11.71/4.79	YES
14.12/5.42	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
14.12/5.42	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
14.12/5.42	
14.12/5.42	
14.12/5.42	H-Termination with start terms of the given HASKELL could be proven:
14.12/5.42	
14.12/5.42	(0) HASKELL
14.12/5.42	(1) CR [EQUIVALENT, 0 ms]
14.12/5.42	(2) HASKELL
14.12/5.42	(3) BR [EQUIVALENT, 0 ms]
14.12/5.42	(4) HASKELL
14.12/5.42	(5) COR [EQUIVALENT, 22 ms]
14.12/5.42	(6) HASKELL
14.12/5.42	(7) Narrow [SOUND, 0 ms]
14.12/5.42	(8) AND
14.12/5.42	    (9) QDP
14.12/5.42	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
14.12/5.42	        (11) YES
14.12/5.42	    (12) QDP
14.12/5.42	        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
14.12/5.42	        (14) YES
14.12/5.42	    (15) QDP
14.12/5.42	        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
14.12/5.42	        (17) QDP
14.12/5.42	        (18) TransformationProof [EQUIVALENT, 0 ms]
14.12/5.42	        (19) QDP
14.12/5.42	        (20) DependencyGraphProof [EQUIVALENT, 0 ms]
14.12/5.42	        (21) QDP
14.12/5.42	        (22) UsableRulesProof [EQUIVALENT, 0 ms]
14.12/5.42	        (23) QDP
14.12/5.42	        (24) QReductionProof [EQUIVALENT, 0 ms]
14.12/5.42	        (25) QDP
14.12/5.42	        (26) TransformationProof [EQUIVALENT, 0 ms]
14.12/5.42	        (27) QDP
14.12/5.42	        (28) UsableRulesProof [EQUIVALENT, 0 ms]
14.12/5.42	        (29) QDP
14.12/5.42	        (30) QReductionProof [EQUIVALENT, 0 ms]
14.12/5.42	        (31) QDP
14.12/5.42	        (32) TransformationProof [EQUIVALENT, 0 ms]
14.12/5.42	        (33) QDP
14.12/5.42	        (34) QDPSizeChangeProof [EQUIVALENT, 0 ms]
14.12/5.42	        (35) YES
14.12/5.42	    (36) QDP
14.12/5.42	        (37) DependencyGraphProof [EQUIVALENT, 0 ms]
14.12/5.42	        (38) QDP
14.12/5.42	        (39) QDPSizeChangeProof [EQUIVALENT, 1 ms]
14.12/5.42	        (40) YES
14.12/5.42	
14.12/5.42	
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(0)
14.12/5.42	Obligation:
14.12/5.42	mainModule Main 
14.12/5.42	module Maybe where {
14.12/5.42	import qualified List;
14.12/5.42	import qualified Main;
14.12/5.42	import qualified Prelude;
14.12/5.42	}
14.12/5.42	module List where {
14.12/5.42	import qualified Main;
14.12/5.42	import qualified Maybe;
14.12/5.42	import qualified Prelude;
14.12/5.42	merge :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a]  ->  [a];
14.12/5.42	merge cmp xs [] = xs;
14.12/5.42	merge cmp [] ys = ys;
14.12/5.42	merge cmp (x : xs) (y : ys) = case x `cmp` y of { 
14.12/5.42	GT-> y : merge cmp (x : xs) ys; 
14.12/5.42	_-> x : merge cmp xs (y : ys); 
14.12/5.42	 } ;
14.12/5.42	
14.12/5.42	merge_pairs :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [[a]];
14.12/5.42	merge_pairs cmp [] = [];
14.12/5.42	merge_pairs cmp (xs : []) = xs : [];
14.12/5.42	merge_pairs cmp (xs : ys : xss) = merge cmp xs ys : merge_pairs cmp xss;
14.12/5.42	
14.12/5.42	mergesort :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a];
14.12/5.42	mergesort cmp = mergesort' cmp . map wrap;
14.12/5.42	
14.12/5.42	mergesort' :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [a];
14.12/5.42	mergesort' cmp [] = [];
14.12/5.42	mergesort' cmp (xs : []) = xs;
14.12/5.42	mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss);
14.12/5.42	
14.12/5.42	sort :: Ord a => [a]  ->  [a];
14.12/5.42	sort l = mergesort compare l;
14.12/5.42	
14.12/5.42	wrap :: a  ->  [a];
14.12/5.42	wrap x = x : [];
14.12/5.42	
14.12/5.42	}
14.12/5.42	module Main where {
14.12/5.42	import qualified List;
14.12/5.42	import qualified Maybe;
14.12/5.42	import qualified Prelude;
14.12/5.42	}
14.12/5.42	
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(1) CR (EQUIVALENT)
14.12/5.42	Case Reductions:
14.12/5.42	The following Case expression
14.12/5.42	"case cmp x y of {
14.12/5.42	GT  -> y : merge cmp (x : xs) ys;
14.12/5.42	_  -> x : merge cmp xs (y : ys)}
14.12/5.42	"
14.12/5.42	is transformed to
14.12/5.42	"merge0 y cmp x xs ys GT = y : merge cmp (x : xs) ys;
14.12/5.42	merge0 y cmp x xs ys _ = x : merge cmp xs (y : ys);
14.12/5.42	"
14.12/5.42	
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(2)
14.12/5.42	Obligation:
14.12/5.42	mainModule Main 
14.12/5.42	module Maybe where {
14.12/5.42	import qualified List;
14.12/5.42	import qualified Main;
14.12/5.42	import qualified Prelude;
14.12/5.42	}
14.12/5.42	module List where {
14.12/5.42	import qualified Main;
14.12/5.42	import qualified Maybe;
14.12/5.42	import qualified Prelude;
14.12/5.42	merge :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a]  ->  [a];
14.12/5.42	merge cmp xs [] = xs;
14.12/5.42	merge cmp [] ys = ys;
14.12/5.42	merge cmp (x : xs) (y : ys) = merge0 y cmp x xs ys (x `cmp` y);
14.12/5.42	
14.12/5.42	merge0 y cmp x xs ys GT = y : merge cmp (x : xs) ys;
14.12/5.42	merge0 y cmp x xs ys _ = x : merge cmp xs (y : ys);
14.12/5.42	
14.12/5.42	merge_pairs :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [[a]];
14.12/5.42	merge_pairs cmp [] = [];
14.12/5.42	merge_pairs cmp (xs : []) = xs : [];
14.12/5.42	merge_pairs cmp (xs : ys : xss) = merge cmp xs ys : merge_pairs cmp xss;
14.12/5.42	
14.12/5.42	mergesort :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a];
14.12/5.42	mergesort cmp = mergesort' cmp . map wrap;
14.12/5.42	
14.12/5.42	mergesort' :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [a];
14.12/5.42	mergesort' cmp [] = [];
14.12/5.42	mergesort' cmp (xs : []) = xs;
14.12/5.42	mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss);
14.12/5.42	
14.12/5.42	sort :: Ord a => [a]  ->  [a];
14.12/5.42	sort l = mergesort compare l;
14.12/5.42	
14.12/5.42	wrap :: a  ->  [a];
14.12/5.42	wrap x = x : [];
14.12/5.42	
14.12/5.42	}
14.12/5.42	module Main where {
14.12/5.42	import qualified List;
14.12/5.42	import qualified Maybe;
14.12/5.42	import qualified Prelude;
14.12/5.42	}
14.12/5.42	
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(3) BR (EQUIVALENT)
14.12/5.42	Replaced joker patterns by fresh variables and removed binding patterns.
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(4)
14.12/5.42	Obligation:
14.12/5.42	mainModule Main 
14.12/5.42	module Maybe where {
14.12/5.42	import qualified List;
14.12/5.42	import qualified Main;
14.12/5.42	import qualified Prelude;
14.12/5.42	}
14.12/5.42	module List where {
14.12/5.42	import qualified Main;
14.12/5.42	import qualified Maybe;
14.12/5.42	import qualified Prelude;
14.12/5.42	merge :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a]  ->  [a];
14.12/5.42	merge cmp xs [] = xs;
14.12/5.42	merge cmp [] ys = ys;
14.12/5.42	merge cmp (x : xs) (y : ys) = merge0 y cmp x xs ys (x `cmp` y);
14.12/5.42	
14.12/5.42	merge0 y cmp x xs ys GT = y : merge cmp (x : xs) ys;
14.12/5.42	merge0 y cmp x xs ys vy = x : merge cmp xs (y : ys);
14.12/5.42	
14.12/5.42	merge_pairs :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [[a]];
14.12/5.42	merge_pairs cmp [] = [];
14.12/5.42	merge_pairs cmp (xs : []) = xs : [];
14.12/5.42	merge_pairs cmp (xs : ys : xss) = merge cmp xs ys : merge_pairs cmp xss;
14.12/5.42	
14.12/5.42	mergesort :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a];
14.12/5.42	mergesort cmp = mergesort' cmp . map wrap;
14.12/5.42	
14.12/5.42	mergesort' :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [a];
14.12/5.42	mergesort' cmp [] = [];
14.12/5.42	mergesort' cmp (xs : []) = xs;
14.12/5.42	mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss);
14.12/5.42	
14.12/5.42	sort :: Ord a => [a]  ->  [a];
14.12/5.42	sort l = mergesort compare l;
14.12/5.42	
14.12/5.42	wrap :: a  ->  [a];
14.12/5.42	wrap x = x : [];
14.12/5.42	
14.12/5.42	}
14.12/5.42	module Main where {
14.12/5.42	import qualified List;
14.12/5.42	import qualified Maybe;
14.12/5.42	import qualified Prelude;
14.12/5.42	}
14.12/5.42	
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(5) COR (EQUIVALENT)
14.12/5.42	Cond Reductions:
14.12/5.42	The following Function with conditions
14.12/5.42	"undefined |Falseundefined;
14.12/5.42	"
14.12/5.42	is transformed to
14.12/5.42	"undefined  = undefined1;
14.12/5.42	"
14.12/5.42	"undefined0 True = undefined;
14.12/5.42	"
14.12/5.42	"undefined1  = undefined0 False;
14.12/5.42	"
14.12/5.42	
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(6)
14.12/5.42	Obligation:
14.12/5.42	mainModule Main 
14.12/5.42	module Maybe where {
14.12/5.42	import qualified List;
14.12/5.42	import qualified Main;
14.12/5.42	import qualified Prelude;
14.12/5.42	}
14.12/5.42	module List where {
14.12/5.42	import qualified Main;
14.12/5.42	import qualified Maybe;
14.12/5.42	import qualified Prelude;
14.12/5.42	merge :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a]  ->  [a];
14.12/5.42	merge cmp xs [] = xs;
14.12/5.42	merge cmp [] ys = ys;
14.12/5.42	merge cmp (x : xs) (y : ys) = merge0 y cmp x xs ys (x `cmp` y);
14.12/5.42	
14.12/5.42	merge0 y cmp x xs ys GT = y : merge cmp (x : xs) ys;
14.12/5.42	merge0 y cmp x xs ys vy = x : merge cmp xs (y : ys);
14.12/5.42	
14.12/5.42	merge_pairs :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [[a]];
14.12/5.42	merge_pairs cmp [] = [];
14.12/5.42	merge_pairs cmp (xs : []) = xs : [];
14.12/5.42	merge_pairs cmp (xs : ys : xss) = merge cmp xs ys : merge_pairs cmp xss;
14.12/5.42	
14.12/5.42	mergesort :: (a  ->  a  ->  Ordering)  ->  [a]  ->  [a];
14.12/5.42	mergesort cmp = mergesort' cmp . map wrap;
14.12/5.42	
14.12/5.42	mergesort' :: (a  ->  a  ->  Ordering)  ->  [[a]]  ->  [a];
14.12/5.42	mergesort' cmp [] = [];
14.12/5.42	mergesort' cmp (xs : []) = xs;
14.12/5.42	mergesort' cmp xss = mergesort' cmp (merge_pairs cmp xss);
14.12/5.42	
14.12/5.42	sort :: Ord a => [a]  ->  [a];
14.12/5.42	sort l = mergesort compare l;
14.12/5.42	
14.12/5.42	wrap :: a  ->  [a];
14.12/5.42	wrap x = x : [];
14.12/5.42	
14.12/5.42	}
14.12/5.42	module Main where {
14.12/5.42	import qualified List;
14.12/5.42	import qualified Maybe;
14.12/5.42	import qualified Prelude;
14.12/5.42	}
14.12/5.42	
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(7) Narrow (SOUND)
14.12/5.42	Haskell To QDPs
14.12/5.42	
14.12/5.42	digraph dp_graph {
14.12/5.42	node [outthreshold=100, inthreshold=100];1[label="List.sort",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
14.12/5.42	3[label="List.sort vz3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
14.12/5.42	4[label="List.mergesort compare vz3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
14.12/5.42	5[label="(List.mergesort' compare) . map List.wrap",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
14.12/5.42	6[label="List.mergesort' compare (map List.wrap vz3)",fontsize=16,color="burlywood",shape="box"];580[label="vz3/vz30 : vz31",fontsize=10,color="white",style="solid",shape="box"];6 -> 580[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	580 -> 7[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	581[label="vz3/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 581[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	581 -> 8[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	7[label="List.mergesort' compare (map List.wrap (vz30 : vz31))",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
14.12/5.42	8[label="List.mergesort' compare (map List.wrap [])",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
14.12/5.42	9[label="List.mergesort' compare (List.wrap vz30 : map List.wrap vz31)",fontsize=16,color="burlywood",shape="box"];582[label="vz31/vz310 : vz311",fontsize=10,color="white",style="solid",shape="box"];9 -> 582[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	582 -> 11[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	583[label="vz31/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 583[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	583 -> 12[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	10[label="List.mergesort' compare []",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3];
14.12/5.42	11[label="List.mergesort' compare (List.wrap vz30 : map List.wrap (vz310 : vz311))",fontsize=16,color="black",shape="box"];11 -> 14[label="",style="solid", color="black", weight=3];
14.12/5.42	12[label="List.mergesort' compare (List.wrap vz30 : map List.wrap [])",fontsize=16,color="black",shape="box"];12 -> 15[label="",style="solid", color="black", weight=3];
14.12/5.42	13[label="[]",fontsize=16,color="green",shape="box"];14[label="List.mergesort' compare (List.wrap vz30 : List.wrap vz310 : map List.wrap vz311)",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3];
14.12/5.42	15[label="List.mergesort' compare (List.wrap vz30 : [])",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
14.12/5.42	16[label="List.mergesort' compare (List.merge_pairs compare (List.wrap vz30 : List.wrap vz310 : map List.wrap vz311))",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3];
14.12/5.42	17[label="List.wrap vz30",fontsize=16,color="black",shape="triangle"];17 -> 19[label="",style="solid", color="black", weight=3];
14.12/5.42	18 -> 245[label="",style="dashed", color="red", weight=0];
14.12/5.42	18[label="List.mergesort' compare (List.merge compare (List.wrap vz30) (List.wrap vz310) : List.merge_pairs compare (map List.wrap vz311))",fontsize=16,color="magenta"];18 -> 246[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	18 -> 247[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	19[label="vz30 : []",fontsize=16,color="green",shape="box"];246[label="map List.wrap vz311",fontsize=16,color="burlywood",shape="triangle"];584[label="vz311/vz3110 : vz3111",fontsize=10,color="white",style="solid",shape="box"];246 -> 584[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	584 -> 400[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	585[label="vz311/[]",fontsize=10,color="white",style="solid",shape="box"];246 -> 585[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	585 -> 401[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	247 -> 402[label="",style="dashed", color="red", weight=0];
14.12/5.42	247[label="List.merge compare (List.wrap vz30) (List.wrap vz310)",fontsize=16,color="magenta"];247 -> 403[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	247 -> 404[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	245[label="List.mergesort' compare (vz34 : List.merge_pairs compare vz35)",fontsize=16,color="burlywood",shape="triangle"];586[label="vz35/vz350 : vz351",fontsize=10,color="white",style="solid",shape="box"];245 -> 586[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	586 -> 405[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	587[label="vz35/[]",fontsize=10,color="white",style="solid",shape="box"];245 -> 587[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	587 -> 406[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	400[label="map List.wrap (vz3110 : vz3111)",fontsize=16,color="black",shape="box"];400 -> 407[label="",style="solid", color="black", weight=3];
