14.04/5.43	YES
16.41/6.09	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
16.41/6.09	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
16.41/6.09	
16.41/6.09	
16.41/6.09	H-Termination with start terms of the given HASKELL could be proven:
16.41/6.09	
16.41/6.09	(0) HASKELL
16.41/6.09	(1) IFR [EQUIVALENT, 0 ms]
16.41/6.09	(2) HASKELL
16.41/6.09	(3) BR [EQUIVALENT, 0 ms]
16.41/6.09	(4) HASKELL
16.41/6.09	(5) COR [EQUIVALENT, 18 ms]
16.41/6.09	(6) HASKELL
16.41/6.09	(7) LetRed [EQUIVALENT, 0 ms]
16.41/6.09	(8) HASKELL
16.41/6.09	(9) Narrow [SOUND, 0 ms]
16.41/6.09	(10) AND
16.41/6.09	    (11) QDP
16.41/6.09	        (12) TransformationProof [EQUIVALENT, 15 ms]
16.41/6.09	        (13) QDP
16.41/6.09	        (14) DependencyGraphProof [EQUIVALENT, 0 ms]
16.41/6.09	        (15) QDP
16.41/6.09	        (16) UsableRulesProof [EQUIVALENT, 0 ms]
16.41/6.09	        (17) QDP
16.41/6.09	        (18) QReductionProof [EQUIVALENT, 0 ms]
16.41/6.09	        (19) QDP
16.41/6.09	        (20) TransformationProof [EQUIVALENT, 0 ms]
16.41/6.09	        (21) QDP
16.41/6.09	        (22) TransformationProof [EQUIVALENT, 0 ms]
16.41/6.09	        (23) QDP
16.41/6.09	        (24) DependencyGraphProof [EQUIVALENT, 0 ms]
16.41/6.09	        (25) QDP
16.41/6.09	        (26) UsableRulesProof [EQUIVALENT, 0 ms]
16.41/6.09	        (27) QDP
16.41/6.09	        (28) QReductionProof [EQUIVALENT, 0 ms]
16.41/6.09	        (29) QDP
16.41/6.09	        (30) TransformationProof [EQUIVALENT, 0 ms]
16.41/6.09	        (31) QDP
16.41/6.09	        (32) UsableRulesProof [EQUIVALENT, 0 ms]
16.41/6.09	        (33) QDP
16.41/6.09	        (34) QReductionProof [EQUIVALENT, 0 ms]
16.41/6.09	        (35) QDP
16.41/6.09	        (36) TransformationProof [EQUIVALENT, 0 ms]
16.41/6.09	        (37) QDP
16.41/6.09	        (38) TransformationProof [EQUIVALENT, 3 ms]
16.41/6.09	        (39) QDP
16.41/6.09	        (40) QDPSizeChangeProof [EQUIVALENT, 0 ms]
16.41/6.09	        (41) YES
16.41/6.09	    (42) QDP
16.41/6.09	        (43) QDPSizeChangeProof [EQUIVALENT, 0 ms]
16.41/6.09	        (44) YES
16.41/6.09	    (45) QDP
16.41/6.09	        (46) TransformationProof [EQUIVALENT, 0 ms]
16.41/6.09	        (47) QDP
16.41/6.09	        (48) DependencyGraphProof [EQUIVALENT, 0 ms]
16.41/6.09	        (49) QDP
16.41/6.09	        (50) UsableRulesProof [EQUIVALENT, 0 ms]
16.41/6.09	        (51) QDP
16.41/6.09	        (52) QReductionProof [EQUIVALENT, 0 ms]
16.41/6.09	        (53) QDP
16.41/6.09	        (54) TransformationProof [EQUIVALENT, 0 ms]
16.41/6.09	        (55) QDP
16.41/6.09	        (56) DependencyGraphProof [EQUIVALENT, 0 ms]
16.41/6.09	        (57) QDP
16.41/6.09	        (58) UsableRulesProof [EQUIVALENT, 0 ms]
16.41/6.09	        (59) QDP
16.41/6.09	        (60) QReductionProof [EQUIVALENT, 1 ms]
16.41/6.09	        (61) QDP
16.41/6.09	        (62) TransformationProof [EQUIVALENT, 0 ms]
16.41/6.09	        (63) QDP
16.41/6.09	        (64) DependencyGraphProof [EQUIVALENT, 0 ms]
16.41/6.09	        (65) AND
16.41/6.09	            (66) QDP
16.41/6.09	                (67) QDPSizeChangeProof [EQUIVALENT, 0 ms]
16.41/6.09	                (68) YES
16.41/6.09	            (69) QDP
16.41/6.09	                (70) QDPSizeChangeProof [EQUIVALENT, 0 ms]
16.41/6.09	                (71) YES
16.41/6.09	            (72) QDP
16.41/6.09	                (73) QDPSizeChangeProof [EQUIVALENT, 0 ms]
16.41/6.09	                (74) YES
16.41/6.09	    (75) QDP
16.41/6.09	        (76) TransformationProof [EQUIVALENT, 0 ms]
16.41/6.09	        (77) QDP
16.41/6.09	        (78) UsableRulesProof [EQUIVALENT, 0 ms]
16.41/6.09	        (79) QDP
16.41/6.09	        (80) QReductionProof [EQUIVALENT, 0 ms]
16.41/6.09	        (81) QDP
16.41/6.09	        (82) QDPSizeChangeProof [EQUIVALENT, 0 ms]
16.41/6.09	        (83) YES
16.41/6.09	
16.41/6.09	
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(0)
16.41/6.09	Obligation:
16.41/6.09	mainModule Main 
16.41/6.09	module Maybe where {
16.41/6.09	import qualified List;
16.41/6.09	import qualified Main;
16.41/6.09	import qualified Prelude;
16.41/6.09	}
16.41/6.09	module List where {
16.41/6.09	import qualified Main;
16.41/6.09	import qualified Maybe;
16.41/6.09	import qualified Prelude;
16.41/6.09	deleteBy :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  [a];
16.41/6.09	deleteBy _ _ [] = [];
16.41/6.09	deleteBy eq x (y : ys) =  if x `eq` y then ys else y : deleteBy eq x ys;
16.41/6.09	
16.41/6.09	elem_by :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  Bool;
16.41/6.09	elem_by _ _ [] = False;
16.41/6.09	elem_by eq y (x : xs) = x `eq` y || elem_by eq y xs;
16.41/6.09	
16.41/6.09	nubBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a];
16.41/6.09	nubBy eq l = nubBy' l [] where { 
16.41/6.09	nubBy' [] _ = [];
16.41/6.09	nubBy' (y : ys) xs  | elem_by eq y xs = nubBy' ys xs
16.41/6.09	 | otherwise = y : nubBy' ys (y : xs);
16.41/6.09	 };
16.41/6.09	
16.41/6.09	union :: Eq a => [a]  ->  [a]  ->  [a];
16.41/6.09	union = unionBy (==);
16.41/6.09	
16.41/6.09	unionBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
16.41/6.09	unionBy eq xs ys = xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs;
16.41/6.09	
16.41/6.09	}
16.41/6.09	module Main where {
16.41/6.09	import qualified List;
16.41/6.09	import qualified Maybe;
16.41/6.09	import qualified Prelude;
16.41/6.09	}
16.41/6.09	
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(1) IFR (EQUIVALENT)
16.41/6.09	If Reductions:
16.41/6.09	The following If expression
16.41/6.09	"if eq x y then ys else y : deleteBy eq x ys"
16.41/6.09	is transformed to
16.41/6.09	"deleteBy0 ys y eq x True = ys;
16.41/6.09	deleteBy0 ys y eq x False = y : deleteBy eq x ys;
16.41/6.09	"
16.41/6.09	
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(2)
16.41/6.09	Obligation:
16.41/6.09	mainModule Main 
16.41/6.09	module Maybe where {
16.41/6.09	import qualified List;
16.41/6.09	import qualified Main;
16.41/6.09	import qualified Prelude;
16.41/6.09	}
16.41/6.09	module List where {
16.41/6.09	import qualified Main;
16.41/6.09	import qualified Maybe;
16.41/6.09	import qualified Prelude;
16.41/6.09	deleteBy :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  [a];
16.41/6.09	deleteBy _ _ [] = [];
16.41/6.09	deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y);
16.41/6.09	
16.41/6.09	deleteBy0 ys y eq x True = ys;
16.41/6.09	deleteBy0 ys y eq x False = y : deleteBy eq x ys;
16.41/6.09	
16.41/6.09	elem_by :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  Bool;
16.41/6.09	elem_by _ _ [] = False;
16.41/6.09	elem_by eq y (x : xs) = x `eq` y || elem_by eq y xs;
16.41/6.09	
16.41/6.09	nubBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a];
16.41/6.09	nubBy eq l = nubBy' l [] where { 
16.41/6.09	nubBy' [] _ = [];
16.41/6.09	nubBy' (y : ys) xs  | elem_by eq y xs = nubBy' ys xs
16.41/6.09	 | otherwise = y : nubBy' ys (y : xs);
16.41/6.09	 };
16.41/6.09	
16.41/6.09	union :: Eq a => [a]  ->  [a]  ->  [a];
16.41/6.09	union = unionBy (==);
16.41/6.09	
16.41/6.09	unionBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
16.41/6.09	unionBy eq xs ys = xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs;
16.41/6.09	
16.41/6.09	}
16.41/6.09	module Main where {
16.41/6.09	import qualified List;
16.41/6.09	import qualified Maybe;
16.41/6.09	import qualified Prelude;
16.41/6.09	}
16.41/6.09	
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(3) BR (EQUIVALENT)
16.41/6.09	Replaced joker patterns by fresh variables and removed binding patterns.
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(4)
16.41/6.09	Obligation:
16.41/6.09	mainModule Main 
16.41/6.09	module Maybe where {
16.41/6.09	import qualified List;
16.41/6.09	import qualified Main;
16.41/6.09	import qualified Prelude;
16.41/6.09	}
16.41/6.09	module List where {
16.41/6.09	import qualified Main;
16.41/6.09	import qualified Maybe;
16.41/6.09	import qualified Prelude;
16.41/6.09	deleteBy :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  [a];
16.41/6.09	deleteBy wv ww [] = [];
16.41/6.09	deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y);
16.41/6.09	
16.41/6.09	deleteBy0 ys y eq x True = ys;
16.41/6.09	deleteBy0 ys y eq x False = y : deleteBy eq x ys;
16.41/6.09	
16.41/6.09	elem_by :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  Bool;
16.41/6.09	elem_by vy vz [] = False;
16.41/6.09	elem_by eq y (x : xs) = x `eq` y || elem_by eq y xs;
16.41/6.09	
16.41/6.09	nubBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a];
16.41/6.09	nubBy eq l = nubBy' l [] where { 
16.41/6.09	nubBy' [] wu = [];
16.41/6.09	nubBy' (y : ys) xs  | elem_by eq y xs = nubBy' ys xs
16.41/6.09	 | otherwise = y : nubBy' ys (y : xs);
16.41/6.09	 };
16.41/6.09	
16.41/6.09	union :: Eq a => [a]  ->  [a]  ->  [a];
16.41/6.09	union = unionBy (==);
16.41/6.09	
16.41/6.09	unionBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
16.41/6.09	unionBy eq xs ys = xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs;
16.41/6.09	
16.41/6.09	}
16.41/6.09	module Main where {
16.41/6.09	import qualified List;
16.41/6.09	import qualified Maybe;
16.41/6.09	import qualified Prelude;
16.41/6.09	}
16.41/6.09	
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(5) COR (EQUIVALENT)
16.41/6.09	Cond Reductions:
16.41/6.09	The following Function with conditions
16.41/6.09	"undefined |Falseundefined;
16.41/6.09	"
16.41/6.09	is transformed to
16.41/6.09	"undefined  = undefined1;
16.41/6.09	"
16.41/6.09	"undefined0 True = undefined;
16.41/6.09	"
16.41/6.09	"undefined1  = undefined0 False;
16.41/6.09	"
16.41/6.09	The following Function with conditions
16.41/6.09	"nubBy' [] wu = [];
16.41/6.09	nubBy' (y : ys) xs|elem_by eq y xsnubBy' ys xs|otherwisey : nubBy' ys (y : xs);
16.41/6.09	"
16.41/6.09	is transformed to
16.41/6.09	"nubBy' [] wu = nubBy'3 [] wu;
16.41/6.09	nubBy' (y : ys) xs = nubBy'2 (y : ys) xs;
16.41/6.09	"
16.41/6.09	"nubBy'0 y ys xs True = y : nubBy' ys (y : xs);
16.41/6.09	"
16.41/6.09	"nubBy'1 y ys xs True = nubBy' ys xs;
16.41/6.09	nubBy'1 y ys xs False = nubBy'0 y ys xs otherwise;
16.41/6.09	"
16.41/6.09	"nubBy'2 (y : ys) xs = nubBy'1 y ys xs (elem_by eq y xs);
16.41/6.09	"
16.41/6.09	"nubBy'3 [] wu = [];
16.41/6.09	nubBy'3 wz xu = nubBy'2 wz xu;
16.41/6.09	"
16.41/6.09	
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(6)
16.41/6.09	Obligation:
16.41/6.09	mainModule Main 
16.41/6.09	module Maybe where {
16.41/6.09	import qualified List;
16.41/6.09	import qualified Main;
16.41/6.09	import qualified Prelude;
16.41/6.09	}
16.41/6.09	module List where {
16.41/6.09	import qualified Main;
16.41/6.09	import qualified Maybe;
16.41/6.09	import qualified Prelude;
16.41/6.09	deleteBy :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  [a];
16.41/6.09	deleteBy wv ww [] = [];
16.41/6.09	deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y);
16.41/6.09	
16.41/6.09	deleteBy0 ys y eq x True = ys;
16.41/6.09	deleteBy0 ys y eq x False = y : deleteBy eq x ys;
16.41/6.09	
16.41/6.09	elem_by :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  Bool;
16.41/6.09	elem_by vy vz [] = False;
16.41/6.09	elem_by eq y (x : xs) = x `eq` y || elem_by eq y xs;
16.41/6.09	
16.41/6.09	nubBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a];
16.41/6.09	nubBy eq l = nubBy' l [] where { 
16.41/6.09	nubBy' [] wu = nubBy'3 [] wu;
16.41/6.09	nubBy' (y : ys) xs = nubBy'2 (y : ys) xs;
16.41/6.09	nubBy'0 y ys xs True = y : nubBy' ys (y : xs);
16.41/6.09	nubBy'1 y ys xs True = nubBy' ys xs;
16.41/6.09	nubBy'1 y ys xs False = nubBy'0 y ys xs otherwise;
16.41/6.09	nubBy'2 (y : ys) xs = nubBy'1 y ys xs (elem_by eq y xs);
16.41/6.09	nubBy'3 [] wu = [];
16.41/6.09	nubBy'3 wz xu = nubBy'2 wz xu;
16.41/6.09	 };
16.41/6.09	
16.41/6.09	union :: Eq a => [a]  ->  [a]  ->  [a];
16.41/6.09	union = unionBy (==);
16.41/6.09	
16.41/6.09	unionBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
16.41/6.09	unionBy eq xs ys = xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs;
16.41/6.09	
16.41/6.09	}
16.41/6.09	module Main where {
16.41/6.09	import qualified List;
16.41/6.09	import qualified Maybe;
16.41/6.09	import qualified Prelude;
16.41/6.09	}
16.41/6.09	
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(7) LetRed (EQUIVALENT)
16.41/6.09	Let/Where Reductions:
16.41/6.09	The bindings of the following Let/Where expression
16.41/6.09	"nubBy' l [] where {
16.41/6.09	nubBy' [] wu = nubBy'3 [] wu;
16.41/6.09	nubBy' (y : ys) xs = nubBy'2 (y : ys) xs;
16.41/6.09	;
16.41/6.09	nubBy'0 y ys xs True = y : nubBy' ys (y : xs);
16.41/6.09	;
16.41/6.09	nubBy'1 y ys xs True = nubBy' ys xs;
16.41/6.09	nubBy'1 y ys xs False = nubBy'0 y ys xs otherwise;
16.41/6.09	;
16.41/6.09	nubBy'2 (y : ys) xs = nubBy'1 y ys xs (elem_by eq y xs);
16.41/6.09	;
16.41/6.09	nubBy'3 [] wu = [];
16.41/6.09	nubBy'3 wz xu = nubBy'2 wz xu;
16.41/6.09	} 
16.41/6.09	"
16.41/6.09	are unpacked to the following functions on top level
16.41/6.09	"nubByNubBy'2 xv (y : ys) xs = nubByNubBy'1 xv y ys xs (elem_by xv y xs);
16.41/6.09	"
16.41/6.09	"nubByNubBy'1 xv y ys xs True = nubByNubBy' xv ys xs;
16.41/6.09	nubByNubBy'1 xv y ys xs False = nubByNubBy'0 xv y ys xs otherwise;
16.41/6.09	"
16.41/6.09	"nubByNubBy' xv [] wu = nubByNubBy'3 xv [] wu;
16.41/6.09	nubByNubBy' xv (y : ys) xs = nubByNubBy'2 xv (y : ys) xs;
16.41/6.09	"
16.41/6.09	"nubByNubBy'0 xv y ys xs True = y : nubByNubBy' xv ys (y : xs);
16.41/6.09	"
16.41/6.09	"nubByNubBy'3 xv [] wu = [];
16.41/6.09	nubByNubBy'3 xv wz xu = nubByNubBy'2 xv wz xu;
16.41/6.09	"
16.41/6.09	
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(8)
16.41/6.09	Obligation:
16.41/6.09	mainModule Main 
16.41/6.09	module Maybe where {
16.41/6.09	import qualified List;
16.41/6.09	import qualified Main;
16.41/6.09	import qualified Prelude;
16.41/6.09	}
16.41/6.09	module List where {
16.41/6.09	import qualified Main;
16.41/6.09	import qualified Maybe;
16.41/6.09	import qualified Prelude;
16.41/6.09	deleteBy :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  [a];
16.41/6.09	deleteBy wv ww [] = [];
16.41/6.09	deleteBy eq x (y : ys) = deleteBy0 ys y eq x (x `eq` y);
16.41/6.09	
16.41/6.09	deleteBy0 ys y eq x True = ys;
16.41/6.09	deleteBy0 ys y eq x False = y : deleteBy eq x ys;
16.41/6.09	
16.41/6.09	elem_by :: (a  ->  a  ->  Bool)  ->  a  ->  [a]  ->  Bool;
16.41/6.09	elem_by vy vz [] = False;
16.41/6.09	elem_by eq y (x : xs) = x `eq` y || elem_by eq y xs;
16.41/6.09	
16.41/6.09	nubBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a];
16.41/6.09	nubBy eq l = nubByNubBy' eq l [];
16.41/6.09	
16.41/6.09	nubByNubBy' xv [] wu = nubByNubBy'3 xv [] wu;
16.41/6.09	nubByNubBy' xv (y : ys) xs = nubByNubBy'2 xv (y : ys) xs;
16.41/6.09	
16.41/6.09	nubByNubBy'0 xv y ys xs True = y : nubByNubBy' xv ys (y : xs);
16.41/6.09	
16.41/6.09	nubByNubBy'1 xv y ys xs True = nubByNubBy' xv ys xs;
16.41/6.09	nubByNubBy'1 xv y ys xs False = nubByNubBy'0 xv y ys xs otherwise;
16.41/6.09	
16.41/6.09	nubByNubBy'2 xv (y : ys) xs = nubByNubBy'1 xv y ys xs (elem_by xv y xs);
16.41/6.09	
16.41/6.09	nubByNubBy'3 xv [] wu = [];
16.41/6.09	nubByNubBy'3 xv wz xu = nubByNubBy'2 xv wz xu;
16.41/6.09	
16.41/6.09	union :: Eq a => [a]  ->  [a]  ->  [a];
16.41/6.09	union = unionBy (==);
16.41/6.09	
16.41/6.09	unionBy :: (a  ->  a  ->  Bool)  ->  [a]  ->  [a]  ->  [a];
16.41/6.09	unionBy eq xs ys = xs ++ foldl (flip (deleteBy eq)) (nubBy eq ys) xs;
16.41/6.09	
16.41/6.09	}
16.41/6.09	module Main where {
16.41/6.09	import qualified List;
16.41/6.09	import qualified Maybe;
16.41/6.09	import qualified Prelude;
16.41/6.09	}
16.41/6.09	
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(9) Narrow (SOUND)
16.41/6.09	Haskell To QDPs
16.41/6.09	
16.41/6.09	digraph dp_graph {
16.41/6.09	node [outthreshold=100, inthreshold=100];1[label="List.union",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
16.41/6.09	3[label="List.union xw3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
16.41/6.09	4[label="List.union xw3 xw4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
16.41/6.09	5[label="List.unionBy (==) xw3 xw4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
16.41/6.09	6[label="xw3 ++ foldl (flip (List.deleteBy (==))) (List.nubBy (==) xw4) xw3",fontsize=16,color="burlywood",shape="box"];2054[label="xw3/xw30 : xw31",fontsize=10,color="white",style="solid",shape="box"];6 -> 2054[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2054 -> 7[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2055[label="xw3/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 2055[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2055 -> 8[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	7[label="(xw30 : xw31) ++ foldl (flip (List.deleteBy (==))) (List.nubBy (==) xw4) (xw30 : xw31)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
16.41/6.09	8[label="[] ++ foldl (flip (List.deleteBy (==))) (List.nubBy (==) xw4) []",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
16.41/6.09	9[label="xw30 : xw31 ++ foldl (flip (List.deleteBy (==))) (List.nubBy (==) xw4) (xw30 : xw31)",fontsize=16,color="green",shape="box"];9 -> 11[label="",style="dashed", color="green", weight=3];
16.41/6.09	10[label="foldl (flip (List.deleteBy (==))) (List.nubBy (==) xw4) []",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3];
16.41/6.09	11 -> 153[label="",style="dashed", color="red", weight=0];
16.41/6.09	11[label="xw31 ++ foldl (flip (List.deleteBy (==))) (List.nubBy (==) xw4) (xw30 : xw31)",fontsize=16,color="magenta"];11 -> 154[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	11 -> 155[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	11 -> 156[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	11 -> 157[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	12[label="List.nubBy (==) xw4",fontsize=16,color="black",shape="triangle"];12 -> 15[label="",style="solid", color="black", weight=3];
16.41/6.09	154[label="xw31",fontsize=16,color="green",shape="box"];155 -> 12[label="",style="dashed", color="red", weight=0];
16.41/6.09	155[label="List.nubBy (==) xw4",fontsize=16,color="magenta"];156[label="xw31",fontsize=16,color="green",shape="box"];157[label="xw30",fontsize=16,color="green",shape="box"];153[label="xw8 ++ foldl (flip (List.deleteBy (==))) xw9 (xw10 : xw11)",fontsize=16,color="burlywood",shape="triangle"];2056[label="xw8/xw80 : xw81",fontsize=10,color="white",style="solid",shape="box"];153 -> 2056[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2056 -> 182[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2057[label="xw8/[]",fontsize=10,color="white",style="solid",shape="box"];153 -> 2057[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2057 -> 183[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	15[label="List.nubByNubBy' (==) xw4 []",fontsize=16,color="burlywood",shape="box"];2058[label="xw4/xw40 : xw41",fontsize=10,color="white",style="solid",shape="box"];15 -> 2058[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2058 -> 18[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2059[label="xw4/[]",fontsize=10,color="white",style="solid",shape="box"];15 -> 2059[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2059 -> 19[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	182[label="(xw80 : xw81) ++ foldl (flip (List.deleteBy (==))) xw9 (xw10 : xw11)",fontsize=16,color="black",shape="box"];182 -> 193[label="",style="solid", color="black", weight=3];
16.41/6.09	183[label="[] ++ foldl (flip (List.deleteBy (==))) xw9 (xw10 : xw11)",fontsize=16,color="black",shape="box"];183 -> 194[label="",style="solid", color="black", weight=3];
16.41/6.09	18[label="List.nubByNubBy' (==) (xw40 : xw41) []",fontsize=16,color="black",shape="box"];18 -> 23[label="",style="solid", color="black", weight=3];
16.41/6.09	19[label="List.nubByNubBy' (==) [] []",fontsize=16,color="black",shape="box"];19 -> 24[label="",style="solid", color="black", weight=3];
16.41/6.09	193[label="xw80 : xw81 ++ foldl (flip (List.deleteBy (==))) xw9 (xw10 : xw11)",fontsize=16,color="green",shape="box"];193 -> 204[label="",style="dashed", color="green", weight=3];
16.41/6.09	194[label="foldl (flip (List.deleteBy (==))) xw9 (xw10 : xw11)",fontsize=16,color="black",shape="box"];194 -> 205[label="",style="solid", color="black", weight=3];
16.41/6.09	23[label="List.nubByNubBy'2 (==) (xw40 : xw41) []",fontsize=16,color="black",shape="box"];23 -> 28[label="",style="solid", color="black", weight=3];
16.41/6.09	24[label="List.nubByNubBy'3 (==) [] []",fontsize=16,color="black",shape="box"];24 -> 29[label="",style="solid", color="black", weight=3];
16.41/6.09	204 -> 153[label="",style="dashed", color="red", weight=0];
16.41/6.09	204[label="xw81 ++ foldl (flip (List.deleteBy (==))) xw9 (xw10 : xw11)",fontsize=16,color="magenta"];204 -> 218[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	205[label="foldl (flip (List.deleteBy (==))) (flip (List.deleteBy (==)) xw9 xw10) xw11",fontsize=16,color="burlywood",shape="triangle"];2060[label="xw11/xw110 : xw111",fontsize=10,color="white",style="solid",shape="box"];205 -> 2060[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2060 -> 219[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2061[label="xw11/[]",fontsize=10,color="white",style="solid",shape="box"];205 -> 2061[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2061 -> 220[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	28[label="List.nubByNubBy'1 (==) xw40 xw41 [] (List.elem_by (==) xw40 [])",fontsize=16,color="black",shape="box"];28 -> 33[label="",style="solid", color="black", weight=3];
16.41/6.09	29[label="[]",fontsize=16,color="green",shape="box"];218[label="xw81",fontsize=16,color="green",shape="box"];219[label="foldl (flip (List.deleteBy (==))) (flip (List.deleteBy (==)) xw9 xw10) (xw110 : xw111)",fontsize=16,color="black",shape="box"];219 -> 227[label="",style="solid", color="black", weight=3];
16.41/6.09	220[label="foldl (flip (List.deleteBy (==))) (flip (List.deleteBy (==)) xw9 xw10) []",fontsize=16,color="black",shape="box"];220 -> 228[label="",style="solid", color="black", weight=3];
16.41/6.09	33[label="List.nubByNubBy'1 (==) xw40 xw41 [] False",fontsize=16,color="black",shape="box"];33 -> 37[label="",style="solid", color="black", weight=3];
16.41/6.09	227 -> 205[label="",style="dashed", color="red", weight=0];
16.41/6.09	227[label="foldl (flip (List.deleteBy (==))) (flip (List.deleteBy (==)) (flip (List.deleteBy (==)) xw9 xw10) xw110) xw111",fontsize=16,color="magenta"];227 -> 235[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	227 -> 236[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	227 -> 237[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	228[label="flip (List.deleteBy (==)) xw9 xw10",fontsize=16,color="black",shape="triangle"];228 -> 238[label="",style="solid", color="black", weight=3];
