNubBy'1(xy363, xy364, xy365, xy366, False, :(xy3680, xy3681)) -> new_nubByNubBy'1(xy363, xy364, xy365, xy366, new_primEqFloat(xy3680, xy363), xy3681)
19.84/8.42	   new_nubByNubBy'1(xy363, :(xy3640, xy3641), xy365, xy366, True, xy368) -> new_nubByNubBy'10(xy3640, xy3641, xy365, xy366, :(xy365, xy366))
19.84/8.42	   new_nubByNubBy'10(z0, z1, z2, z3, :(z2, z3)) -> new_nubByNubBy'1(z0, z1, z2, z3, new_primEqFloat(z2, z0), z3)
19.84/8.42	
19.84/8.42	The TRS R consists of the following rules:
19.84/8.42	
19.84/8.42	   new_primEqFloat(Float(xy100, xy101), Float(xy900, xy901)) -> new_esEs(new_sr(xy100, xy901), new_sr(xy101, xy900))
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Zero)) -> True
19.84/8.42	   new_primEqNat0(Zero, Zero) -> True
19.84/8.42	   new_primMulNat0(Zero, Zero) -> Zero
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Zero)) -> True
19.84/8.42	   new_primEqInt(Neg(Succ(xy1000)), Neg(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.84/8.42	   new_primMulNat0(Succ(xy10100), Succ(xy90000)) -> new_primPlusNat0(new_primMulNat0(xy10100, Succ(xy90000)), xy90000)
19.84/8.42	   new_primEqInt(Neg(Succ(xy1000)), Neg(Zero)) -> False
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Succ(xy9000))) -> False
19.84/8.42	   new_primPlusNat0(Succ(xy400), xy90000) -> Succ(Succ(new_primPlusNat1(xy400, xy90000)))
19.84/8.42	   new_primEqInt(Pos(Succ(xy1000)), Pos(Zero)) -> False
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Succ(xy9000))) -> False
19.84/8.42	   new_primEqInt(Pos(Succ(xy1000)), Pos(Succ(xy9000))) -> new_primEqNat0(xy1000, xy9000)
19.84/8.42	   new_sr(Neg(xy1010), Neg(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_esEs(xy10, xy90) -> new_primEqInt(xy10, xy90)
19.84/8.42	   new_primPlusNat1(Succ(xy4000), Zero) -> Succ(xy4000)
19.84/8.42	   new_primPlusNat1(Zero, Succ(xy900000)) -> Succ(xy900000)
19.84/8.42	   new_sr(Pos(xy1010), Neg(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_sr(Neg(xy1010), Pos(xy9000)) -> Neg(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_primEqNat0(Succ(xy10000), Zero) -> False
19.84/8.42	   new_primEqNat0(Zero, Succ(xy90000)) -> False
19.84/8.42	   new_primPlusNat1(Succ(xy4000), Succ(xy900000)) -> Succ(Succ(new_primPlusNat1(xy4000, xy900000)))
19.84/8.42	   new_primPlusNat1(Zero, Zero) -> Zero
19.84/8.42	   new_primEqNat0(Succ(xy10000), Succ(xy90000)) -> new_primEqNat0(xy10000, xy90000)
19.84/8.42	   new_primMulNat0(Succ(xy10100), Zero) -> Zero
19.84/8.42	   new_primMulNat0(Zero, Succ(xy90000)) -> Zero