14.12/5.42	401[label="map List.wrap []",fontsize=16,color="black",shape="box"];401 -> 408[label="",style="solid", color="black", weight=3];
14.12/5.42	403 -> 17[label="",style="dashed", color="red", weight=0];
14.12/5.42	403[label="List.wrap vz310",fontsize=16,color="magenta"];403 -> 409[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	404 -> 17[label="",style="dashed", color="red", weight=0];
14.12/5.42	404[label="List.wrap vz30",fontsize=16,color="magenta"];402[label="List.merge compare vz37 vz36",fontsize=16,color="burlywood",shape="triangle"];588[label="vz36/vz360 : vz361",fontsize=10,color="white",style="solid",shape="box"];402 -> 588[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	588 -> 410[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	589[label="vz36/[]",fontsize=10,color="white",style="solid",shape="box"];402 -> 589[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	589 -> 411[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	405[label="List.mergesort' compare (vz34 : List.merge_pairs compare (vz350 : vz351))",fontsize=16,color="burlywood",shape="box"];590[label="vz351/vz3510 : vz3511",fontsize=10,color="white",style="solid",shape="box"];405 -> 590[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	590 -> 412[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	591[label="vz351/[]",fontsize=10,color="white",style="solid",shape="box"];405 -> 591[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	591 -> 413[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	406[label="List.mergesort' compare (vz34 : List.merge_pairs compare [])",fontsize=16,color="black",shape="box"];406 -> 414[label="",style="solid", color="black", weight=3];
14.12/5.42	407[label="List.wrap vz3110 : map List.wrap vz3111",fontsize=16,color="green",shape="box"];407 -> 415[label="",style="dashed", color="green", weight=3];
14.12/5.42	407 -> 416[label="",style="dashed", color="green", weight=3];
14.12/5.42	408[label="[]",fontsize=16,color="green",shape="box"];409[label="vz310",fontsize=16,color="green",shape="box"];410[label="List.merge compare vz37 (vz360 : vz361)",fontsize=16,color="burlywood",shape="box"];592[label="vz37/vz370 : vz371",fontsize=10,color="white",style="solid",shape="box"];410 -> 592[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	592 -> 417[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	593[label="vz37/[]",fontsize=10,color="white",style="solid",shape="box"];410 -> 593[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	593 -> 418[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	411[label="List.merge compare vz37 []",fontsize=16,color="black",shape="box"];411 -> 419[label="",style="solid", color="black", weight=3];
14.12/5.42	412[label="List.mergesort' compare (vz34 : List.merge_pairs compare (vz350 : vz3510 : vz3511))",fontsize=16,color="black",shape="box"];412 -> 420[label="",style="solid", color="black", weight=3];
14.12/5.42	413[label="List.mergesort' compare (vz34 : List.merge_pairs compare (vz350 : []))",fontsize=16,color="black",shape="box"];413 -> 421[label="",style="solid", color="black", weight=3];
14.12/5.42	414[label="List.mergesort' compare (vz34 : [])",fontsize=16,color="black",shape="box"];414 -> 422[label="",style="solid", color="black", weight=3];
14.12/5.42	415 -> 17[label="",style="dashed", color="red", weight=0];
14.12/5.42	415[label="List.wrap vz3110",fontsize=16,color="magenta"];415 -> 423[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	416 -> 246[label="",style="dashed", color="red", weight=0];
14.12/5.42	416[label="map List.wrap vz3111",fontsize=16,color="magenta"];416 -> 424[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	417[label="List.merge compare (vz370 : vz371) (vz360 : vz361)",fontsize=16,color="black",shape="box"];417 -> 425[label="",style="solid", color="black", weight=3];
14.12/5.42	418[label="List.merge compare [] (vz360 : vz361)",fontsize=16,color="black",shape="box"];418 -> 426[label="",style="solid", color="black", weight=3];
14.12/5.42	419[label="vz37",fontsize=16,color="green",shape="box"];420[label="List.mergesort' compare (vz34 : List.merge compare vz350 vz3510 : List.merge_pairs compare vz3511)",fontsize=16,color="black",shape="box"];420 -> 427[label="",style="solid", color="black", weight=3];
14.12/5.42	421[label="List.mergesort' compare (vz34 : vz350 : [])",fontsize=16,color="black",shape="box"];421 -> 428[label="",style="solid", color="black", weight=3];
14.12/5.42	422[label="vz34",fontsize=16,color="green",shape="box"];423[label="vz3110",fontsize=16,color="green",shape="box"];424[label="vz3111",fontsize=16,color="green",shape="box"];425 -> 467[label="",style="dashed", color="red", weight=0];
14.12/5.42	425[label="List.merge0 vz360 compare vz370 vz371 vz361 (compare vz370 vz360)",fontsize=16,color="magenta"];425 -> 468[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	425 -> 469[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	425 -> 470[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	425 -> 471[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	425 -> 472[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	426[label="vz360 : vz361",fontsize=16,color="green",shape="box"];427[label="List.mergesort' compare (List.merge_pairs compare (vz34 : List.merge compare vz350 vz3510 : List.merge_pairs compare vz3511))",fontsize=16,color="black",shape="box"];427 -> 430[label="",style="solid", color="black", weight=3];
14.12/5.42	428[label="List.mergesort' compare (List.merge_pairs compare (vz34 : vz350 : []))",fontsize=16,color="black",shape="box"];428 -> 431[label="",style="solid", color="black", weight=3];
14.12/5.42	468[label="vz361",fontsize=16,color="green",shape="box"];469[label="vz360",fontsize=16,color="green",shape="box"];470[label="compare vz370 vz360",fontsize=16,color="burlywood",shape="triangle"];594[label="vz370/()",fontsize=10,color="white",style="solid",shape="box"];470 -> 594[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	594 -> 488[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	471[label="vz370",fontsize=16,color="green",shape="box"];472[label="vz371",fontsize=16,color="green",shape="box"];467[label="List.merge0 vz44 compare vz45 vz46 vz47 vz48",fontsize=16,color="burlywood",shape="triangle"];595[label="vz48/LT",fontsize=10,color="white",style="solid",shape="box"];467 -> 595[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	595 -> 489[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	596[label="vz48/EQ",fontsize=10,color="white",style="solid",shape="box"];467 -> 596[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	596 -> 490[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	597[label="vz48/GT",fontsize=10,color="white",style="solid",shape="box"];467 -> 597[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	597 -> 491[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	430 -> 245[label="",style="dashed", color="red", weight=0];
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14.12/5.42	430 -> 434[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	431 -> 245[label="",style="dashed", color="red", weight=0];
14.12/5.42	431[label="List.mergesort' compare (List.merge compare vz34 vz350 : List.merge_pairs compare [])",fontsize=16,color="magenta"];431 -> 435[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	431 -> 436[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	488[label="compare () vz360",fontsize=16,color="burlywood",shape="box"];598[label="vz360/()",fontsize=10,color="white",style="solid",shape="box"];488 -> 598[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	598 -> 523[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	489[label="List.merge0 vz44 compare vz45 vz46 vz47 LT",fontsize=16,color="black",shape="box"];489 -> 524[label="",style="solid", color="black", weight=3];
14.12/5.42	490[label="List.merge0 vz44 compare vz45 vz46 vz47 EQ",fontsize=16,color="black",shape="box"];490 -> 525[label="",style="solid", color="black", weight=3];
14.12/5.42	491[label="List.merge0 vz44 compare vz45 vz46 vz47 GT",fontsize=16,color="black",shape="box"];491 -> 526[label="",style="solid", color="black", weight=3];
14.12/5.42	433[label="List.merge_pairs compare vz3511",fontsize=16,color="burlywood",shape="triangle"];599[label="vz3511/vz35110 : vz35111",fontsize=10,color="white",style="solid",shape="box"];433 -> 599[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	599 -> 438[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	600[label="vz3511/[]",fontsize=10,color="white",style="solid",shape="box"];433 -> 600[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	600 -> 439[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	434[label="List.merge compare vz34 (List.merge compare vz350 vz3510)",fontsize=16,color="burlywood",shape="box"];601[label="vz3510/vz35100 : vz35101",fontsize=10,color="white",style="solid",shape="box"];434 -> 601[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	601 -> 440[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	602[label="vz3510/[]",fontsize=10,color="white",style="solid",shape="box"];434 -> 602[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	602 -> 441[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	435[label="[]",fontsize=16,color="green",shape="box"];436[label="List.merge compare vz34 vz350",fontsize=16,color="burlywood",shape="triangle"];603[label="vz350/vz3500 : vz3501",fontsize=10,color="white",style="solid",shape="box"];436 -> 603[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	603 -> 442[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	604[label="vz350/[]",fontsize=10,color="white",style="solid",shape="box"];436 -> 604[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	604 -> 443[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	523[label="compare () ()",fontsize=16,color="black",shape="box"];523 -> 570[label="",style="solid", color="black", weight=3];
14.12/5.42	524[label="vz45 : List.merge compare vz46 (vz44 : vz47)",fontsize=16,color="green",shape="box"];524 -> 571[label="",style="dashed", color="green", weight=3];
14.12/5.42	525[label="vz45 : List.merge compare vz46 (vz44 : vz47)",fontsize=16,color="green",shape="box"];525 -> 572[label="",style="dashed", color="green", weight=3];
14.12/5.42	526[label="vz44 : List.merge compare (vz45 : vz46) vz47",fontsize=16,color="green",shape="box"];526 -> 573[label="",style="dashed", color="green", weight=3];
14.12/5.42	438[label="List.merge_pairs compare (vz35110 : vz35111)",fontsize=16,color="burlywood",shape="box"];605[label="vz35111/vz351110 : vz351111",fontsize=10,color="white",style="solid",shape="box"];438 -> 605[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	605 -> 445[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	606[label="vz35111/[]",fontsize=10,color="white",style="solid",shape="box"];438 -> 606[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	606 -> 446[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	439[label="List.merge_pairs compare []",fontsize=16,color="black",shape="box"];439 -> 447[label="",style="solid", color="black", weight=3];
14.12/5.42	440[label="List.merge compare vz34 (List.merge compare vz350 (vz35100 : vz35101))",fontsize=16,color="burlywood",shape="box"];607[label="vz350/vz3500 : vz3501",fontsize=10,color="white",style="solid",shape="box"];440 -> 607[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	607 -> 448[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	608[label="vz350/[]",fontsize=10,color="white",style="solid",shape="box"];440 -> 608[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	608 -> 449[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	441[label="List.merge compare vz34 (List.merge compare vz350 [])",fontsize=16,color="black",shape="box"];441 -> 450[label="",style="solid", color="black", weight=3];
14.12/5.42	442[label="List.merge compare vz34 (vz3500 : vz3501)",fontsize=16,color="burlywood",shape="box"];609[label="vz34/vz340 : vz341",fontsize=10,color="white",style="solid",shape="box"];442 -> 609[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	609 -> 451[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	610[label="vz34/[]",fontsize=10,color="white",style="solid",shape="box"];442 -> 610[label="",style="solid", color="burlywood", weight=9];
14.12/5.42	610 -> 452[label="",style="solid", color="burlywood", weight=3];
14.12/5.42	443[label="List.merge compare vz34 []",fontsize=16,color="black",shape="box"];443 -> 453[label="",style="solid", color="black", weight=3];
14.12/5.42	570[label="EQ",fontsize=16,color="green",shape="box"];571 -> 436[label="",style="dashed", color="red", weight=0];
14.12/5.42	571[label="List.merge compare vz46 (vz44 : vz47)",fontsize=16,color="magenta"];571 -> 574[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	571 -> 575[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	572 -> 436[label="",style="dashed", color="red", weight=0];
14.12/5.42	572[label="List.merge compare vz46 (vz44 : vz47)",fontsize=16,color="magenta"];572 -> 576[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	572 -> 577[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	573 -> 436[label="",style="dashed", color="red", weight=0];
14.12/5.42	573[label="List.merge compare (vz45 : vz46) vz47",fontsize=16,color="magenta"];573 -> 578[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	573 -> 579[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	445[label="List.merge_pairs compare (vz35110 : vz351110 : vz351111)",fontsize=16,color="black",shape="box"];445 -> 455[label="",style="solid", color="black", weight=3];
14.12/5.42	446[label="List.merge_pairs compare (vz35110 : [])",fontsize=16,color="black",shape="box"];446 -> 456[label="",style="solid", color="black", weight=3];
14.12/5.42	447[label="[]",fontsize=16,color="green",shape="box"];448[label="List.merge compare vz34 (List.merge compare (vz3500 : vz3501) (vz35100 : vz35101))",fontsize=16,color="black",shape="box"];448 -> 457[label="",style="solid", color="black", weight=3];
14.12/5.42	449[label="List.merge compare vz34 (List.merge compare [] (vz35100 : vz35101))",fontsize=16,color="black",shape="box"];449 -> 458[label="",style="solid", color="black", weight=3];
14.12/5.42	450 -> 436[label="",style="dashed", color="red", weight=0];