16.41/6.09	37[label="List.nubByNubBy'0 (==) xw40 xw41 [] otherwise",fontsize=16,color="black",shape="box"];37 -> 42[label="",style="solid", color="black", weight=3];
16.41/6.09	235 -> 228[label="",style="dashed", color="red", weight=0];
16.41/6.09	235[label="flip (List.deleteBy (==)) xw9 xw10",fontsize=16,color="magenta"];236[label="xw111",fontsize=16,color="green",shape="box"];237[label="xw110",fontsize=16,color="green",shape="box"];238[label="List.deleteBy (==) xw10 xw9",fontsize=16,color="burlywood",shape="triangle"];2062[label="xw9/xw90 : xw91",fontsize=10,color="white",style="solid",shape="box"];238 -> 2062[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2062 -> 245[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2063[label="xw9/[]",fontsize=10,color="white",style="solid",shape="box"];238 -> 2063[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2063 -> 246[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	42[label="List.nubByNubBy'0 (==) xw40 xw41 [] True",fontsize=16,color="black",shape="box"];42 -> 49[label="",style="solid", color="black", weight=3];
16.41/6.09	245[label="List.deleteBy (==) xw10 (xw90 : xw91)",fontsize=16,color="black",shape="box"];245 -> 259[label="",style="solid", color="black", weight=3];
16.41/6.09	246[label="List.deleteBy (==) xw10 []",fontsize=16,color="black",shape="box"];246 -> 260[label="",style="solid", color="black", weight=3];
16.41/6.09	49[label="xw40 : List.nubByNubBy' (==) xw41 (xw40 : [])",fontsize=16,color="green",shape="box"];49 -> 56[label="",style="dashed", color="green", weight=3];
16.41/6.09	259 -> 273[label="",style="dashed", color="red", weight=0];
16.41/6.09	259[label="List.deleteBy0 xw91 xw90 (==) xw10 ((==) xw10 xw90)",fontsize=16,color="magenta"];259 -> 274[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	259 -> 275[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	259 -> 276[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	259 -> 277[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	260[label="[]",fontsize=16,color="green",shape="box"];56 -> 1379[label="",style="dashed", color="red", weight=0];
16.41/6.09	56[label="List.nubByNubBy' (==) xw41 (xw40 : [])",fontsize=16,color="magenta"];56 -> 1380[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	56 -> 1381[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	56 -> 1382[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	274[label="xw10",fontsize=16,color="green",shape="box"];275[label="xw90",fontsize=16,color="green",shape="box"];276[label="xw91",fontsize=16,color="green",shape="box"];277[label="(==) xw10 xw90",fontsize=16,color="blue",shape="box"];2064[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];277 -> 2064[label="",style="solid", color="blue", weight=9];
16.41/6.09	2064 -> 278[label="",style="solid", color="blue", weight=3];
16.41/6.09	2065[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];277 -> 2065[label="",style="solid", color="blue", weight=9];
16.41/6.09	2065 -> 279[label="",style="solid", color="blue", weight=3];
16.41/6.09	2066[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];277 -> 2066[label="",style="solid", color="blue", weight=9];
16.41/6.09	2066 -> 280[label="",style="solid", color="blue", weight=3];
16.41/6.09	2067[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];277 -> 2067[label="",style="solid", color="blue", weight=9];
16.41/6.09	2067 -> 281[label="",style="solid", color="blue", weight=3];
16.41/6.09	2068[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];277 -> 2068[label="",style="solid", color="blue", weight=9];
16.41/6.09	2068 -> 282[label="",style="solid", color="blue", weight=3];
16.41/6.09	2069[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];277 -> 2069[label="",style="solid", color="blue", weight=9];
16.41/6.09	2069 -> 283[label="",style="solid", color="blue", weight=3];
16.41/6.09	2070[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];277 -> 2070[label="",style="solid", color="blue", weight=9];
16.41/6.09	2070 -> 284[label="",style="solid", color="blue", weight=3];
16.41/6.09	2071[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];277 -> 2071[label="",style="solid", color="blue", weight=9];
16.41/6.09	2071 -> 285[label="",style="solid", color="blue", weight=3];
16.41/6.09	2072[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];277 -> 2072[label="",style="solid", color="blue", weight=9];
16.41/6.09	2072 -> 286[label="",style="solid", color="blue", weight=3];
16.41/6.09	2073[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];277 -> 2073[label="",style="solid", color="blue", weight=9];
16.41/6.09	2073 -> 287[label="",style="solid", color="blue", weight=3];
16.41/6.09	2074[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];277 -> 2074[label="",style="solid", color="blue", weight=9];
16.41/6.09	2074 -> 288[label="",style="solid", color="blue", weight=3];
16.41/6.09	2075[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];277 -> 2075[label="",style="solid", color="blue", weight=9];
16.41/6.09	2075 -> 289[label="",style="solid", color="blue", weight=3];
16.41/6.09	2076[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];277 -> 2076[label="",style="solid", color="blue", weight=9];
16.41/6.09	2076 -> 290[label="",style="solid", color="blue", weight=3];
16.41/6.09	2077[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];277 -> 2077[label="",style="solid", color="blue", weight=9];
16.41/6.09	2077 -> 291[label="",style="solid", color="blue", weight=3];
16.41/6.09	273[label="List.deleteBy0 xw17 xw18 (==) xw19 xw20",fontsize=16,color="burlywood",shape="triangle"];2078[label="xw20/False",fontsize=10,color="white",style="solid",shape="box"];273 -> 2078[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2078 -> 292[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2079[label="xw20/True",fontsize=10,color="white",style="solid",shape="box"];273 -> 2079[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2079 -> 293[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	1380[label="xw40",fontsize=16,color="green",shape="box"];1381[label="xw41",fontsize=16,color="green",shape="box"];1382[label="[]",fontsize=16,color="green",shape="box"];1379[label="List.nubByNubBy' (==) xw106 (xw107 : xw108)",fontsize=16,color="burlywood",shape="triangle"];2080[label="xw106/xw1060 : xw1061",fontsize=10,color="white",style="solid",shape="box"];1379 -> 2080[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2080 -> 1554[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2081[label="xw106/[]",fontsize=10,color="white",style="solid",shape="box"];1379 -> 2081[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2081 -> 1555[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	278[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];278 -> 306[label="",style="solid", color="black", weight=3];
16.41/6.09	279[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];279 -> 307[label="",style="solid", color="black", weight=3];
16.41/6.09	280[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];280 -> 308[label="",style="solid", color="black", weight=3];
16.41/6.09	281[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];281 -> 309[label="",style="solid", color="black", weight=3];
16.41/6.09	282[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];282 -> 310[label="",style="solid", color="black", weight=3];
16.41/6.09	283[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];283 -> 311[label="",style="solid", color="black", weight=3];
16.41/6.09	284[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];284 -> 312[label="",style="solid", color="black", weight=3];
16.41/6.09	285[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];285 -> 313[label="",style="solid", color="black", weight=3];
16.41/6.09	286[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];286 -> 314[label="",style="solid", color="black", weight=3];
16.41/6.09	287[label="(==) xw10 xw90",fontsize=16,color="burlywood",shape="triangle"];2082[label="xw10/LT",fontsize=10,color="white",style="solid",shape="box"];287 -> 2082[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2082 -> 315[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2083[label="xw10/EQ",fontsize=10,color="white",style="solid",shape="box"];287 -> 2083[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2083 -> 316[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2084[label="xw10/GT",fontsize=10,color="white",style="solid",shape="box"];287 -> 2084[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2084 -> 317[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	288[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];288 -> 318[label="",style="solid", color="black", weight=3];
16.41/6.09	289[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];289 -> 319[label="",style="solid", color="black", weight=3];
16.41/6.09	290[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];290 -> 320[label="",style="solid", color="black", weight=3];
16.41/6.09	291[label="(==) xw10 xw90",fontsize=16,color="black",shape="triangle"];291 -> 321[label="",style="solid", color="black", weight=3];
16.41/6.09	292[label="List.deleteBy0 xw17 xw18 (==) xw19 False",fontsize=16,color="black",shape="box"];292 -> 322[label="",style="solid", color="black", weight=3];
16.41/6.09	293[label="List.deleteBy0 xw17 xw18 (==) xw19 True",fontsize=16,color="black",shape="box"];293 -> 323[label="",style="solid", color="black", weight=3];
16.41/6.09	1554[label="List.nubByNubBy' (==) (xw1060 : xw1061) (xw107 : xw108)",fontsize=16,color="black",shape="box"];1554 -> 1556[label="",style="solid", color="black", weight=3];
16.41/6.09	1555[label="List.nubByNubBy' (==) [] (xw107 : xw108)",fontsize=16,color="black",shape="box"];1555 -> 1557[label="",style="solid", color="black", weight=3];
16.41/6.09	306[label="error []",fontsize=16,color="red",shape="box"];307[label="error []",fontsize=16,color="red",shape="box"];308[label="error []",fontsize=16,color="red",shape="box"];309[label="error []",fontsize=16,color="red",shape="box"];310[label="error []",fontsize=16,color="red",shape="box"];311[label="error []",fontsize=16,color="red",shape="box"];312[label="error []",fontsize=16,color="red",shape="box"];313[label="error []",fontsize=16,color="red",shape="box"];314[label="error []",fontsize=16,color="red",shape="box"];315[label="(==) LT xw90",fontsize=16,color="burlywood",shape="box"];2085[label="xw90/LT",fontsize=10,color="white",style="solid",shape="box"];315 -> 2085[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2085 -> 330[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2086[label="xw90/EQ",fontsize=10,color="white",style="solid",shape="box"];315 -> 2086[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2086 -> 331[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2087[label="xw90/GT",fontsize=10,color="white",style="solid",shape="box"];315 -> 2087[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2087 -> 332[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	316[label="(==) EQ xw90",fontsize=16,color="burlywood",shape="box"];2088[label="xw90/LT",fontsize=10,color="white",style="solid",shape="box"];316 -> 2088[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2088 -> 333[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2089[label="xw90/EQ",fontsize=10,color="white",style="solid",shape="box"];316 -> 2089[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2089 -> 334[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2090[label="xw90/GT",fontsize=10,color="white",style="solid",shape="box"];316 -> 2090[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2090 -> 335[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	317[label="(==) GT xw90",fontsize=16,color="burlywood",shape="box"];2091[label="xw90/LT",fontsize=10,color="white",style="solid",shape="box"];317 -> 2091[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2091 -> 336[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2092[label="xw90/EQ",fontsize=10,color="white",style="solid",shape="box"];317 -> 2092[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2092 -> 337[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2093[label="xw90/GT",fontsize=10,color="white",style="solid",shape="box"];317 -> 2093[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2093 -> 338[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	318[label="error []",fontsize=16,color="red",shape="box"];319[label="error []",fontsize=16,color="red",shape="box"];320[label="error []",fontsize=16,color="red",shape="box"];321[label="error []",fontsize=16,color="red",shape="box"];322[label="xw18 : List.deleteBy (==) xw19 xw17",fontsize=16,color="green",shape="box"];322 -> 339[label="",style="dashed", color="green", weight=3];
16.41/6.09	323[label="xw17",fontsize=16,color="green",shape="box"];1556[label="List.nubByNubBy'2 (==) (xw1060 : xw1061) (xw107 : xw108)",fontsize=16,color="black",shape="box"];1556 -> 1558[label="",style="solid", color="black", weight=3];
16.41/6.09	1557[label="List.nubByNubBy'3 (==) [] (xw107 : xw108)",fontsize=16,color="black",shape="box"];1557 -> 1559[label="",style="solid", color="black", weight=3];
16.41/6.09	330[label="(==) LT LT",fontsize=16,color="black",shape="box"];330 -> 342[label="",style="solid", color="black", weight=3];
16.41/6.09	331[label="(==) LT EQ",fontsize=16,color="black",shape="box"];331 -> 343[label="",style="solid", color="black", weight=3];
16.41/6.09	332[label="(==) LT GT",fontsize=16,color="black",shape="box"];332 -> 344[label="",style="solid", color="black", weight=3];
16.41/6.09	333[label="(==) EQ LT",fontsize=16,color="black",shape="box"];333 -> 345[label="",style="solid", color="black", weight=3];
16.41/6.09	334[label="(==) EQ EQ",fontsize=16,color="black",shape="box"];334 -> 346[label="",style="solid", color="black", weight=3];
16.41/6.09	335[label="(==) EQ GT",fontsize=16,color="black",shape="box"];335 -> 347[label="",style="solid", color="black", weight=3];
16.41/6.09	336[label="(==) GT LT",fontsize=16,color="black",shape="box"];336 -> 348[label="",style="solid", color="black", weight=3];
16.41/6.09	337[label="(==) GT EQ",fontsize=16,color="black",shape="box"];337 -> 349[label="",style="solid", color="black", weight=3];
16.41/6.09	338[label="(==) GT GT",fontsize=16,color="black",shape="box"];338 -> 350[label="",style="solid", color="black", weight=3];
16.41/6.09	339 -> 238[label="",style="dashed", color="red", weight=0];
16.41/6.09	339[label="List.deleteBy (==) xw19 xw17",fontsize=16,color="magenta"];339 -> 351[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	339 -> 352[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1558[label="List.nubByNubBy'1 (==) xw1060 xw1061 (xw107 : xw108) (List.elem_by (==) xw1060 (xw107 : xw108))",fontsize=16,color="black",shape="box"];1558 -> 1560[label="",style="solid", color="black", weight=3];
16.41/6.09	1559[label="[]",fontsize=16,color="green",shape="box"];342[label="True",fontsize=16,color="green",shape="box"];343[label="False",fontsize=16,color="green",shape="box"];344[label="False",fontsize=16,color="green",shape="box"];345[label="False",fontsize=16,color="green",shape="box"];346[label="True",fontsize=16,color="green",shape="box"];347[label="False",fontsize=16,color="green",shape="box"];348[label="False",fontsize=16,color="green",shape="box"];349[label="False",fontsize=16,color="green",shape="box"];350[label="True",fontsize=16,color="green",shape="box"];351[label="xw17",fontsize=16,color="green",shape="box"];352[label="xw19",fontsize=16,color="green",shape="box"];1560 -> 1936[label="",style="dashed", color="red", weight=0];
16.41/6.09	1560[label="List.nubByNubBy'1 (==) xw1060 xw1061 (xw107 : xw108) ((==) xw107 xw1060 || List.elem_by (==) xw1060 xw108)",fontsize=16,color="magenta"];1560 -> 1937[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1560 -> 1938[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1560 -> 1939[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1560 -> 1940[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1560 -> 1941[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1560 -> 1942[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1937[label="xw107",fontsize=16,color="green",shape="box"];1938[label="xw108",fontsize=16,color="green",shape="box"];1939[label="xw1061",fontsize=16,color="green",shape="box"];1940[label="(==) xw107 xw1060",fontsize=16,color="blue",shape="box"];2094[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];1940 -> 2094[label="",style="solid", color="blue", weight=9];
16.41/6.09	2094 -> 1949[label="",style="solid", color="blue", weight=3];
16.41/6.09	2095[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];1940 -> 2095[label="",style="solid", color="blue", weight=9];
16.41/6.09	2095 -> 1950[label="",style="solid", color="blue", weight=3];
16.41/6.09	2096[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];1940 -> 2096[label="",style="solid", color="blue", weight=9];
16.41/6.09	2096 -> 1951[label="",style="solid", color="blue", weight=3];
16.41/6.09	2097[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];1940 -> 2097[label="",style="solid", color="blue", weight=9];
16.41/6.09	2097 -> 1952[label="",style="solid", color="blue", weight=3];
16.41/6.09	2098[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];1940 -> 2098[label="",style="solid", color="blue", weight=9];
16.41/6.09	2098 -> 1953[label="",style="solid", color="blue", weight=3];
16.41/6.09	2099[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];1940 -> 2099[label="",style="solid", color="blue", weight=9];
16.41/6.09	2099 -> 1954[label="",style="solid", color="blue", weight=3];
16.41/6.09	2100[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];1940 -> 2100[label="",style="solid", color="blue", weight=9];
16.41/6.09	2100 -> 1955[label="",style="solid", color="blue", weight=3];
16.41/6.09	2101[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];1940 -> 2101[label="",style="solid", color="blue", weight=9];
16.41/6.09	2101 -> 1956[label="",style="solid", color="blue", weight=3];
16.41/6.09	2102[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];1940 -> 2102[label="",style="solid", color="blue", weight=9];
16.41/6.09	2102 -> 1957[label="",style="solid", color="blue", weight=3];
16.41/6.09	2103[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];1940 -> 2103[label="",style="solid", color="blue", weight=9];
16.41/6.09	2103 -> 1958[label="",style="solid", color="blue", weight=3];
16.41/6.09	2104[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];1940 -> 2104[label="",style="solid", color="blue", weight=9];
16.41/6.09	2104 -> 1959[label="",style="solid", color="blue", weight=3];
16.41/6.09	2105[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];1940 -> 2105[label="",style="solid", color="blue", weight=9];
16.41/6.09	2105 -> 1960[label="",style="solid", color="blue", weight=3];
16.41/6.09	2106[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];1940 -> 2106[label="",style="solid", color="blue", weight=9];
16.41/6.09	2106 -> 1961[label="",style="solid", color="blue", weight=3];
16.41/6.09	2107[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];1940 -> 2107[label="",style="solid", color="blue", weight=9];
16.41/6.09	2107 -> 1962[label="",style="solid", color="blue", weight=3];
16.41/6.09	1941[label="xw1060",fontsize=16,color="green",shape="box"];1942[label="xw108",fontsize=16,color="green",shape="box"];1936[label="List.nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) (xw202 || List.elem_by (==) xw198 xw203)",fontsize=16,color="burlywood",shape="triangle"];2108[label="xw202/False",fontsize=10,color="white",style="solid",shape="box"];1936 -> 2108[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2108 -> 1963[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2109[label="xw202/True",fontsize=10,color="white",style="solid",shape="box"];1936 -> 2109[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2109 -> 1964[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	1949 -> 278[label="",style="dashed", color="red", weight=0];
16.41/6.09	1949[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1949 -> 1965[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1949 -> 1966[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1950 -> 279[label="",style="dashed", color="red", weight=0];
16.41/6.09	1950[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1950 -> 1967[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1950 -> 1968[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1951 -> 280[label="",style="dashed", color="red", weight=0];
16.41/6.09	1951[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1951 -> 1969[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1951 -> 1970[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1952 -> 281[label="",style="dashed", color="red", weight=0];
16.41/6.09	1952[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1952 -> 1971[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1952 -> 1972[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1953 -> 282[label="",style="dashed", color="red", weight=0];
16.41/6.09	1953[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1953 -> 1973[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1953 -> 1974[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1954 -> 283[label="",style="dashed", color="red", weight=0];
16.41/6.09	1954[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1954 -> 1975[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1954 -> 1976[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1955 -> 284[label="",style="dashed", color="red", weight=0];
16.41/6.09	1955[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1955 -> 1977[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1955 -> 1978[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1956 -> 285[label="",style="dashed", color="red", weight=0];
16.41/6.09	1956[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1956 -> 1979[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1956 -> 1980[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1957 -> 286[label="",style="dashed", color="red", weight=0];
16.41/6.09	1957[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1957 -> 1981[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1957 -> 1982[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1958 -> 287[label="",style="dashed", color="red", weight=0];