19.84/8.42	   new_primEqInt(Pos(Succ(xy1000)), Neg(xy900)) -> False
19.84/8.42	   new_primEqInt(Neg(Succ(xy1000)), Pos(xy900)) -> False
19.84/8.42	   new_sr(Pos(xy1010), Pos(xy9000)) -> Pos(new_primMulNat0(xy1010, xy9000))
19.84/8.42	   new_primPlusNat0(Zero, xy90000) -> Succ(xy90000)
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Succ(xy9000))) -> False
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Succ(xy9000))) -> False
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Zero)) -> True
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Zero)) -> True
19.84/8.42	
19.84/8.42	The set Q consists of the following terms:
19.84/8.42	
19.84/8.42	   new_primEqNat0(Zero, Zero)
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Succ(x0)))
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Zero))
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Zero))
19.84/8.42	   new_primEqInt(Pos(Succ(x0)), Neg(x1))
19.84/8.42	   new_primEqInt(Neg(Succ(x0)), Pos(x1))
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Zero))
19.84/8.42	   new_primPlusNat1(Succ(x0), Succ(x1))
19.84/8.42	   new_sr(Neg(x0), Neg(x1))
19.84/8.42	   new_primMulNat0(Zero, Succ(x0))
19.84/8.42	   new_primMulNat0(Succ(x0), Succ(x1))
19.84/8.42	   new_primPlusNat1(Succ(x0), Zero)
19.84/8.42	   new_primPlusNat0(Zero, x0)
19.84/8.42	   new_primEqNat0(Succ(x0), Zero)
19.84/8.42	   new_primEqInt(Pos(Succ(x0)), Pos(Succ(x1)))
19.84/8.42	   new_primEqInt(Pos(Zero), Neg(Succ(x0)))
19.84/8.42	   new_primEqInt(Neg(Zero), Pos(Succ(x0)))
19.84/8.42	   new_sr(Pos(x0), Neg(x1))
19.84/8.42	   new_sr(Neg(x0), Pos(x1))
19.84/8.42	   new_primEqInt(Neg(Succ(x0)), Neg(Succ(x1)))
19.84/8.42	   new_esEs(x0, x1)
19.84/8.42	   new_primEqInt(Pos(Succ(x0)), Pos(Zero))
19.84/8.42	   new_sr(Pos(x0), Pos(x1))
19.84/8.42	   new_primMulNat0(Zero, Zero)
19.84/8.42	   new_primEqInt(Neg(Succ(x0)), Neg(Zero))
19.84/8.42	   new_primMulNat0(Succ(x0), Zero)
19.84/8.42	   new_primEqNat0(Succ(x0), Succ(x1))
19.84/8.42	   new_primPlusNat0(Succ(x0), x1)
19.84/8.42	   new_primPlusNat1(Zero, Zero)
19.84/8.42	   new_primPlusNat1(Zero, Succ(x0))
19.84/8.42	   new_primEqFloat(Float(x0, x1), Float(x2, x3))
19.84/8.42	   new_primEqNat0(Zero, Succ(x0))
19.84/8.42	   new_primEqInt(Pos(Zero), Pos(Succ(x0)))
19.84/8.42	   new_primEqInt(Neg(Zero), Neg(Zero))
19.84/8.42	
19.84/8.42	We have to consider all minimal (P,Q,R)-chains.
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(31) QDPSizeChangeProof (EQUIVALENT)
19.84/8.42	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. 