14.12/5.42	450[label="List.merge compare vz34 vz350",fontsize=16,color="magenta"];451[label="List.merge compare (vz340 : vz341) (vz3500 : vz3501)",fontsize=16,color="black",shape="box"];451 -> 459[label="",style="solid", color="black", weight=3];
14.12/5.42	452[label="List.merge compare [] (vz3500 : vz3501)",fontsize=16,color="black",shape="box"];452 -> 460[label="",style="solid", color="black", weight=3];
14.12/5.42	453[label="vz34",fontsize=16,color="green",shape="box"];574[label="vz44 : vz47",fontsize=16,color="green",shape="box"];575[label="vz46",fontsize=16,color="green",shape="box"];576[label="vz44 : vz47",fontsize=16,color="green",shape="box"];577[label="vz46",fontsize=16,color="green",shape="box"];578[label="vz47",fontsize=16,color="green",shape="box"];579[label="vz45 : vz46",fontsize=16,color="green",shape="box"];455[label="List.merge compare vz35110 vz351110 : List.merge_pairs compare vz351111",fontsize=16,color="green",shape="box"];455 -> 463[label="",style="dashed", color="green", weight=3];
14.12/5.42	455 -> 464[label="",style="dashed", color="green", weight=3];
14.12/5.42	456[label="vz35110 : []",fontsize=16,color="green",shape="box"];457 -> 436[label="",style="dashed", color="red", weight=0];
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14.12/5.42	458 -> 436[label="",style="dashed", color="red", weight=0];
14.12/5.42	458[label="List.merge compare vz34 (vz35100 : vz35101)",fontsize=16,color="magenta"];458 -> 466[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	459 -> 467[label="",style="dashed", color="red", weight=0];
14.12/5.42	459[label="List.merge0 vz3500 compare vz340 vz341 vz3501 (compare vz340 vz3500)",fontsize=16,color="magenta"];459 -> 478[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	459 -> 479[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	459 -> 480[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	459 -> 481[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	459 -> 482[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	460[label="vz3500 : vz3501",fontsize=16,color="green",shape="box"];463 -> 436[label="",style="dashed", color="red", weight=0];
14.12/5.42	463[label="List.merge compare vz35110 vz351110",fontsize=16,color="magenta"];463 -> 492[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	463 -> 493[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	464 -> 433[label="",style="dashed", color="red", weight=0];
14.12/5.42	464[label="List.merge_pairs compare vz351111",fontsize=16,color="magenta"];464 -> 494[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	465 -> 467[label="",style="dashed", color="red", weight=0];
14.12/5.42	465[label="List.merge0 vz35100 compare vz3500 vz3501 vz35101 (compare vz3500 vz35100)",fontsize=16,color="magenta"];465 -> 483[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	465 -> 484[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	465 -> 485[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	465 -> 486[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	465 -> 487[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	466[label="vz35100 : vz35101",fontsize=16,color="green",shape="box"];478[label="vz3501",fontsize=16,color="green",shape="box"];479[label="vz3500",fontsize=16,color="green",shape="box"];480[label="compare vz340 vz3500",fontsize=16,color="blue",shape="box"];611[label="compare :: Double -> Double -> Ordering",fontsize=10,color="white",style="solid",shape="box"];480 -> 611[label="",style="solid", color="blue", weight=9];
14.12/5.42	611 -> 495[label="",style="solid", color="blue", weight=3];
14.12/5.42	612[label="compare :: (Either a b) -> (Either a b) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];480 -> 612[label="",style="solid", color="blue", weight=9];
14.12/5.42	612 -> 496[label="",style="solid", color="blue", weight=3];
14.12/5.42	613[label="compare :: Integer -> Integer -> Ordering",fontsize=10,color="white",style="solid",shape="box"];480 -> 613[label="",style="solid", color="blue", weight=9];
14.12/5.42	613 -> 497[label="",style="solid", color="blue", weight=3];
14.12/5.42	614[label="compare :: ([] a) -> ([] a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];480 -> 614[label="",style="solid", color="blue", weight=9];
14.12/5.42	614 -> 498[label="",style="solid", color="blue", weight=3];
14.12/5.42	615[label="compare :: Bool -> Bool -> Ordering",fontsize=10,color="white",style="solid",shape="box"];480 -> 615[label="",style="solid", color="blue", weight=9];
14.12/5.42	615 -> 499[label="",style="solid", color="blue", weight=3];
14.12/5.42	616[label="compare :: () -> () -> Ordering",fontsize=10,color="white",style="solid",shape="box"];480 -> 616[label="",style="solid", color="blue", weight=9];
14.12/5.42	616 -> 500[label="",style="solid", color="blue", weight=3];
14.12/5.42	617[label="compare :: ((@3) a b c) -> ((@3) a b c) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];480 -> 617[label="",style="solid", color="blue", weight=9];
14.12/5.42	617 -> 501[label="",style="solid", color="blue", weight=3];
14.12/5.42	618[label="compare :: ((@2) a b) -> ((@2) a b) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];480 -> 618[label="",style="solid", color="blue", weight=9];
14.12/5.42	618 -> 502[label="",style="solid", color="blue", weight=3];
14.12/5.42	619[label="compare :: Int -> Int -> Ordering",fontsize=10,color="white",style="solid",shape="box"];480 -> 619[label="",style="solid", color="blue", weight=9];
14.12/5.42	619 -> 503[label="",style="solid", color="blue", weight=3];
14.12/5.42	620[label="compare :: Ordering -> Ordering -> Ordering",fontsize=10,color="white",style="solid",shape="box"];480 -> 620[label="",style="solid", color="blue", weight=9];
14.12/5.42	620 -> 504[label="",style="solid", color="blue", weight=3];
14.12/5.42	621[label="compare :: (Maybe a) -> (Maybe a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];480 -> 621[label="",style="solid", color="blue", weight=9];
14.12/5.42	621 -> 505[label="",style="solid", color="blue", weight=3];
14.12/5.42	622[label="compare :: Float -> Float -> Ordering",fontsize=10,color="white",style="solid",shape="box"];480 -> 622[label="",style="solid", color="blue", weight=9];
14.12/5.42	622 -> 506[label="",style="solid", color="blue", weight=3];
14.12/5.42	623[label="compare :: (Ratio a) -> (Ratio a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];480 -> 623[label="",style="solid", color="blue", weight=9];
14.12/5.42	623 -> 507[label="",style="solid", color="blue", weight=3];
14.12/5.42	624[label="compare :: Char -> Char -> Ordering",fontsize=10,color="white",style="solid",shape="box"];480 -> 624[label="",style="solid", color="blue", weight=9];
14.12/5.42	624 -> 508[label="",style="solid", color="blue", weight=3];
14.12/5.42	481[label="vz340",fontsize=16,color="green",shape="box"];482[label="vz341",fontsize=16,color="green",shape="box"];492[label="vz351110",fontsize=16,color="green",shape="box"];493[label="vz35110",fontsize=16,color="green",shape="box"];494[label="vz351111",fontsize=16,color="green",shape="box"];483[label="vz35101",fontsize=16,color="green",shape="box"];484[label="vz35100",fontsize=16,color="green",shape="box"];485[label="compare vz3500 vz35100",fontsize=16,color="blue",shape="box"];625[label="compare :: Double -> Double -> Ordering",fontsize=10,color="white",style="solid",shape="box"];485 -> 625[label="",style="solid", color="blue", weight=9];
14.12/5.42	625 -> 509[label="",style="solid", color="blue", weight=3];
14.12/5.42	626[label="compare :: (Either a b) -> (Either a b) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];485 -> 626[label="",style="solid", color="blue", weight=9];
14.12/5.42	626 -> 510[label="",style="solid", color="blue", weight=3];
14.12/5.42	627[label="compare :: Integer -> Integer -> Ordering",fontsize=10,color="white",style="solid",shape="box"];485 -> 627[label="",style="solid", color="blue", weight=9];
14.12/5.42	627 -> 511[label="",style="solid", color="blue", weight=3];
14.12/5.42	628[label="compare :: ([] a) -> ([] a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];485 -> 628[label="",style="solid", color="blue", weight=9];
14.12/5.42	628 -> 512[label="",style="solid", color="blue", weight=3];
14.12/5.42	629[label="compare :: Bool -> Bool -> Ordering",fontsize=10,color="white",style="solid",shape="box"];485 -> 629[label="",style="solid", color="blue", weight=9];
14.12/5.42	629 -> 513[label="",style="solid", color="blue", weight=3];
14.12/5.42	630[label="compare :: () -> () -> Ordering",fontsize=10,color="white",style="solid",shape="box"];485 -> 630[label="",style="solid", color="blue", weight=9];
14.12/5.42	630 -> 514[label="",style="solid", color="blue", weight=3];
14.12/5.42	631[label="compare :: ((@3) a b c) -> ((@3) a b c) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];485 -> 631[label="",style="solid", color="blue", weight=9];
14.12/5.42	631 -> 515[label="",style="solid", color="blue", weight=3];
14.12/5.42	632[label="compare :: ((@2) a b) -> ((@2) a b) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];485 -> 632[label="",style="solid", color="blue", weight=9];
14.12/5.42	632 -> 516[label="",style="solid", color="blue", weight=3];
14.12/5.42	633[label="compare :: Int -> Int -> Ordering",fontsize=10,color="white",style="solid",shape="box"];485 -> 633[label="",style="solid", color="blue", weight=9];
14.12/5.42	633 -> 517[label="",style="solid", color="blue", weight=3];
14.12/5.42	634[label="compare :: Ordering -> Ordering -> Ordering",fontsize=10,color="white",style="solid",shape="box"];485 -> 634[label="",style="solid", color="blue", weight=9];
14.12/5.42	634 -> 518[label="",style="solid", color="blue", weight=3];
14.12/5.42	635[label="compare :: (Maybe a) -> (Maybe a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];485 -> 635[label="",style="solid", color="blue", weight=9];
14.12/5.42	635 -> 519[label="",style="solid", color="blue", weight=3];
14.12/5.42	636[label="compare :: Float -> Float -> Ordering",fontsize=10,color="white",style="solid",shape="box"];485 -> 636[label="",style="solid", color="blue", weight=9];
14.12/5.42	636 -> 520[label="",style="solid", color="blue", weight=3];
14.12/5.42	637[label="compare :: (Ratio a) -> (Ratio a) -> Ordering",fontsize=10,color="white",style="solid",shape="box"];485 -> 637[label="",style="solid", color="blue", weight=9];
14.12/5.42	637 -> 521[label="",style="solid", color="blue", weight=3];
14.12/5.42	638[label="compare :: Char -> Char -> Ordering",fontsize=10,color="white",style="solid",shape="box"];485 -> 638[label="",style="solid", color="blue", weight=9];
14.12/5.42	638 -> 522[label="",style="solid", color="blue", weight=3];
14.12/5.42	486[label="vz3500",fontsize=16,color="green",shape="box"];487[label="vz3501",fontsize=16,color="green",shape="box"];495[label="compare vz340 vz3500",fontsize=16,color="black",shape="triangle"];495 -> 527[label="",style="solid", color="black", weight=3];
14.12/5.42	496[label="compare vz340 vz3500",fontsize=16,color="black",shape="triangle"];496 -> 528[label="",style="solid", color="black", weight=3];
14.12/5.42	497[label="compare vz340 vz3500",fontsize=16,color="black",shape="triangle"];497 -> 529[label="",style="solid", color="black", weight=3];
14.12/5.42	498[label="compare vz340 vz3500",fontsize=16,color="black",shape="triangle"];498 -> 530[label="",style="solid", color="black", weight=3];
14.12/5.42	499[label="compare vz340 vz3500",fontsize=16,color="black",shape="triangle"];499 -> 531[label="",style="solid", color="black", weight=3];
14.12/5.42	500 -> 470[label="",style="dashed", color="red", weight=0];
14.12/5.42	500[label="compare vz340 vz3500",fontsize=16,color="magenta"];500 -> 532[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	500 -> 533[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	501[label="compare vz340 vz3500",fontsize=16,color="black",shape="triangle"];501 -> 534[label="",style="solid", color="black", weight=3];
14.12/5.42	502[label="compare vz340 vz3500",fontsize=16,color="black",shape="triangle"];502 -> 535[label="",style="solid", color="black", weight=3];
14.12/5.42	503[label="compare vz340 vz3500",fontsize=16,color="black",shape="triangle"];503 -> 536[label="",style="solid", color="black", weight=3];
14.12/5.42	504[label="compare vz340 vz3500",fontsize=16,color="black",shape="triangle"];504 -> 537[label="",style="solid", color="black", weight=3];
14.12/5.42	505[label="compare vz340 vz3500",fontsize=16,color="black",shape="triangle"];505 -> 538[label="",style="solid", color="black", weight=3];
14.12/5.42	506[label="compare vz340 vz3500",fontsize=16,color="black",shape="triangle"];506 -> 539[label="",style="solid", color="black", weight=3];
14.12/5.42	507[label="compare vz340 vz3500",fontsize=16,color="black",shape="triangle"];507 -> 540[label="",style="solid", color="black", weight=3];
14.12/5.42	508[label="compare vz340 vz3500",fontsize=16,color="black",shape="triangle"];508 -> 541[label="",style="solid", color="black", weight=3];
14.12/5.42	509 -> 495[label="",style="dashed", color="red", weight=0];
14.12/5.42	509[label="compare vz3500 vz35100",fontsize=16,color="magenta"];509 -> 542[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	509 -> 543[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	510 -> 496[label="",style="dashed", color="red", weight=0];
14.12/5.42	510[label="compare vz3500 vz35100",fontsize=16,color="magenta"];510 -> 544[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	510 -> 545[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	511 -> 497[label="",style="dashed", color="red", weight=0];
14.12/5.42	511[label="compare vz3500 vz35100",fontsize=16,color="magenta"];511 -> 546[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	511 -> 547[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	512 -> 498[label="",style="dashed", color="red", weight=0];
14.12/5.42	512[label="compare vz3500 vz35100",fontsize=16,color="magenta"];512 -> 548[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	512 -> 549[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	513 -> 499[label="",style="dashed", color="red", weight=0];
14.12/5.42	513[label="compare vz3500 vz35100",fontsize=16,color="magenta"];513 -> 550[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	513 -> 551[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	514 -> 470[label="",style="dashed", color="red", weight=0];
14.12/5.42	514[label="compare vz3500 vz35100",fontsize=16,color="magenta"];514 -> 552[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	514 -> 553[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	515 -> 501[label="",style="dashed", color="red", weight=0];