16.41/6.09	1958[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1958 -> 1983[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1958 -> 1984[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1959 -> 288[label="",style="dashed", color="red", weight=0];
16.41/6.09	1959[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1959 -> 1985[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1959 -> 1986[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1960 -> 289[label="",style="dashed", color="red", weight=0];
16.41/6.09	1960[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1960 -> 1987[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1960 -> 1988[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1961 -> 290[label="",style="dashed", color="red", weight=0];
16.41/6.09	1961[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1961 -> 1989[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1961 -> 1990[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1962 -> 291[label="",style="dashed", color="red", weight=0];
16.41/6.09	1962[label="(==) xw107 xw1060",fontsize=16,color="magenta"];1962 -> 1991[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1962 -> 1992[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1963[label="List.nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) (False || List.elem_by (==) xw198 xw203)",fontsize=16,color="black",shape="box"];1963 -> 1993[label="",style="solid", color="black", weight=3];
16.41/6.09	1964[label="List.nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) (True || List.elem_by (==) xw198 xw203)",fontsize=16,color="black",shape="box"];1964 -> 1994[label="",style="solid", color="black", weight=3];
16.41/6.09	1965[label="xw1060",fontsize=16,color="green",shape="box"];1966[label="xw107",fontsize=16,color="green",shape="box"];1967[label="xw1060",fontsize=16,color="green",shape="box"];1968[label="xw107",fontsize=16,color="green",shape="box"];1969[label="xw1060",fontsize=16,color="green",shape="box"];1970[label="xw107",fontsize=16,color="green",shape="box"];1971[label="xw1060",fontsize=16,color="green",shape="box"];1972[label="xw107",fontsize=16,color="green",shape="box"];1973[label="xw1060",fontsize=16,color="green",shape="box"];1974[label="xw107",fontsize=16,color="green",shape="box"];1975[label="xw1060",fontsize=16,color="green",shape="box"];1976[label="xw107",fontsize=16,color="green",shape="box"];1977[label="xw1060",fontsize=16,color="green",shape="box"];1978[label="xw107",fontsize=16,color="green",shape="box"];1979[label="xw1060",fontsize=16,color="green",shape="box"];1980[label="xw107",fontsize=16,color="green",shape="box"];1981[label="xw1060",fontsize=16,color="green",shape="box"];1982[label="xw107",fontsize=16,color="green",shape="box"];1983[label="xw1060",fontsize=16,color="green",shape="box"];1984[label="xw107",fontsize=16,color="green",shape="box"];1985[label="xw1060",fontsize=16,color="green",shape="box"];1986[label="xw107",fontsize=16,color="green",shape="box"];1987[label="xw1060",fontsize=16,color="green",shape="box"];1988[label="xw107",fontsize=16,color="green",shape="box"];1989[label="xw1060",fontsize=16,color="green",shape="box"];1990[label="xw107",fontsize=16,color="green",shape="box"];1991[label="xw1060",fontsize=16,color="green",shape="box"];1992[label="xw107",fontsize=16,color="green",shape="box"];1993[label="List.nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) (List.elem_by (==) xw198 xw203)",fontsize=16,color="burlywood",shape="box"];2110[label="xw203/xw2030 : xw2031",fontsize=10,color="white",style="solid",shape="box"];1993 -> 2110[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2110 -> 1995[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	2111[label="xw203/[]",fontsize=10,color="white",style="solid",shape="box"];1993 -> 2111[label="",style="solid", color="burlywood", weight=9];
16.41/6.09	2111 -> 1996[label="",style="solid", color="burlywood", weight=3];
16.41/6.09	1994[label="List.nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) True",fontsize=16,color="black",shape="box"];1994 -> 1997[label="",style="solid", color="black", weight=3];
16.41/6.09	1995[label="List.nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) (List.elem_by (==) xw198 (xw2030 : xw2031))",fontsize=16,color="black",shape="box"];1995 -> 1998[label="",style="solid", color="black", weight=3];
16.41/6.09	1996[label="List.nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) (List.elem_by (==) xw198 [])",fontsize=16,color="black",shape="box"];1996 -> 1999[label="",style="solid", color="black", weight=3];
16.41/6.09	1997 -> 1379[label="",style="dashed", color="red", weight=0];
16.41/6.09	1997[label="List.nubByNubBy' (==) xw199 (xw200 : xw201)",fontsize=16,color="magenta"];1997 -> 2000[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1997 -> 2001[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1997 -> 2002[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1998 -> 1936[label="",style="dashed", color="red", weight=0];
16.41/6.09	1998[label="List.nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) ((==) xw2030 xw198 || List.elem_by (==) xw198 xw2031)",fontsize=16,color="magenta"];1998 -> 2003[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1998 -> 2004[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	1999[label="List.nubByNubBy'1 (==) xw198 xw199 (xw200 : xw201) False",fontsize=16,color="black",shape="box"];1999 -> 2005[label="",style="solid", color="black", weight=3];
16.41/6.09	2000[label="xw200",fontsize=16,color="green",shape="box"];2001[label="xw199",fontsize=16,color="green",shape="box"];2002[label="xw201",fontsize=16,color="green",shape="box"];2003[label="(==) xw2030 xw198",fontsize=16,color="blue",shape="box"];2112[label="== :: ((@3) a b c) -> ((@3) a b c) -> Bool",fontsize=10,color="white",style="solid",shape="box"];2003 -> 2112[label="",style="solid", color="blue", weight=9];
16.41/6.09	2112 -> 2006[label="",style="solid", color="blue", weight=3];
16.41/6.09	2113[label="== :: (Either a b) -> (Either a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];2003 -> 2113[label="",style="solid", color="blue", weight=9];
16.41/6.09	2113 -> 2007[label="",style="solid", color="blue", weight=3];
16.41/6.09	2114[label="== :: Bool -> Bool -> Bool",fontsize=10,color="white",style="solid",shape="box"];2003 -> 2114[label="",style="solid", color="blue", weight=9];
16.41/6.09	2114 -> 2008[label="",style="solid", color="blue", weight=3];
16.41/6.09	2115[label="== :: ((@2) a b) -> ((@2) a b) -> Bool",fontsize=10,color="white",style="solid",shape="box"];2003 -> 2115[label="",style="solid", color="blue", weight=9];
16.41/6.09	2115 -> 2009[label="",style="solid", color="blue", weight=3];
16.41/6.09	2116[label="== :: Float -> Float -> Bool",fontsize=10,color="white",style="solid",shape="box"];2003 -> 2116[label="",style="solid", color="blue", weight=9];
16.41/6.09	2116 -> 2010[label="",style="solid", color="blue", weight=3];
16.41/6.09	2117[label="== :: Char -> Char -> Bool",fontsize=10,color="white",style="solid",shape="box"];2003 -> 2117[label="",style="solid", color="blue", weight=9];
16.41/6.09	2117 -> 2011[label="",style="solid", color="blue", weight=3];
16.41/6.09	2118[label="== :: ([] a) -> ([] a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];2003 -> 2118[label="",style="solid", color="blue", weight=9];
16.41/6.09	2118 -> 2012[label="",style="solid", color="blue", weight=3];
16.41/6.09	2119[label="== :: Double -> Double -> Bool",fontsize=10,color="white",style="solid",shape="box"];2003 -> 2119[label="",style="solid", color="blue", weight=9];
16.41/6.09	2119 -> 2013[label="",style="solid", color="blue", weight=3];
16.41/6.09	2120[label="== :: Integer -> Integer -> Bool",fontsize=10,color="white",style="solid",shape="box"];2003 -> 2120[label="",style="solid", color="blue", weight=9];
16.41/6.09	2120 -> 2014[label="",style="solid", color="blue", weight=3];
16.41/6.09	2121[label="== :: Ordering -> Ordering -> Bool",fontsize=10,color="white",style="solid",shape="box"];2003 -> 2121[label="",style="solid", color="blue", weight=9];
16.41/6.09	2121 -> 2015[label="",style="solid", color="blue", weight=3];
16.41/6.09	2122[label="== :: Int -> Int -> Bool",fontsize=10,color="white",style="solid",shape="box"];2003 -> 2122[label="",style="solid", color="blue", weight=9];
16.41/6.09	2122 -> 2016[label="",style="solid", color="blue", weight=3];
16.41/6.09	2123[label="== :: (Maybe a) -> (Maybe a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];2003 -> 2123[label="",style="solid", color="blue", weight=9];
16.41/6.09	2123 -> 2017[label="",style="solid", color="blue", weight=3];
16.41/6.09	2124[label="== :: (Ratio a) -> (Ratio a) -> Bool",fontsize=10,color="white",style="solid",shape="box"];2003 -> 2124[label="",style="solid", color="blue", weight=9];
16.41/6.09	2124 -> 2018[label="",style="solid", color="blue", weight=3];
16.41/6.09	2125[label="== :: () -> () -> Bool",fontsize=10,color="white",style="solid",shape="box"];2003 -> 2125[label="",style="solid", color="blue", weight=9];
16.41/6.09	2125 -> 2019[label="",style="solid", color="blue", weight=3];
16.41/6.09	2004[label="xw2031",fontsize=16,color="green",shape="box"];2005[label="List.nubByNubBy'0 (==) xw198 xw199 (xw200 : xw201) otherwise",fontsize=16,color="black",shape="box"];2005 -> 2020[label="",style="solid", color="black", weight=3];
16.41/6.09	2006 -> 278[label="",style="dashed", color="red", weight=0];
16.41/6.09	2006[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2006 -> 2021[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2006 -> 2022[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2007 -> 279[label="",style="dashed", color="red", weight=0];
16.41/6.09	2007[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2007 -> 2023[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2007 -> 2024[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2008 -> 280[label="",style="dashed", color="red", weight=0];
16.41/6.09	2008[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2008 -> 2025[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2008 -> 2026[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2009 -> 281[label="",style="dashed", color="red", weight=0];
16.41/6.09	2009[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2009 -> 2027[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2009 -> 2028[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2010 -> 282[label="",style="dashed", color="red", weight=0];
16.41/6.09	2010[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2010 -> 2029[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2010 -> 2030[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2011 -> 283[label="",style="dashed", color="red", weight=0];
16.41/6.09	2011[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2011 -> 2031[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2011 -> 2032[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2012 -> 284[label="",style="dashed", color="red", weight=0];
16.41/6.09	2012[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2012 -> 2033[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2012 -> 2034[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2013 -> 285[label="",style="dashed", color="red", weight=0];
16.41/6.09	2013[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2013 -> 2035[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2013 -> 2036[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2014 -> 286[label="",style="dashed", color="red", weight=0];
16.41/6.09	2014[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2014 -> 2037[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2014 -> 2038[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2015 -> 287[label="",style="dashed", color="red", weight=0];
16.41/6.09	2015[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2015 -> 2039[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2015 -> 2040[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2016 -> 288[label="",style="dashed", color="red", weight=0];
16.41/6.09	2016[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2016 -> 2041[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2016 -> 2042[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2017 -> 289[label="",style="dashed", color="red", weight=0];
16.41/6.09	2017[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2017 -> 2043[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2017 -> 2044[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2018 -> 290[label="",style="dashed", color="red", weight=0];
16.41/6.09	2018[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2018 -> 2045[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2018 -> 2046[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2019 -> 291[label="",style="dashed", color="red", weight=0];
16.41/6.09	2019[label="(==) xw2030 xw198",fontsize=16,color="magenta"];2019 -> 2047[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2019 -> 2048[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2020[label="List.nubByNubBy'0 (==) xw198 xw199 (xw200 : xw201) True",fontsize=16,color="black",shape="box"];2020 -> 2049[label="",style="solid", color="black", weight=3];
16.41/6.09	2021[label="xw198",fontsize=16,color="green",shape="box"];2022[label="xw2030",fontsize=16,color="green",shape="box"];2023[label="xw198",fontsize=16,color="green",shape="box"];2024[label="xw2030",fontsize=16,color="green",shape="box"];2025[label="xw198",fontsize=16,color="green",shape="box"];2026[label="xw2030",fontsize=16,color="green",shape="box"];2027[label="xw198",fontsize=16,color="green",shape="box"];2028[label="xw2030",fontsize=16,color="green",shape="box"];2029[label="xw198",fontsize=16,color="green",shape="box"];2030[label="xw2030",fontsize=16,color="green",shape="box"];2031[label="xw198",fontsize=16,color="green",shape="box"];2032[label="xw2030",fontsize=16,color="green",shape="box"];2033[label="xw198",fontsize=16,color="green",shape="box"];2034[label="xw2030",fontsize=16,color="green",shape="box"];2035[label="xw198",fontsize=16,color="green",shape="box"];2036[label="xw2030",fontsize=16,color="green",shape="box"];2037[label="xw198",fontsize=16,color="green",shape="box"];2038[label="xw2030",fontsize=16,color="green",shape="box"];2039[label="xw198",fontsize=16,color="green",shape="box"];2040[label="xw2030",fontsize=16,color="green",shape="box"];2041[label="xw198",fontsize=16,color="green",shape="box"];2042[label="xw2030",fontsize=16,color="green",shape="box"];2043[label="xw198",fontsize=16,color="green",shape="box"];2044[label="xw2030",fontsize=16,color="green",shape="box"];2045[label="xw198",fontsize=16,color="green",shape="box"];2046[label="xw2030",fontsize=16,color="green",shape="box"];2047[label="xw198",fontsize=16,color="green",shape="box"];2048[label="xw2030",fontsize=16,color="green",shape="box"];2049[label="xw198 : List.nubByNubBy' (==) xw199 (xw198 : xw200 : xw201)",fontsize=16,color="green",shape="box"];2049 -> 2050[label="",style="dashed", color="green", weight=3];
16.41/6.09	2050 -> 1379[label="",style="dashed", color="red", weight=0];
16.41/6.09	2050[label="List.nubByNubBy' (==) xw199 (xw198 : xw200 : xw201)",fontsize=16,color="magenta"];2050 -> 2051[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2050 -> 2052[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2050 -> 2053[label="",style="dashed", color="magenta", weight=3];
16.41/6.09	2051[label="xw198",fontsize=16,color="green",shape="box"];2052[label="xw199",fontsize=16,color="green",shape="box"];2053[label="xw200 : xw201",fontsize=16,color="green",shape="box"];}
16.41/6.09	
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(10)
16.41/6.09	Complex Obligation (AND)
16.41/6.09	
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(11)
16.41/6.09	Obligation:
16.41/6.09	Q DP problem:
16.41/6.09	The TRS P consists of the following rules:
16.41/6.09	
16.41/6.09	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) -> new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba)
16.41/6.09	   new_nubByNubBy'(:(xw1060, xw1061), xw107, xw108, bb) -> new_nubByNubBy'1(xw1060, xw1061, xw107, xw108, new_esEs0(xw107, xw1060, bb), xw108, bb)
16.41/6.09	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) -> new_nubByNubBy'(xw199, xw200, xw201, ba)
16.41/6.09	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, :(xw2030, xw2031), ba) -> new_nubByNubBy'1(xw198, xw199, xw200, xw201, new_esEs(xw2030, xw198, ba), xw2031, ba)
16.41/6.09	
16.41/6.09	The TRS R consists of the following rules:
16.41/6.09	
16.41/6.09	   new_esEs10(EQ, GT) -> False
16.41/6.09	   new_esEs10(GT, EQ) -> False
16.41/6.09	   new_esEs5(xw10, xw90) -> error([])
16.41/6.09	   new_esEs10(LT, GT) -> False
16.41/6.09	   new_esEs10(GT, LT) -> False
16.41/6.09	   new_esEs1(xw10, xw90) -> error([])
16.41/6.09	   new_esEs2(xw10, xw90, bc, bd) -> error([])
16.41/6.09	   new_esEs0(xw107, xw1060, app(ty_Maybe, ed)) -> new_esEs12(xw107, xw1060, ed)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Bool) -> new_esEs5(xw2030, xw198)
16.41/6.09	   new_esEs(xw2030, xw198, ty_@0) -> new_esEs14(xw2030, xw198)
16.41/6.09	   new_esEs4(xw10, xw90, da, db, dc) -> error([])
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Ordering) -> new_esEs10(xw107, xw1060)
16.41/6.09	   new_esEs(xw2030, xw198, app(app(ty_@2, cc), cd)) -> new_esEs6(xw2030, xw198, cc, cd)
16.41/6.09	   new_esEs(xw2030, xw198, app(app(ty_Either, ca), cb)) -> new_esEs2(xw2030, xw198, ca, cb)
16.41/6.09	   new_esEs9(xw10, xw90) -> error([])
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Integer) -> new_esEs9(xw107, xw1060)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Char) -> new_esEs7(xw2030, xw198)
16.41/6.09	   new_esEs6(xw10, xw90, eg, eh) -> error([])
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Double) -> new_esEs8(xw107, xw1060)
16.41/6.09	   new_esEs(xw2030, xw198, app(ty_Maybe, cf)) -> new_esEs12(xw2030, xw198, cf)
16.41/6.09	   new_esEs0(xw107, xw1060, app(ty_[], ec)) -> new_esEs3(xw107, xw1060, ec)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Double) -> new_esEs8(xw2030, xw198)
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Char) -> new_esEs7(xw107, xw1060)
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Int) -> new_esEs11(xw107, xw1060)
16.41/6.09	   new_esEs3(xw10, xw90, be) -> error([])
16.41/6.09	   new_esEs8(xw10, xw90) -> error([])
16.41/6.09	   new_esEs(xw2030, xw198, ty_Ordering) -> new_esEs10(xw2030, xw198)
16.41/6.09	   new_esEs10(EQ, EQ) -> True
16.41/6.09	   new_esEs0(xw107, xw1060, ty_@0) -> new_esEs14(xw107, xw1060)
16.41/6.09	   new_esEs11(xw10, xw90) -> error([])
16.41/6.09	   new_esEs0(xw107, xw1060, app(app(ty_@2, ea), eb)) -> new_esEs6(xw107, xw1060, ea, eb)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Integer) -> new_esEs9(xw2030, xw198)
16.41/6.09	   new_esEs7(xw10, xw90) -> error([])
16.41/6.09	   new_esEs(xw2030, xw198, app(ty_[], ce)) -> new_esEs3(xw2030, xw198, ce)
16.41/6.09	   new_esEs0(xw107, xw1060, app(ty_Ratio, ee)) -> new_esEs13(xw107, xw1060, ee)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Int) -> new_esEs11(xw2030, xw198)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Float) -> new_esEs1(xw2030, xw198)
16.41/6.09	   new_esEs(xw2030, xw198, app(ty_Ratio, cg)) -> new_esEs13(xw2030, xw198, cg)
16.41/6.09	   new_esEs0(xw107, xw1060, app(app(app(ty_@3, dd), de), df)) -> new_esEs4(xw107, xw1060, dd, de, df)
16.41/6.09	   new_esEs10(LT, LT) -> True
16.41/6.09	   new_esEs14(xw10, xw90) -> error([])
16.41/6.09	   new_esEs12(xw10, xw90, ef) -> error([])
16.41/6.09	   new_esEs13(xw10, xw90, fa) -> error([])
16.41/6.09	   new_esEs10(LT, EQ) -> False
16.41/6.09	   new_esEs10(EQ, LT) -> False
16.41/6.09	   new_esEs10(GT, GT) -> True
16.41/6.09	   new_esEs0(xw107, xw1060, app(app(ty_Either, dg), dh)) -> new_esEs2(xw107, xw1060, dg, dh)
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Bool) -> new_esEs5(xw107, xw1060)
16.41/6.09	   new_esEs(xw2030, xw198, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs4(xw2030, xw198, bf, bg, bh)
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Float) -> new_esEs1(xw107, xw1060)
16.41/6.09	
16.41/6.09	The set Q consists of the following terms:
16.41/6.09	
16.41/6.09	   new_esEs0(x0, x1, ty_Int)
16.41/6.09	   new_esEs(x0, x1, ty_Integer)
16.41/6.09	   new_esEs7(x0, x1)
16.41/6.09	   new_esEs10(GT, GT)
16.41/6.09	   new_esEs0(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.09	   new_esEs0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.09	   new_esEs14(x0, x1)
16.41/6.09	   new_esEs5(x0, x1)
16.41/6.09	   new_esEs(x0, x1, ty_Char)
16.41/6.09	   new_esEs13(x0, x1, x2)
16.41/6.09	   new_esEs10(LT, EQ)
16.41/6.09	   new_esEs10(EQ, LT)
16.41/6.09	   new_esEs3(x0, x1, x2)
16.41/6.09	   new_esEs(x0, x1, ty_Double)
16.41/6.09	   new_esEs10(LT, GT)
16.41/6.09	   new_esEs10(GT, LT)
16.41/6.09	   new_esEs11(x0, x1)
16.41/6.09	   new_esEs0(x0, x1, ty_Integer)
16.41/6.09	   new_esEs0(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.09	   new_esEs(x0, x1, ty_Float)
16.41/6.09	   new_esEs8(x0, x1)
16.41/6.09	   new_esEs10(EQ, EQ)
16.41/6.09	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.09	   new_esEs(x0, x1, ty_Ordering)
16.41/6.09	   new_esEs0(x0, x1, ty_Float)
16.41/6.09	   new_esEs6(x0, x1, x2, x3)
16.41/6.09	   new_esEs0(x0, x1, app(ty_[], x2))
16.41/6.09	   new_esEs0(x0, x1, ty_Bool)
16.41/6.09	   new_esEs0(x0, x1, app(ty_Maybe, x2))
16.41/6.09	   new_esEs0(x0, x1, app(ty_Ratio, x2))
16.41/6.09	   new_esEs(x0, x1, ty_Bool)
16.41/6.09	   new_esEs0(x0, x1, ty_Ordering)
16.41/6.09	   new_esEs0(x0, x1, ty_Double)
16.41/6.09	   new_esEs(x0, x1, app(ty_Maybe, x2))
16.41/6.09	   new_esEs(x0, x1, app(ty_Ratio, x2))
16.41/6.09	   new_esEs1(x0, x1)
16.41/6.09	   new_esEs(x0, x1, app(ty_[], x2))
16.41/6.09	   new_esEs0(x0, x1, ty_Char)
16.41/6.09	   new_esEs2(x0, x1, x2, x3)
16.41/6.09	   new_esEs9(x0, x1)
16.41/6.09	   new_esEs0(x0, x1, ty_@0)
16.41/6.09	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.09	   new_esEs(x0, x1, ty_@0)
16.41/6.09	   new_esEs10(EQ, GT)
16.41/6.09	   new_esEs10(GT, EQ)
16.41/6.09	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.09	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.09	   new_esEs12(x0, x1, x2)
16.41/6.09	   new_esEs10(LT, LT)
16.41/6.09	   new_esEs(x0, x1, ty_Int)
16.41/6.09	
16.41/6.09	We have to consider all minimal (P,Q,R)-chains.