19.84/8.42	
19.84/8.42	From the DPs we obtained the following set of size-change graphs:
19.84/8.42	*new_nubByNubBy'10(z0, z1, z2, z3, :(z2, z3)) -> new_nubByNubBy'1(z0, z1, z2, z3, new_primEqFloat(z2, z0), z3)
19.84/8.42	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 5 > 3, 4 >= 4, 5 > 4, 4 >= 6, 5 > 6
19.84/8.42	
19.84/8.42	
19.84/8.42	*new_nubByNubBy'1(xy363, xy364, xy365, xy366, False, []) -> new_nubByNubBy'(xy364, xy363, :(xy365, xy366))
19.84/8.42	The graph contains the following edges 2 >= 1, 1 >= 2
19.84/8.42	
19.84/8.42	
19.84/8.42	*new_nubByNubBy'(:(xy3640, xy3641), xy365, xy366) -> new_nubByNubBy'10(xy3640, xy3641, xy365, xy366, :(xy365, xy366))
19.84/8.42	The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3, 3 >= 4
19.84/8.42	
19.84/8.42	
19.84/8.42	*new_nubByNubBy'1(xy363, xy364, xy365, xy366, False, :(xy3680, xy3681)) -> new_nubByNubBy'1(xy363, xy364, xy365, xy366, new_primEqFloat(xy3680, xy363), xy3681)
19.84/8.42	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 > 6
19.84/8.42	
19.84/8.42	
19.84/8.42	*new_nubByNubBy'1(xy363, :(xy3640, xy3641), xy365, xy366, True, xy368) -> new_nubByNubBy'10(xy3640, xy3641, xy365, xy366, :(xy365, xy366))
19.84/8.42	The graph contains the following edges 2 > 1, 2 > 2, 3 >= 3, 4 >= 4
19.84/8.42	
19.84/8.42	
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(32)
19.84/8.42	YES
19.84/8.42	
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(33)
19.84/8.42	Obligation:
19.84/8.42	Q DP problem:
19.84/8.42	The TRS P consists of the following rules:
19.84/8.42	
19.84/8.42	   new_primMulNat(Succ(xy10100), Succ(xy90000)) -> new_primMulNat(xy10100, Succ(xy90000))
19.84/8.42	
19.84/8.42	R is empty.
19.84/8.42	Q is empty.
19.84/8.42	We have to consider all minimal (P,Q,R)-chains.
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(34) QDPSizeChangeProof (EQUIVALENT)
19.84/8.42	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. 
19.84/8.42	
19.84/8.42	From the DPs we obtained the following set of size-change graphs:
19.84/8.42	*new_primMulNat(Succ(xy10100), Succ(xy90000)) -> new_primMulNat(xy10100, Succ(xy90000))
19.84/8.42	The graph contains the following edges 1 > 1, 2 >= 2
19.84/8.42	
19.84/8.42	
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(35)
19.84/8.42	YES
19.84/8.42	
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(36)
19.84/8.42	Obligation:
19.84/8.42	Q DP problem:
19.84/8.42	The TRS P consists of the following rules:
19.84/8.42	
19.84/8.42	   new_primPlusNat(Succ(xy4000), Succ(xy900000)) -> new_primPlusNat(xy4000, xy900000)
19.84/8.42	
19.84/8.42	R is empty.
19.84/8.42	Q is empty.
19.84/8.42	We have to consider all minimal (P,Q,R)-chains.
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(37) QDPSizeChangeProof (EQUIVALENT)
19.84/8.42	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. 
19.84/8.42	
19.84/8.42	From the DPs we obtained the following set of size-change graphs:
19.84/8.42	*new_primPlusNat(Succ(xy4000), Succ(xy900000)) -> new_primPlusNat(xy4000, xy900000)
19.84/8.42	The graph contains the following edges 1 > 1, 2 > 2
19.84/8.42	
19.84/8.42	
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(38)
19.84/8.42	YES
19.84/8.42	
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(39)
19.84/8.42	Obligation:
19.84/8.42	Q DP problem:
19.84/8.42	The TRS P consists of the following rules:
19.84/8.42	
19.84/8.42	   new_primEqNat(Succ(xy10000), Succ(xy90000)) -> new_primEqNat(xy10000, xy90000)
19.84/8.42	
19.84/8.42	R is empty.
19.84/8.42	Q is empty.
19.84/8.42	We have to consider all minimal (P,Q,R)-chains.
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(40) QDPSizeChangeProof (EQUIVALENT)
19.84/8.42	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. 
19.84/8.42	
19.84/8.42	From the DPs we obtained the following set of size-change graphs:
19.84/8.42	*new_primEqNat(Succ(xy10000), Succ(xy90000)) -> new_primEqNat(xy10000, xy90000)
19.84/8.42	The graph contains the following edges 1 > 1, 2 > 2
19.84/8.42	
19.84/8.42	
19.84/8.42	----------------------------------------
19.84/8.42	
19.84/8.42	(41)
19.84/8.42	YES
19.87/8.45	EOF