14.12/5.42	515[label="compare vz3500 vz35100",fontsize=16,color="magenta"];515 -> 554[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	515 -> 555[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	516 -> 502[label="",style="dashed", color="red", weight=0];
14.12/5.42	516[label="compare vz3500 vz35100",fontsize=16,color="magenta"];516 -> 556[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	516 -> 557[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	517 -> 503[label="",style="dashed", color="red", weight=0];
14.12/5.42	517[label="compare vz3500 vz35100",fontsize=16,color="magenta"];517 -> 558[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	517 -> 559[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	518 -> 504[label="",style="dashed", color="red", weight=0];
14.12/5.42	518[label="compare vz3500 vz35100",fontsize=16,color="magenta"];518 -> 560[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	518 -> 561[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	519 -> 505[label="",style="dashed", color="red", weight=0];
14.12/5.42	519[label="compare vz3500 vz35100",fontsize=16,color="magenta"];519 -> 562[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	519 -> 563[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	520 -> 506[label="",style="dashed", color="red", weight=0];
14.12/5.42	520[label="compare vz3500 vz35100",fontsize=16,color="magenta"];520 -> 564[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	520 -> 565[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	521 -> 507[label="",style="dashed", color="red", weight=0];
14.12/5.42	521[label="compare vz3500 vz35100",fontsize=16,color="magenta"];521 -> 566[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	521 -> 567[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	522 -> 508[label="",style="dashed", color="red", weight=0];
14.12/5.42	522[label="compare vz3500 vz35100",fontsize=16,color="magenta"];522 -> 568[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	522 -> 569[label="",style="dashed", color="magenta", weight=3];
14.12/5.42	527[label="error []",fontsize=16,color="red",shape="box"];528[label="error []",fontsize=16,color="red",shape="box"];529[label="error []",fontsize=16,color="red",shape="box"];530[label="error []",fontsize=16,color="red",shape="box"];531[label="error []",fontsize=16,color="red",shape="box"];532[label="vz340",fontsize=16,color="green",shape="box"];533[label="vz3500",fontsize=16,color="green",shape="box"];534[label="error []",fontsize=16,color="red",shape="box"];535[label="error []",fontsize=16,color="red",shape="box"];536[label="error []",fontsize=16,color="red",shape="box"];537[label="error []",fontsize=16,color="red",shape="box"];538[label="error []",fontsize=16,color="red",shape="box"];539[label="error []",fontsize=16,color="red",shape="box"];540[label="error []",fontsize=16,color="red",shape="box"];541[label="error []",fontsize=16,color="red",shape="box"];542[label="vz3500",fontsize=16,color="green",shape="box"];543[label="vz35100",fontsize=16,color="green",shape="box"];544[label="vz3500",fontsize=16,color="green",shape="box"];545[label="vz35100",fontsize=16,color="green",shape="box"];546[label="vz3500",fontsize=16,color="green",shape="box"];547[label="vz35100",fontsize=16,color="green",shape="box"];548[label="vz3500",fontsize=16,color="green",shape="box"];549[label="vz35100",fontsize=16,color="green",shape="box"];550[label="vz3500",fontsize=16,color="green",shape="box"];551[label="vz35100",fontsize=16,color="green",shape="box"];552[label="vz3500",fontsize=16,color="green",shape="box"];553[label="vz35100",fontsize=16,color="green",shape="box"];554[label="vz3500",fontsize=16,color="green",shape="box"];555[label="vz35100",fontsize=16,color="green",shape="box"];556[label="vz3500",fontsize=16,color="green",shape="box"];557[label="vz35100",fontsize=16,color="green",shape="box"];558[label="vz3500",fontsize=16,color="green",shape="box"];559[label="vz35100",fontsize=16,color="green",shape="box"];560[label="vz3500",fontsize=16,color="green",shape="box"];561[label="vz35100",fontsize=16,color="green",shape="box"];562[label="vz3500",fontsize=16,color="green",shape="box"];563[label="vz35100",fontsize=16,color="green",shape="box"];564[label="vz3500",fontsize=16,color="green",shape="box"];565[label="vz35100",fontsize=16,color="green",shape="box"];566[label="vz3500",fontsize=16,color="green",shape="box"];567[label="vz35100",fontsize=16,color="green",shape="box"];568[label="vz3500",fontsize=16,color="green",shape="box"];569[label="vz35100",fontsize=16,color="green",shape="box"];}
14.12/5.42	
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(8)
14.12/5.42	Complex Obligation (AND)
14.12/5.42	
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(9)
14.12/5.42	Obligation:
14.12/5.42	Q DP problem:
14.12/5.42	The TRS P consists of the following rules:
14.12/5.42	
14.12/5.42	   new_merge_pairs(:(vz35110, :(vz351110, vz351111)), ba) -> new_merge_pairs(vz351111, ba)
14.12/5.42	
14.12/5.42	R is empty.
14.12/5.42	Q is empty.
14.12/5.42	We have to consider all minimal (P,Q,R)-chains.
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(10) QDPSizeChangeProof (EQUIVALENT)
14.12/5.42	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
14.12/5.42	
14.12/5.42	From the DPs we obtained the following set of size-change graphs:
14.12/5.42	*new_merge_pairs(:(vz35110, :(vz351110, vz351111)), ba) -> new_merge_pairs(vz351111, ba)
14.12/5.42	The graph contains the following edges 1 > 1, 2 >= 2
14.12/5.42	
14.12/5.42	
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(11)
14.12/5.42	YES
14.12/5.42	
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(12)
14.12/5.42	Obligation:
14.12/5.42	Q DP problem:
14.12/5.42	The TRS P consists of the following rules:
14.12/5.42	
14.12/5.42	   new_map(:(vz3110, vz3111)) -> new_map(vz3111)
14.12/5.42	
14.12/5.42	R is empty.
14.12/5.42	Q is empty.
14.12/5.42	We have to consider all minimal (P,Q,R)-chains.
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(13) QDPSizeChangeProof (EQUIVALENT)
14.12/5.42	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
14.12/5.42	
14.12/5.42	From the DPs we obtained the following set of size-change graphs:
14.12/5.42	*new_map(:(vz3110, vz3111)) -> new_map(vz3111)
14.12/5.42	The graph contains the following edges 1 > 1
14.12/5.42	
14.12/5.42	
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(14)
14.12/5.42	YES
14.12/5.42	
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(15)
14.12/5.42	Obligation:
14.12/5.42	Q DP problem:
14.12/5.42	The TRS P consists of the following rules:
14.12/5.42	
14.12/5.42	   new_merge0(vz44, vz45, vz46, vz47, EQ, ba) -> new_merge(vz46, :(vz44, vz47), ba)
14.12/5.42	   new_merge0(vz44, vz45, vz46, vz47, GT, ba) -> new_merge(:(vz45, vz46), vz47, ba)
14.12/5.42	   new_merge0(vz44, vz45, vz46, vz47, LT, ba) -> new_merge(vz46, :(vz44, vz47), ba)
14.12/5.42	   new_merge(:(vz340, vz341), :(vz3500, vz3501), bb) -> new_merge0(vz3500, vz340, vz341, vz3501, new_compare(vz340, vz3500, bb), bb)
14.12/5.42	
14.12/5.42	The TRS R consists of the following rules:
14.12/5.42	
14.12/5.42	   new_compare1(vz340, vz3500, bd, be) -> error([])
14.12/5.42	   new_compare10(vz340, vz3500, bh, ca) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, ty_Bool) -> new_compare9(vz340, vz3500)
14.12/5.42	   new_compare(vz340, vz3500, app(ty_Maybe, bg)) -> new_compare8(vz340, vz3500, bg)
14.12/5.42	   new_compare13(vz340, vz3500) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, ty_Integer) -> new_compare2(vz340, vz3500)
14.12/5.42	   new_compare(vz340, vz3500, app(app(app(ty_@3, cb), cc), cd)) -> new_compare11(vz340, vz3500, cb, cc, cd)
14.12/5.42	   new_compare2(vz340, vz3500) -> error([])
14.12/5.42	   new_compare11(vz340, vz3500, cb, cc, cd) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, app(ty_Ratio, bf)) -> new_compare6(vz340, vz3500, bf)
14.12/5.42	   new_compare(vz340, vz3500, ty_Int) -> new_compare12(vz340, vz3500)
14.12/5.42	   new_compare(vz340, vz3500, ty_@0) -> new_compare4(vz340, vz3500)
14.12/5.42	   new_compare5(vz340, vz3500) -> error([])
14.12/5.42	   new_compare12(vz340, vz3500) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, app(app(ty_Either, bh), ca)) -> new_compare10(vz340, vz3500, bh, ca)
14.12/5.42	   new_compare(vz340, vz3500, ty_Char) -> new_compare7(vz340, vz3500)
14.12/5.42	   new_compare(vz340, vz3500, app(ty_[], bc)) -> new_compare0(vz340, vz3500, bc)
14.12/5.42	   new_compare6(vz340, vz3500, bf) -> error([])
14.12/5.42	   new_compare0(vz340, vz3500, bc) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, app(app(ty_@2, bd), be)) -> new_compare1(vz340, vz3500, bd, be)
14.12/5.42	   new_compare(vz340, vz3500, ty_Double) -> new_compare13(vz340, vz3500)
14.12/5.42	   new_compare3(vz340, vz3500) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, ty_Ordering) -> new_compare5(vz340, vz3500)
14.12/5.42	   new_compare8(vz340, vz3500, bg) -> error([])
14.12/5.42	   new_compare4(@0, @0) -> EQ
14.12/5.42	   new_compare9(vz340, vz3500) -> error([])
14.12/5.42	   new_compare7(vz340, vz3500) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, ty_Float) -> new_compare3(vz340, vz3500)
14.12/5.42	
14.12/5.42	The set Q consists of the following terms:
14.12/5.42	
14.12/5.42	   new_compare(x0, x1, app(app(ty_Either, x2), x3))
14.12/5.42	   new_compare11(x0, x1, x2, x3, x4)
14.12/5.42	   new_compare5(x0, x1)
14.12/5.42	   new_compare10(x0, x1, x2, x3)
14.12/5.42	   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.12/5.42	   new_compare(x0, x1, ty_Integer)
14.12/5.42	   new_compare(x0, x1, ty_Bool)
14.12/5.42	   new_compare4(@0, @0)
14.12/5.42	   new_compare2(x0, x1)
14.12/5.42	   new_compare(x0, x1, ty_Float)
14.12/5.42	   new_compare8(x0, x1, x2)
14.12/5.42	   new_compare12(x0, x1)
14.12/5.42	   new_compare7(x0, x1)
14.12/5.42	   new_compare13(x0, x1)
14.12/5.42	   new_compare(x0, x1, ty_Int)
14.12/5.42	   new_compare3(x0, x1)
14.12/5.42	   new_compare(x0, x1, ty_Char)
14.12/5.42	   new_compare0(x0, x1, x2)
14.12/5.42	   new_compare6(x0, x1, x2)
14.12/5.42	   new_compare(x0, x1, app(ty_Maybe, x2))
14.12/5.42	   new_compare(x0, x1, app(app(ty_@2, x2), x3))
14.12/5.42	   new_compare(x0, x1, app(ty_Ratio, x2))
14.12/5.42	   new_compare(x0, x1, ty_Double)
14.12/5.42	   new_compare9(x0, x1)
14.12/5.42	   new_compare1(x0, x1, x2, x3)
14.12/5.42	   new_compare(x0, x1, ty_@0)
14.12/5.42	   new_compare(x0, x1, app(ty_[], x2))
14.12/5.42	   new_compare(x0, x1, ty_Ordering)
14.12/5.42	
14.12/5.42	We have to consider all minimal (P,Q,R)-chains.
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(16) DependencyGraphProof (EQUIVALENT)
14.12/5.42	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(17)
14.12/5.42	Obligation:
14.12/5.42	Q DP problem:
14.12/5.42	The TRS P consists of the following rules:
14.12/5.42	
14.12/5.42	   new_merge(:(vz340, vz341), :(vz3500, vz3501), bb) -> new_merge0(vz3500, vz340, vz341, vz3501, new_compare(vz340, vz3500, bb), bb)
14.12/5.42	   new_merge0(vz44, vz45, vz46, vz47, EQ, ba) -> new_merge(vz46, :(vz44, vz47), ba)
14.12/5.42	
14.12/5.42	The TRS R consists of the following rules:
14.12/5.42	
14.12/5.42	   new_compare1(vz340, vz3500, bd, be) -> error([])
14.12/5.42	   new_compare10(vz340, vz3500, bh, ca) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, ty_Bool) -> new_compare9(vz340, vz3500)
14.12/5.42	   new_compare(vz340, vz3500, app(ty_Maybe, bg)) -> new_compare8(vz340, vz3500, bg)
14.12/5.42	   new_compare13(vz340, vz3500) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, ty_Integer) -> new_compare2(vz340, vz3500)
14.12/5.42	   new_compare(vz340, vz3500, app(app(app(ty_@3, cb), cc), cd)) -> new_compare11(vz340, vz3500, cb, cc, cd)
14.12/5.42	   new_compare2(vz340, vz3500) -> error([])
14.12/5.42	   new_compare11(vz340, vz3500, cb, cc, cd) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, app(ty_Ratio, bf)) -> new_compare6(vz340, vz3500, bf)
14.12/5.42	   new_compare(vz340, vz3500, ty_Int) -> new_compare12(vz340, vz3500)
14.12/5.42	   new_compare(vz340, vz3500, ty_@0) -> new_compare4(vz340, vz3500)
14.12/5.42	   new_compare5(vz340, vz3500) -> error([])
14.12/5.42	   new_compare12(vz340, vz3500) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, app(app(ty_Either, bh), ca)) -> new_compare10(vz340, vz3500, bh, ca)
14.12/5.42	   new_compare(vz340, vz3500, ty_Char) -> new_compare7(vz340, vz3500)
14.12/5.42	   new_compare(vz340, vz3500, app(ty_[], bc)) -> new_compare0(vz340, vz3500, bc)
14.12/5.42	   new_compare6(vz340, vz3500, bf) -> error([])
14.12/5.42	   new_compare0(vz340, vz3500, bc) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, app(app(ty_@2, bd), be)) -> new_compare1(vz340, vz3500, bd, be)
14.12/5.42	   new_compare(vz340, vz3500, ty_Double) -> new_compare13(vz340, vz3500)
14.12/5.42	   new_compare3(vz340, vz3500) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, ty_Ordering) -> new_compare5(vz340, vz3500)
14.12/5.42	   new_compare8(vz340, vz3500, bg) -> error([])
14.12/5.42	   new_compare4(@0, @0) -> EQ
14.12/5.42	   new_compare9(vz340, vz3500) -> error([])
14.12/5.42	   new_compare7(vz340, vz3500) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, ty_Float) -> new_compare3(vz340, vz3500)
14.12/5.42	
14.12/5.42	The set Q consists of the following terms:
14.12/5.42	
14.12/5.42	   new_compare(x0, x1, app(app(ty_Either, x2), x3))
14.12/5.42	   new_compare11(x0, x1, x2, x3, x4)
14.12/5.42	   new_compare5(x0, x1)
14.12/5.42	   new_compare10(x0, x1, x2, x3)
14.12/5.42	   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.12/5.42	   new_compare(x0, x1, ty_Integer)
14.12/5.42	   new_compare(x0, x1, ty_Bool)
14.12/5.42	   new_compare4(@0, @0)
14.12/5.42	   new_compare2(x0, x1)
14.12/5.42	   new_compare(x0, x1, ty_Float)
14.12/5.42	   new_compare8(x0, x1, x2)
14.12/5.42	   new_compare12(x0, x1)
14.12/5.42	   new_compare7(x0, x1)
14.12/5.42	   new_compare13(x0, x1)
14.12/5.42	   new_compare(x0, x1, ty_Int)
14.12/5.42	   new_compare3(x0, x1)
14.12/5.42	   new_compare(x0, x1, ty_Char)
14.12/5.42	   new_compare0(x0, x1, x2)
14.12/5.42	   new_compare6(x0, x1, x2)
14.12/5.42	   new_compare(x0, x1, app(ty_Maybe, x2))
14.12/5.42	   new_compare(x0, x1, app(app(ty_@2, x2), x3))
14.12/5.42	   new_compare(x0, x1, app(ty_Ratio, x2))
14.12/5.42	   new_compare(x0, x1, ty_Double)
14.12/5.42	   new_compare9(x0, x1)
14.12/5.42	   new_compare1(x0, x1, x2, x3)
14.12/5.42	   new_compare(x0, x1, ty_@0)
14.12/5.42	   new_compare(x0, x1, app(ty_[], x2))
14.12/5.42	   new_compare(x0, x1, ty_Ordering)
14.12/5.42	
14.12/5.42	We have to consider all minimal (P,Q,R)-chains.