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(12) TransformationProof (EQUIVALENT)
16.41/6.09	By narrowing [LPAR04] the rule new_nubByNubBy'(:(xw1060, xw1061), xw107, xw108, bb) -> new_nubByNubBy'1(xw1060, xw1061, xw107, xw108, new_esEs0(xw107, xw1060, bb), xw108, bb) at position [4] we obtained the following new rules [LPAR04]:
16.41/6.09	
16.41/6.09	   (new_nubByNubBy'(:(x1, y1), x0, y3, app(ty_Maybe, x2)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs12(x0, x1, x2), y3, app(ty_Maybe, x2)),new_nubByNubBy'(:(x1, y1), x0, y3, app(ty_Maybe, x2)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs12(x0, x1, x2), y3, app(ty_Maybe, x2)))
16.41/6.09	   (new_nubByNubBy'(:(x1, y1), x0, y3, ty_Ordering) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs10(x0, x1), y3, ty_Ordering),new_nubByNubBy'(:(x1, y1), x0, y3, ty_Ordering) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs10(x0, x1), y3, ty_Ordering))
16.41/6.09	   (new_nubByNubBy'(:(x1, y1), x0, y3, ty_Integer) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs9(x0, x1), y3, ty_Integer),new_nubByNubBy'(:(x1, y1), x0, y3, ty_Integer) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs9(x0, x1), y3, ty_Integer))
16.41/6.09	   (new_nubByNubBy'(:(x1, y1), x0, y3, ty_Double) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs8(x0, x1), y3, ty_Double),new_nubByNubBy'(:(x1, y1), x0, y3, ty_Double) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs8(x0, x1), y3, ty_Double))
16.41/6.09	   (new_nubByNubBy'(:(x1, y1), x0, y3, app(ty_[], x2)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs3(x0, x1, x2), y3, app(ty_[], x2)),new_nubByNubBy'(:(x1, y1), x0, y3, app(ty_[], x2)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs3(x0, x1, x2), y3, app(ty_[], x2)))
16.41/6.09	   (new_nubByNubBy'(:(x1, y1), x0, y3, ty_Char) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs7(x0, x1), y3, ty_Char),new_nubByNubBy'(:(x1, y1), x0, y3, ty_Char) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs7(x0, x1), y3, ty_Char))
16.41/6.09	   (new_nubByNubBy'(:(x1, y1), x0, y3, ty_Int) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs11(x0, x1), y3, ty_Int),new_nubByNubBy'(:(x1, y1), x0, y3, ty_Int) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs11(x0, x1), y3, ty_Int))
16.41/6.09	   (new_nubByNubBy'(:(x1, y1), x0, y3, ty_@0) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs14(x0, x1), y3, ty_@0),new_nubByNubBy'(:(x1, y1), x0, y3, ty_@0) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs14(x0, x1), y3, ty_@0))
16.41/6.09	   (new_nubByNubBy'(:(x1, y1), x0, y3, app(app(ty_@2, x2), x3)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs6(x0, x1, x2, x3), y3, app(app(ty_@2, x2), x3)),new_nubByNubBy'(:(x1, y1), x0, y3, app(app(ty_@2, x2), x3)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs6(x0, x1, x2, x3), y3, app(app(ty_@2, x2), x3)))
16.41/6.09	   (new_nubByNubBy'(:(x1, y1), x0, y3, app(ty_Ratio, x2)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs13(x0, x1, x2), y3, app(ty_Ratio, x2)),new_nubByNubBy'(:(x1, y1), x0, y3, app(ty_Ratio, x2)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs13(x0, x1, x2), y3, app(ty_Ratio, x2)))
16.41/6.09	   (new_nubByNubBy'(:(x1, y1), x0, y3, app(app(app(ty_@3, x2), x3), x4)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs4(x0, x1, x2, x3, x4), y3, app(app(app(ty_@3, x2), x3), x4)),new_nubByNubBy'(:(x1, y1), x0, y3, app(app(app(ty_@3, x2), x3), x4)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs4(x0, x1, x2, x3, x4), y3, app(app(app(ty_@3, x2), x3), x4)))
16.41/6.09	   (new_nubByNubBy'(:(x1, y1), x0, y3, app(app(ty_Either, x2), x3)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs2(x0, x1, x2, x3), y3, app(app(ty_Either, x2), x3)),new_nubByNubBy'(:(x1, y1), x0, y3, app(app(ty_Either, x2), x3)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs2(x0, x1, x2, x3), y3, app(app(ty_Either, x2), x3)))
16.41/6.09	   (new_nubByNubBy'(:(x1, y1), x0, y3, ty_Bool) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs5(x0, x1), y3, ty_Bool),new_nubByNubBy'(:(x1, y1), x0, y3, ty_Bool) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs5(x0, x1), y3, ty_Bool))
16.41/6.09	   (new_nubByNubBy'(:(x1, y1), x0, y3, ty_Float) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs1(x0, x1), y3, ty_Float),new_nubByNubBy'(:(x1, y1), x0, y3, ty_Float) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs1(x0, x1), y3, ty_Float))
16.41/6.09	
16.41/6.09	
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(13)
16.41/6.09	Obligation:
16.41/6.09	Q DP problem:
16.41/6.09	The TRS P consists of the following rules:
16.41/6.09	
16.41/6.09	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) -> new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba)
16.41/6.09	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) -> new_nubByNubBy'(xw199, xw200, xw201, ba)
16.41/6.09	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, :(xw2030, xw2031), ba) -> new_nubByNubBy'1(xw198, xw199, xw200, xw201, new_esEs(xw2030, xw198, ba), xw2031, ba)
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, app(ty_Maybe, x2)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs12(x0, x1, x2), y3, app(ty_Maybe, x2))
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, ty_Ordering) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs10(x0, x1), y3, ty_Ordering)
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, ty_Integer) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs9(x0, x1), y3, ty_Integer)
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, ty_Double) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs8(x0, x1), y3, ty_Double)
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, app(ty_[], x2)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs3(x0, x1, x2), y3, app(ty_[], x2))
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, ty_Char) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs7(x0, x1), y3, ty_Char)
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, ty_Int) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs11(x0, x1), y3, ty_Int)
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, ty_@0) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs14(x0, x1), y3, ty_@0)
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, app(app(ty_@2, x2), x3)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs6(x0, x1, x2, x3), y3, app(app(ty_@2, x2), x3))
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, app(ty_Ratio, x2)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs13(x0, x1, x2), y3, app(ty_Ratio, x2))
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, app(app(app(ty_@3, x2), x3), x4)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs4(x0, x1, x2, x3, x4), y3, app(app(app(ty_@3, x2), x3), x4))
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, app(app(ty_Either, x2), x3)) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs2(x0, x1, x2, x3), y3, app(app(ty_Either, x2), x3))
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, ty_Bool) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs5(x0, x1), y3, ty_Bool)
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, ty_Float) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs1(x0, x1), y3, ty_Float)
16.41/6.09	
16.41/6.09	The TRS R consists of the following rules:
16.41/6.09	
16.41/6.09	   new_esEs10(EQ, GT) -> False
16.41/6.09	   new_esEs10(GT, EQ) -> False
16.41/6.09	   new_esEs5(xw10, xw90) -> error([])
16.41/6.09	   new_esEs10(LT, GT) -> False
16.41/6.09	   new_esEs10(GT, LT) -> False
16.41/6.09	   new_esEs1(xw10, xw90) -> error([])
16.41/6.09	   new_esEs2(xw10, xw90, bc, bd) -> error([])
16.41/6.09	   new_esEs0(xw107, xw1060, app(ty_Maybe, ed)) -> new_esEs12(xw107, xw1060, ed)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Bool) -> new_esEs5(xw2030, xw198)
16.41/6.09	   new_esEs(xw2030, xw198, ty_@0) -> new_esEs14(xw2030, xw198)
16.41/6.09	   new_esEs4(xw10, xw90, da, db, dc) -> error([])
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Ordering) -> new_esEs10(xw107, xw1060)
16.41/6.09	   new_esEs(xw2030, xw198, app(app(ty_@2, cc), cd)) -> new_esEs6(xw2030, xw198, cc, cd)
16.41/6.09	   new_esEs(xw2030, xw198, app(app(ty_Either, ca), cb)) -> new_esEs2(xw2030, xw198, ca, cb)
16.41/6.09	   new_esEs9(xw10, xw90) -> error([])
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Integer) -> new_esEs9(xw107, xw1060)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Char) -> new_esEs7(xw2030, xw198)
16.41/6.09	   new_esEs6(xw10, xw90, eg, eh) -> error([])
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Double) -> new_esEs8(xw107, xw1060)
16.41/6.09	   new_esEs(xw2030, xw198, app(ty_Maybe, cf)) -> new_esEs12(xw2030, xw198, cf)
16.41/6.09	   new_esEs0(xw107, xw1060, app(ty_[], ec)) -> new_esEs3(xw107, xw1060, ec)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Double) -> new_esEs8(xw2030, xw198)
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Char) -> new_esEs7(xw107, xw1060)
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Int) -> new_esEs11(xw107, xw1060)
16.41/6.09	   new_esEs3(xw10, xw90, be) -> error([])
16.41/6.09	   new_esEs8(xw10, xw90) -> error([])
16.41/6.09	   new_esEs(xw2030, xw198, ty_Ordering) -> new_esEs10(xw2030, xw198)
16.41/6.09	   new_esEs10(EQ, EQ) -> True
16.41/6.09	   new_esEs0(xw107, xw1060, ty_@0) -> new_esEs14(xw107, xw1060)
16.41/6.09	   new_esEs11(xw10, xw90) -> error([])
16.41/6.09	   new_esEs0(xw107, xw1060, app(app(ty_@2, ea), eb)) -> new_esEs6(xw107, xw1060, ea, eb)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Integer) -> new_esEs9(xw2030, xw198)
16.41/6.09	   new_esEs7(xw10, xw90) -> error([])
16.41/6.09	   new_esEs(xw2030, xw198, app(ty_[], ce)) -> new_esEs3(xw2030, xw198, ce)
16.41/6.09	   new_esEs0(xw107, xw1060, app(ty_Ratio, ee)) -> new_esEs13(xw107, xw1060, ee)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Int) -> new_esEs11(xw2030, xw198)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Float) -> new_esEs1(xw2030, xw198)
16.41/6.09	   new_esEs(xw2030, xw198, app(ty_Ratio, cg)) -> new_esEs13(xw2030, xw198, cg)
16.41/6.09	   new_esEs0(xw107, xw1060, app(app(app(ty_@3, dd), de), df)) -> new_esEs4(xw107, xw1060, dd, de, df)
16.41/6.09	   new_esEs10(LT, LT) -> True
16.41/6.09	   new_esEs14(xw10, xw90) -> error([])
16.41/6.09	   new_esEs12(xw10, xw90, ef) -> error([])
16.41/6.09	   new_esEs13(xw10, xw90, fa) -> error([])
16.41/6.09	   new_esEs10(LT, EQ) -> False
16.41/6.09	   new_esEs10(EQ, LT) -> False
16.41/6.09	   new_esEs10(GT, GT) -> True
16.41/6.09	   new_esEs0(xw107, xw1060, app(app(ty_Either, dg), dh)) -> new_esEs2(xw107, xw1060, dg, dh)
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Bool) -> new_esEs5(xw107, xw1060)
16.41/6.09	   new_esEs(xw2030, xw198, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs4(xw2030, xw198, bf, bg, bh)
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Float) -> new_esEs1(xw107, xw1060)
16.41/6.09	
16.41/6.09	The set Q consists of the following terms:
16.41/6.09	
16.41/6.09	   new_esEs0(x0, x1, ty_Int)
16.41/6.09	   new_esEs(x0, x1, ty_Integer)
16.41/6.09	   new_esEs7(x0, x1)
16.41/6.09	   new_esEs10(GT, GT)
16.41/6.09	   new_esEs0(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.09	   new_esEs0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.09	   new_esEs14(x0, x1)
16.41/6.09	   new_esEs5(x0, x1)
16.41/6.09	   new_esEs(x0, x1, ty_Char)
16.41/6.09	   new_esEs13(x0, x1, x2)
16.41/6.09	   new_esEs10(LT, EQ)
16.41/6.09	   new_esEs10(EQ, LT)
16.41/6.09	   new_esEs3(x0, x1, x2)
16.41/6.09	   new_esEs(x0, x1, ty_Double)
16.41/6.09	   new_esEs10(LT, GT)
16.41/6.09	   new_esEs10(GT, LT)
16.41/6.09	   new_esEs11(x0, x1)
16.41/6.09	   new_esEs0(x0, x1, ty_Integer)
16.41/6.09	   new_esEs0(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.09	   new_esEs(x0, x1, ty_Float)
16.41/6.09	   new_esEs8(x0, x1)
16.41/6.09	   new_esEs10(EQ, EQ)
16.41/6.09	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.09	   new_esEs(x0, x1, ty_Ordering)
16.41/6.09	   new_esEs0(x0, x1, ty_Float)
16.41/6.09	   new_esEs6(x0, x1, x2, x3)
16.41/6.09	   new_esEs0(x0, x1, app(ty_[], x2))
16.41/6.09	   new_esEs0(x0, x1, ty_Bool)
16.41/6.09	   new_esEs0(x0, x1, app(ty_Maybe, x2))
16.41/6.09	   new_esEs0(x0, x1, app(ty_Ratio, x2))
16.41/6.09	   new_esEs(x0, x1, ty_Bool)
16.41/6.09	   new_esEs0(x0, x1, ty_Ordering)
16.41/6.09	   new_esEs0(x0, x1, ty_Double)
16.41/6.09	   new_esEs(x0, x1, app(ty_Maybe, x2))
16.41/6.09	   new_esEs(x0, x1, app(ty_Ratio, x2))
16.41/6.09	   new_esEs1(x0, x1)
16.41/6.09	   new_esEs(x0, x1, app(ty_[], x2))
16.41/6.09	   new_esEs0(x0, x1, ty_Char)
16.41/6.09	   new_esEs2(x0, x1, x2, x3)
16.41/6.09	   new_esEs9(x0, x1)
16.41/6.09	   new_esEs0(x0, x1, ty_@0)
16.41/6.09	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.09	   new_esEs(x0, x1, ty_@0)
16.41/6.09	   new_esEs10(EQ, GT)
16.41/6.09	   new_esEs10(GT, EQ)
16.41/6.09	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.09	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.09	   new_esEs12(x0, x1, x2)
16.41/6.09	   new_esEs10(LT, LT)
16.41/6.09	   new_esEs(x0, x1, ty_Int)
16.41/6.09	
16.41/6.09	We have to consider all minimal (P,Q,R)-chains.
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(14) DependencyGraphProof (EQUIVALENT)
16.41/6.09	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 13 less nodes.
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(15)
16.41/6.09	Obligation:
16.41/6.09	Q DP problem:
16.41/6.09	The TRS P consists of the following rules:
16.41/6.09	
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, ty_Ordering) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs10(x0, x1), y3, ty_Ordering)
16.41/6.09	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) -> new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba)
16.41/6.09	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) -> new_nubByNubBy'(xw199, xw200, xw201, ba)
16.41/6.09	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, :(xw2030, xw2031), ba) -> new_nubByNubBy'1(xw198, xw199, xw200, xw201, new_esEs(xw2030, xw198, ba), xw2031, ba)
16.41/6.09	
16.41/6.09	The TRS R consists of the following rules:
16.41/6.09	
16.41/6.09	   new_esEs10(EQ, GT) -> False
16.41/6.09	   new_esEs10(GT, EQ) -> False
16.41/6.09	   new_esEs5(xw10, xw90) -> error([])
16.41/6.09	   new_esEs10(LT, GT) -> False
16.41/6.09	   new_esEs10(GT, LT) -> False
16.41/6.09	   new_esEs1(xw10, xw90) -> error([])
16.41/6.09	   new_esEs2(xw10, xw90, bc, bd) -> error([])
16.41/6.09	   new_esEs0(xw107, xw1060, app(ty_Maybe, ed)) -> new_esEs12(xw107, xw1060, ed)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Bool) -> new_esEs5(xw2030, xw198)
16.41/6.09	   new_esEs(xw2030, xw198, ty_@0) -> new_esEs14(xw2030, xw198)
16.41/6.09	   new_esEs4(xw10, xw90, da, db, dc) -> error([])
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Ordering) -> new_esEs10(xw107, xw1060)
16.41/6.09	   new_esEs(xw2030, xw198, app(app(ty_@2, cc), cd)) -> new_esEs6(xw2030, xw198, cc, cd)
16.41/6.09	   new_esEs(xw2030, xw198, app(app(ty_Either, ca), cb)) -> new_esEs2(xw2030, xw198, ca, cb)
16.41/6.09	   new_esEs9(xw10, xw90) -> error([])
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Integer) -> new_esEs9(xw107, xw1060)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Char) -> new_esEs7(xw2030, xw198)
16.41/6.09	   new_esEs6(xw10, xw90, eg, eh) -> error([])
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Double) -> new_esEs8(xw107, xw1060)
16.41/6.09	   new_esEs(xw2030, xw198, app(ty_Maybe, cf)) -> new_esEs12(xw2030, xw198, cf)
16.41/6.09	   new_esEs0(xw107, xw1060, app(ty_[], ec)) -> new_esEs3(xw107, xw1060, ec)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Double) -> new_esEs8(xw2030, xw198)
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Char) -> new_esEs7(xw107, xw1060)
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Int) -> new_esEs11(xw107, xw1060)
16.41/6.09	   new_esEs3(xw10, xw90, be) -> error([])
16.41/6.09	   new_esEs8(xw10, xw90) -> error([])
16.41/6.09	   new_esEs(xw2030, xw198, ty_Ordering) -> new_esEs10(xw2030, xw198)
16.41/6.09	   new_esEs10(EQ, EQ) -> True
16.41/6.09	   new_esEs0(xw107, xw1060, ty_@0) -> new_esEs14(xw107, xw1060)
16.41/6.09	   new_esEs11(xw10, xw90) -> error([])
16.41/6.09	   new_esEs0(xw107, xw1060, app(app(ty_@2, ea), eb)) -> new_esEs6(xw107, xw1060, ea, eb)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Integer) -> new_esEs9(xw2030, xw198)
16.41/6.09	   new_esEs7(xw10, xw90) -> error([])
16.41/6.09	   new_esEs(xw2030, xw198, app(ty_[], ce)) -> new_esEs3(xw2030, xw198, ce)
16.41/6.09	   new_esEs0(xw107, xw1060, app(ty_Ratio, ee)) -> new_esEs13(xw107, xw1060, ee)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Int) -> new_esEs11(xw2030, xw198)
16.41/6.09	   new_esEs(xw2030, xw198, ty_Float) -> new_esEs1(xw2030, xw198)
16.41/6.09	   new_esEs(xw2030, xw198, app(ty_Ratio, cg)) -> new_esEs13(xw2030, xw198, cg)
16.41/6.09	   new_esEs0(xw107, xw1060, app(app(app(ty_@3, dd), de), df)) -> new_esEs4(xw107, xw1060, dd, de, df)
16.41/6.09	   new_esEs10(LT, LT) -> True
16.41/6.09	   new_esEs14(xw10, xw90) -> error([])
16.41/6.09	   new_esEs12(xw10, xw90, ef) -> error([])
16.41/6.09	   new_esEs13(xw10, xw90, fa) -> error([])
16.41/6.09	   new_esEs10(LT, EQ) -> False
16.41/6.09	   new_esEs10(EQ, LT) -> False
16.41/6.09	   new_esEs10(GT, GT) -> True
16.41/6.09	   new_esEs0(xw107, xw1060, app(app(ty_Either, dg), dh)) -> new_esEs2(xw107, xw1060, dg, dh)
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Bool) -> new_esEs5(xw107, xw1060)
16.41/6.09	   new_esEs(xw2030, xw198, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs4(xw2030, xw198, bf, bg, bh)
16.41/6.09	   new_esEs0(xw107, xw1060, ty_Float) -> new_esEs1(xw107, xw1060)
16.41/6.09	
16.41/6.09	The set Q consists of the following terms:
16.41/6.09	
16.41/6.09	   new_esEs0(x0, x1, ty_Int)
16.41/6.09	   new_esEs(x0, x1, ty_Integer)
16.41/6.09	   new_esEs7(x0, x1)
16.41/6.09	   new_esEs10(GT, GT)
16.41/6.09	   new_esEs0(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.09	   new_esEs0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.09	   new_esEs14(x0, x1)
16.41/6.09	   new_esEs5(x0, x1)
16.41/6.09	   new_esEs(x0, x1, ty_Char)
16.41/6.09	   new_esEs13(x0, x1, x2)
16.41/6.09	   new_esEs10(LT, EQ)
16.41/6.09	   new_esEs10(EQ, LT)
16.41/6.09	   new_esEs3(x0, x1, x2)
16.41/6.09	   new_esEs(x0, x1, ty_Double)
16.41/6.09	   new_esEs10(LT, GT)
16.41/6.09	   new_esEs10(GT, LT)
16.41/6.09	   new_esEs11(x0, x1)
16.41/6.09	   new_esEs0(x0, x1, ty_Integer)
16.41/6.09	   new_esEs0(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.09	   new_esEs(x0, x1, ty_Float)
16.41/6.09	   new_esEs8(x0, x1)
16.41/6.09	   new_esEs10(EQ, EQ)
16.41/6.09	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.09	   new_esEs(x0, x1, ty_Ordering)
16.41/6.09	   new_esEs0(x0, x1, ty_Float)
16.41/6.09	   new_esEs6(x0, x1, x2, x3)
16.41/6.09	   new_esEs0(x0, x1, app(ty_[], x2))
16.41/6.09	   new_esEs0(x0, x1, ty_Bool)
16.41/6.09	   new_esEs0(x0, x1, app(ty_Maybe, x2))
16.41/6.09	   new_esEs0(x0, x1, app(ty_Ratio, x2))
16.41/6.09	   new_esEs(x0, x1, ty_Bool)
16.41/6.09	   new_esEs0(x0, x1, ty_Ordering)
16.41/6.09	   new_esEs0(x0, x1, ty_Double)
16.41/6.09	   new_esEs(x0, x1, app(ty_Maybe, x2))
16.41/6.09	   new_esEs(x0, x1, app(ty_Ratio, x2))
16.41/6.09	   new_esEs1(x0, x1)
16.41/6.09	   new_esEs(x0, x1, app(ty_[], x2))
16.41/6.09	   new_esEs0(x0, x1, ty_Char)
16.41/6.09	   new_esEs2(x0, x1, x2, x3)
16.41/6.09	   new_esEs9(x0, x1)
16.41/6.09	   new_esEs0(x0, x1, ty_@0)
16.41/6.09	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.09	   new_esEs(x0, x1, ty_@0)
16.41/6.09	   new_esEs10(EQ, GT)
16.41/6.09	   new_esEs10(GT, EQ)
16.41/6.09	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.09	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.09	   new_esEs12(x0, x1, x2)
16.41/6.09	   new_esEs10(LT, LT)
16.41/6.09	   new_esEs(x0, x1, ty_Int)
16.41/6.09	
16.41/6.09	We have to consider all minimal (P,Q,R)-chains.
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(16) UsableRulesProof (EQUIVALENT)
16.41/6.09	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.
16.41/6.09	----------------------------------------
16.41/6.09	
16.41/6.09	(17)
16.41/6.09	Obligation:
16.41/6.09	Q DP problem:
16.41/6.09	The TRS P consists of the following rules:
16.41/6.09	
16.41/6.09	   new_nubByNubBy'(:(x1, y1), x0, y3, ty_Ordering) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs10(x0, x1), y3, ty_Ordering)
16.41/6.09	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) -> new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) -> new_nubByNubBy'(xw199, xw200, xw201, ba)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, :(xw2030, xw2031), ba) -> new_nubByNubBy'1(xw198, xw199, xw200, xw201, new_esEs(xw2030, xw198, ba), xw2031, ba)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs(xw2030, xw198, ty_Bool) -> new_esEs5(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_@0) -> new_esEs14(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(app(ty_@2, cc), cd)) -> new_esEs6(xw2030, xw198, cc, cd)
16.41/6.10	   new_esEs(xw2030, xw198, app(app(ty_Either, ca), cb)) -> new_esEs2(xw2030, xw198, ca, cb)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Char) -> new_esEs7(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(ty_Maybe, cf)) -> new_esEs12(xw2030, xw198, cf)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Double) -> new_esEs8(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Ordering) -> new_esEs10(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Integer) -> new_esEs9(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(ty_[], ce)) -> new_esEs3(xw2030, xw198, ce)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Int) -> new_esEs11(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Float) -> new_esEs1(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(ty_Ratio, cg)) -> new_esEs13(xw2030, xw198, cg)
16.41/6.10	   new_esEs(xw2030, xw198, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs4(xw2030, xw198, bf, bg, bh)
16.41/6.10	   new_esEs4(xw10, xw90, da, db, dc) -> error([])
16.41/6.10	   new_esEs13(xw10, xw90, fa) -> error([])
16.41/6.10	   new_esEs1(xw10, xw90) -> error([])
16.41/6.10	   new_esEs11(xw10, xw90) -> error([])
16.41/6.10	   new_esEs3(xw10, xw90, be) -> error([])
16.41/6.10	   new_esEs9(xw10, xw90) -> error([])
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	   new_esEs8(xw10, xw90) -> error([])
16.41/6.10	   new_esEs12(xw10, xw90, ef) -> error([])
16.41/6.10	   new_esEs7(xw10, xw90) -> error([])
16.41/6.10	   new_esEs2(xw10, xw90, bc, bd) -> error([])
16.41/6.10	   new_esEs6(xw10, xw90, eg, eh) -> error([])
16.41/6.10	   new_esEs14(xw10, xw90) -> error([])
16.41/6.10	   new_esEs5(xw10, xw90) -> error([])
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs0(x0, x1, ty_Int)
16.41/6.10	   new_esEs(x0, x1, ty_Integer)
16.41/6.10	   new_esEs7(x0, x1)
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs0(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.10	   new_esEs0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_esEs14(x0, x1)
16.41/6.10	   new_esEs5(x0, x1)
16.41/6.10	   new_esEs(x0, x1, ty_Char)
16.41/6.10	   new_esEs13(x0, x1, x2)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs3(x0, x1, x2)
16.41/6.10	   new_esEs(x0, x1, ty_Double)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs11(x0, x1)
16.41/6.10	   new_esEs0(x0, x1, ty_Integer)
16.41/6.10	   new_esEs0(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.10	   new_esEs(x0, x1, ty_Float)
16.41/6.10	   new_esEs8(x0, x1)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.10	   new_esEs(x0, x1, ty_Ordering)
16.41/6.10	   new_esEs0(x0, x1, ty_Float)
16.41/6.10	   new_esEs6(x0, x1, x2, x3)
16.41/6.10	   new_esEs0(x0, x1, app(ty_[], x2))
16.41/6.10	   new_esEs0(x0, x1, ty_Bool)
16.41/6.10	   new_esEs0(x0, x1, app(ty_Maybe, x2))
16.41/6.10	   new_esEs0(x0, x1, app(ty_Ratio, x2))
16.41/6.10	   new_esEs(x0, x1, ty_Bool)
16.41/6.10	   new_esEs0(x0, x1, ty_Ordering)
16.41/6.10	   new_esEs0(x0, x1, ty_Double)
16.41/6.10	   new_esEs(x0, x1, app(ty_Maybe, x2))
16.41/6.10	   new_esEs(x0, x1, app(ty_Ratio, x2))
16.41/6.10	   new_esEs1(x0, x1)
16.41/6.10	   new_esEs(x0, x1, app(ty_[], x2))
16.41/6.10	   new_esEs0(x0, x1, ty_Char)
16.41/6.10	   new_esEs2(x0, x1, x2, x3)
16.41/6.10	   new_esEs9(x0, x1)
16.41/6.10	   new_esEs0(x0, x1, ty_@0)
16.41/6.10	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_esEs(x0, x1, ty_@0)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.10	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.10	   new_esEs12(x0, x1, x2)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs(x0, x1, ty_Int)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(18) QReductionProof (EQUIVALENT)
16.41/6.10	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
16.41/6.10	
16.41/6.10	   new_esEs0(x0, x1, ty_Int)
16.41/6.10	   new_esEs0(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.10	   new_esEs0(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_esEs0(x0, x1, ty_Integer)
16.41/6.10	   new_esEs0(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.10	   new_esEs0(x0, x1, ty_Float)
16.41/6.10	   new_esEs0(x0, x1, app(ty_[], x2))
16.41/6.10	   new_esEs0(x0, x1, ty_Bool)
16.41/6.10	   new_esEs0(x0, x1, app(ty_Maybe, x2))
16.41/6.10	   new_esEs0(x0, x1, app(ty_Ratio, x2))
16.41/6.10	   new_esEs0(x0, x1, ty_Ordering)
16.41/6.10	   new_esEs0(x0, x1, ty_Double)
16.41/6.10	   new_esEs0(x0, x1, ty_Char)
16.41/6.10	   new_esEs0(x0, x1, ty_@0)
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(19)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_nubByNubBy'(:(x1, y1), x0, y3, ty_Ordering) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs10(x0, x1), y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) -> new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) -> new_nubByNubBy'(xw199, xw200, xw201, ba)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, :(xw2030, xw2031), ba) -> new_nubByNubBy'1(xw198, xw199, xw200, xw201, new_esEs(xw2030, xw198, ba), xw2031, ba)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs(xw2030, xw198, ty_Bool) -> new_esEs5(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_@0) -> new_esEs14(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(app(ty_@2, cc), cd)) -> new_esEs6(xw2030, xw198, cc, cd)
16.41/6.10	   new_esEs(xw2030, xw198, app(app(ty_Either, ca), cb)) -> new_esEs2(xw2030, xw198, ca, cb)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Char) -> new_esEs7(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(ty_Maybe, cf)) -> new_esEs12(xw2030, xw198, cf)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Double) -> new_esEs8(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Ordering) -> new_esEs10(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Integer) -> new_esEs9(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(ty_[], ce)) -> new_esEs3(xw2030, xw198, ce)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Int) -> new_esEs11(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Float) -> new_esEs1(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(ty_Ratio, cg)) -> new_esEs13(xw2030, xw198, cg)
16.41/6.10	   new_esEs(xw2030, xw198, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs4(xw2030, xw198, bf, bg, bh)
16.41/6.10	   new_esEs4(xw10, xw90, da, db, dc) -> error([])
16.41/6.10	   new_esEs13(xw10, xw90, fa) -> error([])
16.41/6.10	   new_esEs1(xw10, xw90) -> error([])
16.41/6.10	   new_esEs11(xw10, xw90) -> error([])
16.41/6.10	   new_esEs3(xw10, xw90, be) -> error([])
16.41/6.10	   new_esEs9(xw10, xw90) -> error([])
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	   new_esEs8(xw10, xw90) -> error([])
16.41/6.10	   new_esEs12(xw10, xw90, ef) -> error([])
16.41/6.10	   new_esEs7(xw10, xw90) -> error([])
16.41/6.10	   new_esEs2(xw10, xw90, bc, bd) -> error([])
16.41/6.10	   new_esEs6(xw10, xw90, eg, eh) -> error([])
16.41/6.10	   new_esEs14(xw10, xw90) -> error([])
16.41/6.10	   new_esEs5(xw10, xw90) -> error([])
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs(x0, x1, ty_Integer)
16.41/6.10	   new_esEs7(x0, x1)
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs14(x0, x1)
16.41/6.10	   new_esEs5(x0, x1)
16.41/6.10	   new_esEs(x0, x1, ty_Char)
16.41/6.10	   new_esEs13(x0, x1, x2)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs3(x0, x1, x2)
16.41/6.10	   new_esEs(x0, x1, ty_Double)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs11(x0, x1)
16.41/6.10	   new_esEs(x0, x1, ty_Float)
16.41/6.10	   new_esEs8(x0, x1)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.10	   new_esEs(x0, x1, ty_Ordering)
16.41/6.10	   new_esEs6(x0, x1, x2, x3)
16.41/6.10	   new_esEs(x0, x1, ty_Bool)
16.41/6.10	   new_esEs(x0, x1, app(ty_Maybe, x2))
16.41/6.10	   new_esEs(x0, x1, app(ty_Ratio, x2))
16.41/6.10	   new_esEs1(x0, x1)
16.41/6.10	   new_esEs(x0, x1, app(ty_[], x2))
16.41/6.10	   new_esEs2(x0, x1, x2, x3)
16.41/6.10	   new_esEs9(x0, x1)
16.41/6.10	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_esEs(x0, x1, ty_@0)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.10	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.10	   new_esEs12(x0, x1, x2)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs(x0, x1, ty_Int)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(20) TransformationProof (EQUIVALENT)
16.41/6.10	By narrowing [LPAR04] the rule new_nubByNubBy'(:(x1, y1), x0, y3, ty_Ordering) -> new_nubByNubBy'1(x1, y1, x0, y3, new_esEs10(x0, x1), y3, ty_Ordering) at position [4] we obtained the following new rules [LPAR04]:
16.41/6.10	
16.41/6.10	   (new_nubByNubBy'(:(GT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, EQ, y3, False, y3, ty_Ordering),new_nubByNubBy'(:(GT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, EQ, y3, False, y3, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'(:(EQ, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, GT, y3, False, y3, ty_Ordering),new_nubByNubBy'(:(EQ, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, GT, y3, False, y3, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'(:(GT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, LT, y3, False, y3, ty_Ordering),new_nubByNubBy'(:(GT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, LT, y3, False, y3, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'(:(LT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, GT, y3, False, y3, ty_Ordering),new_nubByNubBy'(:(LT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, GT, y3, False, y3, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'(:(EQ, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, EQ, y3, True, y3, ty_Ordering),new_nubByNubBy'(:(EQ, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, EQ, y3, True, y3, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'(:(LT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, LT, y3, True, y3, ty_Ordering),new_nubByNubBy'(:(LT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, LT, y3, True, y3, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'(:(EQ, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, LT, y3, False, y3, ty_Ordering),new_nubByNubBy'(:(EQ, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, LT, y3, False, y3, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'(:(LT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, EQ, y3, False, y3, ty_Ordering),new_nubByNubBy'(:(LT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, EQ, y3, False, y3, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'(:(GT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, GT, y3, True, y3, ty_Ordering),new_nubByNubBy'(:(GT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, GT, y3, True, y3, ty_Ordering))
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(21)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) -> new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) -> new_nubByNubBy'(xw199, xw200, xw201, ba)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, :(xw2030, xw2031), ba) -> new_nubByNubBy'1(xw198, xw199, xw200, xw201, new_esEs(xw2030, xw198, ba), xw2031, ba)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, EQ, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, LT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, GT, y3, True, y3, ty_Ordering)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs(xw2030, xw198, ty_Bool) -> new_esEs5(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_@0) -> new_esEs14(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(app(ty_@2, cc), cd)) -> new_esEs6(xw2030, xw198, cc, cd)
16.41/6.10	   new_esEs(xw2030, xw198, app(app(ty_Either, ca), cb)) -> new_esEs2(xw2030, xw198, ca, cb)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Char) -> new_esEs7(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(ty_Maybe, cf)) -> new_esEs12(xw2030, xw198, cf)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Double) -> new_esEs8(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Ordering) -> new_esEs10(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Integer) -> new_esEs9(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(ty_[], ce)) -> new_esEs3(xw2030, xw198, ce)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Int) -> new_esEs11(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Float) -> new_esEs1(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(ty_Ratio, cg)) -> new_esEs13(xw2030, xw198, cg)
16.41/6.10	   new_esEs(xw2030, xw198, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs4(xw2030, xw198, bf, bg, bh)
16.41/6.10	   new_esEs4(xw10, xw90, da, db, dc) -> error([])
16.41/6.10	   new_esEs13(xw10, xw90, fa) -> error([])
16.41/6.10	   new_esEs1(xw10, xw90) -> error([])
16.41/6.10	   new_esEs11(xw10, xw90) -> error([])
16.41/6.10	   new_esEs3(xw10, xw90, be) -> error([])
16.41/6.10	   new_esEs9(xw10, xw90) -> error([])
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	   new_esEs8(xw10, xw90) -> error([])
16.41/6.10	   new_esEs12(xw10, xw90, ef) -> error([])
16.41/6.10	   new_esEs7(xw10, xw90) -> error([])
16.41/6.10	   new_esEs2(xw10, xw90, bc, bd) -> error([])
16.41/6.10	   new_esEs6(xw10, xw90, eg, eh) -> error([])
16.41/6.10	   new_esEs14(xw10, xw90) -> error([])
16.41/6.10	   new_esEs5(xw10, xw90) -> error([])
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs(x0, x1, ty_Integer)
16.41/6.10	   new_esEs7(x0, x1)
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs14(x0, x1)
16.41/6.10	   new_esEs5(x0, x1)
16.41/6.10	   new_esEs(x0, x1, ty_Char)
16.41/6.10	   new_esEs13(x0, x1, x2)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs3(x0, x1, x2)
16.41/6.10	   new_esEs(x0, x1, ty_Double)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs11(x0, x1)
16.41/6.10	   new_esEs(x0, x1, ty_Float)
16.41/6.10	   new_esEs8(x0, x1)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.10	   new_esEs(x0, x1, ty_Ordering)
16.41/6.10	   new_esEs6(x0, x1, x2, x3)
16.41/6.10	   new_esEs(x0, x1, ty_Bool)
16.41/6.10	   new_esEs(x0, x1, app(ty_Maybe, x2))
16.41/6.10	   new_esEs(x0, x1, app(ty_Ratio, x2))
16.41/6.10	   new_esEs1(x0, x1)
16.41/6.10	   new_esEs(x0, x1, app(ty_[], x2))
16.41/6.10	   new_esEs2(x0, x1, x2, x3)
16.41/6.10	   new_esEs9(x0, x1)
16.41/6.10	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_esEs(x0, x1, ty_@0)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.10	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.10	   new_esEs12(x0, x1, x2)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs(x0, x1, ty_Int)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(22) TransformationProof (EQUIVALENT)
16.41/6.10	By narrowing [LPAR04] the rule new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, :(xw2030, xw2031), ba) -> new_nubByNubBy'1(xw198, xw199, xw200, xw201, new_esEs(xw2030, xw198, ba), xw2031, ba) at position [4] we obtained the following new rules [LPAR04]:
16.41/6.10	
16.41/6.10	   (new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Bool) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs5(x0, x1), y5, ty_Bool),new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Bool) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs5(x0, x1), y5, ty_Bool))
16.41/6.10	   (new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_@0) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs14(x0, x1), y5, ty_@0),new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_@0) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs14(x0, x1), y5, ty_@0))
16.41/6.10	   (new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(app(ty_@2, x2), x3)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs6(x0, x1, x2, x3), y5, app(app(ty_@2, x2), x3)),new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(app(ty_@2, x2), x3)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs6(x0, x1, x2, x3), y5, app(app(ty_@2, x2), x3)))
16.41/6.10	   (new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(app(ty_Either, x2), x3)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs2(x0, x1, x2, x3), y5, app(app(ty_Either, x2), x3)),new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(app(ty_Either, x2), x3)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs2(x0, x1, x2, x3), y5, app(app(ty_Either, x2), x3)))
16.41/6.10	   (new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Char) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs7(x0, x1), y5, ty_Char),new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Char) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs7(x0, x1), y5, ty_Char))
16.41/6.10	   (new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(ty_Maybe, x2)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs12(x0, x1, x2), y5, app(ty_Maybe, x2)),new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(ty_Maybe, x2)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs12(x0, x1, x2), y5, app(ty_Maybe, x2)))
16.41/6.10	   (new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Double) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs8(x0, x1), y5, ty_Double),new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Double) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs8(x0, x1), y5, ty_Double))
16.41/6.10	   (new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Ordering) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs10(x0, x1), y5, ty_Ordering),new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Ordering) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs10(x0, x1), y5, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Integer) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs9(x0, x1), y5, ty_Integer),new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Integer) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs9(x0, x1), y5, ty_Integer))
16.41/6.10	   (new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(ty_[], x2)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs3(x0, x1, x2), y5, app(ty_[], x2)),new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(ty_[], x2)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs3(x0, x1, x2), y5, app(ty_[], x2)))
16.41/6.10	   (new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Int) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs11(x0, x1), y5, ty_Int),new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Int) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs11(x0, x1), y5, ty_Int))
16.41/6.10	   (new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Float) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs1(x0, x1), y5, ty_Float),new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Float) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs1(x0, x1), y5, ty_Float))
16.41/6.10	   (new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(ty_Ratio, x2)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs13(x0, x1, x2), y5, app(ty_Ratio, x2)),new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(ty_Ratio, x2)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs13(x0, x1, x2), y5, app(ty_Ratio, x2)))
16.41/6.10	   (new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(app(app(ty_@3, x2), x3), x4)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs4(x0, x1, x2, x3, x4), y5, app(app(app(ty_@3, x2), x3), x4)),new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(app(app(ty_@3, x2), x3), x4)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs4(x0, x1, x2, x3, x4), y5, app(app(app(ty_@3, x2), x3), x4)))
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(23)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) -> new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) -> new_nubByNubBy'(xw199, xw200, xw201, ba)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, EQ, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, LT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, GT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Bool) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs5(x0, x1), y5, ty_Bool)
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_@0) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs14(x0, x1), y5, ty_@0)
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(app(ty_@2, x2), x3)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs6(x0, x1, x2, x3), y5, app(app(ty_@2, x2), x3))
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(app(ty_Either, x2), x3)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs2(x0, x1, x2, x3), y5, app(app(ty_Either, x2), x3))
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Char) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs7(x0, x1), y5, ty_Char)
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(ty_Maybe, x2)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs12(x0, x1, x2), y5, app(ty_Maybe, x2))
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Double) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs8(x0, x1), y5, ty_Double)
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Ordering) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs10(x0, x1), y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Integer) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs9(x0, x1), y5, ty_Integer)
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(ty_[], x2)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs3(x0, x1, x2), y5, app(ty_[], x2))
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Int) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs11(x0, x1), y5, ty_Int)
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Float) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs1(x0, x1), y5, ty_Float)
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(ty_Ratio, x2)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs13(x0, x1, x2), y5, app(ty_Ratio, x2))
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), app(app(app(ty_@3, x2), x3), x4)) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs4(x0, x1, x2, x3, x4), y5, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs(xw2030, xw198, ty_Bool) -> new_esEs5(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_@0) -> new_esEs14(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(app(ty_@2, cc), cd)) -> new_esEs6(xw2030, xw198, cc, cd)
16.41/6.10	   new_esEs(xw2030, xw198, app(app(ty_Either, ca), cb)) -> new_esEs2(xw2030, xw198, ca, cb)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Char) -> new_esEs7(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(ty_Maybe, cf)) -> new_esEs12(xw2030, xw198, cf)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Double) -> new_esEs8(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Ordering) -> new_esEs10(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Integer) -> new_esEs9(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(ty_[], ce)) -> new_esEs3(xw2030, xw198, ce)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Int) -> new_esEs11(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Float) -> new_esEs1(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(ty_Ratio, cg)) -> new_esEs13(xw2030, xw198, cg)
16.41/6.10	   new_esEs(xw2030, xw198, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs4(xw2030, xw198, bf, bg, bh)
16.41/6.10	   new_esEs4(xw10, xw90, da, db, dc) -> error([])
16.41/6.10	   new_esEs13(xw10, xw90, fa) -> error([])
16.41/6.10	   new_esEs1(xw10, xw90) -> error([])
16.41/6.10	   new_esEs11(xw10, xw90) -> error([])
16.41/6.10	   new_esEs3(xw10, xw90, be) -> error([])
16.41/6.10	   new_esEs9(xw10, xw90) -> error([])
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	   new_esEs8(xw10, xw90) -> error([])
16.41/6.10	   new_esEs12(xw10, xw90, ef) -> error([])
16.41/6.10	   new_esEs7(xw10, xw90) -> error([])
16.41/6.10	   new_esEs2(xw10, xw90, bc, bd) -> error([])
16.41/6.10	   new_esEs6(xw10, xw90, eg, eh) -> error([])
16.41/6.10	   new_esEs14(xw10, xw90) -> error([])
16.41/6.10	   new_esEs5(xw10, xw90) -> error([])
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs(x0, x1, ty_Integer)
16.41/6.10	   new_esEs7(x0, x1)
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs14(x0, x1)
16.41/6.10	   new_esEs5(x0, x1)
16.41/6.10	   new_esEs(x0, x1, ty_Char)
16.41/6.10	   new_esEs13(x0, x1, x2)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs3(x0, x1, x2)
16.41/6.10	   new_esEs(x0, x1, ty_Double)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs11(x0, x1)
16.41/6.10	   new_esEs(x0, x1, ty_Float)
16.41/6.10	   new_esEs8(x0, x1)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.10	   new_esEs(x0, x1, ty_Ordering)
16.41/6.10	   new_esEs6(x0, x1, x2, x3)
16.41/6.10	   new_esEs(x0, x1, ty_Bool)
16.41/6.10	   new_esEs(x0, x1, app(ty_Maybe, x2))
16.41/6.10	   new_esEs(x0, x1, app(ty_Ratio, x2))
16.41/6.10	   new_esEs1(x0, x1)
16.41/6.10	   new_esEs(x0, x1, app(ty_[], x2))
16.41/6.10	   new_esEs2(x0, x1, x2, x3)
16.41/6.10	   new_esEs9(x0, x1)
16.41/6.10	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_esEs(x0, x1, ty_@0)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.10	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.10	   new_esEs12(x0, x1, x2)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs(x0, x1, ty_Int)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(24) DependencyGraphProof (EQUIVALENT)
16.41/6.10	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 13 less nodes.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(25)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_nubByNubBy'(:(GT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) -> new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Ordering) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs10(x0, x1), y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) -> new_nubByNubBy'(xw199, xw200, xw201, ba)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, EQ, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, LT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, GT, y3, True, y3, ty_Ordering)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs(xw2030, xw198, ty_Bool) -> new_esEs5(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_@0) -> new_esEs14(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(app(ty_@2, cc), cd)) -> new_esEs6(xw2030, xw198, cc, cd)
16.41/6.10	   new_esEs(xw2030, xw198, app(app(ty_Either, ca), cb)) -> new_esEs2(xw2030, xw198, ca, cb)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Char) -> new_esEs7(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(ty_Maybe, cf)) -> new_esEs12(xw2030, xw198, cf)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Double) -> new_esEs8(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Ordering) -> new_esEs10(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Integer) -> new_esEs9(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(ty_[], ce)) -> new_esEs3(xw2030, xw198, ce)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Int) -> new_esEs11(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, ty_Float) -> new_esEs1(xw2030, xw198)
16.41/6.10	   new_esEs(xw2030, xw198, app(ty_Ratio, cg)) -> new_esEs13(xw2030, xw198, cg)
16.41/6.10	   new_esEs(xw2030, xw198, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs4(xw2030, xw198, bf, bg, bh)
16.41/6.10	   new_esEs4(xw10, xw90, da, db, dc) -> error([])
16.41/6.10	   new_esEs13(xw10, xw90, fa) -> error([])
16.41/6.10	   new_esEs1(xw10, xw90) -> error([])
16.41/6.10	   new_esEs11(xw10, xw90) -> error([])
16.41/6.10	   new_esEs3(xw10, xw90, be) -> error([])
16.41/6.10	   new_esEs9(xw10, xw90) -> error([])
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	   new_esEs8(xw10, xw90) -> error([])
16.41/6.10	   new_esEs12(xw10, xw90, ef) -> error([])
16.41/6.10	   new_esEs7(xw10, xw90) -> error([])
16.41/6.10	   new_esEs2(xw10, xw90, bc, bd) -> error([])
16.41/6.10	   new_esEs6(xw10, xw90, eg, eh) -> error([])
16.41/6.10	   new_esEs14(xw10, xw90) -> error([])
16.41/6.10	   new_esEs5(xw10, xw90) -> error([])
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs(x0, x1, ty_Integer)
16.41/6.10	   new_esEs7(x0, x1)
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs14(x0, x1)
16.41/6.10	   new_esEs5(x0, x1)
16.41/6.10	   new_esEs(x0, x1, ty_Char)
16.41/6.10	   new_esEs13(x0, x1, x2)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs3(x0, x1, x2)
16.41/6.10	   new_esEs(x0, x1, ty_Double)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs11(x0, x1)
16.41/6.10	   new_esEs(x0, x1, ty_Float)
16.41/6.10	   new_esEs8(x0, x1)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.10	   new_esEs(x0, x1, ty_Ordering)
16.41/6.10	   new_esEs6(x0, x1, x2, x3)
16.41/6.10	   new_esEs(x0, x1, ty_Bool)
16.41/6.10	   new_esEs(x0, x1, app(ty_Maybe, x2))
16.41/6.10	   new_esEs(x0, x1, app(ty_Ratio, x2))
16.41/6.10	   new_esEs1(x0, x1)
16.41/6.10	   new_esEs(x0, x1, app(ty_[], x2))
16.41/6.10	   new_esEs2(x0, x1, x2, x3)
16.41/6.10	   new_esEs9(x0, x1)
16.41/6.10	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_esEs(x0, x1, ty_@0)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.10	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.10	   new_esEs12(x0, x1, x2)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs(x0, x1, ty_Int)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(26) UsableRulesProof (EQUIVALENT)
16.41/6.10	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.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(27)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_nubByNubBy'(:(GT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) -> new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Ordering) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs10(x0, x1), y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) -> new_nubByNubBy'(xw199, xw200, xw201, ba)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, EQ, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, LT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, GT, y3, True, y3, ty_Ordering)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs(x0, x1, ty_Integer)
16.41/6.10	   new_esEs7(x0, x1)
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs14(x0, x1)
16.41/6.10	   new_esEs5(x0, x1)
16.41/6.10	   new_esEs(x0, x1, ty_Char)
16.41/6.10	   new_esEs13(x0, x1, x2)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs3(x0, x1, x2)
16.41/6.10	   new_esEs(x0, x1, ty_Double)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs11(x0, x1)
16.41/6.10	   new_esEs(x0, x1, ty_Float)
16.41/6.10	   new_esEs8(x0, x1)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.10	   new_esEs(x0, x1, ty_Ordering)
16.41/6.10	   new_esEs6(x0, x1, x2, x3)
16.41/6.10	   new_esEs(x0, x1, ty_Bool)
16.41/6.10	   new_esEs(x0, x1, app(ty_Maybe, x2))
16.41/6.10	   new_esEs(x0, x1, app(ty_Ratio, x2))
16.41/6.10	   new_esEs1(x0, x1)
16.41/6.10	   new_esEs(x0, x1, app(ty_[], x2))
16.41/6.10	   new_esEs2(x0, x1, x2, x3)
16.41/6.10	   new_esEs9(x0, x1)
16.41/6.10	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_esEs(x0, x1, ty_@0)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.10	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.10	   new_esEs12(x0, x1, x2)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs(x0, x1, ty_Int)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(28) QReductionProof (EQUIVALENT)
16.41/6.10	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
16.41/6.10	
16.41/6.10	   new_esEs(x0, x1, ty_Integer)
16.41/6.10	   new_esEs7(x0, x1)
16.41/6.10	   new_esEs14(x0, x1)
16.41/6.10	   new_esEs5(x0, x1)
16.41/6.10	   new_esEs(x0, x1, ty_Char)
16.41/6.10	   new_esEs13(x0, x1, x2)
16.41/6.10	   new_esEs3(x0, x1, x2)
16.41/6.10	   new_esEs(x0, x1, ty_Double)
16.41/6.10	   new_esEs11(x0, x1)
16.41/6.10	   new_esEs(x0, x1, ty_Float)
16.41/6.10	   new_esEs8(x0, x1)
16.41/6.10	   new_esEs(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.10	   new_esEs(x0, x1, ty_Ordering)
16.41/6.10	   new_esEs6(x0, x1, x2, x3)
16.41/6.10	   new_esEs(x0, x1, ty_Bool)
16.41/6.10	   new_esEs(x0, x1, app(ty_Maybe, x2))
16.41/6.10	   new_esEs(x0, x1, app(ty_Ratio, x2))
16.41/6.10	   new_esEs1(x0, x1)
16.41/6.10	   new_esEs(x0, x1, app(ty_[], x2))
16.41/6.10	   new_esEs2(x0, x1, x2, x3)
16.41/6.10	   new_esEs9(x0, x1)
16.41/6.10	   new_esEs(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_esEs(x0, x1, ty_@0)
16.41/6.10	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.10	   new_esEs(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.10	   new_esEs12(x0, x1, x2)
16.41/6.10	   new_esEs(x0, x1, ty_Int)
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(29)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_nubByNubBy'(:(GT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) -> new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Ordering) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs10(x0, x1), y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) -> new_nubByNubBy'(xw199, xw200, xw201, ba)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, EQ, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, LT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, GT, y3, True, y3, ty_Ordering)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(30) TransformationProof (EQUIVALENT)
16.41/6.10	By narrowing [LPAR04] the rule new_nubByNubBy'1(x1, y1, y2, y3, False, :(x0, y5), ty_Ordering) -> new_nubByNubBy'1(x1, y1, y2, y3, new_esEs10(x0, x1), y5, ty_Ordering) at position [4] we obtained the following new rules [LPAR04]:
16.41/6.10	
16.41/6.10	   (new_nubByNubBy'1(GT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering),new_nubByNubBy'1(GT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(EQ, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering),new_nubByNubBy'1(EQ, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(GT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering),new_nubByNubBy'1(GT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(LT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering),new_nubByNubBy'1(LT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(EQ, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, True, y5, ty_Ordering),new_nubByNubBy'1(EQ, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, True, y5, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(LT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, True, y5, ty_Ordering),new_nubByNubBy'1(LT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, True, y5, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(EQ, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering),new_nubByNubBy'1(EQ, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(LT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering),new_nubByNubBy'1(LT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(GT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, True, y5, ty_Ordering),new_nubByNubBy'1(GT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, True, y5, ty_Ordering))
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(31)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_nubByNubBy'(:(GT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) -> new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) -> new_nubByNubBy'(xw199, xw200, xw201, ba)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, EQ, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, LT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, GT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(32) UsableRulesProof (EQUIVALENT)
16.41/6.10	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.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(33)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_nubByNubBy'(:(GT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) -> new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) -> new_nubByNubBy'(xw199, xw200, xw201, ba)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, EQ, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, LT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, GT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	
16.41/6.10	R is empty.
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(34) QReductionProof (EQUIVALENT)
16.41/6.10	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
16.41/6.10	
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(35)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_nubByNubBy'(:(GT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) -> new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) -> new_nubByNubBy'(xw199, xw200, xw201, ba)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, EQ, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, LT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, GT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	
16.41/6.10	R is empty.
16.41/6.10	Q is empty.