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(18) TransformationProof (EQUIVALENT)
14.12/5.42	By narrowing [LPAR04] the rule new_merge(:(vz340, vz341), :(vz3500, vz3501), bb) -> new_merge0(vz3500, vz340, vz341, vz3501, new_compare(vz340, vz3500, bb), bb) at position [4] we obtained the following new rules [LPAR04]:
14.12/5.42	
14.12/5.42	   (new_merge(:(x0, y1), :(x1, y3), ty_Bool) -> new_merge0(x1, x0, y1, y3, new_compare9(x0, x1), ty_Bool),new_merge(:(x0, y1), :(x1, y3), ty_Bool) -> new_merge0(x1, x0, y1, y3, new_compare9(x0, x1), ty_Bool))
14.12/5.42	   (new_merge(:(x0, y1), :(x1, y3), app(ty_Maybe, x2)) -> new_merge0(x1, x0, y1, y3, new_compare8(x0, x1, x2), app(ty_Maybe, x2)),new_merge(:(x0, y1), :(x1, y3), app(ty_Maybe, x2)) -> new_merge0(x1, x0, y1, y3, new_compare8(x0, x1, x2), app(ty_Maybe, x2)))
14.12/5.42	   (new_merge(:(x0, y1), :(x1, y3), ty_Integer) -> new_merge0(x1, x0, y1, y3, new_compare2(x0, x1), ty_Integer),new_merge(:(x0, y1), :(x1, y3), ty_Integer) -> new_merge0(x1, x0, y1, y3, new_compare2(x0, x1), ty_Integer))
14.12/5.42	   (new_merge(:(x0, y1), :(x1, y3), app(app(app(ty_@3, x2), x3), x4)) -> new_merge0(x1, x0, y1, y3, new_compare11(x0, x1, x2, x3, x4), app(app(app(ty_@3, x2), x3), x4)),new_merge(:(x0, y1), :(x1, y3), app(app(app(ty_@3, x2), x3), x4)) -> new_merge0(x1, x0, y1, y3, new_compare11(x0, x1, x2, x3, x4), app(app(app(ty_@3, x2), x3), x4)))
14.12/5.42	   (new_merge(:(x0, y1), :(x1, y3), app(ty_Ratio, x2)) -> new_merge0(x1, x0, y1, y3, new_compare6(x0, x1, x2), app(ty_Ratio, x2)),new_merge(:(x0, y1), :(x1, y3), app(ty_Ratio, x2)) -> new_merge0(x1, x0, y1, y3, new_compare6(x0, x1, x2), app(ty_Ratio, x2)))
14.12/5.42	   (new_merge(:(x0, y1), :(x1, y3), ty_Int) -> new_merge0(x1, x0, y1, y3, new_compare12(x0, x1), ty_Int),new_merge(:(x0, y1), :(x1, y3), ty_Int) -> new_merge0(x1, x0, y1, y3, new_compare12(x0, x1), ty_Int))
14.12/5.42	   (new_merge(:(x0, y1), :(x1, y3), ty_@0) -> new_merge0(x1, x0, y1, y3, new_compare4(x0, x1), ty_@0),new_merge(:(x0, y1), :(x1, y3), ty_@0) -> new_merge0(x1, x0, y1, y3, new_compare4(x0, x1), ty_@0))
14.12/5.42	   (new_merge(:(x0, y1), :(x1, y3), app(app(ty_Either, x2), x3)) -> new_merge0(x1, x0, y1, y3, new_compare10(x0, x1, x2, x3), app(app(ty_Either, x2), x3)),new_merge(:(x0, y1), :(x1, y3), app(app(ty_Either, x2), x3)) -> new_merge0(x1, x0, y1, y3, new_compare10(x0, x1, x2, x3), app(app(ty_Either, x2), x3)))
14.12/5.42	   (new_merge(:(x0, y1), :(x1, y3), ty_Char) -> new_merge0(x1, x0, y1, y3, new_compare7(x0, x1), ty_Char),new_merge(:(x0, y1), :(x1, y3), ty_Char) -> new_merge0(x1, x0, y1, y3, new_compare7(x0, x1), ty_Char))
14.12/5.42	   (new_merge(:(x0, y1), :(x1, y3), app(ty_[], x2)) -> new_merge0(x1, x0, y1, y3, new_compare0(x0, x1, x2), app(ty_[], x2)),new_merge(:(x0, y1), :(x1, y3), app(ty_[], x2)) -> new_merge0(x1, x0, y1, y3, new_compare0(x0, x1, x2), app(ty_[], x2)))
14.12/5.42	   (new_merge(:(x0, y1), :(x1, y3), app(app(ty_@2, x2), x3)) -> new_merge0(x1, x0, y1, y3, new_compare1(x0, x1, x2, x3), app(app(ty_@2, x2), x3)),new_merge(:(x0, y1), :(x1, y3), app(app(ty_@2, x2), x3)) -> new_merge0(x1, x0, y1, y3, new_compare1(x0, x1, x2, x3), app(app(ty_@2, x2), x3)))
14.12/5.42	   (new_merge(:(x0, y1), :(x1, y3), ty_Double) -> new_merge0(x1, x0, y1, y3, new_compare13(x0, x1), ty_Double),new_merge(:(x0, y1), :(x1, y3), ty_Double) -> new_merge0(x1, x0, y1, y3, new_compare13(x0, x1), ty_Double))
14.12/5.42	   (new_merge(:(x0, y1), :(x1, y3), ty_Ordering) -> new_merge0(x1, x0, y1, y3, new_compare5(x0, x1), ty_Ordering),new_merge(:(x0, y1), :(x1, y3), ty_Ordering) -> new_merge0(x1, x0, y1, y3, new_compare5(x0, x1), ty_Ordering))
14.12/5.42	   (new_merge(:(x0, y1), :(x1, y3), ty_Float) -> new_merge0(x1, x0, y1, y3, new_compare3(x0, x1), ty_Float),new_merge(:(x0, y1), :(x1, y3), ty_Float) -> new_merge0(x1, x0, y1, y3, new_compare3(x0, x1), ty_Float))
14.12/5.42	
14.12/5.42	
14.12/5.42	----------------------------------------
14.12/5.42	
14.12/5.42	(19)
14.12/5.42	Obligation:
14.12/5.42	Q DP problem:
14.12/5.42	The TRS P consists of the following rules:
14.12/5.42	
14.12/5.42	   new_merge0(vz44, vz45, vz46, vz47, EQ, ba) -> new_merge(vz46, :(vz44, vz47), ba)
14.12/5.42	   new_merge(:(x0, y1), :(x1, y3), ty_Bool) -> new_merge0(x1, x0, y1, y3, new_compare9(x0, x1), ty_Bool)
14.12/5.42	   new_merge(:(x0, y1), :(x1, y3), app(ty_Maybe, x2)) -> new_merge0(x1, x0, y1, y3, new_compare8(x0, x1, x2), app(ty_Maybe, x2))
14.12/5.42	   new_merge(:(x0, y1), :(x1, y3), ty_Integer) -> new_merge0(x1, x0, y1, y3, new_compare2(x0, x1), ty_Integer)
14.12/5.42	   new_merge(:(x0, y1), :(x1, y3), app(app(app(ty_@3, x2), x3), x4)) -> new_merge0(x1, x0, y1, y3, new_compare11(x0, x1, x2, x3, x4), app(app(app(ty_@3, x2), x3), x4))
14.12/5.42	   new_merge(:(x0, y1), :(x1, y3), app(ty_Ratio, x2)) -> new_merge0(x1, x0, y1, y3, new_compare6(x0, x1, x2), app(ty_Ratio, x2))
14.12/5.42	   new_merge(:(x0, y1), :(x1, y3), ty_Int) -> new_merge0(x1, x0, y1, y3, new_compare12(x0, x1), ty_Int)
14.12/5.42	   new_merge(:(x0, y1), :(x1, y3), ty_@0) -> new_merge0(x1, x0, y1, y3, new_compare4(x0, x1), ty_@0)
14.12/5.42	   new_merge(:(x0, y1), :(x1, y3), app(app(ty_Either, x2), x3)) -> new_merge0(x1, x0, y1, y3, new_compare10(x0, x1, x2, x3), app(app(ty_Either, x2), x3))
14.12/5.42	   new_merge(:(x0, y1), :(x1, y3), ty_Char) -> new_merge0(x1, x0, y1, y3, new_compare7(x0, x1), ty_Char)
14.12/5.42	   new_merge(:(x0, y1), :(x1, y3), app(ty_[], x2)) -> new_merge0(x1, x0, y1, y3, new_compare0(x0, x1, x2), app(ty_[], x2))
14.12/5.42	   new_merge(:(x0, y1), :(x1, y3), app(app(ty_@2, x2), x3)) -> new_merge0(x1, x0, y1, y3, new_compare1(x0, x1, x2, x3), app(app(ty_@2, x2), x3))
14.12/5.42	   new_merge(:(x0, y1), :(x1, y3), ty_Double) -> new_merge0(x1, x0, y1, y3, new_compare13(x0, x1), ty_Double)
14.12/5.42	   new_merge(:(x0, y1), :(x1, y3), ty_Ordering) -> new_merge0(x1, x0, y1, y3, new_compare5(x0, x1), ty_Ordering)
14.12/5.42	   new_merge(:(x0, y1), :(x1, y3), ty_Float) -> new_merge0(x1, x0, y1, y3, new_compare3(x0, x1), ty_Float)
14.12/5.42	
14.12/5.42	The TRS R consists of the following rules:
14.12/5.42	
14.12/5.42	   new_compare1(vz340, vz3500, bd, be) -> error([])
14.12/5.42	   new_compare10(vz340, vz3500, bh, ca) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, ty_Bool) -> new_compare9(vz340, vz3500)
14.12/5.42	   new_compare(vz340, vz3500, app(ty_Maybe, bg)) -> new_compare8(vz340, vz3500, bg)
14.12/5.42	   new_compare13(vz340, vz3500) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, ty_Integer) -> new_compare2(vz340, vz3500)
14.12/5.42	   new_compare(vz340, vz3500, app(app(app(ty_@3, cb), cc), cd)) -> new_compare11(vz340, vz3500, cb, cc, cd)
14.12/5.42	   new_compare2(vz340, vz3500) -> error([])
14.12/5.42	   new_compare11(vz340, vz3500, cb, cc, cd) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, app(ty_Ratio, bf)) -> new_compare6(vz340, vz3500, bf)
14.12/5.42	   new_compare(vz340, vz3500, ty_Int) -> new_compare12(vz340, vz3500)
14.12/5.42	   new_compare(vz340, vz3500, ty_@0) -> new_compare4(vz340, vz3500)
14.12/5.42	   new_compare5(vz340, vz3500) -> error([])
14.12/5.42	   new_compare12(vz340, vz3500) -> error([])
14.12/5.42	   new_compare(vz340, vz3500, app(app(ty_Either, bh), ca)) -> new_compare10(vz340, vz3500, bh, ca)
14.12/5.42	   new_compare(vz340, vz3500, ty_Char) -> new_compare7(vz340, vz3500)
14.12/5.42	   new_compare(vz340, vz3500, app(ty_[], bc)) -> new_compare0(vz340, vz3500, bc)
14.12/5.43	   new_compare6(vz340, vz3500, bf) -> error([])
14.12/5.43	   new_compare0(vz340, vz3500, bc) -> error([])
14.12/5.43	   new_compare(vz340, vz3500, app(app(ty_@2, bd), be)) -> new_compare1(vz340, vz3500, bd, be)
14.12/5.43	   new_compare(vz340, vz3500, ty_Double) -> new_compare13(vz340, vz3500)
14.12/5.43	   new_compare3(vz340, vz3500) -> error([])
14.12/5.43	   new_compare(vz340, vz3500, ty_Ordering) -> new_compare5(vz340, vz3500)
14.12/5.43	   new_compare8(vz340, vz3500, bg) -> error([])
14.12/5.43	   new_compare4(@0, @0) -> EQ
14.12/5.43	   new_compare9(vz340, vz3500) -> error([])
14.12/5.43	   new_compare7(vz340, vz3500) -> error([])
14.12/5.43	   new_compare(vz340, vz3500, ty_Float) -> new_compare3(vz340, vz3500)
14.12/5.43	
14.12/5.43	The set Q consists of the following terms:
14.12/5.43	
14.12/5.43	   new_compare(x0, x1, app(app(ty_Either, x2), x3))
14.12/5.43	   new_compare11(x0, x1, x2, x3, x4)
14.12/5.43	   new_compare5(x0, x1)
14.12/5.43	   new_compare10(x0, x1, x2, x3)
14.12/5.43	   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.12/5.43	   new_compare(x0, x1, ty_Integer)
14.12/5.43	   new_compare(x0, x1, ty_Bool)
14.12/5.43	   new_compare4(@0, @0)
14.12/5.43	   new_compare2(x0, x1)
14.12/5.43	   new_compare(x0, x1, ty_Float)
14.12/5.43	   new_compare8(x0, x1, x2)
14.12/5.43	   new_compare12(x0, x1)
14.12/5.43	   new_compare7(x0, x1)
14.12/5.43	   new_compare13(x0, x1)
14.12/5.43	   new_compare(x0, x1, ty_Int)
14.12/5.43	   new_compare3(x0, x1)
14.12/5.43	   new_compare(x0, x1, ty_Char)
14.12/5.43	   new_compare0(x0, x1, x2)
14.12/5.43	   new_compare6(x0, x1, x2)
14.12/5.43	   new_compare(x0, x1, app(ty_Maybe, x2))
14.12/5.43	   new_compare(x0, x1, app(app(ty_@2, x2), x3))
14.12/5.43	   new_compare(x0, x1, app(ty_Ratio, x2))
14.12/5.43	   new_compare(x0, x1, ty_Double)
14.12/5.43	   new_compare9(x0, x1)
14.12/5.43	   new_compare1(x0, x1, x2, x3)
14.12/5.43	   new_compare(x0, x1, ty_@0)
14.12/5.43	   new_compare(x0, x1, app(ty_[], x2))
14.12/5.43	   new_compare(x0, x1, ty_Ordering)
14.12/5.43	
14.12/5.43	We have to consider all minimal (P,Q,R)-chains.
14.12/5.43	----------------------------------------
14.12/5.43	
14.12/5.43	(20) DependencyGraphProof (EQUIVALENT)
14.12/5.43	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 13 less nodes.
14.12/5.43	----------------------------------------
14.12/5.43	
14.12/5.43	(21)
14.12/5.43	Obligation:
14.12/5.43	Q DP problem:
14.12/5.43	The TRS P consists of the following rules:
14.12/5.43	
14.12/5.43	   new_merge(:(x0, y1), :(x1, y3), ty_@0) -> new_merge0(x1, x0, y1, y3, new_compare4(x0, x1), ty_@0)
14.12/5.43	   new_merge0(vz44, vz45, vz46, vz47, EQ, ba) -> new_merge(vz46, :(vz44, vz47), ba)
14.12/5.43	
14.12/5.43	The TRS R consists of the following rules:
14.12/5.43	
14.12/5.43	   new_compare1(vz340, vz3500, bd, be) -> error([])
14.12/5.43	   new_compare10(vz340, vz3500, bh, ca) -> error([])
14.12/5.43	   new_compare(vz340, vz3500, ty_Bool) -> new_compare9(vz340, vz3500)
14.12/5.43	   new_compare(vz340, vz3500, app(ty_Maybe, bg)) -> new_compare8(vz340, vz3500, bg)
14.12/5.43	   new_compare13(vz340, vz3500) -> error([])
14.12/5.43	   new_compare(vz340, vz3500, ty_Integer) -> new_compare2(vz340, vz3500)
14.12/5.43	   new_compare(vz340, vz3500, app(app(app(ty_@3, cb), cc), cd)) -> new_compare11(vz340, vz3500, cb, cc, cd)
14.12/5.43	   new_compare2(vz340, vz3500) -> error([])
14.12/5.43	   new_compare11(vz340, vz3500, cb, cc, cd) -> error([])
14.12/5.43	   new_compare(vz340, vz3500, app(ty_Ratio, bf)) -> new_compare6(vz340, vz3500, bf)
14.12/5.43	   new_compare(vz340, vz3500, ty_Int) -> new_compare12(vz340, vz3500)
14.12/5.43	   new_compare(vz340, vz3500, ty_@0) -> new_compare4(vz340, vz3500)
14.12/5.43	   new_compare5(vz340, vz3500) -> error([])
14.12/5.43	   new_compare12(vz340, vz3500) -> error([])
14.12/5.43	   new_compare(vz340, vz3500, app(app(ty_Either, bh), ca)) -> new_compare10(vz340, vz3500, bh, ca)
14.12/5.43	   new_compare(vz340, vz3500, ty_Char) -> new_compare7(vz340, vz3500)
14.12/5.43	   new_compare(vz340, vz3500, app(ty_[], bc)) -> new_compare0(vz340, vz3500, bc)
14.12/5.43	   new_compare6(vz340, vz3500, bf) -> error([])
14.12/5.43	   new_compare0(vz340, vz3500, bc) -> error([])
14.12/5.43	   new_compare(vz340, vz3500, app(app(ty_@2, bd), be)) -> new_compare1(vz340, vz3500, bd, be)
14.12/5.43	   new_compare(vz340, vz3500, ty_Double) -> new_compare13(vz340, vz3500)
14.12/5.43	   new_compare3(vz340, vz3500) -> error([])
14.12/5.43	   new_compare(vz340, vz3500, ty_Ordering) -> new_compare5(vz340, vz3500)
14.12/5.43	   new_compare8(vz340, vz3500, bg) -> error([])
14.12/5.43	   new_compare4(@0, @0) -> EQ
14.12/5.43	   new_compare9(vz340, vz3500) -> error([])
14.12/5.43	   new_compare7(vz340, vz3500) -> error([])
14.12/5.43	   new_compare(vz340, vz3500, ty_Float) -> new_compare3(vz340, vz3500)
14.12/5.43	
14.12/5.43	The set Q consists of the following terms:
14.12/5.43	
14.12/5.43	   new_compare(x0, x1, app(app(ty_Either, x2), x3))
14.12/5.43	   new_compare11(x0, x1, x2, x3, x4)
14.12/5.43	   new_compare5(x0, x1)
14.12/5.43	   new_compare10(x0, x1, x2, x3)
14.12/5.43	   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.12/5.43	   new_compare(x0, x1, ty_Integer)
14.12/5.43	   new_compare(x0, x1, ty_Bool)
14.12/5.43	   new_compare4(@0, @0)
14.12/5.43	   new_compare2(x0, x1)
14.12/5.43	   new_compare(x0, x1, ty_Float)
14.12/5.43	   new_compare8(x0, x1, x2)
14.12/5.43	   new_compare12(x0, x1)
14.12/5.43	   new_compare7(x0, x1)
14.12/5.43	   new_compare13(x0, x1)
14.12/5.43	   new_compare(x0, x1, ty_Int)
14.12/5.43	   new_compare3(x0, x1)
14.12/5.43	   new_compare(x0, x1, ty_Char)
14.12/5.43	   new_compare0(x0, x1, x2)
14.12/5.43	   new_compare6(x0, x1, x2)
14.12/5.43	   new_compare(x0, x1, app(ty_Maybe, x2))
14.12/5.43	   new_compare(x0, x1, app(app(ty_@2, x2), x3))
14.12/5.43	   new_compare(x0, x1, app(ty_Ratio, x2))
14.12/5.43	   new_compare(x0, x1, ty_Double)
14.12/5.43	   new_compare9(x0, x1)
14.12/5.43	   new_compare1(x0, x1, x2, x3)
14.12/5.43	   new_compare(x0, x1, ty_@0)
14.12/5.43	   new_compare(x0, x1, app(ty_[], x2))
14.12/5.43	   new_compare(x0, x1, ty_Ordering)
14.12/5.43	
14.12/5.43	We have to consider all minimal (P,Q,R)-chains.
14.12/5.43	----------------------------------------
14.12/5.43	
14.12/5.43	(22) UsableRulesProof (EQUIVALENT)
14.12/5.43	As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.
14.12/5.43	----------------------------------------
14.12/5.43	
14.12/5.43	(23)
14.12/5.43	Obligation:
14.12/5.43	Q DP problem:
14.12/5.43	The TRS P consists of the following rules:
14.12/5.43	
14.12/5.43	   new_merge(:(x0, y1), :(x1, y3), ty_@0) -> new_merge0(x1, x0, y1, y3, new_compare4(x0, x1), ty_@0)
14.12/5.43	   new_merge0(vz44, vz45, vz46, vz47, EQ, ba) -> new_merge(vz46, :(vz44, vz47), ba)
14.12/5.43	
14.12/5.43	The TRS R consists of the following rules:
14.12/5.43	
14.12/5.43	   new_compare4(@0, @0) -> EQ
14.12/5.43	
14.12/5.43	The set Q consists of the following terms:
14.12/5.43	
14.12/5.43	   new_compare(x0, x1, app(app(ty_Either, x2), x3))
14.12/5.43	   new_compare11(x0, x1, x2, x3, x4)
14.12/5.43	   new_compare5(x0, x1)
14.12/5.43	   new_compare10(x0, x1, x2, x3)
14.12/5.43	   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.12/5.43	   new_compare(x0, x1, ty_Integer)
14.12/5.43	   new_compare(x0, x1, ty_Bool)
14.12/5.43	   new_compare4(@0, @0)
14.12/5.43	   new_compare2(x0, x1)
14.12/5.43	   new_compare(x0, x1, ty_Float)
14.12/5.43	   new_compare8(x0, x1, x2)
14.12/5.43	   new_compare12(x0, x1)
14.12/5.43	   new_compare7(x0, x1)
14.12/5.43	   new_compare13(x0, x1)
14.12/5.43	   new_compare(x0, x1, ty_Int)
14.12/5.44	   new_compare3(x0, x1)
14.12/5.44	   new_compare(x0, x1, ty_Char)
14.12/5.44	   new_compare0(x0, x1, x2)
14.12/5.44	   new_compare6(x0, x1, x2)
14.12/5.44	   new_compare(x0, x1, app(ty_Maybe, x2))
14.12/5.44	   new_compare(x0, x1, app(app(ty_@2, x2), x3))
14.12/5.44	   new_compare(x0, x1, app(ty_Ratio, x2))
14.12/5.44	   new_compare(x0, x1, ty_Double)
14.12/5.44	   new_compare9(x0, x1)
14.12/5.44	   new_compare1(x0, x1, x2, x3)
14.12/5.44	   new_compare(x0, x1, ty_@0)
14.12/5.44	   new_compare(x0, x1, app(ty_[], x2))
14.12/5.44	   new_compare(x0, x1, ty_Ordering)
14.12/5.44	
14.12/5.44	We have to consider all minimal (P,Q,R)-chains.
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(24) QReductionProof (EQUIVALENT)
14.12/5.44	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
14.12/5.44	
14.12/5.44	   new_compare(x0, x1, app(app(ty_Either, x2), x3))
14.12/5.44	   new_compare11(x0, x1, x2, x3, x4)
14.12/5.44	   new_compare5(x0, x1)
14.12/5.44	   new_compare10(x0, x1, x2, x3)
14.12/5.44	   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.12/5.44	   new_compare(x0, x1, ty_Integer)
14.12/5.44	   new_compare(x0, x1, ty_Bool)
14.12/5.44	   new_compare2(x0, x1)
14.12/5.44	   new_compare(x0, x1, ty_Float)
14.12/5.44	   new_compare8(x0, x1, x2)
14.12/5.44	   new_compare12(x0, x1)
14.12/5.44	   new_compare7(x0, x1)
14.12/5.44	   new_compare13(x0, x1)
14.12/5.44	   new_compare(x0, x1, ty_Int)
14.12/5.44	   new_compare3(x0, x1)
14.12/5.44	   new_compare(x0, x1, ty_Char)
14.12/5.44	   new_compare0(x0, x1, x2)
14.12/5.44	   new_compare6(x0, x1, x2)
14.12/5.44	   new_compare(x0, x1, app(ty_Maybe, x2))
14.12/5.44	   new_compare(x0, x1, app(app(ty_@2, x2), x3))
14.12/5.44	   new_compare(x0, x1, app(ty_Ratio, x2))
14.12/5.44	   new_compare(x0, x1, ty_Double)
14.12/5.44	   new_compare9(x0, x1)
14.12/5.44	   new_compare1(x0, x1, x2, x3)
14.12/5.44	   new_compare(x0, x1, ty_@0)
14.12/5.44	   new_compare(x0, x1, app(ty_[], x2))
14.12/5.44	   new_compare(x0, x1, ty_Ordering)
14.12/5.44	
14.12/5.44	
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(25)
14.12/5.44	Obligation:
14.12/5.44	Q DP problem:
14.12/5.44	The TRS P consists of the following rules:
14.12/5.44	
14.12/5.44	   new_merge(:(x0, y1), :(x1, y3), ty_@0) -> new_merge0(x1, x0, y1, y3, new_compare4(x0, x1), ty_@0)
14.12/5.44	   new_merge0(vz44, vz45, vz46, vz47, EQ, ba) -> new_merge(vz46, :(vz44, vz47), ba)
14.12/5.44	
14.12/5.44	The TRS R consists of the following rules:
14.12/5.44	
14.12/5.44	   new_compare4(@0, @0) -> EQ
14.12/5.44	
14.12/5.44	The set Q consists of the following terms:
14.12/5.44	
14.12/5.44	   new_compare4(@0, @0)
14.12/5.44	
14.12/5.44	We have to consider all minimal (P,Q,R)-chains.
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(26) TransformationProof (EQUIVALENT)
14.12/5.44	By narrowing [LPAR04] the rule new_merge(:(x0, y1), :(x1, y3), ty_@0) -> new_merge0(x1, x0, y1, y3, new_compare4(x0, x1), ty_@0) at position [4] we obtained the following new rules [LPAR04]:
14.12/5.44	
14.12/5.44	   (new_merge(:(@0, y1), :(@0, y3), ty_@0) -> new_merge0(@0, @0, y1, y3, EQ, ty_@0),new_merge(:(@0, y1), :(@0, y3), ty_@0) -> new_merge0(@0, @0, y1, y3, EQ, ty_@0))
14.12/5.44	
14.12/5.44	
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(27)
14.12/5.44	Obligation:
14.12/5.44	Q DP problem:
14.12/5.44	The TRS P consists of the following rules:
14.12/5.44	
14.12/5.44	   new_merge0(vz44, vz45, vz46, vz47, EQ, ba) -> new_merge(vz46, :(vz44, vz47), ba)
14.12/5.44	   new_merge(:(@0, y1), :(@0, y3), ty_@0) -> new_merge0(@0, @0, y1, y3, EQ, ty_@0)
14.12/5.44	
14.12/5.44	The TRS R consists of the following rules:
14.12/5.44	
14.12/5.44	   new_compare4(@0, @0) -> EQ
14.12/5.44	
14.12/5.44	The set Q consists of the following terms:
14.12/5.44	
14.12/5.44	   new_compare4(@0, @0)
14.12/5.44	
14.12/5.44	We have to consider all minimal (P,Q,R)-chains.