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(36) TransformationProof (EQUIVALENT)
16.41/6.10	By instantiating [LPAR04] the rule new_nubByNubBy'1(xw198, xw199, xw200, xw201, False, [], ba) -> new_nubByNubBy'(xw199, xw198, :(xw200, xw201), ba) we obtained the following new rules [LPAR04]:
16.41/6.10	
16.41/6.10	   (new_nubByNubBy'1(GT, z0, EQ, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, GT, :(EQ, []), ty_Ordering),new_nubByNubBy'1(GT, z0, EQ, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, GT, :(EQ, []), ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(EQ, z0, GT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, EQ, :(GT, []), ty_Ordering),new_nubByNubBy'1(EQ, z0, GT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, EQ, :(GT, []), ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(GT, z0, LT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, GT, :(LT, []), ty_Ordering),new_nubByNubBy'1(GT, z0, LT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, GT, :(LT, []), ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(LT, z0, GT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, LT, :(GT, []), ty_Ordering),new_nubByNubBy'1(LT, z0, GT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, LT, :(GT, []), ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(EQ, z0, LT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, EQ, :(LT, []), ty_Ordering),new_nubByNubBy'1(EQ, z0, LT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, EQ, :(LT, []), ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(LT, z0, EQ, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, LT, :(EQ, []), ty_Ordering),new_nubByNubBy'1(LT, z0, EQ, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, LT, :(EQ, []), ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(GT, z0, z1, z2, False, [], ty_Ordering) -> new_nubByNubBy'(z0, GT, :(z1, z2), ty_Ordering),new_nubByNubBy'1(GT, z0, z1, z2, False, [], ty_Ordering) -> new_nubByNubBy'(z0, GT, :(z1, z2), ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(EQ, z0, z1, z2, False, [], ty_Ordering) -> new_nubByNubBy'(z0, EQ, :(z1, z2), ty_Ordering),new_nubByNubBy'1(EQ, z0, z1, z2, False, [], ty_Ordering) -> new_nubByNubBy'(z0, EQ, :(z1, z2), ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(LT, z0, z1, z2, False, [], ty_Ordering) -> new_nubByNubBy'(z0, LT, :(z1, z2), ty_Ordering),new_nubByNubBy'1(LT, z0, z1, z2, False, [], ty_Ordering) -> new_nubByNubBy'(z0, LT, :(z1, z2), ty_Ordering))
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(37)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_nubByNubBy'(:(GT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) -> new_nubByNubBy'(xw199, xw200, xw201, ba)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, EQ, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, LT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, GT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, z0, EQ, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, GT, :(EQ, []), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, z0, GT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, EQ, :(GT, []), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, z0, LT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, GT, :(LT, []), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, z0, GT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, LT, :(GT, []), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, z0, LT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, EQ, :(LT, []), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, z0, EQ, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, LT, :(EQ, []), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, z0, z1, z2, False, [], ty_Ordering) -> new_nubByNubBy'(z0, GT, :(z1, z2), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, z0, z1, z2, False, [], ty_Ordering) -> new_nubByNubBy'(z0, EQ, :(z1, z2), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, z0, z1, z2, False, [], ty_Ordering) -> new_nubByNubBy'(z0, LT, :(z1, z2), ty_Ordering)
16.41/6.10	
16.41/6.10	R is empty.
16.41/6.10	Q is empty.
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(38) TransformationProof (EQUIVALENT)
16.41/6.10	By instantiating [LPAR04] the rule new_nubByNubBy'1(xw198, xw199, xw200, xw201, True, xw203, ba) -> new_nubByNubBy'(xw199, xw200, xw201, ba) we obtained the following new rules [LPAR04]:
16.41/6.10	
16.41/6.10	   (new_nubByNubBy'1(EQ, z0, EQ, z1, True, z1, ty_Ordering) -> new_nubByNubBy'(z0, EQ, z1, ty_Ordering),new_nubByNubBy'1(EQ, z0, EQ, z1, True, z1, ty_Ordering) -> new_nubByNubBy'(z0, EQ, z1, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(LT, z0, LT, z1, True, z1, ty_Ordering) -> new_nubByNubBy'(z0, LT, z1, ty_Ordering),new_nubByNubBy'1(LT, z0, LT, z1, True, z1, ty_Ordering) -> new_nubByNubBy'(z0, LT, z1, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(GT, z0, GT, z1, True, z1, ty_Ordering) -> new_nubByNubBy'(z0, GT, z1, ty_Ordering),new_nubByNubBy'1(GT, z0, GT, z1, True, z1, ty_Ordering) -> new_nubByNubBy'(z0, GT, z1, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(EQ, z0, z1, z2, True, z3, ty_Ordering) -> new_nubByNubBy'(z0, z1, z2, ty_Ordering),new_nubByNubBy'1(EQ, z0, z1, z2, True, z3, ty_Ordering) -> new_nubByNubBy'(z0, z1, z2, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(LT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubByNubBy'(z0, z1, z2, ty_Ordering),new_nubByNubBy'1(LT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubByNubBy'(z0, z1, z2, ty_Ordering))
16.41/6.10	   (new_nubByNubBy'1(GT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubByNubBy'(z0, z1, z2, ty_Ordering),new_nubByNubBy'1(GT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubByNubBy'(z0, z1, z2, ty_Ordering))
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(39)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_nubByNubBy'(:(GT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, EQ, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, LT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(EQ, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(LT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'(:(GT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, GT, y3, True, y3, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, z0, EQ, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, GT, :(EQ, []), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, z0, GT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, EQ, :(GT, []), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, z0, LT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, GT, :(LT, []), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, z0, GT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, LT, :(GT, []), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, z0, LT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, EQ, :(LT, []), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, z0, EQ, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, LT, :(EQ, []), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, z0, z1, z2, False, [], ty_Ordering) -> new_nubByNubBy'(z0, GT, :(z1, z2), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, z0, z1, z2, False, [], ty_Ordering) -> new_nubByNubBy'(z0, EQ, :(z1, z2), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, z0, z1, z2, False, [], ty_Ordering) -> new_nubByNubBy'(z0, LT, :(z1, z2), ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, z0, EQ, z1, True, z1, ty_Ordering) -> new_nubByNubBy'(z0, EQ, z1, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, z0, LT, z1, True, z1, ty_Ordering) -> new_nubByNubBy'(z0, LT, z1, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, z0, GT, z1, True, z1, ty_Ordering) -> new_nubByNubBy'(z0, GT, z1, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(EQ, z0, z1, z2, True, z3, ty_Ordering) -> new_nubByNubBy'(z0, z1, z2, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(LT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubByNubBy'(z0, z1, z2, ty_Ordering)
16.41/6.10	   new_nubByNubBy'1(GT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubByNubBy'(z0, z1, z2, ty_Ordering)
16.41/6.10	
16.41/6.10	R is empty.
16.41/6.10	Q is empty.
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(40) QDPSizeChangeProof (EQUIVALENT)
16.41/6.10	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. 
16.41/6.10	
16.41/6.10	From the DPs we obtained the following set of size-change graphs:
16.41/6.10	*new_nubByNubBy'1(GT, z0, z1, z2, False, [], ty_Ordering) -> new_nubByNubBy'(z0, GT, :(z1, z2), ty_Ordering)
16.41/6.10	The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(GT, z0, EQ, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, GT, :(EQ, []), ty_Ordering)
16.41/6.10	The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(GT, z0, LT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, GT, :(LT, []), ty_Ordering)
16.41/6.10	The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(GT, z0, GT, z1, True, z1, ty_Ordering) -> new_nubByNubBy'(z0, GT, z1, ty_Ordering)
16.41/6.10	The graph contains the following edges 2 >= 1, 1 >= 2, 3 >= 2, 4 >= 3, 6 >= 3, 7 >= 4
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(EQ, z0, z1, z2, True, z3, ty_Ordering) -> new_nubByNubBy'(z0, z1, z2, ty_Ordering)
16.41/6.10	The graph contains the following edges 2 >= 1, 3 >= 2, 4 >= 3, 7 >= 4
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(EQ, z0, EQ, z1, True, z1, ty_Ordering) -> new_nubByNubBy'(z0, EQ, z1, ty_Ordering)
16.41/6.10	The graph contains the following edges 2 >= 1, 1 >= 2, 3 >= 2, 4 >= 3, 6 >= 3, 7 >= 4
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(EQ, z0, LT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, EQ, :(LT, []), ty_Ordering)
16.41/6.10	The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(LT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubByNubBy'(z0, z1, z2, ty_Ordering)
16.41/6.10	The graph contains the following edges 2 >= 1, 3 >= 2, 4 >= 3, 7 >= 4
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(GT, z0, z1, z2, True, z3, ty_Ordering) -> new_nubByNubBy'(z0, z1, z2, ty_Ordering)
16.41/6.10	The graph contains the following edges 2 >= 1, 3 >= 2, 4 >= 3, 7 >= 4
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(LT, z0, LT, z1, True, z1, ty_Ordering) -> new_nubByNubBy'(z0, LT, z1, ty_Ordering)
16.41/6.10	The graph contains the following edges 2 >= 1, 1 >= 2, 3 >= 2, 4 >= 3, 6 >= 3, 7 >= 4
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(LT, z0, EQ, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, LT, :(EQ, []), ty_Ordering)
16.41/6.10	The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(EQ, z0, z1, z2, False, [], ty_Ordering) -> new_nubByNubBy'(z0, EQ, :(z1, z2), ty_Ordering)
16.41/6.10	The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(EQ, z0, GT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, EQ, :(GT, []), ty_Ordering)
16.41/6.10	The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(LT, z0, z1, z2, False, [], ty_Ordering) -> new_nubByNubBy'(z0, LT, :(z1, z2), ty_Ordering)
16.41/6.10	The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(LT, z0, GT, [], False, [], ty_Ordering) -> new_nubByNubBy'(z0, LT, :(GT, []), ty_Ordering)
16.41/6.10	The graph contains the following edges 2 >= 1, 1 >= 2, 7 >= 4
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(GT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 >= 1, 6 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 > 6, 7 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(EQ, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 >= 1, 6 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 > 6, 7 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(LT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, True, y5, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 >= 1, 6 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 6 > 6, 7 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'(:(GT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3, 3 >= 4, 3 >= 6, 4 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'(:(GT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3, 3 >= 4, 3 >= 6, 4 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'(:(EQ, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3, 3 >= 4, 3 >= 6, 4 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'(:(EQ, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, LT, y3, False, y3, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3, 3 >= 4, 3 >= 6, 4 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'(:(LT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, GT, y3, False, y3, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3, 3 >= 4, 3 >= 6, 4 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'(:(LT, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, EQ, y3, False, y3, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 > 1, 1 > 2, 2 >= 3, 3 >= 4, 3 >= 6, 4 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'(:(GT, y1), GT, y3, ty_Ordering) -> new_nubByNubBy'1(GT, y1, GT, y3, True, y3, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 > 1, 2 >= 1, 1 > 2, 1 > 3, 2 >= 3, 3 >= 4, 3 >= 6, 4 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'(:(EQ, y1), EQ, y3, ty_Ordering) -> new_nubByNubBy'1(EQ, y1, EQ, y3, True, y3, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 > 1, 2 >= 1, 1 > 2, 1 > 3, 2 >= 3, 3 >= 4, 3 >= 6, 4 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'(:(LT, y1), LT, y3, ty_Ordering) -> new_nubByNubBy'1(LT, y1, LT, y3, True, y3, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 > 1, 2 >= 1, 1 > 2, 1 > 3, 2 >= 3, 3 >= 4, 3 >= 6, 4 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(GT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(GT, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(GT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(EQ, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(EQ, y1, y2, y3, False, :(LT, y5), ty_Ordering) -> new_nubByNubBy'1(EQ, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(LT, y1, y2, y3, False, :(GT, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_nubByNubBy'1(LT, y1, y2, y3, False, :(EQ, y5), ty_Ordering) -> new_nubByNubBy'1(LT, y1, y2, y3, False, y5, ty_Ordering)
16.41/6.10	The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5, 6 > 6, 7 >= 7
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(41)
16.41/6.10	YES
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(42)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_psPs(:(xw80, xw81), xw9, xw10, xw11, ba) -> new_psPs(xw81, xw9, xw10, xw11, ba)
16.41/6.10	
16.41/6.10	R is empty.
16.41/6.10	Q is empty.
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(43) QDPSizeChangeProof (EQUIVALENT)
16.41/6.10	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. 
16.41/6.10	
16.41/6.10	From the DPs we obtained the following set of size-change graphs:
16.41/6.10	*new_psPs(:(xw80, xw81), xw9, xw10, xw11, ba) -> new_psPs(xw81, xw9, xw10, xw11, ba)
16.41/6.10	The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(44)
16.41/6.10	YES
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(45)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_deleteBy(xw10, :(xw90, xw91), bb) -> new_deleteBy0(xw91, xw90, xw10, new_esEs15(xw10, xw90, bb), bb)
16.41/6.10	   new_deleteBy0(xw17, xw18, xw19, False, ba) -> new_deleteBy(xw19, xw17, ba)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs15(xw10, xw90, ty_@0) -> new_esEs14(xw10, xw90)
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs11(xw10, xw90) -> error([])
16.41/6.10	   new_esEs5(xw10, xw90) -> error([])
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs1(xw10, xw90) -> error([])
16.41/6.10	   new_esEs2(xw10, xw90, bc, bd) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, app(app(ty_@2, ca), cb)) -> new_esEs6(xw10, xw90, ca, cb)
16.41/6.10	   new_esEs4(xw10, xw90, bf, bg, bh) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Ordering) -> new_esEs10(xw10, xw90)
16.41/6.10	   new_esEs7(xw10, xw90) -> error([])
16.41/6.10	   new_esEs9(xw10, xw90) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, app(ty_Ratio, cd)) -> new_esEs13(xw10, xw90, cd)
16.41/6.10	   new_esEs15(xw10, xw90, app(ty_Maybe, cc)) -> new_esEs12(xw10, xw90, cc)
16.41/6.10	   new_esEs6(xw10, xw90, ca, cb) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Bool) -> new_esEs5(xw10, xw90)
16.41/6.10	   new_esEs15(xw10, xw90, ty_Integer) -> new_esEs9(xw10, xw90)
16.41/6.10	   new_esEs15(xw10, xw90, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs4(xw10, xw90, bf, bg, bh)
16.41/6.10	   new_esEs15(xw10, xw90, ty_Double) -> new_esEs8(xw10, xw90)
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs15(xw10, xw90, app(ty_[], be)) -> new_esEs3(xw10, xw90, be)
16.41/6.10	   new_esEs14(xw10, xw90) -> error([])
16.41/6.10	   new_esEs12(xw10, xw90, cc) -> error([])
16.41/6.10	   new_esEs13(xw10, xw90, cd) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Char) -> new_esEs7(xw10, xw90)
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs15(xw10, xw90, ty_Int) -> new_esEs11(xw10, xw90)
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	   new_esEs3(xw10, xw90, be) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, app(app(ty_Either, bc), bd)) -> new_esEs2(xw10, xw90, bc, bd)
16.41/6.10	   new_esEs8(xw10, xw90) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Float) -> new_esEs1(xw10, xw90)
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs7(x0, x1)
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.10	   new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.10	   new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.10	   new_esEs15(x0, x1, ty_Char)
16.41/6.10	   new_esEs14(x0, x1)
16.41/6.10	   new_esEs12(x0, x1, x2)
16.41/6.10	   new_esEs13(x0, x1, x2)
16.41/6.10	   new_esEs15(x0, x1, app(ty_Ratio, x2))
16.41/6.10	   new_esEs15(x0, x1, app(ty_Maybe, x2))
16.41/6.10	   new_esEs5(x0, x1)
16.41/6.10	   new_esEs1(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Double)
16.41/6.10	   new_esEs15(x0, x1, ty_@0)
16.41/6.10	   new_esEs15(x0, x1, ty_Ordering)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_esEs15(x0, x1, ty_Float)
16.41/6.10	   new_esEs2(x0, x1, x2, x3)
16.41/6.10	   new_esEs6(x0, x1, x2, x3)
16.41/6.10	   new_esEs3(x0, x1, x2)
16.41/6.10	   new_esEs9(x0, x1)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs15(x0, x1, ty_Int)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs11(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Integer)
16.41/6.10	   new_esEs8(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Bool)
16.41/6.10	   new_esEs15(x0, x1, app(ty_[], x2))
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(46) TransformationProof (EQUIVALENT)
16.41/6.10	By narrowing [LPAR04] the rule new_deleteBy(xw10, :(xw90, xw91), bb) -> new_deleteBy0(xw91, xw90, xw10, new_esEs15(xw10, xw90, bb), bb) at position [3] we obtained the following new rules [LPAR04]:
16.41/6.10	
16.41/6.10	   (new_deleteBy(x0, :(x1, y2), ty_@0) -> new_deleteBy0(y2, x1, x0, new_esEs14(x0, x1), ty_@0),new_deleteBy(x0, :(x1, y2), ty_@0) -> new_deleteBy0(y2, x1, x0, new_esEs14(x0, x1), ty_@0))
16.41/6.10	   (new_deleteBy(x0, :(x1, y2), app(app(ty_@2, x2), x3)) -> new_deleteBy0(y2, x1, x0, new_esEs6(x0, x1, x2, x3), app(app(ty_@2, x2), x3)),new_deleteBy(x0, :(x1, y2), app(app(ty_@2, x2), x3)) -> new_deleteBy0(y2, x1, x0, new_esEs6(x0, x1, x2, x3), app(app(ty_@2, x2), x3)))
16.41/6.10	   (new_deleteBy(x0, :(x1, y2), ty_Ordering) -> new_deleteBy0(y2, x1, x0, new_esEs10(x0, x1), ty_Ordering),new_deleteBy(x0, :(x1, y2), ty_Ordering) -> new_deleteBy0(y2, x1, x0, new_esEs10(x0, x1), ty_Ordering))
16.41/6.10	   (new_deleteBy(x0, :(x1, y2), app(ty_Ratio, x2)) -> new_deleteBy0(y2, x1, x0, new_esEs13(x0, x1, x2), app(ty_Ratio, x2)),new_deleteBy(x0, :(x1, y2), app(ty_Ratio, x2)) -> new_deleteBy0(y2, x1, x0, new_esEs13(x0, x1, x2), app(ty_Ratio, x2)))
16.41/6.10	   (new_deleteBy(x0, :(x1, y2), app(ty_Maybe, x2)) -> new_deleteBy0(y2, x1, x0, new_esEs12(x0, x1, x2), app(ty_Maybe, x2)),new_deleteBy(x0, :(x1, y2), app(ty_Maybe, x2)) -> new_deleteBy0(y2, x1, x0, new_esEs12(x0, x1, x2), app(ty_Maybe, x2)))
16.41/6.10	   (new_deleteBy(x0, :(x1, y2), ty_Bool) -> new_deleteBy0(y2, x1, x0, new_esEs5(x0, x1), ty_Bool),new_deleteBy(x0, :(x1, y2), ty_Bool) -> new_deleteBy0(y2, x1, x0, new_esEs5(x0, x1), ty_Bool))
16.41/6.10	   (new_deleteBy(x0, :(x1, y2), ty_Integer) -> new_deleteBy0(y2, x1, x0, new_esEs9(x0, x1), ty_Integer),new_deleteBy(x0, :(x1, y2), ty_Integer) -> new_deleteBy0(y2, x1, x0, new_esEs9(x0, x1), ty_Integer))
16.41/6.10	   (new_deleteBy(x0, :(x1, y2), app(app(app(ty_@3, x2), x3), x4)) -> new_deleteBy0(y2, x1, x0, new_esEs4(x0, x1, x2, x3, x4), app(app(app(ty_@3, x2), x3), x4)),new_deleteBy(x0, :(x1, y2), app(app(app(ty_@3, x2), x3), x4)) -> new_deleteBy0(y2, x1, x0, new_esEs4(x0, x1, x2, x3, x4), app(app(app(ty_@3, x2), x3), x4)))
16.41/6.10	   (new_deleteBy(x0, :(x1, y2), ty_Double) -> new_deleteBy0(y2, x1, x0, new_esEs8(x0, x1), ty_Double),new_deleteBy(x0, :(x1, y2), ty_Double) -> new_deleteBy0(y2, x1, x0, new_esEs8(x0, x1), ty_Double))
16.41/6.10	   (new_deleteBy(x0, :(x1, y2), app(ty_[], x2)) -> new_deleteBy0(y2, x1, x0, new_esEs3(x0, x1, x2), app(ty_[], x2)),new_deleteBy(x0, :(x1, y2), app(ty_[], x2)) -> new_deleteBy0(y2, x1, x0, new_esEs3(x0, x1, x2), app(ty_[], x2)))
16.41/6.10	   (new_deleteBy(x0, :(x1, y2), ty_Char) -> new_deleteBy0(y2, x1, x0, new_esEs7(x0, x1), ty_Char),new_deleteBy(x0, :(x1, y2), ty_Char) -> new_deleteBy0(y2, x1, x0, new_esEs7(x0, x1), ty_Char))
16.41/6.10	   (new_deleteBy(x0, :(x1, y2), ty_Int) -> new_deleteBy0(y2, x1, x0, new_esEs11(x0, x1), ty_Int),new_deleteBy(x0, :(x1, y2), ty_Int) -> new_deleteBy0(y2, x1, x0, new_esEs11(x0, x1), ty_Int))
16.41/6.10	   (new_deleteBy(x0, :(x1, y2), app(app(ty_Either, x2), x3)) -> new_deleteBy0(y2, x1, x0, new_esEs2(x0, x1, x2, x3), app(app(ty_Either, x2), x3)),new_deleteBy(x0, :(x1, y2), app(app(ty_Either, x2), x3)) -> new_deleteBy0(y2, x1, x0, new_esEs2(x0, x1, x2, x3), app(app(ty_Either, x2), x3)))
16.41/6.10	   (new_deleteBy(x0, :(x1, y2), ty_Float) -> new_deleteBy0(y2, x1, x0, new_esEs1(x0, x1), ty_Float),new_deleteBy(x0, :(x1, y2), ty_Float) -> new_deleteBy0(y2, x1, x0, new_esEs1(x0, x1), ty_Float))
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(47)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_deleteBy0(xw17, xw18, xw19, False, ba) -> new_deleteBy(xw19, xw17, ba)
16.41/6.10	   new_deleteBy(x0, :(x1, y2), ty_@0) -> new_deleteBy0(y2, x1, x0, new_esEs14(x0, x1), ty_@0)
16.41/6.10	   new_deleteBy(x0, :(x1, y2), app(app(ty_@2, x2), x3)) -> new_deleteBy0(y2, x1, x0, new_esEs6(x0, x1, x2, x3), app(app(ty_@2, x2), x3))
16.41/6.10	   new_deleteBy(x0, :(x1, y2), ty_Ordering) -> new_deleteBy0(y2, x1, x0, new_esEs10(x0, x1), ty_Ordering)
16.41/6.10	   new_deleteBy(x0, :(x1, y2), app(ty_Ratio, x2)) -> new_deleteBy0(y2, x1, x0, new_esEs13(x0, x1, x2), app(ty_Ratio, x2))
16.41/6.10	   new_deleteBy(x0, :(x1, y2), app(ty_Maybe, x2)) -> new_deleteBy0(y2, x1, x0, new_esEs12(x0, x1, x2), app(ty_Maybe, x2))
16.41/6.10	   new_deleteBy(x0, :(x1, y2), ty_Bool) -> new_deleteBy0(y2, x1, x0, new_esEs5(x0, x1), ty_Bool)
16.41/6.10	   new_deleteBy(x0, :(x1, y2), ty_Integer) -> new_deleteBy0(y2, x1, x0, new_esEs9(x0, x1), ty_Integer)
16.41/6.10	   new_deleteBy(x0, :(x1, y2), app(app(app(ty_@3, x2), x3), x4)) -> new_deleteBy0(y2, x1, x0, new_esEs4(x0, x1, x2, x3, x4), app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_deleteBy(x0, :(x1, y2), ty_Double) -> new_deleteBy0(y2, x1, x0, new_esEs8(x0, x1), ty_Double)
16.41/6.10	   new_deleteBy(x0, :(x1, y2), app(ty_[], x2)) -> new_deleteBy0(y2, x1, x0, new_esEs3(x0, x1, x2), app(ty_[], x2))
16.41/6.10	   new_deleteBy(x0, :(x1, y2), ty_Char) -> new_deleteBy0(y2, x1, x0, new_esEs7(x0, x1), ty_Char)
16.41/6.10	   new_deleteBy(x0, :(x1, y2), ty_Int) -> new_deleteBy0(y2, x1, x0, new_esEs11(x0, x1), ty_Int)
16.41/6.10	   new_deleteBy(x0, :(x1, y2), app(app(ty_Either, x2), x3)) -> new_deleteBy0(y2, x1, x0, new_esEs2(x0, x1, x2, x3), app(app(ty_Either, x2), x3))
16.41/6.10	   new_deleteBy(x0, :(x1, y2), ty_Float) -> new_deleteBy0(y2, x1, x0, new_esEs1(x0, x1), ty_Float)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs15(xw10, xw90, ty_@0) -> new_esEs14(xw10, xw90)
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs11(xw10, xw90) -> error([])
16.41/6.10	   new_esEs5(xw10, xw90) -> error([])
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs1(xw10, xw90) -> error([])
16.41/6.10	   new_esEs2(xw10, xw90, bc, bd) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, app(app(ty_@2, ca), cb)) -> new_esEs6(xw10, xw90, ca, cb)
16.41/6.10	   new_esEs4(xw10, xw90, bf, bg, bh) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Ordering) -> new_esEs10(xw10, xw90)
16.41/6.10	   new_esEs7(xw10, xw90) -> error([])
16.41/6.10	   new_esEs9(xw10, xw90) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, app(ty_Ratio, cd)) -> new_esEs13(xw10, xw90, cd)
16.41/6.10	   new_esEs15(xw10, xw90, app(ty_Maybe, cc)) -> new_esEs12(xw10, xw90, cc)
16.41/6.10	   new_esEs6(xw10, xw90, ca, cb) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Bool) -> new_esEs5(xw10, xw90)
16.41/6.10	   new_esEs15(xw10, xw90, ty_Integer) -> new_esEs9(xw10, xw90)
16.41/6.10	   new_esEs15(xw10, xw90, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs4(xw10, xw90, bf, bg, bh)
16.41/6.10	   new_esEs15(xw10, xw90, ty_Double) -> new_esEs8(xw10, xw90)
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs15(xw10, xw90, app(ty_[], be)) -> new_esEs3(xw10, xw90, be)
16.41/6.10	   new_esEs14(xw10, xw90) -> error([])
16.41/6.10	   new_esEs12(xw10, xw90, cc) -> error([])
16.41/6.10	   new_esEs13(xw10, xw90, cd) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Char) -> new_esEs7(xw10, xw90)
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs15(xw10, xw90, ty_Int) -> new_esEs11(xw10, xw90)
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	   new_esEs3(xw10, xw90, be) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, app(app(ty_Either, bc), bd)) -> new_esEs2(xw10, xw90, bc, bd)
16.41/6.10	   new_esEs8(xw10, xw90) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Float) -> new_esEs1(xw10, xw90)
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs7(x0, x1)
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.10	   new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.10	   new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.10	   new_esEs15(x0, x1, ty_Char)
16.41/6.10	   new_esEs14(x0, x1)
16.41/6.10	   new_esEs12(x0, x1, x2)
16.41/6.10	   new_esEs13(x0, x1, x2)
16.41/6.10	   new_esEs15(x0, x1, app(ty_Ratio, x2))
16.41/6.10	   new_esEs15(x0, x1, app(ty_Maybe, x2))
16.41/6.10	   new_esEs5(x0, x1)