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(28) UsableRulesProof (EQUIVALENT)
14.12/5.44	As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(29)
14.12/5.44	Obligation:
14.12/5.44	Q DP problem:
14.12/5.44	The TRS P consists of the following rules:
14.12/5.44	
14.12/5.44	   new_merge0(vz44, vz45, vz46, vz47, EQ, ba) -> new_merge(vz46, :(vz44, vz47), ba)
14.12/5.44	   new_merge(:(@0, y1), :(@0, y3), ty_@0) -> new_merge0(@0, @0, y1, y3, EQ, ty_@0)
14.12/5.44	
14.12/5.44	R is empty.
14.12/5.44	The set Q consists of the following terms:
14.12/5.44	
14.12/5.44	   new_compare4(@0, @0)
14.12/5.44	
14.12/5.44	We have to consider all minimal (P,Q,R)-chains.
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(30) QReductionProof (EQUIVALENT)
14.12/5.44	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
14.12/5.44	
14.12/5.44	   new_compare4(@0, @0)
14.12/5.44	
14.12/5.44	
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(31)
14.12/5.44	Obligation:
14.12/5.44	Q DP problem:
14.12/5.44	The TRS P consists of the following rules:
14.12/5.44	
14.12/5.44	   new_merge0(vz44, vz45, vz46, vz47, EQ, ba) -> new_merge(vz46, :(vz44, vz47), ba)
14.12/5.44	   new_merge(:(@0, y1), :(@0, y3), ty_@0) -> new_merge0(@0, @0, y1, y3, EQ, ty_@0)
14.12/5.44	
14.12/5.44	R is empty.
14.12/5.44	Q is empty.
14.12/5.44	We have to consider all minimal (P,Q,R)-chains.
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(32) TransformationProof (EQUIVALENT)
14.12/5.44	By instantiating [LPAR04] the rule new_merge0(vz44, vz45, vz46, vz47, EQ, ba) -> new_merge(vz46, :(vz44, vz47), ba) we obtained the following new rules [LPAR04]:
14.12/5.44	
14.12/5.44	   (new_merge0(@0, @0, z0, z1, EQ, ty_@0) -> new_merge(z0, :(@0, z1), ty_@0),new_merge0(@0, @0, z0, z1, EQ, ty_@0) -> new_merge(z0, :(@0, z1), ty_@0))
14.12/5.44	
14.12/5.44	
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(33)
14.12/5.44	Obligation:
14.12/5.44	Q DP problem:
14.12/5.44	The TRS P consists of the following rules:
14.12/5.44	
14.12/5.44	   new_merge(:(@0, y1), :(@0, y3), ty_@0) -> new_merge0(@0, @0, y1, y3, EQ, ty_@0)
14.12/5.44	   new_merge0(@0, @0, z0, z1, EQ, ty_@0) -> new_merge(z0, :(@0, z1), ty_@0)
14.12/5.44	
14.12/5.44	R is empty.
14.12/5.44	Q is empty.
14.12/5.44	We have to consider all minimal (P,Q,R)-chains.
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(34) QDPSizeChangeProof (EQUIVALENT)
14.12/5.44	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
14.12/5.44	
14.12/5.44	From the DPs we obtained the following set of size-change graphs:
14.12/5.44	*new_merge0(@0, @0, z0, z1, EQ, ty_@0) -> new_merge(z0, :(@0, z1), ty_@0)
14.12/5.44	The graph contains the following edges 3 >= 1, 6 >= 3
14.12/5.44	
14.12/5.44	
14.12/5.44	*new_merge(:(@0, y1), :(@0, y3), ty_@0) -> new_merge0(@0, @0, y1, y3, EQ, ty_@0)
14.12/5.44	The graph contains the following edges 1 > 1, 2 > 1, 1 > 2, 2 > 2, 1 > 3, 2 > 4, 3 >= 6
14.12/5.44	
14.12/5.44	
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(35)
14.12/5.44	YES
14.12/5.44	
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(36)
14.12/5.44	Obligation:
14.12/5.44	Q DP problem:
14.12/5.44	The TRS P consists of the following rules:
14.12/5.44	
14.12/5.44	   new_mergesort'(vz34, :(vz350, []), ba) -> new_mergesort'(new_merge2(vz34, vz350, ba), [], ba)
14.12/5.44	   new_mergesort'(vz34, :(vz350, :(vz3510, vz3511)), ba) -> new_mergesort'(new_merge1(vz34, vz350, vz3510, ba), new_merge_pairs0(vz3511, ba), ba)
14.12/5.44	
14.12/5.44	The TRS R consists of the following rules:
14.12/5.44	
14.12/5.44	   new_compare1(vz340, vz3500, bc, bd) -> error([])
14.12/5.44	   new_compare14(vz3500, vz35100, app(app(app(ty_@3, bg), bh), ca)) -> new_compare11(vz3500, vz35100, bg, bh, ca)
14.12/5.44	   new_compare14(vz3500, vz35100, ty_Double) -> new_compare13(vz3500, vz35100)
14.12/5.44	   new_compare14(vz3500, vz35100, ty_Char) -> new_compare7(vz3500, vz35100)
14.12/5.44	   new_compare(vz340, vz3500, app(ty_Maybe, cb)) -> new_compare8(vz340, vz3500, cb)
14.12/5.44	   new_merge_pairs0(:(vz35110, []), ba) -> :(vz35110, [])
14.12/5.44	   new_compare11(vz340, vz3500, bg, bh, ca) -> error([])
14.12/5.44	   new_compare14(vz3500, vz35100, app(app(ty_Either, be), bf)) -> new_compare10(vz3500, vz35100, be, bf)
14.12/5.44	   new_compare(vz340, vz3500, ty_Int) -> new_compare12(vz340, vz3500)
14.12/5.44	   new_merge1(vz34, :(vz3500, vz3501), :(vz35100, vz35101), ba) -> new_merge2(vz34, new_merge00(vz35100, vz3500, vz3501, vz35101, new_compare14(vz3500, vz35100, ba), ba), ba)
14.12/5.44	   new_compare12(vz340, vz3500) -> error([])
14.12/5.44	   new_merge2([], :(vz3500, vz3501), ba) -> :(vz3500, vz3501)
14.12/5.44	   new_compare(vz340, vz3500, ty_Char) -> new_compare7(vz340, vz3500)
14.12/5.44	   new_compare14(vz3500, vz35100, app(ty_Maybe, cb)) -> new_compare8(vz3500, vz35100, cb)
14.12/5.44	   new_compare(vz340, vz3500, app(ty_[], bb)) -> new_compare0(vz340, vz3500, bb)
14.12/5.44	   new_compare6(vz340, vz3500, cc) -> error([])
14.12/5.44	   new_compare(vz340, vz3500, app(app(ty_@2, bc), bd)) -> new_compare1(vz340, vz3500, bc, bd)
14.12/5.44	   new_compare(vz340, vz3500, ty_Double) -> new_compare13(vz340, vz3500)
14.12/5.44	   new_merge_pairs0(:(vz35110, :(vz351110, vz351111)), ba) -> :(new_merge2(vz35110, vz351110, ba), new_merge_pairs0(vz351111, ba))
14.12/5.44	   new_compare3(vz340, vz3500) -> error([])
14.12/5.44	   new_compare14(vz3500, vz35100, ty_Bool) -> new_compare9(vz3500, vz35100)
14.12/5.44	   new_compare(vz340, vz3500, ty_Ordering) -> new_compare5(vz340, vz3500)
14.12/5.44	   new_merge00(vz44, vz45, vz46, vz47, LT, cd) -> :(vz45, new_merge2(vz46, :(vz44, vz47), cd))
14.12/5.44	   new_compare4(@0, @0) -> EQ
14.12/5.44	   new_compare7(vz340, vz3500) -> error([])
14.12/5.44	   new_compare14(vz3500, vz35100, app(ty_[], bb)) -> new_compare0(vz3500, vz35100, bb)
14.12/5.44	   new_merge2(:(vz340, vz341), :(vz3500, vz3501), ba) -> new_merge00(vz3500, vz340, vz341, vz3501, new_compare(vz340, vz3500, ba), ba)
14.12/5.44	   new_compare14(vz3500, vz35100, app(app(ty_@2, bc), bd)) -> new_compare1(vz3500, vz35100, bc, bd)
14.12/5.44	   new_compare10(vz340, vz3500, be, bf) -> error([])
14.12/5.44	   new_compare(vz340, vz3500, ty_Bool) -> new_compare9(vz340, vz3500)
14.12/5.44	   new_compare13(vz340, vz3500) -> error([])
14.12/5.44	   new_merge2(vz34, [], ba) -> vz34
14.12/5.44	   new_compare(vz340, vz3500, ty_Integer) -> new_compare2(vz340, vz3500)
14.12/5.44	   new_compare(vz340, vz3500, app(app(app(ty_@3, bg), bh), ca)) -> new_compare11(vz340, vz3500, bg, bh, ca)
14.12/5.44	   new_merge_pairs0([], ba) -> []
14.12/5.44	   new_merge1(vz34, [], :(vz35100, vz35101), ba) -> new_merge2(vz34, :(vz35100, vz35101), ba)
14.12/5.44	   new_compare14(vz3500, vz35100, ty_Ordering) -> new_compare5(vz3500, vz35100)
14.12/5.44	   new_compare2(vz340, vz3500) -> error([])
14.12/5.44	   new_compare(vz340, vz3500, app(ty_Ratio, cc)) -> new_compare6(vz340, vz3500, cc)
14.12/5.44	   new_compare14(vz3500, vz35100, ty_Float) -> new_compare3(vz3500, vz35100)
14.12/5.44	   new_merge00(vz44, vz45, vz46, vz47, GT, cd) -> :(vz44, new_merge2(:(vz45, vz46), vz47, cd))
14.12/5.44	   new_compare(vz340, vz3500, ty_@0) -> new_compare4(vz340, vz3500)
14.12/5.44	   new_compare5(vz340, vz3500) -> error([])
14.12/5.44	   new_compare(vz340, vz3500, app(app(ty_Either, be), bf)) -> new_compare10(vz340, vz3500, be, bf)
14.12/5.44	   new_compare14(vz3500, vz35100, ty_Integer) -> new_compare2(vz3500, vz35100)
14.12/5.44	   new_merge00(vz44, vz45, vz46, vz47, EQ, cd) -> :(vz45, new_merge2(vz46, :(vz44, vz47), cd))
14.12/5.44	   new_compare14(vz3500, vz35100, ty_Int) -> new_compare12(vz3500, vz35100)
14.12/5.44	   new_compare0(vz340, vz3500, bb) -> error([])
14.12/5.44	   new_compare14(vz3500, vz35100, app(ty_Ratio, cc)) -> new_compare6(vz3500, vz35100, cc)
14.12/5.44	   new_compare8(vz340, vz3500, cb) -> error([])
14.12/5.44	   new_compare9(vz340, vz3500) -> error([])
14.12/5.44	   new_merge1(vz34, vz350, [], ba) -> new_merge2(vz34, vz350, ba)
14.12/5.44	   new_compare14(vz3500, vz35100, ty_@0) -> new_compare4(vz3500, vz35100)
14.12/5.44	   new_compare(vz340, vz3500, ty_Float) -> new_compare3(vz340, vz3500)
14.12/5.44	
14.12/5.44	The set Q consists of the following terms:
14.12/5.44	
14.12/5.44	   new_compare14(x0, x1, ty_Double)
14.12/5.44	   new_merge1(x0, :(x1, x2), :(x3, x4), x5)
14.12/5.44	   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.12/5.44	   new_compare14(x0, x1, ty_Bool)
14.12/5.44	   new_compare10(x0, x1, x2, x3)
14.12/5.44	   new_merge2([], :(x0, x1), x2)
14.12/5.44	   new_compare14(x0, x1, app(app(ty_@2, x2), x3))
14.12/5.44	   new_compare14(x0, x1, ty_@0)
14.12/5.44	   new_merge_pairs0(:(x0, :(x1, x2)), x3)
14.12/5.44	   new_compare(x0, x1, ty_Bool)
14.12/5.44	   new_compare4(@0, @0)
14.12/5.44	   new_compare14(x0, x1, ty_Char)
14.12/5.44	   new_merge00(x0, x1, x2, x3, EQ, x4)
14.12/5.44	   new_compare14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.12/5.44	   new_merge1(x0, [], :(x1, x2), x3)
14.12/5.44	   new_compare14(x0, x1, ty_Ordering)
14.12/5.44	   new_compare7(x0, x1)
14.12/5.44	   new_merge2(x0, [], x1)
14.12/5.44	   new_compare13(x0, x1)
14.12/5.44	   new_compare(x0, x1, ty_Int)
14.12/5.44	   new_merge00(x0, x1, x2, x3, GT, x4)
14.12/5.44	   new_merge1(x0, x1, [], x2)
14.12/5.44	   new_compare8(x0, x1, x2)
14.12/5.44	   new_compare14(x0, x1, ty_Int)
14.12/5.44	   new_compare9(x0, x1)
14.12/5.44	   new_compare1(x0, x1, x2, x3)
14.12/5.44	   new_compare14(x0, x1, app(app(ty_Either, x2), x3))
14.12/5.44	   new_compare(x0, x1, ty_@0)
14.12/5.44	   new_compare(x0, x1, ty_Ordering)
14.12/5.44	   new_compare(x0, x1, app(ty_Ratio, x2))
14.12/5.44	   new_compare(x0, x1, app(app(ty_Either, x2), x3))
14.12/5.44	   new_compare5(x0, x1)
14.12/5.44	   new_compare(x0, x1, app(ty_[], x2))
14.12/5.44	   new_compare(x0, x1, ty_Integer)
14.12/5.44	   new_compare14(x0, x1, app(ty_Maybe, x2))
14.12/5.44	   new_compare11(x0, x1, x2, x3, x4)
14.12/5.44	   new_compare2(x0, x1)
14.12/5.44	   new_compare(x0, x1, ty_Float)
14.12/5.44	   new_compare(x0, x1, app(ty_Maybe, x2))
14.12/5.44	   new_compare12(x0, x1)
14.12/5.44	   new_compare14(x0, x1, app(ty_[], x2))
14.12/5.44	   new_compare14(x0, x1, app(ty_Ratio, x2))
14.12/5.44	   new_compare3(x0, x1)
14.12/5.44	   new_compare0(x0, x1, x2)
14.12/5.44	   new_compare(x0, x1, ty_Char)
14.12/5.44	   new_merge_pairs0(:(x0, []), x1)
14.12/5.44	   new_compare(x0, x1, app(app(ty_@2, x2), x3))
14.12/5.44	   new_merge_pairs0([], x0)
14.12/5.44	   new_compare14(x0, x1, ty_Float)
14.12/5.44	   new_compare(x0, x1, ty_Double)
14.12/5.44	   new_merge2(:(x0, x1), :(x2, x3), x4)
14.12/5.44	   new_compare6(x0, x1, x2)
14.12/5.44	   new_compare14(x0, x1, ty_Integer)
14.12/5.44	   new_merge00(x0, x1, x2, x3, LT, x4)
14.12/5.44	
14.12/5.44	We have to consider all minimal (P,Q,R)-chains.
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(37) DependencyGraphProof (EQUIVALENT)
14.12/5.44	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(38)
14.12/5.44	Obligation:
14.12/5.44	Q DP problem:
14.12/5.44	The TRS P consists of the following rules:
14.12/5.44	
14.12/5.44	   new_mergesort'(vz34, :(vz350, :(vz3510, vz3511)), ba) -> new_mergesort'(new_merge1(vz34, vz350, vz3510, ba), new_merge_pairs0(vz3511, ba), ba)
14.12/5.44	
14.12/5.44	The TRS R consists of the following rules:
14.12/5.44	
14.12/5.44	   new_compare1(vz340, vz3500, bc, bd) -> error([])
14.12/5.44	   new_compare14(vz3500, vz35100, app(app(app(ty_@3, bg), bh), ca)) -> new_compare11(vz3500, vz35100, bg, bh, ca)
14.12/5.44	   new_compare14(vz3500, vz35100, ty_Double) -> new_compare13(vz3500, vz35100)
14.12/5.44	   new_compare14(vz3500, vz35100, ty_Char) -> new_compare7(vz3500, vz35100)
14.12/5.44	   new_compare(vz340, vz3500, app(ty_Maybe, cb)) -> new_compare8(vz340, vz3500, cb)
14.12/5.44	   new_merge_pairs0(:(vz35110, []), ba) -> :(vz35110, [])
14.12/5.44	   new_compare11(vz340, vz3500, bg, bh, ca) -> error([])
14.12/5.44	   new_compare14(vz3500, vz35100, app(app(ty_Either, be), bf)) -> new_compare10(vz3500, vz35100, be, bf)
14.12/5.44	   new_compare(vz340, vz3500, ty_Int) -> new_compare12(vz340, vz3500)
14.12/5.44	   new_merge1(vz34, :(vz3500, vz3501), :(vz35100, vz35101), ba) -> new_merge2(vz34, new_merge00(vz35100, vz3500, vz3501, vz35101, new_compare14(vz3500, vz35100, ba), ba), ba)
14.12/5.44	   new_compare12(vz340, vz3500) -> error([])
14.12/5.44	   new_merge2([], :(vz3500, vz3501), ba) -> :(vz3500, vz3501)
14.12/5.44	   new_compare(vz340, vz3500, ty_Char) -> new_compare7(vz340, vz3500)
14.12/5.44	   new_compare14(vz3500, vz35100, app(ty_Maybe, cb)) -> new_compare8(vz3500, vz35100, cb)
14.12/5.44	   new_compare(vz340, vz3500, app(ty_[], bb)) -> new_compare0(vz340, vz3500, bb)
14.12/5.44	   new_compare6(vz340, vz3500, cc) -> error([])
14.12/5.44	   new_compare(vz340, vz3500, app(app(ty_@2, bc), bd)) -> new_compare1(vz340, vz3500, bc, bd)
14.12/5.44	   new_compare(vz340, vz3500, ty_Double) -> new_compare13(vz340, vz3500)
14.12/5.44	   new_merge_pairs0(:(vz35110, :(vz351110, vz351111)), ba) -> :(new_merge2(vz35110, vz351110, ba), new_merge_pairs0(vz351111, ba))
14.12/5.44	   new_compare3(vz340, vz3500) -> error([])
14.12/5.44	   new_compare14(vz3500, vz35100, ty_Bool) -> new_compare9(vz3500, vz35100)
14.12/5.44	   new_compare(vz340, vz3500, ty_Ordering) -> new_compare5(vz340, vz3500)
14.12/5.44	   new_merge00(vz44, vz45, vz46, vz47, LT, cd) -> :(vz45, new_merge2(vz46, :(vz44, vz47), cd))
14.12/5.44	   new_compare4(@0, @0) -> EQ
14.12/5.44	   new_compare7(vz340, vz3500) -> error([])
14.12/5.44	   new_compare14(vz3500, vz35100, app(ty_[], bb)) -> new_compare0(vz3500, vz35100, bb)
14.12/5.44	   new_merge2(:(vz340, vz341), :(vz3500, vz3501), ba) -> new_merge00(vz3500, vz340, vz341, vz3501, new_compare(vz340, vz3500, ba), ba)
14.12/5.44	   new_compare14(vz3500, vz35100, app(app(ty_@2, bc), bd)) -> new_compare1(vz3500, vz35100, bc, bd)
14.12/5.44	   new_compare10(vz340, vz3500, be, bf) -> error([])
14.12/5.44	   new_compare(vz340, vz3500, ty_Bool) -> new_compare9(vz340, vz3500)
14.12/5.44	   new_compare13(vz340, vz3500) -> error([])
14.12/5.44	   new_merge2(vz34, [], ba) -> vz34
14.12/5.44	   new_compare(vz340, vz3500, ty_Integer) -> new_compare2(vz340, vz3500)
14.12/5.44	   new_compare(vz340, vz3500, app(app(app(ty_@3, bg), bh), ca)) -> new_compare11(vz340, vz3500, bg, bh, ca)
14.12/5.44	   new_merge_pairs0([], ba) -> []
14.12/5.44	   new_merge1(vz34, [], :(vz35100, vz35101), ba) -> new_merge2(vz34, :(vz35100, vz35101), ba)
14.12/5.44	   new_compare14(vz3500, vz35100, ty_Ordering) -> new_compare5(vz3500, vz35100)
14.12/5.44	   new_compare2(vz340, vz3500) -> error([])
14.12/5.44	   new_compare(vz340, vz3500, app(ty_Ratio, cc)) -> new_compare6(vz340, vz3500, cc)
14.12/5.44	   new_compare14(vz3500, vz35100, ty_Float) -> new_compare3(vz3500, vz35100)
14.12/5.44	   new_merge00(vz44, vz45, vz46, vz47, GT, cd) -> :(vz44, new_merge2(:(vz45, vz46), vz47, cd))
14.12/5.44	   new_compare(vz340, vz3500, ty_@0) -> new_compare4(vz340, vz3500)
14.12/5.44	   new_compare5(vz340, vz3500) -> error([])
14.12/5.44	   new_compare(vz340, vz3500, app(app(ty_Either, be), bf)) -> new_compare10(vz340, vz3500, be, bf)
14.12/5.44	   new_compare14(vz3500, vz35100, ty_Integer) -> new_compare2(vz3500, vz35100)
14.12/5.44	   new_merge00(vz44, vz45, vz46, vz47, EQ, cd) -> :(vz45, new_merge2(vz46, :(vz44, vz47), cd))
14.12/5.44	   new_compare14(vz3500, vz35100, ty_Int) -> new_compare12(vz3500, vz35100)
14.12/5.44	   new_compare0(vz340, vz3500, bb) -> error([])
14.12/5.44	   new_compare14(vz3500, vz35100, app(ty_Ratio, cc)) -> new_compare6(vz3500, vz35100, cc)
14.12/5.44	   new_compare8(vz340, vz3500, cb) -> error([])
14.12/5.44	   new_compare9(vz340, vz3500) -> error([])
14.12/5.44	   new_merge1(vz34, vz350, [], ba) -> new_merge2(vz34, vz350, ba)
14.12/5.44	   new_compare14(vz3500, vz35100, ty_@0) -> new_compare4(vz3500, vz35100)
14.12/5.44	   new_compare(vz340, vz3500, ty_Float) -> new_compare3(vz340, vz3500)
14.12/5.44	
14.12/5.44	The set Q consists of the following terms:
14.12/5.44	
14.12/5.44	   new_compare14(x0, x1, ty_Double)
14.12/5.44	   new_merge1(x0, :(x1, x2), :(x3, x4), x5)
14.12/5.44	   new_compare(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.12/5.44	   new_compare14(x0, x1, ty_Bool)
14.12/5.44	   new_compare10(x0, x1, x2, x3)
14.12/5.44	   new_merge2([], :(x0, x1), x2)
14.12/5.44	   new_compare14(x0, x1, app(app(ty_@2, x2), x3))
14.12/5.44	   new_compare14(x0, x1, ty_@0)
14.12/5.44	   new_merge_pairs0(:(x0, :(x1, x2)), x3)
14.12/5.44	   new_compare(x0, x1, ty_Bool)
14.12/5.44	   new_compare4(@0, @0)
14.12/5.44	   new_compare14(x0, x1, ty_Char)
14.12/5.44	   new_merge00(x0, x1, x2, x3, EQ, x4)
14.12/5.44	   new_compare14(x0, x1, app(app(app(ty_@3, x2), x3), x4))
14.12/5.44	   new_merge1(x0, [], :(x1, x2), x3)
14.12/5.44	   new_compare14(x0, x1, ty_Ordering)
14.12/5.44	   new_compare7(x0, x1)
14.12/5.44	   new_merge2(x0, [], x1)
14.12/5.44	   new_compare13(x0, x1)
14.12/5.44	   new_compare(x0, x1, ty_Int)
14.12/5.44	   new_merge00(x0, x1, x2, x3, GT, x4)
14.12/5.44	   new_merge1(x0, x1, [], x2)
14.12/5.44	   new_compare8(x0, x1, x2)
14.12/5.44	   new_compare14(x0, x1, ty_Int)
14.12/5.44	   new_compare9(x0, x1)
14.12/5.44	   new_compare1(x0, x1, x2, x3)
14.12/5.44	   new_compare14(x0, x1, app(app(ty_Either, x2), x3))
14.12/5.44	   new_compare(x0, x1, ty_@0)
14.12/5.44	   new_compare(x0, x1, ty_Ordering)
14.12/5.44	   new_compare(x0, x1, app(ty_Ratio, x2))
14.12/5.44	   new_compare(x0, x1, app(app(ty_Either, x2), x3))
14.12/5.44	   new_compare5(x0, x1)
14.12/5.44	   new_compare(x0, x1, app(ty_[], x2))
14.12/5.44	   new_compare(x0, x1, ty_Integer)
14.12/5.44	   new_compare14(x0, x1, app(ty_Maybe, x2))
14.12/5.44	   new_compare11(x0, x1, x2, x3, x4)
14.12/5.44	   new_compare2(x0, x1)
14.12/5.44	   new_compare(x0, x1, ty_Float)
14.12/5.44	   new_compare(x0, x1, app(ty_Maybe, x2))
14.12/5.44	   new_compare12(x0, x1)
14.12/5.44	   new_compare14(x0, x1, app(ty_[], x2))
14.12/5.44	   new_compare14(x0, x1, app(ty_Ratio, x2))
14.12/5.44	   new_compare3(x0, x1)
14.12/5.44	   new_compare0(x0, x1, x2)
14.12/5.44	   new_compare(x0, x1, ty_Char)
14.12/5.44	   new_merge_pairs0(:(x0, []), x1)
14.12/5.44	   new_compare(x0, x1, app(app(ty_@2, x2), x3))
14.12/5.44	   new_merge_pairs0([], x0)
14.12/5.44	   new_compare14(x0, x1, ty_Float)
14.12/5.44	   new_compare(x0, x1, ty_Double)
14.12/5.44	   new_merge2(:(x0, x1), :(x2, x3), x4)
14.12/5.44	   new_compare6(x0, x1, x2)
14.12/5.44	   new_compare14(x0, x1, ty_Integer)
14.12/5.44	   new_merge00(x0, x1, x2, x3, LT, x4)
14.12/5.44	
14.12/5.44	We have to consider all minimal (P,Q,R)-chains.
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(39) QDPSizeChangeProof (EQUIVALENT)
14.12/5.44	We used the following order together with the size-change analysis [AAECC05] to show that there are no infinite chains for this DP problem. 
14.12/5.44	
14.12/5.44	Order:Polynomial interpretation [POLO]:
14.12/5.44	
14.12/5.44	   POL(:(x_1, x_2)) = 1 + x_2
14.12/5.44	   POL([]) = 0
14.12/5.44	   POL(new_merge2(x_1, x_2, x_3)) = 0
14.12/5.44	   POL(new_merge_pairs0(x_1, x_2)) = x_1
14.12/5.44	
14.12/5.44	
14.12/5.44	
14.12/5.44	
14.12/5.44	From the DPs we obtained the following set of size-change graphs:
14.12/5.44	*new_mergesort'(vz34, :(vz350, :(vz3510, vz3511)), ba) -> new_mergesort'(new_merge1(vz34, vz350, vz3510, ba), new_merge_pairs0(vz3511, ba), ba) (allowed arguments on rhs = {2, 3})
14.12/5.44	The graph contains the following edges 2 > 2, 3 >= 3
14.12/5.44	
14.12/5.44	
14.12/5.44	
14.12/5.44	We oriented the following set of usable rules [AAECC05,FROCOS05].
14.12/5.44	
14.12/5.44	   new_merge_pairs0([], ba) -> []
14.12/5.44	   new_merge_pairs0(:(vz35110, []), ba) -> :(vz35110, [])
14.12/5.44	   new_merge_pairs0(:(vz35110, :(vz351110, vz351111)), ba) -> :(new_merge2(vz35110, vz351110, ba), new_merge_pairs0(vz351111, ba))
14.12/5.44	
14.12/5.44	----------------------------------------
14.12/5.44	
14.12/5.44	(40)
14.12/5.44	YES
14.22/5.52	EOF