16.41/6.10	   new_esEs1(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Double)
16.41/6.10	   new_esEs15(x0, x1, ty_@0)
16.41/6.10	   new_esEs15(x0, x1, ty_Ordering)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_esEs15(x0, x1, ty_Float)
16.41/6.10	   new_esEs2(x0, x1, x2, x3)
16.41/6.10	   new_esEs6(x0, x1, x2, x3)
16.41/6.10	   new_esEs3(x0, x1, x2)
16.41/6.10	   new_esEs9(x0, x1)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs15(x0, x1, ty_Int)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs11(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Integer)
16.41/6.10	   new_esEs8(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Bool)
16.41/6.10	   new_esEs15(x0, x1, app(ty_[], x2))
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(48) DependencyGraphProof (EQUIVALENT)
16.41/6.10	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 13 less nodes.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(49)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_deleteBy(x0, :(x1, y2), ty_Ordering) -> new_deleteBy0(y2, x1, x0, new_esEs10(x0, x1), ty_Ordering)
16.41/6.10	   new_deleteBy0(xw17, xw18, xw19, False, ba) -> new_deleteBy(xw19, xw17, ba)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs15(xw10, xw90, ty_@0) -> new_esEs14(xw10, xw90)
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs11(xw10, xw90) -> error([])
16.41/6.10	   new_esEs5(xw10, xw90) -> error([])
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs1(xw10, xw90) -> error([])
16.41/6.10	   new_esEs2(xw10, xw90, bc, bd) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, app(app(ty_@2, ca), cb)) -> new_esEs6(xw10, xw90, ca, cb)
16.41/6.10	   new_esEs4(xw10, xw90, bf, bg, bh) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Ordering) -> new_esEs10(xw10, xw90)
16.41/6.10	   new_esEs7(xw10, xw90) -> error([])
16.41/6.10	   new_esEs9(xw10, xw90) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, app(ty_Ratio, cd)) -> new_esEs13(xw10, xw90, cd)
16.41/6.10	   new_esEs15(xw10, xw90, app(ty_Maybe, cc)) -> new_esEs12(xw10, xw90, cc)
16.41/6.10	   new_esEs6(xw10, xw90, ca, cb) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Bool) -> new_esEs5(xw10, xw90)
16.41/6.10	   new_esEs15(xw10, xw90, ty_Integer) -> new_esEs9(xw10, xw90)
16.41/6.10	   new_esEs15(xw10, xw90, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs4(xw10, xw90, bf, bg, bh)
16.41/6.10	   new_esEs15(xw10, xw90, ty_Double) -> new_esEs8(xw10, xw90)
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs15(xw10, xw90, app(ty_[], be)) -> new_esEs3(xw10, xw90, be)
16.41/6.10	   new_esEs14(xw10, xw90) -> error([])
16.41/6.10	   new_esEs12(xw10, xw90, cc) -> error([])
16.41/6.10	   new_esEs13(xw10, xw90, cd) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Char) -> new_esEs7(xw10, xw90)
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs15(xw10, xw90, ty_Int) -> new_esEs11(xw10, xw90)
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	   new_esEs3(xw10, xw90, be) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, app(app(ty_Either, bc), bd)) -> new_esEs2(xw10, xw90, bc, bd)
16.41/6.10	   new_esEs8(xw10, xw90) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Float) -> new_esEs1(xw10, xw90)
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs7(x0, x1)
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.10	   new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.10	   new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.10	   new_esEs15(x0, x1, ty_Char)
16.41/6.10	   new_esEs14(x0, x1)
16.41/6.10	   new_esEs12(x0, x1, x2)
16.41/6.10	   new_esEs13(x0, x1, x2)
16.41/6.10	   new_esEs15(x0, x1, app(ty_Ratio, x2))
16.41/6.10	   new_esEs15(x0, x1, app(ty_Maybe, x2))
16.41/6.10	   new_esEs5(x0, x1)
16.41/6.10	   new_esEs1(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Double)
16.41/6.10	   new_esEs15(x0, x1, ty_@0)
16.41/6.10	   new_esEs15(x0, x1, ty_Ordering)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_esEs15(x0, x1, ty_Float)
16.41/6.10	   new_esEs2(x0, x1, x2, x3)
16.41/6.10	   new_esEs6(x0, x1, x2, x3)
16.41/6.10	   new_esEs3(x0, x1, x2)
16.41/6.10	   new_esEs9(x0, x1)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs15(x0, x1, ty_Int)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs11(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Integer)
16.41/6.10	   new_esEs8(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Bool)
16.41/6.10	   new_esEs15(x0, x1, app(ty_[], x2))
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(50) UsableRulesProof (EQUIVALENT)
16.41/6.10	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.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(51)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_deleteBy(x0, :(x1, y2), ty_Ordering) -> new_deleteBy0(y2, x1, x0, new_esEs10(x0, x1), ty_Ordering)
16.41/6.10	   new_deleteBy0(xw17, xw18, xw19, False, ba) -> new_deleteBy(xw19, xw17, ba)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs7(x0, x1)
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.10	   new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.10	   new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.10	   new_esEs15(x0, x1, ty_Char)
16.41/6.10	   new_esEs14(x0, x1)
16.41/6.10	   new_esEs12(x0, x1, x2)
16.41/6.10	   new_esEs13(x0, x1, x2)
16.41/6.10	   new_esEs15(x0, x1, app(ty_Ratio, x2))
16.41/6.10	   new_esEs15(x0, x1, app(ty_Maybe, x2))
16.41/6.10	   new_esEs5(x0, x1)
16.41/6.10	   new_esEs1(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Double)
16.41/6.10	   new_esEs15(x0, x1, ty_@0)
16.41/6.10	   new_esEs15(x0, x1, ty_Ordering)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_esEs15(x0, x1, ty_Float)
16.41/6.10	   new_esEs2(x0, x1, x2, x3)
16.41/6.10	   new_esEs6(x0, x1, x2, x3)
16.41/6.10	   new_esEs3(x0, x1, x2)
16.41/6.10	   new_esEs9(x0, x1)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs15(x0, x1, ty_Int)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs11(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Integer)
16.41/6.10	   new_esEs8(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Bool)
16.41/6.10	   new_esEs15(x0, x1, app(ty_[], x2))
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(52) QReductionProof (EQUIVALENT)
16.41/6.10	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
16.41/6.10	
16.41/6.10	   new_esEs7(x0, x1)
16.41/6.10	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.10	   new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.10	   new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.10	   new_esEs15(x0, x1, ty_Char)
16.41/6.10	   new_esEs14(x0, x1)
16.41/6.10	   new_esEs12(x0, x1, x2)
16.41/6.10	   new_esEs13(x0, x1, x2)
16.41/6.10	   new_esEs15(x0, x1, app(ty_Ratio, x2))
16.41/6.10	   new_esEs15(x0, x1, app(ty_Maybe, x2))
16.41/6.10	   new_esEs5(x0, x1)
16.41/6.10	   new_esEs1(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Double)
16.41/6.10	   new_esEs15(x0, x1, ty_@0)
16.41/6.10	   new_esEs15(x0, x1, ty_Ordering)
16.41/6.10	   new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_esEs15(x0, x1, ty_Float)
16.41/6.10	   new_esEs2(x0, x1, x2, x3)
16.41/6.10	   new_esEs6(x0, x1, x2, x3)
16.41/6.10	   new_esEs3(x0, x1, x2)
16.41/6.10	   new_esEs9(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Int)
16.41/6.10	   new_esEs11(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Integer)
16.41/6.10	   new_esEs8(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Bool)
16.41/6.10	   new_esEs15(x0, x1, app(ty_[], x2))
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(53)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_deleteBy(x0, :(x1, y2), ty_Ordering) -> new_deleteBy0(y2, x1, x0, new_esEs10(x0, x1), ty_Ordering)
16.41/6.10	   new_deleteBy0(xw17, xw18, xw19, False, ba) -> new_deleteBy(xw19, xw17, ba)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(54) TransformationProof (EQUIVALENT)
16.41/6.10	By narrowing [LPAR04] the rule new_deleteBy(x0, :(x1, y2), ty_Ordering) -> new_deleteBy0(y2, x1, x0, new_esEs10(x0, x1), ty_Ordering) at position [3] we obtained the following new rules [LPAR04]:
16.41/6.10	
16.41/6.10	   (new_deleteBy(EQ, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, EQ, False, ty_Ordering),new_deleteBy(EQ, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, EQ, False, ty_Ordering))
16.41/6.10	   (new_deleteBy(GT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, GT, False, ty_Ordering),new_deleteBy(GT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, GT, False, ty_Ordering))
16.41/6.10	   (new_deleteBy(LT, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, LT, False, ty_Ordering),new_deleteBy(LT, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, LT, False, ty_Ordering))
16.41/6.10	   (new_deleteBy(GT, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, GT, False, ty_Ordering),new_deleteBy(GT, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, GT, False, ty_Ordering))
16.41/6.10	   (new_deleteBy(LT, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, LT, True, ty_Ordering),new_deleteBy(LT, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, LT, True, ty_Ordering))
16.41/6.10	   (new_deleteBy(LT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, LT, False, ty_Ordering),new_deleteBy(LT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, LT, False, ty_Ordering))
16.41/6.10	   (new_deleteBy(EQ, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, EQ, False, ty_Ordering),new_deleteBy(EQ, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, EQ, False, ty_Ordering))
16.41/6.10	   (new_deleteBy(GT, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, GT, True, ty_Ordering),new_deleteBy(GT, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, GT, True, ty_Ordering))
16.41/6.10	   (new_deleteBy(EQ, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, EQ, True, ty_Ordering),new_deleteBy(EQ, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, EQ, True, ty_Ordering))
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(55)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_deleteBy0(xw17, xw18, xw19, False, ba) -> new_deleteBy(xw19, xw17, ba)
16.41/6.10	   new_deleteBy(EQ, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, EQ, False, ty_Ordering)
16.41/6.10	   new_deleteBy(GT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, GT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(LT, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, LT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(GT, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, GT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(LT, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, LT, True, ty_Ordering)
16.41/6.10	   new_deleteBy(LT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, LT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(EQ, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, EQ, False, ty_Ordering)
16.41/6.10	   new_deleteBy(GT, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, GT, True, ty_Ordering)
16.41/6.10	   new_deleteBy(EQ, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, EQ, True, ty_Ordering)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(56) DependencyGraphProof (EQUIVALENT)
16.41/6.10	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(57)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_deleteBy(EQ, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, EQ, False, ty_Ordering)
16.41/6.10	   new_deleteBy0(xw17, xw18, xw19, False, ba) -> new_deleteBy(xw19, xw17, ba)
16.41/6.10	   new_deleteBy(GT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, GT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(LT, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, LT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(GT, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, GT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(LT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, LT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(EQ, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, EQ, False, ty_Ordering)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(58) UsableRulesProof (EQUIVALENT)
16.41/6.10	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.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(59)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_deleteBy(EQ, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, EQ, False, ty_Ordering)
16.41/6.10	   new_deleteBy0(xw17, xw18, xw19, False, ba) -> new_deleteBy(xw19, xw17, ba)
16.41/6.10	   new_deleteBy(GT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, GT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(LT, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, LT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(GT, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, GT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(LT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, LT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(EQ, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, EQ, False, ty_Ordering)
16.41/6.10	
16.41/6.10	R is empty.
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(60) QReductionProof (EQUIVALENT)
16.41/6.10	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
16.41/6.10	
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(61)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_deleteBy(EQ, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, EQ, False, ty_Ordering)
16.41/6.10	   new_deleteBy0(xw17, xw18, xw19, False, ba) -> new_deleteBy(xw19, xw17, ba)
16.41/6.10	   new_deleteBy(GT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, GT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(LT, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, LT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(GT, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, GT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(LT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, LT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(EQ, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, EQ, False, ty_Ordering)
16.41/6.10	
16.41/6.10	R is empty.
16.41/6.10	Q is empty.
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(62) TransformationProof (EQUIVALENT)
16.41/6.10	By instantiating [LPAR04] the rule new_deleteBy0(xw17, xw18, xw19, False, ba) -> new_deleteBy(xw19, xw17, ba) we obtained the following new rules [LPAR04]:
16.41/6.10	
16.41/6.10	   (new_deleteBy0(z0, GT, EQ, False, ty_Ordering) -> new_deleteBy(EQ, z0, ty_Ordering),new_deleteBy0(z0, GT, EQ, False, ty_Ordering) -> new_deleteBy(EQ, z0, ty_Ordering))
16.41/6.10	   (new_deleteBy0(z0, EQ, GT, False, ty_Ordering) -> new_deleteBy(GT, z0, ty_Ordering),new_deleteBy0(z0, EQ, GT, False, ty_Ordering) -> new_deleteBy(GT, z0, ty_Ordering))
16.41/6.10	   (new_deleteBy0(z0, GT, LT, False, ty_Ordering) -> new_deleteBy(LT, z0, ty_Ordering),new_deleteBy0(z0, GT, LT, False, ty_Ordering) -> new_deleteBy(LT, z0, ty_Ordering))
16.41/6.10	   (new_deleteBy0(z0, LT, GT, False, ty_Ordering) -> new_deleteBy(GT, z0, ty_Ordering),new_deleteBy0(z0, LT, GT, False, ty_Ordering) -> new_deleteBy(GT, z0, ty_Ordering))
16.41/6.10	   (new_deleteBy0(z0, EQ, LT, False, ty_Ordering) -> new_deleteBy(LT, z0, ty_Ordering),new_deleteBy0(z0, EQ, LT, False, ty_Ordering) -> new_deleteBy(LT, z0, ty_Ordering))
16.41/6.10	   (new_deleteBy0(z0, LT, EQ, False, ty_Ordering) -> new_deleteBy(EQ, z0, ty_Ordering),new_deleteBy0(z0, LT, EQ, False, ty_Ordering) -> new_deleteBy(EQ, z0, ty_Ordering))
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(63)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_deleteBy(EQ, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, EQ, False, ty_Ordering)
16.41/6.10	   new_deleteBy(GT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, GT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(LT, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, LT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(GT, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, GT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(LT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, LT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(EQ, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, EQ, False, ty_Ordering)
16.41/6.10	   new_deleteBy0(z0, GT, EQ, False, ty_Ordering) -> new_deleteBy(EQ, z0, ty_Ordering)
16.41/6.10	   new_deleteBy0(z0, EQ, GT, False, ty_Ordering) -> new_deleteBy(GT, z0, ty_Ordering)
16.41/6.10	   new_deleteBy0(z0, GT, LT, False, ty_Ordering) -> new_deleteBy(LT, z0, ty_Ordering)
16.41/6.10	   new_deleteBy0(z0, LT, GT, False, ty_Ordering) -> new_deleteBy(GT, z0, ty_Ordering)
16.41/6.10	   new_deleteBy0(z0, EQ, LT, False, ty_Ordering) -> new_deleteBy(LT, z0, ty_Ordering)
16.41/6.10	   new_deleteBy0(z0, LT, EQ, False, ty_Ordering) -> new_deleteBy(EQ, z0, ty_Ordering)
16.41/6.10	
16.41/6.10	R is empty.
16.41/6.10	Q is empty.
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(64) DependencyGraphProof (EQUIVALENT)
16.41/6.10	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(65)
16.41/6.10	Complex Obligation (AND)
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(66)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_deleteBy0(z0, GT, LT, False, ty_Ordering) -> new_deleteBy(LT, z0, ty_Ordering)
16.41/6.10	   new_deleteBy(LT, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, LT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(LT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, LT, False, ty_Ordering)
16.41/6.10	   new_deleteBy0(z0, EQ, LT, False, ty_Ordering) -> new_deleteBy(LT, z0, ty_Ordering)
16.41/6.10	
16.41/6.10	R is empty.
16.41/6.10	Q is empty.
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(67) QDPSizeChangeProof (EQUIVALENT)
16.41/6.10	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. 
16.41/6.10	
16.41/6.10	From the DPs we obtained the following set of size-change graphs:
16.41/6.10	*new_deleteBy(LT, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, LT, False, ty_Ordering)
16.41/6.10	The graph contains the following edges 2 > 1, 2 > 2, 1 >= 3, 3 >= 5
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_deleteBy(LT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, LT, False, ty_Ordering)
16.41/6.10	The graph contains the following edges 2 > 1, 2 > 2, 1 >= 3, 3 >= 5
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_deleteBy0(z0, GT, LT, False, ty_Ordering) -> new_deleteBy(LT, z0, ty_Ordering)
16.41/6.10	The graph contains the following edges 3 >= 1, 1 >= 2, 5 >= 3
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_deleteBy0(z0, EQ, LT, False, ty_Ordering) -> new_deleteBy(LT, z0, ty_Ordering)
16.41/6.10	The graph contains the following edges 3 >= 1, 1 >= 2, 5 >= 3
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(68)
16.41/6.10	YES
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(69)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_deleteBy0(z0, EQ, GT, False, ty_Ordering) -> new_deleteBy(GT, z0, ty_Ordering)
16.41/6.10	   new_deleteBy(GT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, GT, False, ty_Ordering)
16.41/6.10	   new_deleteBy(GT, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, GT, False, ty_Ordering)
16.41/6.10	   new_deleteBy0(z0, LT, GT, False, ty_Ordering) -> new_deleteBy(GT, z0, ty_Ordering)
16.41/6.10	
16.41/6.10	R is empty.
16.41/6.10	Q is empty.
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(70) QDPSizeChangeProof (EQUIVALENT)
16.41/6.10	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. 
16.41/6.10	
16.41/6.10	From the DPs we obtained the following set of size-change graphs:
16.41/6.10	*new_deleteBy(GT, :(EQ, y2), ty_Ordering) -> new_deleteBy0(y2, EQ, GT, False, ty_Ordering)
16.41/6.10	The graph contains the following edges 2 > 1, 2 > 2, 1 >= 3, 3 >= 5
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_deleteBy(GT, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, GT, False, ty_Ordering)
16.41/6.10	The graph contains the following edges 2 > 1, 2 > 2, 1 >= 3, 3 >= 5
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_deleteBy0(z0, EQ, GT, False, ty_Ordering) -> new_deleteBy(GT, z0, ty_Ordering)
16.41/6.10	The graph contains the following edges 3 >= 1, 1 >= 2, 5 >= 3
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_deleteBy0(z0, LT, GT, False, ty_Ordering) -> new_deleteBy(GT, z0, ty_Ordering)
16.41/6.10	The graph contains the following edges 3 >= 1, 1 >= 2, 5 >= 3
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(71)
16.41/6.10	YES
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(72)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_deleteBy0(z0, GT, EQ, False, ty_Ordering) -> new_deleteBy(EQ, z0, ty_Ordering)
16.41/6.10	   new_deleteBy(EQ, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, EQ, False, ty_Ordering)
16.41/6.10	   new_deleteBy(EQ, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, EQ, False, ty_Ordering)
16.41/6.10	   new_deleteBy0(z0, LT, EQ, False, ty_Ordering) -> new_deleteBy(EQ, z0, ty_Ordering)
16.41/6.10	
16.41/6.10	R is empty.
16.41/6.10	Q is empty.
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(73) QDPSizeChangeProof (EQUIVALENT)
16.41/6.10	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. 
16.41/6.10	
16.41/6.10	From the DPs we obtained the following set of size-change graphs:
16.41/6.10	*new_deleteBy(EQ, :(GT, y2), ty_Ordering) -> new_deleteBy0(y2, GT, EQ, False, ty_Ordering)
16.41/6.10	The graph contains the following edges 2 > 1, 2 > 2, 1 >= 3, 3 >= 5
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_deleteBy(EQ, :(LT, y2), ty_Ordering) -> new_deleteBy0(y2, LT, EQ, False, ty_Ordering)
16.41/6.10	The graph contains the following edges 2 > 1, 2 > 2, 1 >= 3, 3 >= 5
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_deleteBy0(z0, GT, EQ, False, ty_Ordering) -> new_deleteBy(EQ, z0, ty_Ordering)
16.41/6.10	The graph contains the following edges 3 >= 1, 1 >= 2, 5 >= 3
16.41/6.10	
16.41/6.10	
16.41/6.10	*new_deleteBy0(z0, LT, EQ, False, ty_Ordering) -> new_deleteBy(EQ, z0, ty_Ordering)
16.41/6.10	The graph contains the following edges 3 >= 1, 1 >= 2, 5 >= 3
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(74)
16.41/6.10	YES
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(75)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_foldl(xw9, xw10, :(xw110, xw111), ba) -> new_foldl(new_flip(xw9, xw10, ba), xw110, xw111, ba)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs15(xw10, xw90, ty_@0) -> new_esEs14(xw10, xw90)
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs11(xw10, xw90) -> error([])
16.41/6.10	   new_esEs5(xw10, xw90) -> error([])
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs1(xw10, xw90) -> error([])
16.41/6.10	   new_esEs2(xw10, xw90, bb, bc) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, app(app(ty_@2, ca), cb)) -> new_esEs6(xw10, xw90, ca, cb)
16.41/6.10	   new_esEs4(xw10, xw90, bf, bg, bh) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Ordering) -> new_esEs10(xw10, xw90)
16.41/6.10	   new_esEs7(xw10, xw90) -> error([])
16.41/6.10	   new_esEs9(xw10, xw90) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, app(ty_Ratio, cd)) -> new_esEs13(xw10, xw90, cd)
16.41/6.10	   new_esEs15(xw10, xw90, app(ty_Maybe, cc)) -> new_esEs12(xw10, xw90, cc)
16.41/6.10	   new_deleteBy00(xw17, xw18, xw19, True, be) -> xw17
16.41/6.10	   new_esEs6(xw10, xw90, ca, cb) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Bool) -> new_esEs5(xw10, xw90)
16.41/6.10	   new_esEs15(xw10, xw90, ty_Integer) -> new_esEs9(xw10, xw90)
16.41/6.10	   new_esEs15(xw10, xw90, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs4(xw10, xw90, bf, bg, bh)
16.41/6.10	   new_deleteBy1(xw10, :(xw90, xw91), ba) -> new_deleteBy00(xw91, xw90, xw10, new_esEs15(xw10, xw90, ba), ba)
16.41/6.10	   new_esEs15(xw10, xw90, ty_Double) -> new_esEs8(xw10, xw90)
16.41/6.10	   new_esEs10(LT, LT) -> True
16.41/6.10	   new_esEs15(xw10, xw90, app(ty_[], bd)) -> new_esEs3(xw10, xw90, bd)
16.41/6.10	   new_flip(xw9, xw10, ba) -> new_deleteBy1(xw10, xw9, ba)
16.41/6.10	   new_esEs14(xw10, xw90) -> error([])
16.41/6.10	   new_esEs12(xw10, xw90, cc) -> error([])
16.41/6.10	   new_esEs13(xw10, xw90, cd) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Char) -> new_esEs7(xw10, xw90)
16.41/6.10	   new_esEs10(LT, EQ) -> False
16.41/6.10	   new_esEs10(EQ, LT) -> False
16.41/6.10	   new_esEs15(xw10, xw90, ty_Int) -> new_esEs11(xw10, xw90)
16.41/6.10	   new_esEs10(GT, GT) -> True
16.41/6.10	   new_esEs3(xw10, xw90, bd) -> error([])
16.41/6.10	   new_deleteBy1(xw10, [], ba) -> []
16.41/6.10	   new_esEs15(xw10, xw90, app(app(ty_Either, bb), bc)) -> new_esEs2(xw10, xw90, bb, bc)
16.41/6.10	   new_esEs8(xw10, xw90) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Float) -> new_esEs1(xw10, xw90)
16.41/6.10	   new_deleteBy00(xw17, xw18, xw19, False, be) -> :(xw18, new_deleteBy1(xw19, xw17, be))
16.41/6.10	   new_esEs10(EQ, EQ) -> True
16.41/6.10	
16.41/6.10	The set Q consists of the following terms:
16.41/6.10	
16.41/6.10	   new_esEs7(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.10	   new_esEs10(GT, GT)
16.41/6.10	   new_esEs2(x0, x1, x2, x3)
16.41/6.10	   new_esEs3(x0, x1, x2)
16.41/6.10	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.10	   new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.10	   new_deleteBy1(x0, :(x1, x2), x3)
16.41/6.10	   new_esEs15(x0, x1, ty_Char)
16.41/6.10	   new_deleteBy1(x0, [], x1)
16.41/6.10	   new_flip(x0, x1, x2)
16.41/6.10	   new_esEs14(x0, x1)
16.41/6.10	   new_esEs12(x0, x1, x2)
16.41/6.10	   new_esEs13(x0, x1, x2)
16.41/6.10	   new_esEs15(x0, x1, app(ty_Ratio, x2))
16.41/6.10	   new_esEs15(x0, x1, app(ty_Maybe, x2))
16.41/6.10	   new_deleteBy00(x0, x1, x2, False, x3)
16.41/6.10	   new_esEs5(x0, x1)
16.41/6.10	   new_esEs1(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Double)
16.41/6.10	   new_esEs15(x0, x1, ty_@0)
16.41/6.10	   new_esEs15(x0, x1, ty_Ordering)
16.41/6.10	   new_esEs10(LT, EQ)
16.41/6.10	   new_esEs10(EQ, LT)
16.41/6.10	   new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.10	   new_esEs15(x0, x1, ty_Float)
16.41/6.10	   new_esEs6(x0, x1, x2, x3)
16.41/6.10	   new_esEs9(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, app(ty_[], x2))
16.41/6.10	   new_esEs10(EQ, GT)
16.41/6.10	   new_esEs10(GT, EQ)
16.41/6.10	   new_esEs15(x0, x1, ty_Int)
16.41/6.10	   new_esEs10(LT, GT)
16.41/6.10	   new_esEs10(GT, LT)
16.41/6.10	   new_esEs11(x0, x1)
16.41/6.10	   new_deleteBy00(x0, x1, x2, True, x3)
16.41/6.10	   new_esEs15(x0, x1, ty_Integer)
16.41/6.10	   new_esEs8(x0, x1)
16.41/6.10	   new_esEs15(x0, x1, ty_Bool)
16.41/6.10	   new_esEs10(LT, LT)
16.41/6.10	   new_esEs10(EQ, EQ)
16.41/6.10	
16.41/6.10	We have to consider all minimal (P,Q,R)-chains.
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(76) TransformationProof (EQUIVALENT)
16.41/6.10	By rewriting [LPAR04] the rule new_foldl(xw9, xw10, :(xw110, xw111), ba) -> new_foldl(new_flip(xw9, xw10, ba), xw110, xw111, ba) at position [0] we obtained the following new rules [LPAR04]:
16.41/6.10	
16.41/6.10	   (new_foldl(xw9, xw10, :(xw110, xw111), ba) -> new_foldl(new_deleteBy1(xw10, xw9, ba), xw110, xw111, ba),new_foldl(xw9, xw10, :(xw110, xw111), ba) -> new_foldl(new_deleteBy1(xw10, xw9, ba), xw110, xw111, ba))
16.41/6.10	
16.41/6.10	
16.41/6.10	----------------------------------------
16.41/6.10	
16.41/6.10	(77)
16.41/6.10	Obligation:
16.41/6.10	Q DP problem:
16.41/6.10	The TRS P consists of the following rules:
16.41/6.10	
16.41/6.10	   new_foldl(xw9, xw10, :(xw110, xw111), ba) -> new_foldl(new_deleteBy1(xw10, xw9, ba), xw110, xw111, ba)
16.41/6.10	
16.41/6.10	The TRS R consists of the following rules:
16.41/6.10	
16.41/6.10	   new_esEs15(xw10, xw90, ty_@0) -> new_esEs14(xw10, xw90)
16.41/6.10	   new_esEs10(EQ, GT) -> False
16.41/6.10	   new_esEs10(GT, EQ) -> False
16.41/6.10	   new_esEs11(xw10, xw90) -> error([])
16.41/6.10	   new_esEs5(xw10, xw90) -> error([])
16.41/6.10	   new_esEs10(LT, GT) -> False
16.41/6.10	   new_esEs10(GT, LT) -> False
16.41/6.10	   new_esEs1(xw10, xw90) -> error([])
16.41/6.10	   new_esEs2(xw10, xw90, bb, bc) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, app(app(ty_@2, ca), cb)) -> new_esEs6(xw10, xw90, ca, cb)
16.41/6.10	   new_esEs4(xw10, xw90, bf, bg, bh) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Ordering) -> new_esEs10(xw10, xw90)
16.41/6.10	   new_esEs7(xw10, xw90) -> error([])
16.41/6.10	   new_esEs9(xw10, xw90) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, app(ty_Ratio, cd)) -> new_esEs13(xw10, xw90, cd)
16.41/6.10	   new_esEs15(xw10, xw90, app(ty_Maybe, cc)) -> new_esEs12(xw10, xw90, cc)
16.41/6.10	   new_deleteBy00(xw17, xw18, xw19, True, be) -> xw17
16.41/6.10	   new_esEs6(xw10, xw90, ca, cb) -> error([])
16.41/6.10	   new_esEs15(xw10, xw90, ty_Bool) -> new_esEs5(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Integer) -> new_esEs9(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs4(xw10, xw90, bf, bg, bh)
16.41/6.11	   new_deleteBy1(xw10, :(xw90, xw91), ba) -> new_deleteBy00(xw91, xw90, xw10, new_esEs15(xw10, xw90, ba), ba)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Double) -> new_esEs8(xw10, xw90)
16.41/6.11	   new_esEs10(LT, LT) -> True
16.41/6.11	   new_esEs15(xw10, xw90, app(ty_[], bd)) -> new_esEs3(xw10, xw90, bd)
16.41/6.11	   new_flip(xw9, xw10, ba) -> new_deleteBy1(xw10, xw9, ba)
16.41/6.11	   new_esEs14(xw10, xw90) -> error([])
16.41/6.11	   new_esEs12(xw10, xw90, cc) -> error([])
16.41/6.11	   new_esEs13(xw10, xw90, cd) -> error([])
16.41/6.11	   new_esEs15(xw10, xw90, ty_Char) -> new_esEs7(xw10, xw90)
16.41/6.11	   new_esEs10(LT, EQ) -> False
16.41/6.11	   new_esEs10(EQ, LT) -> False
16.41/6.11	   new_esEs15(xw10, xw90, ty_Int) -> new_esEs11(xw10, xw90)
16.41/6.11	   new_esEs10(GT, GT) -> True
16.41/6.11	   new_esEs3(xw10, xw90, bd) -> error([])
16.41/6.11	   new_deleteBy1(xw10, [], ba) -> []
16.41/6.11	   new_esEs15(xw10, xw90, app(app(ty_Either, bb), bc)) -> new_esEs2(xw10, xw90, bb, bc)
16.41/6.11	   new_esEs8(xw10, xw90) -> error([])
16.41/6.11	   new_esEs15(xw10, xw90, ty_Float) -> new_esEs1(xw10, xw90)
16.41/6.11	   new_deleteBy00(xw17, xw18, xw19, False, be) -> :(xw18, new_deleteBy1(xw19, xw17, be))
16.41/6.11	   new_esEs10(EQ, EQ) -> True
16.41/6.11	
16.41/6.11	The set Q consists of the following terms:
16.41/6.11	
16.41/6.11	   new_esEs7(x0, x1)
16.41/6.11	   new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.11	   new_esEs10(GT, GT)
16.41/6.11	   new_esEs2(x0, x1, x2, x3)
16.41/6.11	   new_esEs3(x0, x1, x2)
16.41/6.11	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.11	   new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.11	   new_deleteBy1(x0, :(x1, x2), x3)
16.41/6.11	   new_esEs15(x0, x1, ty_Char)
16.41/6.11	   new_deleteBy1(x0, [], x1)
16.41/6.11	   new_flip(x0, x1, x2)
16.41/6.11	   new_esEs14(x0, x1)
16.41/6.11	   new_esEs12(x0, x1, x2)
16.41/6.11	   new_esEs13(x0, x1, x2)
16.41/6.11	   new_esEs15(x0, x1, app(ty_Ratio, x2))
16.41/6.11	   new_esEs15(x0, x1, app(ty_Maybe, x2))
16.41/6.11	   new_deleteBy00(x0, x1, x2, False, x3)
16.41/6.11	   new_esEs5(x0, x1)
16.41/6.11	   new_esEs1(x0, x1)
16.41/6.11	   new_esEs15(x0, x1, ty_Double)
16.41/6.11	   new_esEs15(x0, x1, ty_@0)
16.41/6.11	   new_esEs15(x0, x1, ty_Ordering)
16.41/6.11	   new_esEs10(LT, EQ)
16.41/6.11	   new_esEs10(EQ, LT)
16.41/6.11	   new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.11	   new_esEs15(x0, x1, ty_Float)
16.41/6.11	   new_esEs6(x0, x1, x2, x3)
16.41/6.11	   new_esEs9(x0, x1)
16.41/6.11	   new_esEs15(x0, x1, app(ty_[], x2))
16.41/6.11	   new_esEs10(EQ, GT)
16.41/6.11	   new_esEs10(GT, EQ)
16.41/6.11	   new_esEs15(x0, x1, ty_Int)
16.41/6.11	   new_esEs10(LT, GT)
16.41/6.11	   new_esEs10(GT, LT)
16.41/6.11	   new_esEs11(x0, x1)
16.41/6.11	   new_deleteBy00(x0, x1, x2, True, x3)
16.41/6.11	   new_esEs15(x0, x1, ty_Integer)
16.41/6.11	   new_esEs8(x0, x1)
16.41/6.11	   new_esEs15(x0, x1, ty_Bool)
16.41/6.11	   new_esEs10(LT, LT)
16.41/6.11	   new_esEs10(EQ, EQ)
16.41/6.11	
16.41/6.11	We have to consider all minimal (P,Q,R)-chains.
16.41/6.11	----------------------------------------
16.41/6.11	
16.41/6.11	(78) UsableRulesProof (EQUIVALENT)
16.41/6.11	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.
16.41/6.11	----------------------------------------
16.41/6.11	
16.41/6.11	(79)
16.41/6.11	Obligation:
16.41/6.11	Q DP problem:
16.41/6.11	The TRS P consists of the following rules:
16.41/6.11	
16.41/6.11	   new_foldl(xw9, xw10, :(xw110, xw111), ba) -> new_foldl(new_deleteBy1(xw10, xw9, ba), xw110, xw111, ba)
16.41/6.11	
16.41/6.11	The TRS R consists of the following rules:
16.41/6.11	
16.41/6.11	   new_deleteBy1(xw10, :(xw90, xw91), ba) -> new_deleteBy00(xw91, xw90, xw10, new_esEs15(xw10, xw90, ba), ba)
16.41/6.11	   new_deleteBy1(xw10, [], ba) -> []
16.41/6.11	   new_esEs15(xw10, xw90, ty_@0) -> new_esEs14(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, app(app(ty_@2, ca), cb)) -> new_esEs6(xw10, xw90, ca, cb)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Ordering) -> new_esEs10(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, app(ty_Ratio, cd)) -> new_esEs13(xw10, xw90, cd)
16.41/6.11	   new_esEs15(xw10, xw90, app(ty_Maybe, cc)) -> new_esEs12(xw10, xw90, cc)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Bool) -> new_esEs5(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Integer) -> new_esEs9(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs4(xw10, xw90, bf, bg, bh)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Double) -> new_esEs8(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, app(ty_[], bd)) -> new_esEs3(xw10, xw90, bd)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Char) -> new_esEs7(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Int) -> new_esEs11(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, app(app(ty_Either, bb), bc)) -> new_esEs2(xw10, xw90, bb, bc)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Float) -> new_esEs1(xw10, xw90)
16.41/6.11	   new_deleteBy00(xw17, xw18, xw19, True, be) -> xw17
16.41/6.11	   new_deleteBy00(xw17, xw18, xw19, False, be) -> :(xw18, new_deleteBy1(xw19, xw17, be))
16.41/6.11	   new_esEs1(xw10, xw90) -> error([])
16.41/6.11	   new_esEs2(xw10, xw90, bb, bc) -> error([])
16.41/6.11	   new_esEs11(xw10, xw90) -> error([])
16.41/6.11	   new_esEs7(xw10, xw90) -> error([])
16.41/6.11	   new_esEs3(xw10, xw90, bd) -> error([])
16.41/6.11	   new_esEs8(xw10, xw90) -> error([])
16.41/6.11	   new_esEs4(xw10, xw90, bf, bg, bh) -> error([])
16.41/6.11	   new_esEs9(xw10, xw90) -> error([])
16.41/6.11	   new_esEs5(xw10, xw90) -> error([])
16.41/6.11	   new_esEs12(xw10, xw90, cc) -> error([])
16.41/6.11	   new_esEs13(xw10, xw90, cd) -> error([])
16.41/6.11	   new_esEs10(EQ, GT) -> False
16.41/6.11	   new_esEs10(GT, EQ) -> False
16.41/6.11	   new_esEs10(LT, GT) -> False
16.41/6.11	   new_esEs10(GT, LT) -> False
16.41/6.11	   new_esEs10(LT, LT) -> True
16.41/6.11	   new_esEs10(LT, EQ) -> False
16.41/6.11	   new_esEs10(EQ, LT) -> False
16.41/6.11	   new_esEs10(GT, GT) -> True
16.41/6.11	   new_esEs10(EQ, EQ) -> True
16.41/6.11	   new_esEs6(xw10, xw90, ca, cb) -> error([])
16.41/6.11	   new_esEs14(xw10, xw90) -> error([])
16.41/6.11	
16.41/6.11	The set Q consists of the following terms:
16.41/6.11	
16.41/6.11	   new_esEs7(x0, x1)
16.41/6.11	   new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.11	   new_esEs10(GT, GT)
16.41/6.11	   new_esEs2(x0, x1, x2, x3)
16.41/6.11	   new_esEs3(x0, x1, x2)
16.41/6.11	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.11	   new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.11	   new_deleteBy1(x0, :(x1, x2), x3)
16.41/6.11	   new_esEs15(x0, x1, ty_Char)
16.41/6.11	   new_deleteBy1(x0, [], x1)
16.41/6.11	   new_flip(x0, x1, x2)
16.41/6.11	   new_esEs14(x0, x1)
16.41/6.11	   new_esEs12(x0, x1, x2)
16.41/6.11	   new_esEs13(x0, x1, x2)
16.41/6.11	   new_esEs15(x0, x1, app(ty_Ratio, x2))
16.41/6.11	   new_esEs15(x0, x1, app(ty_Maybe, x2))
16.41/6.11	   new_deleteBy00(x0, x1, x2, False, x3)
16.41/6.11	   new_esEs5(x0, x1)
16.41/6.11	   new_esEs1(x0, x1)
16.41/6.11	   new_esEs15(x0, x1, ty_Double)
16.41/6.11	   new_esEs15(x0, x1, ty_@0)
16.41/6.11	   new_esEs15(x0, x1, ty_Ordering)
16.41/6.11	   new_esEs10(LT, EQ)
16.41/6.11	   new_esEs10(EQ, LT)
16.41/6.11	   new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.11	   new_esEs15(x0, x1, ty_Float)
16.41/6.11	   new_esEs6(x0, x1, x2, x3)
16.41/6.11	   new_esEs9(x0, x1)
16.41/6.11	   new_esEs15(x0, x1, app(ty_[], x2))
16.41/6.11	   new_esEs10(EQ, GT)
16.41/6.11	   new_esEs10(GT, EQ)
16.41/6.11	   new_esEs15(x0, x1, ty_Int)
16.41/6.11	   new_esEs10(LT, GT)
16.41/6.11	   new_esEs10(GT, LT)
16.41/6.11	   new_esEs11(x0, x1)
16.41/6.11	   new_deleteBy00(x0, x1, x2, True, x3)
16.41/6.11	   new_esEs15(x0, x1, ty_Integer)
16.41/6.11	   new_esEs8(x0, x1)
16.41/6.11	   new_esEs15(x0, x1, ty_Bool)
16.41/6.11	   new_esEs10(LT, LT)
16.41/6.11	   new_esEs10(EQ, EQ)
16.41/6.11	
16.41/6.11	We have to consider all minimal (P,Q,R)-chains.
16.41/6.11	----------------------------------------
16.41/6.11	
16.41/6.11	(80) QReductionProof (EQUIVALENT)
16.41/6.11	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
16.41/6.11	
16.41/6.11	   new_flip(x0, x1, x2)
16.41/6.11	
16.41/6.11	
16.41/6.11	----------------------------------------
16.41/6.11	
16.41/6.11	(81)
16.41/6.11	Obligation:
16.41/6.11	Q DP problem:
16.41/6.11	The TRS P consists of the following rules:
16.41/6.11	
16.41/6.11	   new_foldl(xw9, xw10, :(xw110, xw111), ba) -> new_foldl(new_deleteBy1(xw10, xw9, ba), xw110, xw111, ba)
16.41/6.11	
16.41/6.11	The TRS R consists of the following rules:
16.41/6.11	
16.41/6.11	   new_deleteBy1(xw10, :(xw90, xw91), ba) -> new_deleteBy00(xw91, xw90, xw10, new_esEs15(xw10, xw90, ba), ba)
16.41/6.11	   new_deleteBy1(xw10, [], ba) -> []
16.41/6.11	   new_esEs15(xw10, xw90, ty_@0) -> new_esEs14(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, app(app(ty_@2, ca), cb)) -> new_esEs6(xw10, xw90, ca, cb)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Ordering) -> new_esEs10(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, app(ty_Ratio, cd)) -> new_esEs13(xw10, xw90, cd)
16.41/6.11	   new_esEs15(xw10, xw90, app(ty_Maybe, cc)) -> new_esEs12(xw10, xw90, cc)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Bool) -> new_esEs5(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Integer) -> new_esEs9(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, app(app(app(ty_@3, bf), bg), bh)) -> new_esEs4(xw10, xw90, bf, bg, bh)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Double) -> new_esEs8(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, app(ty_[], bd)) -> new_esEs3(xw10, xw90, bd)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Char) -> new_esEs7(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Int) -> new_esEs11(xw10, xw90)
16.41/6.11	   new_esEs15(xw10, xw90, app(app(ty_Either, bb), bc)) -> new_esEs2(xw10, xw90, bb, bc)
16.41/6.11	   new_esEs15(xw10, xw90, ty_Float) -> new_esEs1(xw10, xw90)
16.41/6.11	   new_deleteBy00(xw17, xw18, xw19, True, be) -> xw17
16.41/6.11	   new_deleteBy00(xw17, xw18, xw19, False, be) -> :(xw18, new_deleteBy1(xw19, xw17, be))
16.41/6.11	   new_esEs1(xw10, xw90) -> error([])
16.41/6.11	   new_esEs2(xw10, xw90, bb, bc) -> error([])
16.41/6.11	   new_esEs11(xw10, xw90) -> error([])
16.41/6.11	   new_esEs7(xw10, xw90) -> error([])
16.41/6.11	   new_esEs3(xw10, xw90, bd) -> error([])
16.41/6.11	   new_esEs8(xw10, xw90) -> error([])
16.41/6.11	   new_esEs4(xw10, xw90, bf, bg, bh) -> error([])
16.41/6.11	   new_esEs9(xw10, xw90) -> error([])
16.41/6.11	   new_esEs5(xw10, xw90) -> error([])
16.41/6.11	   new_esEs12(xw10, xw90, cc) -> error([])
16.41/6.11	   new_esEs13(xw10, xw90, cd) -> error([])
16.41/6.11	   new_esEs10(EQ, GT) -> False
16.41/6.11	   new_esEs10(GT, EQ) -> False
16.41/6.11	   new_esEs10(LT, GT) -> False
16.41/6.11	   new_esEs10(GT, LT) -> False
16.41/6.11	   new_esEs10(LT, LT) -> True
16.41/6.11	   new_esEs10(LT, EQ) -> False
16.41/6.11	   new_esEs10(EQ, LT) -> False
16.41/6.11	   new_esEs10(GT, GT) -> True
16.41/6.11	   new_esEs10(EQ, EQ) -> True
16.41/6.11	   new_esEs6(xw10, xw90, ca, cb) -> error([])
16.41/6.11	   new_esEs14(xw10, xw90) -> error([])
16.41/6.11	
16.41/6.11	The set Q consists of the following terms:
16.41/6.11	
16.41/6.11	   new_esEs7(x0, x1)
16.41/6.11	   new_esEs15(x0, x1, app(app(ty_Either, x2), x3))
16.41/6.11	   new_esEs10(GT, GT)
16.41/6.11	   new_esEs2(x0, x1, x2, x3)
16.41/6.11	   new_esEs3(x0, x1, x2)
16.41/6.11	   new_esEs4(x0, x1, x2, x3, x4)
16.41/6.11	   new_esEs15(x0, x1, app(app(ty_@2, x2), x3))
16.41/6.11	   new_deleteBy1(x0, :(x1, x2), x3)
16.41/6.11	   new_esEs15(x0, x1, ty_Char)
16.41/6.11	   new_deleteBy1(x0, [], x1)
16.41/6.11	   new_esEs14(x0, x1)
16.41/6.11	   new_esEs12(x0, x1, x2)
16.41/6.11	   new_esEs13(x0, x1, x2)
16.41/6.11	   new_esEs15(x0, x1, app(ty_Ratio, x2))
16.41/6.11	   new_esEs15(x0, x1, app(ty_Maybe, x2))
16.41/6.11	   new_deleteBy00(x0, x1, x2, False, x3)
16.41/6.11	   new_esEs5(x0, x1)
16.41/6.11	   new_esEs1(x0, x1)
16.41/6.11	   new_esEs15(x0, x1, ty_Double)
16.41/6.11	   new_esEs15(x0, x1, ty_@0)
16.41/6.11	   new_esEs15(x0, x1, ty_Ordering)
16.41/6.11	   new_esEs10(LT, EQ)
16.41/6.11	   new_esEs10(EQ, LT)
16.41/6.11	   new_esEs15(x0, x1, app(app(app(ty_@3, x2), x3), x4))
16.41/6.11	   new_esEs15(x0, x1, ty_Float)
16.41/6.11	   new_esEs6(x0, x1, x2, x3)
16.41/6.11	   new_esEs9(x0, x1)
16.41/6.11	   new_esEs15(x0, x1, app(ty_[], x2))
16.41/6.11	   new_esEs10(EQ, GT)
16.41/6.11	   new_esEs10(GT, EQ)
16.41/6.11	   new_esEs15(x0, x1, ty_Int)
16.41/6.11	   new_esEs10(LT, GT)
16.41/6.11	   new_esEs10(GT, LT)
16.41/6.11	   new_esEs11(x0, x1)
16.41/6.11	   new_deleteBy00(x0, x1, x2, True, x3)
16.41/6.11	   new_esEs15(x0, x1, ty_Integer)
16.41/6.11	   new_esEs8(x0, x1)
16.41/6.11	   new_esEs15(x0, x1, ty_Bool)
16.41/6.11	   new_esEs10(LT, LT)
16.41/6.11	   new_esEs10(EQ, EQ)
16.41/6.11	
16.41/6.11	We have to consider all minimal (P,Q,R)-chains.
16.41/6.11	----------------------------------------
16.41/6.11	
16.41/6.11	(82) QDPSizeChangeProof (EQUIVALENT)
16.41/6.11	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. 
16.41/6.11	
16.41/6.11	From the DPs we obtained the following set of size-change graphs:
16.41/6.11	*new_foldl(xw9, xw10, :(xw110, xw111), ba) -> new_foldl(new_deleteBy1(xw10, xw9, ba), xw110, xw111, ba)
16.41/6.11	The graph contains the following edges 3 > 2, 3 > 3, 4 >= 4
16.41/6.11	
16.41/6.11	
16.41/6.11	----------------------------------------
16.41/6.11	
16.41/6.11	(83)
16.41/6.11	YES
16.60/6.15	EOF